diff options
Diffstat (limited to 'kernel/arch/m68k/ifpsp060/src/fplsp.S')
| -rw-r--r-- | kernel/arch/m68k/ifpsp060/src/fplsp.S | 10980 |
1 files changed, 10980 insertions, 0 deletions
diff --git a/kernel/arch/m68k/ifpsp060/src/fplsp.S b/kernel/arch/m68k/ifpsp060/src/fplsp.S new file mode 100644 index 000000000..3b7ea2dc9 --- /dev/null +++ b/kernel/arch/m68k/ifpsp060/src/fplsp.S @@ -0,0 +1,10980 @@ +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP +M68000 Hi-Performance Microprocessor Division +M68060 Software Package +Production Release P1.00 -- October 10, 1994 + +M68060 Software Package Copyright © 1993, 1994 Motorola Inc. All rights reserved. + +THE SOFTWARE is provided on an "AS IS" basis and without warranty. +To the maximum extent permitted by applicable law, +MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, +INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE +and any warranty against infringement with regard to the SOFTWARE +(INCLUDING ANY MODIFIED VERSIONS THEREOF) and any accompanying written materials. + +To the maximum extent permitted by applicable law, +IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER +(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS PROFITS, +BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR OTHER PECUNIARY LOSS) +ARISING OF THE USE OR INABILITY TO USE THE SOFTWARE. +Motorola assumes no responsibility for the maintenance and support of the SOFTWARE. + +You are hereby granted a copyright license to use, modify, and distribute the SOFTWARE +so long as this entire notice is retained without alteration in any modified and/or +redistributed versions, and that such modified versions are clearly identified as such. +No licenses are granted by implication, estoppel or otherwise under any patents +or trademarks of Motorola, Inc. +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# lfptop.s: +# This file is appended to the top of the 060ILSP package +# and contains the entry points into the package. The user, in +# effect, branches to one of the branch table entries located here. +# + + bra.l _facoss_ + short 0x0000 + bra.l _facosd_ + short 0x0000 + bra.l _facosx_ + short 0x0000 + + bra.l _fasins_ + short 0x0000 + bra.l _fasind_ + short 0x0000 + bra.l _fasinx_ + short 0x0000 + + bra.l _fatans_ + short 0x0000 + bra.l _fatand_ + short 0x0000 + bra.l _fatanx_ + short 0x0000 + + bra.l _fatanhs_ + short 0x0000 + bra.l _fatanhd_ + short 0x0000 + bra.l _fatanhx_ + short 0x0000 + + bra.l _fcoss_ + short 0x0000 + bra.l _fcosd_ + short 0x0000 + bra.l _fcosx_ + short 0x0000 + + bra.l _fcoshs_ + short 0x0000 + bra.l _fcoshd_ + short 0x0000 + bra.l _fcoshx_ + short 0x0000 + + bra.l _fetoxs_ + short 0x0000 + bra.l _fetoxd_ + short 0x0000 + bra.l _fetoxx_ + short 0x0000 + + bra.l _fetoxm1s_ + short 0x0000 + bra.l _fetoxm1d_ + short 0x0000 + bra.l _fetoxm1x_ + short 0x0000 + + bra.l _fgetexps_ + short 0x0000 + bra.l _fgetexpd_ + short 0x0000 + bra.l _fgetexpx_ + short 0x0000 + + bra.l _fgetmans_ + short 0x0000 + bra.l _fgetmand_ + short 0x0000 + bra.l _fgetmanx_ + short 0x0000 + + bra.l _flog10s_ + short 0x0000 + bra.l _flog10d_ + short 0x0000 + bra.l _flog10x_ + short 0x0000 + + bra.l _flog2s_ + short 0x0000 + bra.l _flog2d_ + short 0x0000 + bra.l _flog2x_ + short 0x0000 + + bra.l _flogns_ + short 0x0000 + bra.l _flognd_ + short 0x0000 + bra.l _flognx_ + short 0x0000 + + bra.l _flognp1s_ + short 0x0000 + bra.l _flognp1d_ + short 0x0000 + bra.l _flognp1x_ + short 0x0000 + + bra.l _fmods_ + short 0x0000 + bra.l _fmodd_ + short 0x0000 + bra.l _fmodx_ + short 0x0000 + + bra.l _frems_ + short 0x0000 + bra.l _fremd_ + short 0x0000 + bra.l _fremx_ + short 0x0000 + + bra.l _fscales_ + short 0x0000 + bra.l _fscaled_ + short 0x0000 + bra.l _fscalex_ + short 0x0000 + + bra.l _fsins_ + short 0x0000 + bra.l _fsind_ + short 0x0000 + bra.l _fsinx_ + short 0x0000 + + bra.l _fsincoss_ + short 0x0000 + bra.l _fsincosd_ + short 0x0000 + bra.l _fsincosx_ + short 0x0000 + + bra.l _fsinhs_ + short 0x0000 + bra.l _fsinhd_ + short 0x0000 + bra.l _fsinhx_ + short 0x0000 + + bra.l _ftans_ + short 0x0000 + bra.l _ftand_ + short 0x0000 + bra.l _ftanx_ + short 0x0000 + + bra.l _ftanhs_ + short 0x0000 + bra.l _ftanhd_ + short 0x0000 + bra.l _ftanhx_ + short 0x0000 + + bra.l _ftentoxs_ + short 0x0000 + bra.l _ftentoxd_ + short 0x0000 + bra.l _ftentoxx_ + short 0x0000 + + bra.l _ftwotoxs_ + short 0x0000 + bra.l _ftwotoxd_ + short 0x0000 + bra.l _ftwotoxx_ + short 0x0000 + + bra.l _fabss_ + short 0x0000 + bra.l _fabsd_ + short 0x0000 + bra.l _fabsx_ + short 0x0000 + + bra.l _fadds_ + short 0x0000 + bra.l _faddd_ + short 0x0000 + bra.l _faddx_ + short 0x0000 + + bra.l _fdivs_ + short 0x0000 + bra.l _fdivd_ + short 0x0000 + bra.l _fdivx_ + short 0x0000 + + bra.l _fints_ + short 0x0000 + bra.l _fintd_ + short 0x0000 + bra.l _fintx_ + short 0x0000 + + bra.l _fintrzs_ + short 0x0000 + bra.l _fintrzd_ + short 0x0000 + bra.l _fintrzx_ + short 0x0000 + + bra.l _fmuls_ + short 0x0000 + bra.l _fmuld_ + short 0x0000 + bra.l _fmulx_ + short 0x0000 + + bra.l _fnegs_ + short 0x0000 + bra.l _fnegd_ + short 0x0000 + bra.l _fnegx_ + short 0x0000 + + bra.l _fsqrts_ + short 0x0000 + bra.l _fsqrtd_ + short 0x0000 + bra.l _fsqrtx_ + short 0x0000 + + bra.l _fsubs_ + short 0x0000 + bra.l _fsubd_ + short 0x0000 + bra.l _fsubx_ + short 0x0000 + +# leave room for future possible additions + align 0x400 + +# +# This file contains a set of define statements for constants +# in order to promote readability within the corecode itself. +# + +set LOCAL_SIZE, 192 # stack frame size(bytes) +set LV, -LOCAL_SIZE # stack offset + +set EXC_SR, 0x4 # stack status register +set EXC_PC, 0x6 # stack pc +set EXC_VOFF, 0xa # stacked vector offset +set EXC_EA, 0xc # stacked <ea> + +set EXC_FP, 0x0 # frame pointer + +set EXC_AREGS, -68 # offset of all address regs +set EXC_DREGS, -100 # offset of all data regs +set EXC_FPREGS, -36 # offset of all fp regs + +set EXC_A7, EXC_AREGS+(7*4) # offset of saved a7 +set OLD_A7, EXC_AREGS+(6*4) # extra copy of saved a7 +set EXC_A6, EXC_AREGS+(6*4) # offset of saved a6 +set EXC_A5, EXC_AREGS+(5*4) +set EXC_A4, EXC_AREGS+(4*4) +set EXC_A3, EXC_AREGS+(3*4) +set EXC_A2, EXC_AREGS+(2*4) +set EXC_A1, EXC_AREGS+(1*4) +set EXC_A0, EXC_AREGS+(0*4) +set EXC_D7, EXC_DREGS+(7*4) +set EXC_D6, EXC_DREGS+(6*4) +set EXC_D5, EXC_DREGS+(5*4) +set EXC_D4, EXC_DREGS+(4*4) +set EXC_D3, EXC_DREGS+(3*4) +set EXC_D2, EXC_DREGS+(2*4) +set EXC_D1, EXC_DREGS+(1*4) +set EXC_D0, EXC_DREGS+(0*4) + +set EXC_FP0, EXC_FPREGS+(0*12) # offset of saved fp0 +set EXC_FP1, EXC_FPREGS+(1*12) # offset of saved fp1 +set EXC_FP2, EXC_FPREGS+(2*12) # offset of saved fp2 (not used) + +set FP_SCR1, LV+80 # fp scratch 1 +set FP_SCR1_EX, FP_SCR1+0 +set FP_SCR1_SGN, FP_SCR1+2 +set FP_SCR1_HI, FP_SCR1+4 +set FP_SCR1_LO, FP_SCR1+8 + +set FP_SCR0, LV+68 # fp scratch 0 +set FP_SCR0_EX, FP_SCR0+0 +set FP_SCR0_SGN, FP_SCR0+2 +set FP_SCR0_HI, FP_SCR0+4 +set FP_SCR0_LO, FP_SCR0+8 + +set FP_DST, LV+56 # fp destination operand +set FP_DST_EX, FP_DST+0 +set FP_DST_SGN, FP_DST+2 +set FP_DST_HI, FP_DST+4 +set FP_DST_LO, FP_DST+8 + +set FP_SRC, LV+44 # fp source operand +set FP_SRC_EX, FP_SRC+0 +set FP_SRC_SGN, FP_SRC+2 +set FP_SRC_HI, FP_SRC+4 +set FP_SRC_LO, FP_SRC+8 + +set USER_FPIAR, LV+40 # FP instr address register + +set USER_FPSR, LV+36 # FP status register +set FPSR_CC, USER_FPSR+0 # FPSR condition codes +set FPSR_QBYTE, USER_FPSR+1 # FPSR qoutient byte +set FPSR_EXCEPT, USER_FPSR+2 # FPSR exception status byte +set FPSR_AEXCEPT, USER_FPSR+3 # FPSR accrued exception byte + +set USER_FPCR, LV+32 # FP control register +set FPCR_ENABLE, USER_FPCR+2 # FPCR exception enable +set FPCR_MODE, USER_FPCR+3 # FPCR rounding mode control + +set L_SCR3, LV+28 # integer scratch 3 +set L_SCR2, LV+24 # integer scratch 2 +set L_SCR1, LV+20 # integer scratch 1 + +set STORE_FLG, LV+19 # flag: operand store (ie. not fcmp/ftst) + +set EXC_TEMP2, LV+24 # temporary space +set EXC_TEMP, LV+16 # temporary space + +set DTAG, LV+15 # destination operand type +set STAG, LV+14 # source operand type + +set SPCOND_FLG, LV+10 # flag: special case (see below) + +set EXC_CC, LV+8 # saved condition codes +set EXC_EXTWPTR, LV+4 # saved current PC (active) +set EXC_EXTWORD, LV+2 # saved extension word +set EXC_CMDREG, LV+2 # saved extension word +set EXC_OPWORD, LV+0 # saved operation word + +################################ + +# Helpful macros + +set FTEMP, 0 # offsets within an +set FTEMP_EX, 0 # extended precision +set FTEMP_SGN, 2 # value saved in memory. +set FTEMP_HI, 4 +set FTEMP_LO, 8 +set FTEMP_GRS, 12 + +set LOCAL, 0 # offsets within an +set LOCAL_EX, 0 # extended precision +set LOCAL_SGN, 2 # value saved in memory. +set LOCAL_HI, 4 +set LOCAL_LO, 8 +set LOCAL_GRS, 12 + +set DST, 0 # offsets within an +set DST_EX, 0 # extended precision +set DST_HI, 4 # value saved in memory. +set DST_LO, 8 + +set SRC, 0 # offsets within an +set SRC_EX, 0 # extended precision +set SRC_HI, 4 # value saved in memory. +set SRC_LO, 8 + +set SGL_LO, 0x3f81 # min sgl prec exponent +set SGL_HI, 0x407e # max sgl prec exponent +set DBL_LO, 0x3c01 # min dbl prec exponent +set DBL_HI, 0x43fe # max dbl prec exponent +set EXT_LO, 0x0 # min ext prec exponent +set EXT_HI, 0x7ffe # max ext prec exponent + +set EXT_BIAS, 0x3fff # extended precision bias +set SGL_BIAS, 0x007f # single precision bias +set DBL_BIAS, 0x03ff # double precision bias + +set NORM, 0x00 # operand type for STAG/DTAG +set ZERO, 0x01 # operand type for STAG/DTAG +set INF, 0x02 # operand type for STAG/DTAG +set QNAN, 0x03 # operand type for STAG/DTAG +set DENORM, 0x04 # operand type for STAG/DTAG +set SNAN, 0x05 # operand type for STAG/DTAG +set UNNORM, 0x06 # operand type for STAG/DTAG + +################## +# FPSR/FPCR bits # +################## +set neg_bit, 0x3 # negative result +set z_bit, 0x2 # zero result +set inf_bit, 0x1 # infinite result +set nan_bit, 0x0 # NAN result + +set q_sn_bit, 0x7 # sign bit of quotient byte + +set bsun_bit, 7 # branch on unordered +set snan_bit, 6 # signalling NAN +set operr_bit, 5 # operand error +set ovfl_bit, 4 # overflow +set unfl_bit, 3 # underflow +set dz_bit, 2 # divide by zero +set inex2_bit, 1 # inexact result 2 +set inex1_bit, 0 # inexact result 1 + +set aiop_bit, 7 # accrued inexact operation bit +set aovfl_bit, 6 # accrued overflow bit +set aunfl_bit, 5 # accrued underflow bit +set adz_bit, 4 # accrued dz bit +set ainex_bit, 3 # accrued inexact bit + +############################# +# FPSR individual bit masks # +############################# +set neg_mask, 0x08000000 # negative bit mask (lw) +set inf_mask, 0x02000000 # infinity bit mask (lw) +set z_mask, 0x04000000 # zero bit mask (lw) +set nan_mask, 0x01000000 # nan bit mask (lw) + +set neg_bmask, 0x08 # negative bit mask (byte) +set inf_bmask, 0x02 # infinity bit mask (byte) +set z_bmask, 0x04 # zero bit mask (byte) +set nan_bmask, 0x01 # nan bit mask (byte) + +set bsun_mask, 0x00008000 # bsun exception mask +set snan_mask, 0x00004000 # snan exception mask +set operr_mask, 0x00002000 # operr exception mask +set ovfl_mask, 0x00001000 # overflow exception mask +set unfl_mask, 0x00000800 # underflow exception mask +set dz_mask, 0x00000400 # dz exception mask +set inex2_mask, 0x00000200 # inex2 exception mask +set inex1_mask, 0x00000100 # inex1 exception mask + +set aiop_mask, 0x00000080 # accrued illegal operation +set aovfl_mask, 0x00000040 # accrued overflow +set aunfl_mask, 0x00000020 # accrued underflow +set adz_mask, 0x00000010 # accrued divide by zero +set ainex_mask, 0x00000008 # accrued inexact + +###################################### +# FPSR combinations used in the FPSP # +###################################### +set dzinf_mask, inf_mask+dz_mask+adz_mask +set opnan_mask, nan_mask+operr_mask+aiop_mask +set nzi_mask, 0x01ffffff #clears N, Z, and I +set unfinx_mask, unfl_mask+inex2_mask+aunfl_mask+ainex_mask +set unf2inx_mask, unfl_mask+inex2_mask+ainex_mask +set ovfinx_mask, ovfl_mask+inex2_mask+aovfl_mask+ainex_mask +set inx1a_mask, inex1_mask+ainex_mask +set inx2a_mask, inex2_mask+ainex_mask +set snaniop_mask, nan_mask+snan_mask+aiop_mask +set snaniop2_mask, snan_mask+aiop_mask +set naniop_mask, nan_mask+aiop_mask +set neginf_mask, neg_mask+inf_mask +set infaiop_mask, inf_mask+aiop_mask +set negz_mask, neg_mask+z_mask +set opaop_mask, operr_mask+aiop_mask +set unfl_inx_mask, unfl_mask+aunfl_mask+ainex_mask +set ovfl_inx_mask, ovfl_mask+aovfl_mask+ainex_mask + +######### +# misc. # +######### +set rnd_stky_bit, 29 # stky bit pos in longword + +set sign_bit, 0x7 # sign bit +set signan_bit, 0x6 # signalling nan bit + +set sgl_thresh, 0x3f81 # minimum sgl exponent +set dbl_thresh, 0x3c01 # minimum dbl exponent + +set x_mode, 0x0 # extended precision +set s_mode, 0x4 # single precision +set d_mode, 0x8 # double precision + +set rn_mode, 0x0 # round-to-nearest +set rz_mode, 0x1 # round-to-zero +set rm_mode, 0x2 # round-tp-minus-infinity +set rp_mode, 0x3 # round-to-plus-infinity + +set mantissalen, 64 # length of mantissa in bits + +set BYTE, 1 # len(byte) == 1 byte +set WORD, 2 # len(word) == 2 bytes +set LONG, 4 # len(longword) == 2 bytes + +set BSUN_VEC, 0xc0 # bsun vector offset +set INEX_VEC, 0xc4 # inexact vector offset +set DZ_VEC, 0xc8 # dz vector offset +set UNFL_VEC, 0xcc # unfl vector offset +set OPERR_VEC, 0xd0 # operr vector offset +set OVFL_VEC, 0xd4 # ovfl vector offset +set SNAN_VEC, 0xd8 # snan vector offset + +########################### +# SPecial CONDition FLaGs # +########################### +set ftrapcc_flg, 0x01 # flag bit: ftrapcc exception +set fbsun_flg, 0x02 # flag bit: bsun exception +set mia7_flg, 0x04 # flag bit: (a7)+ <ea> +set mda7_flg, 0x08 # flag bit: -(a7) <ea> +set fmovm_flg, 0x40 # flag bit: fmovm instruction +set immed_flg, 0x80 # flag bit: &<data> <ea> + +set ftrapcc_bit, 0x0 +set fbsun_bit, 0x1 +set mia7_bit, 0x2 +set mda7_bit, 0x3 +set immed_bit, 0x7 + +################################## +# TRANSCENDENTAL "LAST-OP" FLAGS # +################################## +set FMUL_OP, 0x0 # fmul instr performed last +set FDIV_OP, 0x1 # fdiv performed last +set FADD_OP, 0x2 # fadd performed last +set FMOV_OP, 0x3 # fmov performed last + +############# +# CONSTANTS # +############# +T1: long 0x40C62D38,0xD3D64634 # 16381 LOG2 LEAD +T2: long 0x3D6F90AE,0xB1E75CC7 # 16381 LOG2 TRAIL + +PI: long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000 +PIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 + +TWOBYPI: + long 0x3FE45F30,0x6DC9C883 + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fsins_ +_fsins_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L0_2s + bsr.l ssin # operand is a NORM + bra.b _L0_6s +_L0_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L0_3s # no + bsr.l src_zero # yes + bra.b _L0_6s +_L0_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L0_4s # no + bsr.l t_operr # yes + bra.b _L0_6s +_L0_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L0_5s # no + bsr.l src_qnan # yes + bra.b _L0_6s +_L0_5s: + bsr.l ssind # operand is a DENORM +_L0_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fsind_ +_fsind_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L0_2d + bsr.l ssin # operand is a NORM + bra.b _L0_6d +_L0_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L0_3d # no + bsr.l src_zero # yes + bra.b _L0_6d +_L0_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L0_4d # no + bsr.l t_operr # yes + bra.b _L0_6d +_L0_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L0_5d # no + bsr.l src_qnan # yes + bra.b _L0_6d +_L0_5d: + bsr.l ssind # operand is a DENORM +_L0_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fsinx_ +_fsinx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L0_2x + bsr.l ssin # operand is a NORM + bra.b _L0_6x +_L0_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L0_3x # no + bsr.l src_zero # yes + bra.b _L0_6x +_L0_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L0_4x # no + bsr.l t_operr # yes + bra.b _L0_6x +_L0_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L0_5x # no + bsr.l src_qnan # yes + bra.b _L0_6x +_L0_5x: + bsr.l ssind # operand is a DENORM +_L0_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fcoss_ +_fcoss_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L1_2s + bsr.l scos # operand is a NORM + bra.b _L1_6s +_L1_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L1_3s # no + bsr.l ld_pone # yes + bra.b _L1_6s +_L1_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L1_4s # no + bsr.l t_operr # yes + bra.b _L1_6s +_L1_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L1_5s # no + bsr.l src_qnan # yes + bra.b _L1_6s +_L1_5s: + bsr.l scosd # operand is a DENORM +_L1_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fcosd_ +_fcosd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L1_2d + bsr.l scos # operand is a NORM + bra.b _L1_6d +_L1_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L1_3d # no + bsr.l ld_pone # yes + bra.b _L1_6d +_L1_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L1_4d # no + bsr.l t_operr # yes + bra.b _L1_6d +_L1_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L1_5d # no + bsr.l src_qnan # yes + bra.b _L1_6d +_L1_5d: + bsr.l scosd # operand is a DENORM +_L1_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fcosx_ +_fcosx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L1_2x + bsr.l scos # operand is a NORM + bra.b _L1_6x +_L1_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L1_3x # no + bsr.l ld_pone # yes + bra.b _L1_6x +_L1_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L1_4x # no + bsr.l t_operr # yes + bra.b _L1_6x +_L1_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L1_5x # no + bsr.l src_qnan # yes + bra.b _L1_6x +_L1_5x: + bsr.l scosd # operand is a DENORM +_L1_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fsinhs_ +_fsinhs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L2_2s + bsr.l ssinh # operand is a NORM + bra.b _L2_6s +_L2_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L2_3s # no + bsr.l src_zero # yes + bra.b _L2_6s +_L2_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L2_4s # no + bsr.l src_inf # yes + bra.b _L2_6s +_L2_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L2_5s # no + bsr.l src_qnan # yes + bra.b _L2_6s +_L2_5s: + bsr.l ssinhd # operand is a DENORM +_L2_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fsinhd_ +_fsinhd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L2_2d + bsr.l ssinh # operand is a NORM + bra.b _L2_6d +_L2_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L2_3d # no + bsr.l src_zero # yes + bra.b _L2_6d +_L2_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L2_4d # no + bsr.l src_inf # yes + bra.b _L2_6d +_L2_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L2_5d # no + bsr.l src_qnan # yes + bra.b _L2_6d +_L2_5d: + bsr.l ssinhd # operand is a DENORM +_L2_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fsinhx_ +_fsinhx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L2_2x + bsr.l ssinh # operand is a NORM + bra.b _L2_6x +_L2_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L2_3x # no + bsr.l src_zero # yes + bra.b _L2_6x +_L2_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L2_4x # no + bsr.l src_inf # yes + bra.b _L2_6x +_L2_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L2_5x # no + bsr.l src_qnan # yes + bra.b _L2_6x +_L2_5x: + bsr.l ssinhd # operand is a DENORM +_L2_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _flognp1s_ +_flognp1s_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L3_2s + bsr.l slognp1 # operand is a NORM + bra.b _L3_6s +_L3_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L3_3s # no + bsr.l src_zero # yes + bra.b _L3_6s +_L3_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L3_4s # no + bsr.l sopr_inf # yes + bra.b _L3_6s +_L3_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L3_5s # no + bsr.l src_qnan # yes + bra.b _L3_6s +_L3_5s: + bsr.l slognp1d # operand is a DENORM +_L3_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flognp1d_ +_flognp1d_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L3_2d + bsr.l slognp1 # operand is a NORM + bra.b _L3_6d +_L3_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L3_3d # no + bsr.l src_zero # yes + bra.b _L3_6d +_L3_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L3_4d # no + bsr.l sopr_inf # yes + bra.b _L3_6d +_L3_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L3_5d # no + bsr.l src_qnan # yes + bra.b _L3_6d +_L3_5d: + bsr.l slognp1d # operand is a DENORM +_L3_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flognp1x_ +_flognp1x_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L3_2x + bsr.l slognp1 # operand is a NORM + bra.b _L3_6x +_L3_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L3_3x # no + bsr.l src_zero # yes + bra.b _L3_6x +_L3_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L3_4x # no + bsr.l sopr_inf # yes + bra.b _L3_6x +_L3_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L3_5x # no + bsr.l src_qnan # yes + bra.b _L3_6x +_L3_5x: + bsr.l slognp1d # operand is a DENORM +_L3_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fetoxm1s_ +_fetoxm1s_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L4_2s + bsr.l setoxm1 # operand is a NORM + bra.b _L4_6s +_L4_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L4_3s # no + bsr.l src_zero # yes + bra.b _L4_6s +_L4_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L4_4s # no + bsr.l setoxm1i # yes + bra.b _L4_6s +_L4_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L4_5s # no + bsr.l src_qnan # yes + bra.b _L4_6s +_L4_5s: + bsr.l setoxm1d # operand is a DENORM +_L4_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fetoxm1d_ +_fetoxm1d_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L4_2d + bsr.l setoxm1 # operand is a NORM + bra.b _L4_6d +_L4_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L4_3d # no + bsr.l src_zero # yes + bra.b _L4_6d +_L4_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L4_4d # no + bsr.l setoxm1i # yes + bra.b _L4_6d +_L4_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L4_5d # no + bsr.l src_qnan # yes + bra.b _L4_6d +_L4_5d: + bsr.l setoxm1d # operand is a DENORM +_L4_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fetoxm1x_ +_fetoxm1x_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L4_2x + bsr.l setoxm1 # operand is a NORM + bra.b _L4_6x +_L4_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L4_3x # no + bsr.l src_zero # yes + bra.b _L4_6x +_L4_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L4_4x # no + bsr.l setoxm1i # yes + bra.b _L4_6x +_L4_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L4_5x # no + bsr.l src_qnan # yes + bra.b _L4_6x +_L4_5x: + bsr.l setoxm1d # operand is a DENORM +_L4_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _ftanhs_ +_ftanhs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L5_2s + bsr.l stanh # operand is a NORM + bra.b _L5_6s +_L5_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L5_3s # no + bsr.l src_zero # yes + bra.b _L5_6s +_L5_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L5_4s # no + bsr.l src_one # yes + bra.b _L5_6s +_L5_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L5_5s # no + bsr.l src_qnan # yes + bra.b _L5_6s +_L5_5s: + bsr.l stanhd # operand is a DENORM +_L5_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftanhd_ +_ftanhd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L5_2d + bsr.l stanh # operand is a NORM + bra.b _L5_6d +_L5_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L5_3d # no + bsr.l src_zero # yes + bra.b _L5_6d +_L5_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L5_4d # no + bsr.l src_one # yes + bra.b _L5_6d +_L5_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L5_5d # no + bsr.l src_qnan # yes + bra.b _L5_6d +_L5_5d: + bsr.l stanhd # operand is a DENORM +_L5_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftanhx_ +_ftanhx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L5_2x + bsr.l stanh # operand is a NORM + bra.b _L5_6x +_L5_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L5_3x # no + bsr.l src_zero # yes + bra.b _L5_6x +_L5_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L5_4x # no + bsr.l src_one # yes + bra.b _L5_6x +_L5_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L5_5x # no + bsr.l src_qnan # yes + bra.b _L5_6x +_L5_5x: + bsr.l stanhd # operand is a DENORM +_L5_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fatans_ +_fatans_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L6_2s + bsr.l satan # operand is a NORM + bra.b _L6_6s +_L6_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L6_3s # no + bsr.l src_zero # yes + bra.b _L6_6s +_L6_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L6_4s # no + bsr.l spi_2 # yes + bra.b _L6_6s +_L6_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L6_5s # no + bsr.l src_qnan # yes + bra.b _L6_6s +_L6_5s: + bsr.l satand # operand is a DENORM +_L6_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fatand_ +_fatand_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L6_2d + bsr.l satan # operand is a NORM + bra.b _L6_6d +_L6_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L6_3d # no + bsr.l src_zero # yes + bra.b _L6_6d +_L6_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L6_4d # no + bsr.l spi_2 # yes + bra.b _L6_6d +_L6_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L6_5d # no + bsr.l src_qnan # yes + bra.b _L6_6d +_L6_5d: + bsr.l satand # operand is a DENORM +_L6_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fatanx_ +_fatanx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L6_2x + bsr.l satan # operand is a NORM + bra.b _L6_6x +_L6_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L6_3x # no + bsr.l src_zero # yes + bra.b _L6_6x +_L6_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L6_4x # no + bsr.l spi_2 # yes + bra.b _L6_6x +_L6_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L6_5x # no + bsr.l src_qnan # yes + bra.b _L6_6x +_L6_5x: + bsr.l satand # operand is a DENORM +_L6_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fasins_ +_fasins_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L7_2s + bsr.l sasin # operand is a NORM + bra.b _L7_6s +_L7_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L7_3s # no + bsr.l src_zero # yes + bra.b _L7_6s +_L7_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L7_4s # no + bsr.l t_operr # yes + bra.b _L7_6s +_L7_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L7_5s # no + bsr.l src_qnan # yes + bra.b _L7_6s +_L7_5s: + bsr.l sasind # operand is a DENORM +_L7_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fasind_ +_fasind_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L7_2d + bsr.l sasin # operand is a NORM + bra.b _L7_6d +_L7_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L7_3d # no + bsr.l src_zero # yes + bra.b _L7_6d +_L7_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L7_4d # no + bsr.l t_operr # yes + bra.b _L7_6d +_L7_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L7_5d # no + bsr.l src_qnan # yes + bra.b _L7_6d +_L7_5d: + bsr.l sasind # operand is a DENORM +_L7_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fasinx_ +_fasinx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L7_2x + bsr.l sasin # operand is a NORM + bra.b _L7_6x +_L7_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L7_3x # no + bsr.l src_zero # yes + bra.b _L7_6x +_L7_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L7_4x # no + bsr.l t_operr # yes + bra.b _L7_6x +_L7_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L7_5x # no + bsr.l src_qnan # yes + bra.b _L7_6x +_L7_5x: + bsr.l sasind # operand is a DENORM +_L7_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fatanhs_ +_fatanhs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L8_2s + bsr.l satanh # operand is a NORM + bra.b _L8_6s +_L8_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L8_3s # no + bsr.l src_zero # yes + bra.b _L8_6s +_L8_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L8_4s # no + bsr.l t_operr # yes + bra.b _L8_6s +_L8_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L8_5s # no + bsr.l src_qnan # yes + bra.b _L8_6s +_L8_5s: + bsr.l satanhd # operand is a DENORM +_L8_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fatanhd_ +_fatanhd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L8_2d + bsr.l satanh # operand is a NORM + bra.b _L8_6d +_L8_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L8_3d # no + bsr.l src_zero # yes + bra.b _L8_6d +_L8_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L8_4d # no + bsr.l t_operr # yes + bra.b _L8_6d +_L8_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L8_5d # no + bsr.l src_qnan # yes + bra.b _L8_6d +_L8_5d: + bsr.l satanhd # operand is a DENORM +_L8_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fatanhx_ +_fatanhx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L8_2x + bsr.l satanh # operand is a NORM + bra.b _L8_6x +_L8_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L8_3x # no + bsr.l src_zero # yes + bra.b _L8_6x +_L8_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L8_4x # no + bsr.l t_operr # yes + bra.b _L8_6x +_L8_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L8_5x # no + bsr.l src_qnan # yes + bra.b _L8_6x +_L8_5x: + bsr.l satanhd # operand is a DENORM +_L8_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _ftans_ +_ftans_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L9_2s + bsr.l stan # operand is a NORM + bra.b _L9_6s +_L9_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L9_3s # no + bsr.l src_zero # yes + bra.b _L9_6s +_L9_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L9_4s # no + bsr.l t_operr # yes + bra.b _L9_6s +_L9_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L9_5s # no + bsr.l src_qnan # yes + bra.b _L9_6s +_L9_5s: + bsr.l stand # operand is a DENORM +_L9_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftand_ +_ftand_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L9_2d + bsr.l stan # operand is a NORM + bra.b _L9_6d +_L9_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L9_3d # no + bsr.l src_zero # yes + bra.b _L9_6d +_L9_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L9_4d # no + bsr.l t_operr # yes + bra.b _L9_6d +_L9_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L9_5d # no + bsr.l src_qnan # yes + bra.b _L9_6d +_L9_5d: + bsr.l stand # operand is a DENORM +_L9_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftanx_ +_ftanx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L9_2x + bsr.l stan # operand is a NORM + bra.b _L9_6x +_L9_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L9_3x # no + bsr.l src_zero # yes + bra.b _L9_6x +_L9_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L9_4x # no + bsr.l t_operr # yes + bra.b _L9_6x +_L9_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L9_5x # no + bsr.l src_qnan # yes + bra.b _L9_6x +_L9_5x: + bsr.l stand # operand is a DENORM +_L9_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fetoxs_ +_fetoxs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L10_2s + bsr.l setox # operand is a NORM + bra.b _L10_6s +_L10_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L10_3s # no + bsr.l ld_pone # yes + bra.b _L10_6s +_L10_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L10_4s # no + bsr.l szr_inf # yes + bra.b _L10_6s +_L10_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L10_5s # no + bsr.l src_qnan # yes + bra.b _L10_6s +_L10_5s: + bsr.l setoxd # operand is a DENORM +_L10_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fetoxd_ +_fetoxd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L10_2d + bsr.l setox # operand is a NORM + bra.b _L10_6d +_L10_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L10_3d # no + bsr.l ld_pone # yes + bra.b _L10_6d +_L10_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L10_4d # no + bsr.l szr_inf # yes + bra.b _L10_6d +_L10_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L10_5d # no + bsr.l src_qnan # yes + bra.b _L10_6d +_L10_5d: + bsr.l setoxd # operand is a DENORM +_L10_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fetoxx_ +_fetoxx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L10_2x + bsr.l setox # operand is a NORM + bra.b _L10_6x +_L10_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L10_3x # no + bsr.l ld_pone # yes + bra.b _L10_6x +_L10_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L10_4x # no + bsr.l szr_inf # yes + bra.b _L10_6x +_L10_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L10_5x # no + bsr.l src_qnan # yes + bra.b _L10_6x +_L10_5x: + bsr.l setoxd # operand is a DENORM +_L10_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _ftwotoxs_ +_ftwotoxs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L11_2s + bsr.l stwotox # operand is a NORM + bra.b _L11_6s +_L11_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L11_3s # no + bsr.l ld_pone # yes + bra.b _L11_6s +_L11_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L11_4s # no + bsr.l szr_inf # yes + bra.b _L11_6s +_L11_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L11_5s # no + bsr.l src_qnan # yes + bra.b _L11_6s +_L11_5s: + bsr.l stwotoxd # operand is a DENORM +_L11_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftwotoxd_ +_ftwotoxd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L11_2d + bsr.l stwotox # operand is a NORM + bra.b _L11_6d +_L11_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L11_3d # no + bsr.l ld_pone # yes + bra.b _L11_6d +_L11_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L11_4d # no + bsr.l szr_inf # yes + bra.b _L11_6d +_L11_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L11_5d # no + bsr.l src_qnan # yes + bra.b _L11_6d +_L11_5d: + bsr.l stwotoxd # operand is a DENORM +_L11_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftwotoxx_ +_ftwotoxx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L11_2x + bsr.l stwotox # operand is a NORM + bra.b _L11_6x +_L11_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L11_3x # no + bsr.l ld_pone # yes + bra.b _L11_6x +_L11_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L11_4x # no + bsr.l szr_inf # yes + bra.b _L11_6x +_L11_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L11_5x # no + bsr.l src_qnan # yes + bra.b _L11_6x +_L11_5x: + bsr.l stwotoxd # operand is a DENORM +_L11_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _ftentoxs_ +_ftentoxs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L12_2s + bsr.l stentox # operand is a NORM + bra.b _L12_6s +_L12_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L12_3s # no + bsr.l ld_pone # yes + bra.b _L12_6s +_L12_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L12_4s # no + bsr.l szr_inf # yes + bra.b _L12_6s +_L12_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L12_5s # no + bsr.l src_qnan # yes + bra.b _L12_6s +_L12_5s: + bsr.l stentoxd # operand is a DENORM +_L12_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftentoxd_ +_ftentoxd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L12_2d + bsr.l stentox # operand is a NORM + bra.b _L12_6d +_L12_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L12_3d # no + bsr.l ld_pone # yes + bra.b _L12_6d +_L12_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L12_4d # no + bsr.l szr_inf # yes + bra.b _L12_6d +_L12_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L12_5d # no + bsr.l src_qnan # yes + bra.b _L12_6d +_L12_5d: + bsr.l stentoxd # operand is a DENORM +_L12_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _ftentoxx_ +_ftentoxx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L12_2x + bsr.l stentox # operand is a NORM + bra.b _L12_6x +_L12_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L12_3x # no + bsr.l ld_pone # yes + bra.b _L12_6x +_L12_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L12_4x # no + bsr.l szr_inf # yes + bra.b _L12_6x +_L12_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L12_5x # no + bsr.l src_qnan # yes + bra.b _L12_6x +_L12_5x: + bsr.l stentoxd # operand is a DENORM +_L12_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _flogns_ +_flogns_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L13_2s + bsr.l slogn # operand is a NORM + bra.b _L13_6s +_L13_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L13_3s # no + bsr.l t_dz2 # yes + bra.b _L13_6s +_L13_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L13_4s # no + bsr.l sopr_inf # yes + bra.b _L13_6s +_L13_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L13_5s # no + bsr.l src_qnan # yes + bra.b _L13_6s +_L13_5s: + bsr.l slognd # operand is a DENORM +_L13_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flognd_ +_flognd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L13_2d + bsr.l slogn # operand is a NORM + bra.b _L13_6d +_L13_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L13_3d # no + bsr.l t_dz2 # yes + bra.b _L13_6d +_L13_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L13_4d # no + bsr.l sopr_inf # yes + bra.b _L13_6d +_L13_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L13_5d # no + bsr.l src_qnan # yes + bra.b _L13_6d +_L13_5d: + bsr.l slognd # operand is a DENORM +_L13_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flognx_ +_flognx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L13_2x + bsr.l slogn # operand is a NORM + bra.b _L13_6x +_L13_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L13_3x # no + bsr.l t_dz2 # yes + bra.b _L13_6x +_L13_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L13_4x # no + bsr.l sopr_inf # yes + bra.b _L13_6x +_L13_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L13_5x # no + bsr.l src_qnan # yes + bra.b _L13_6x +_L13_5x: + bsr.l slognd # operand is a DENORM +_L13_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _flog10s_ +_flog10s_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L14_2s + bsr.l slog10 # operand is a NORM + bra.b _L14_6s +_L14_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L14_3s # no + bsr.l t_dz2 # yes + bra.b _L14_6s +_L14_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L14_4s # no + bsr.l sopr_inf # yes + bra.b _L14_6s +_L14_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L14_5s # no + bsr.l src_qnan # yes + bra.b _L14_6s +_L14_5s: + bsr.l slog10d # operand is a DENORM +_L14_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flog10d_ +_flog10d_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L14_2d + bsr.l slog10 # operand is a NORM + bra.b _L14_6d +_L14_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L14_3d # no + bsr.l t_dz2 # yes + bra.b _L14_6d +_L14_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L14_4d # no + bsr.l sopr_inf # yes + bra.b _L14_6d +_L14_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L14_5d # no + bsr.l src_qnan # yes + bra.b _L14_6d +_L14_5d: + bsr.l slog10d # operand is a DENORM +_L14_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flog10x_ +_flog10x_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L14_2x + bsr.l slog10 # operand is a NORM + bra.b _L14_6x +_L14_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L14_3x # no + bsr.l t_dz2 # yes + bra.b _L14_6x +_L14_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L14_4x # no + bsr.l sopr_inf # yes + bra.b _L14_6x +_L14_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L14_5x # no + bsr.l src_qnan # yes + bra.b _L14_6x +_L14_5x: + bsr.l slog10d # operand is a DENORM +_L14_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _flog2s_ +_flog2s_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L15_2s + bsr.l slog2 # operand is a NORM + bra.b _L15_6s +_L15_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L15_3s # no + bsr.l t_dz2 # yes + bra.b _L15_6s +_L15_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L15_4s # no + bsr.l sopr_inf # yes + bra.b _L15_6s +_L15_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L15_5s # no + bsr.l src_qnan # yes + bra.b _L15_6s +_L15_5s: + bsr.l slog2d # operand is a DENORM +_L15_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flog2d_ +_flog2d_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L15_2d + bsr.l slog2 # operand is a NORM + bra.b _L15_6d +_L15_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L15_3d # no + bsr.l t_dz2 # yes + bra.b _L15_6d +_L15_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L15_4d # no + bsr.l sopr_inf # yes + bra.b _L15_6d +_L15_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L15_5d # no + bsr.l src_qnan # yes + bra.b _L15_6d +_L15_5d: + bsr.l slog2d # operand is a DENORM +_L15_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _flog2x_ +_flog2x_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L15_2x + bsr.l slog2 # operand is a NORM + bra.b _L15_6x +_L15_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L15_3x # no + bsr.l t_dz2 # yes + bra.b _L15_6x +_L15_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L15_4x # no + bsr.l sopr_inf # yes + bra.b _L15_6x +_L15_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L15_5x # no + bsr.l src_qnan # yes + bra.b _L15_6x +_L15_5x: + bsr.l slog2d # operand is a DENORM +_L15_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fcoshs_ +_fcoshs_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L16_2s + bsr.l scosh # operand is a NORM + bra.b _L16_6s +_L16_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L16_3s # no + bsr.l ld_pone # yes + bra.b _L16_6s +_L16_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L16_4s # no + bsr.l ld_pinf # yes + bra.b _L16_6s +_L16_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L16_5s # no + bsr.l src_qnan # yes + bra.b _L16_6s +_L16_5s: + bsr.l scoshd # operand is a DENORM +_L16_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fcoshd_ +_fcoshd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L16_2d + bsr.l scosh # operand is a NORM + bra.b _L16_6d +_L16_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L16_3d # no + bsr.l ld_pone # yes + bra.b _L16_6d +_L16_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L16_4d # no + bsr.l ld_pinf # yes + bra.b _L16_6d +_L16_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L16_5d # no + bsr.l src_qnan # yes + bra.b _L16_6d +_L16_5d: + bsr.l scoshd # operand is a DENORM +_L16_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fcoshx_ +_fcoshx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L16_2x + bsr.l scosh # operand is a NORM + bra.b _L16_6x +_L16_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L16_3x # no + bsr.l ld_pone # yes + bra.b _L16_6x +_L16_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L16_4x # no + bsr.l ld_pinf # yes + bra.b _L16_6x +_L16_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L16_5x # no + bsr.l src_qnan # yes + bra.b _L16_6x +_L16_5x: + bsr.l scoshd # operand is a DENORM +_L16_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _facoss_ +_facoss_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L17_2s + bsr.l sacos # operand is a NORM + bra.b _L17_6s +_L17_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L17_3s # no + bsr.l ld_ppi2 # yes + bra.b _L17_6s +_L17_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L17_4s # no + bsr.l t_operr # yes + bra.b _L17_6s +_L17_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L17_5s # no + bsr.l src_qnan # yes + bra.b _L17_6s +_L17_5s: + bsr.l sacosd # operand is a DENORM +_L17_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _facosd_ +_facosd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L17_2d + bsr.l sacos # operand is a NORM + bra.b _L17_6d +_L17_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L17_3d # no + bsr.l ld_ppi2 # yes + bra.b _L17_6d +_L17_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L17_4d # no + bsr.l t_operr # yes + bra.b _L17_6d +_L17_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L17_5d # no + bsr.l src_qnan # yes + bra.b _L17_6d +_L17_5d: + bsr.l sacosd # operand is a DENORM +_L17_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _facosx_ +_facosx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L17_2x + bsr.l sacos # operand is a NORM + bra.b _L17_6x +_L17_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L17_3x # no + bsr.l ld_ppi2 # yes + bra.b _L17_6x +_L17_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L17_4x # no + bsr.l t_operr # yes + bra.b _L17_6x +_L17_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L17_5x # no + bsr.l src_qnan # yes + bra.b _L17_6x +_L17_5x: + bsr.l sacosd # operand is a DENORM +_L17_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fgetexps_ +_fgetexps_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L18_2s + bsr.l sgetexp # operand is a NORM + bra.b _L18_6s +_L18_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L18_3s # no + bsr.l src_zero # yes + bra.b _L18_6s +_L18_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L18_4s # no + bsr.l t_operr # yes + bra.b _L18_6s +_L18_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L18_5s # no + bsr.l src_qnan # yes + bra.b _L18_6s +_L18_5s: + bsr.l sgetexpd # operand is a DENORM +_L18_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fgetexpd_ +_fgetexpd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L18_2d + bsr.l sgetexp # operand is a NORM + bra.b _L18_6d +_L18_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L18_3d # no + bsr.l src_zero # yes + bra.b _L18_6d +_L18_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L18_4d # no + bsr.l t_operr # yes + bra.b _L18_6d +_L18_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L18_5d # no + bsr.l src_qnan # yes + bra.b _L18_6d +_L18_5d: + bsr.l sgetexpd # operand is a DENORM +_L18_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fgetexpx_ +_fgetexpx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L18_2x + bsr.l sgetexp # operand is a NORM + bra.b _L18_6x +_L18_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L18_3x # no + bsr.l src_zero # yes + bra.b _L18_6x +_L18_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L18_4x # no + bsr.l t_operr # yes + bra.b _L18_6x +_L18_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L18_5x # no + bsr.l src_qnan # yes + bra.b _L18_6x +_L18_5x: + bsr.l sgetexpd # operand is a DENORM +_L18_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fgetmans_ +_fgetmans_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L19_2s + bsr.l sgetman # operand is a NORM + bra.b _L19_6s +_L19_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L19_3s # no + bsr.l src_zero # yes + bra.b _L19_6s +_L19_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L19_4s # no + bsr.l t_operr # yes + bra.b _L19_6s +_L19_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L19_5s # no + bsr.l src_qnan # yes + bra.b _L19_6s +_L19_5s: + bsr.l sgetmand # operand is a DENORM +_L19_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fgetmand_ +_fgetmand_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L19_2d + bsr.l sgetman # operand is a NORM + bra.b _L19_6d +_L19_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L19_3d # no + bsr.l src_zero # yes + bra.b _L19_6d +_L19_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L19_4d # no + bsr.l t_operr # yes + bra.b _L19_6d +_L19_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L19_5d # no + bsr.l src_qnan # yes + bra.b _L19_6d +_L19_5d: + bsr.l sgetmand # operand is a DENORM +_L19_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fgetmanx_ +_fgetmanx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L19_2x + bsr.l sgetman # operand is a NORM + bra.b _L19_6x +_L19_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L19_3x # no + bsr.l src_zero # yes + bra.b _L19_6x +_L19_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L19_4x # no + bsr.l t_operr # yes + bra.b _L19_6x +_L19_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L19_5x # no + bsr.l src_qnan # yes + bra.b _L19_6x +_L19_5x: + bsr.l sgetmand # operand is a DENORM +_L19_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# MONADIC TEMPLATE # +######################################################################### + global _fsincoss_ +_fsincoss_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L20_2s + bsr.l ssincos # operand is a NORM + bra.b _L20_6s +_L20_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L20_3s # no + bsr.l ssincosz # yes + bra.b _L20_6s +_L20_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L20_4s # no + bsr.l ssincosi # yes + bra.b _L20_6s +_L20_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L20_5s # no + bsr.l ssincosqnan # yes + bra.b _L20_6s +_L20_5s: + bsr.l ssincosd # operand is a DENORM +_L20_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x &0x03,-(%sp) # store off fp0/fp1 + fmovm.x (%sp)+,&0x40 # fp0 now in fp1 + fmovm.x (%sp)+,&0x80 # fp1 now in fp0 + unlk %a6 + rts + + global _fsincosd_ +_fsincosd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl input + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + mov.b %d1,STAG(%a6) + tst.b %d1 + bne.b _L20_2d + bsr.l ssincos # operand is a NORM + bra.b _L20_6d +_L20_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L20_3d # no + bsr.l ssincosz # yes + bra.b _L20_6d +_L20_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L20_4d # no + bsr.l ssincosi # yes + bra.b _L20_6d +_L20_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L20_5d # no + bsr.l ssincosqnan # yes + bra.b _L20_6d +_L20_5d: + bsr.l ssincosd # operand is a DENORM +_L20_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x &0x03,-(%sp) # store off fp0/fp1 + fmovm.x (%sp)+,&0x40 # fp0 now in fp1 + fmovm.x (%sp)+,&0x80 # fp1 now in fp0 + unlk %a6 + rts + + global _fsincosx_ +_fsincosx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_SRC(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext input + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.b %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + tst.b %d1 + bne.b _L20_2x + bsr.l ssincos # operand is a NORM + bra.b _L20_6x +_L20_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L20_3x # no + bsr.l ssincosz # yes + bra.b _L20_6x +_L20_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L20_4x # no + bsr.l ssincosi # yes + bra.b _L20_6x +_L20_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L20_5x # no + bsr.l ssincosqnan # yes + bra.b _L20_6x +_L20_5x: + bsr.l ssincosd # operand is a DENORM +_L20_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x &0x03,-(%sp) # store off fp0/fp1 + fmovm.x (%sp)+,&0x40 # fp0 now in fp1 + fmovm.x (%sp)+,&0x80 # fp1 now in fp0 + unlk %a6 + rts + + +######################################################################### +# DYADIC TEMPLATE # +######################################################################### + global _frems_ +_frems_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.s 0xc(%a6),%fp0 # load sgl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L21_2s + bsr.l srem_snorm # operand is a NORM + bra.b _L21_6s +_L21_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L21_3s # no + bsr.l srem_szero # yes + bra.b _L21_6s +_L21_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L21_4s # no + bsr.l srem_sinf # yes + bra.b _L21_6s +_L21_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L21_5s # no + bsr.l sop_sqnan # yes + bra.b _L21_6s +_L21_5s: + bsr.l srem_sdnrm # operand is a DENORM +_L21_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fremd_ +_fremd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.d 0x10(%a6),%fp0 # load dbl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L21_2d + bsr.l srem_snorm # operand is a NORM + bra.b _L21_6d +_L21_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L21_3d # no + bsr.l srem_szero # yes + bra.b _L21_6d +_L21_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L21_4d # no + bsr.l srem_sinf # yes + bra.b _L21_6d +_L21_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L21_5d # no + bsr.l sop_sqnan # yes + bra.b _L21_6d +_L21_5d: + bsr.l srem_sdnrm # operand is a DENORM +_L21_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fremx_ +_fremx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_DST(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext dst + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + lea FP_SRC(%a6),%a0 + mov.l 0x14+0x0(%a6),0x0(%a0) # load ext src + mov.l 0x14+0x4(%a6),0x4(%a0) + mov.l 0x14+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L21_2x + bsr.l srem_snorm # operand is a NORM + bra.b _L21_6x +_L21_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L21_3x # no + bsr.l srem_szero # yes + bra.b _L21_6x +_L21_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L21_4x # no + bsr.l srem_sinf # yes + bra.b _L21_6x +_L21_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L21_5x # no + bsr.l sop_sqnan # yes + bra.b _L21_6x +_L21_5x: + bsr.l srem_sdnrm # operand is a DENORM +_L21_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# DYADIC TEMPLATE # +######################################################################### + global _fmods_ +_fmods_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.s 0xc(%a6),%fp0 # load sgl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L22_2s + bsr.l smod_snorm # operand is a NORM + bra.b _L22_6s +_L22_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L22_3s # no + bsr.l smod_szero # yes + bra.b _L22_6s +_L22_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L22_4s # no + bsr.l smod_sinf # yes + bra.b _L22_6s +_L22_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L22_5s # no + bsr.l sop_sqnan # yes + bra.b _L22_6s +_L22_5s: + bsr.l smod_sdnrm # operand is a DENORM +_L22_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fmodd_ +_fmodd_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.d 0x10(%a6),%fp0 # load dbl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L22_2d + bsr.l smod_snorm # operand is a NORM + bra.b _L22_6d +_L22_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L22_3d # no + bsr.l smod_szero # yes + bra.b _L22_6d +_L22_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L22_4d # no + bsr.l smod_sinf # yes + bra.b _L22_6d +_L22_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L22_5d # no + bsr.l sop_sqnan # yes + bra.b _L22_6d +_L22_5d: + bsr.l smod_sdnrm # operand is a DENORM +_L22_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fmodx_ +_fmodx_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_DST(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext dst + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + lea FP_SRC(%a6),%a0 + mov.l 0x14+0x0(%a6),0x0(%a0) # load ext src + mov.l 0x14+0x4(%a6),0x4(%a0) + mov.l 0x14+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L22_2x + bsr.l smod_snorm # operand is a NORM + bra.b _L22_6x +_L22_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L22_3x # no + bsr.l smod_szero # yes + bra.b _L22_6x +_L22_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L22_4x # no + bsr.l smod_sinf # yes + bra.b _L22_6x +_L22_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L22_5x # no + bsr.l sop_sqnan # yes + bra.b _L22_6x +_L22_5x: + bsr.l smod_sdnrm # operand is a DENORM +_L22_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# DYADIC TEMPLATE # +######################################################################### + global _fscales_ +_fscales_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.s 0x8(%a6),%fp0 # load sgl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.s 0xc(%a6),%fp0 # load sgl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L23_2s + bsr.l sscale_snorm # operand is a NORM + bra.b _L23_6s +_L23_2s: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L23_3s # no + bsr.l sscale_szero # yes + bra.b _L23_6s +_L23_3s: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L23_4s # no + bsr.l sscale_sinf # yes + bra.b _L23_6s +_L23_4s: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L23_5s # no + bsr.l sop_sqnan # yes + bra.b _L23_6s +_L23_5s: + bsr.l sscale_sdnrm # operand is a DENORM +_L23_6s: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fscaled_ +_fscaled_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + fmov.d 0x8(%a6),%fp0 # load dbl dst + fmov.x %fp0,FP_DST(%a6) + lea FP_DST(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + fmov.d 0x10(%a6),%fp0 # load dbl src + fmov.x %fp0,FP_SRC(%a6) + lea FP_SRC(%a6),%a0 + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L23_2d + bsr.l sscale_snorm # operand is a NORM + bra.b _L23_6d +_L23_2d: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L23_3d # no + bsr.l sscale_szero # yes + bra.b _L23_6d +_L23_3d: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L23_4d # no + bsr.l sscale_sinf # yes + bra.b _L23_6d +_L23_4d: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L23_5d # no + bsr.l sop_sqnan # yes + bra.b _L23_6d +_L23_5d: + bsr.l sscale_sdnrm # operand is a DENORM +_L23_6d: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + global _fscalex_ +_fscalex_: + link %a6,&-LOCAL_SIZE + + movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1 + fmovm.l %fpcr,%fpsr,USER_FPCR(%a6) # save ctrl regs + fmovm.x &0xc0,EXC_FP0(%a6) # save fp0/fp1 + + fmov.l &0x0,%fpcr # zero FPCR + +# +# copy, convert, and tag input argument +# + lea FP_DST(%a6),%a0 + mov.l 0x8+0x0(%a6),0x0(%a0) # load ext dst + mov.l 0x8+0x4(%a6),0x4(%a0) + mov.l 0x8+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,DTAG(%a6) + + lea FP_SRC(%a6),%a0 + mov.l 0x14+0x0(%a6),0x0(%a0) # load ext src + mov.l 0x14+0x4(%a6),0x4(%a0) + mov.l 0x14+0x8(%a6),0x8(%a0) + bsr.l tag # fetch operand type + mov.b %d0,STAG(%a6) + mov.l %d0,%d1 + + andi.l &0x00ff00ff,USER_FPSR(%a6) + + clr.l %d0 + mov.b FPCR_MODE(%a6),%d0 # pass rnd mode,prec + + lea FP_SRC(%a6),%a0 # pass ptr to src + lea FP_DST(%a6),%a1 # pass ptr to dst + + tst.b %d1 + bne.b _L23_2x + bsr.l sscale_snorm # operand is a NORM + bra.b _L23_6x +_L23_2x: + cmpi.b %d1,&ZERO # is operand a ZERO? + bne.b _L23_3x # no + bsr.l sscale_szero # yes + bra.b _L23_6x +_L23_3x: + cmpi.b %d1,&INF # is operand an INF? + bne.b _L23_4x # no + bsr.l sscale_sinf # yes + bra.b _L23_6x +_L23_4x: + cmpi.b %d1,&QNAN # is operand a QNAN? + bne.b _L23_5x # no + bsr.l sop_sqnan # yes + bra.b _L23_6x +_L23_5x: + bsr.l sscale_sdnrm # operand is a DENORM +_L23_6x: + +# +# Result is now in FP0 +# + movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1 + fmovm.l USER_FPCR(%a6),%fpcr,%fpsr # restore ctrl regs + fmovm.x EXC_FP1(%a6),&0x40 # restore fp1 + unlk %a6 + rts + + +######################################################################### +# ssin(): computes the sine of a normalized input # +# ssind(): computes the sine of a denormalized input # +# scos(): computes the cosine of a normalized input # +# scosd(): computes the cosine of a denormalized input # +# ssincos(): computes the sine and cosine of a normalized input # +# ssincosd(): computes the sine and cosine of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = sin(X) or cos(X) # +# # +# For ssincos(X): # +# fp0 = sin(X) # +# fp1 = cos(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 1 ulp in 64 significant bit, i.e. # +# within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# SIN and COS: # +# 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1. # +# # +# 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7. # +# # +# 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let # +# k = N mod 4, so in particular, k = 0,1,2,or 3. # +# Overwrite k by k := k + AdjN. # +# # +# 4. If k is even, go to 6. # +# # +# 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. # +# Return sgn*cos(r) where cos(r) is approximated by an # +# even polynomial in r, 1 + r*r*(B1+s*(B2+ ... + s*B8)), # +# s = r*r. # +# Exit. # +# # +# 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r) # +# where sin(r) is approximated by an odd polynomial in r # +# r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r. # +# Exit. # +# # +# 7. If |X| > 1, go to 9. # +# # +# 8. (|X|<2**(-40)) If SIN is invoked, return X; # +# otherwise return 1. # +# # +# 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, # +# go back to 3. # +# # +# SINCOS: # +# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. # +# # +# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let # +# k = N mod 4, so in particular, k = 0,1,2,or 3. # +# # +# 3. If k is even, go to 5. # +# # +# 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), ie. # +# j1 exclusive or with the l.s.b. of k. # +# sgn1 := (-1)**j1, sgn2 := (-1)**j2. # +# SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where # +# sin(r) and cos(r) are computed as odd and even # +# polynomials in r, respectively. Exit # +# # +# 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1. # +# SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where # +# sin(r) and cos(r) are computed as odd and even # +# polynomials in r, respectively. Exit # +# # +# 6. If |X| > 1, go to 8. # +# # +# 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit. # +# # +# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, # +# go back to 2. # +# # +######################################################################### + +SINA7: long 0xBD6AAA77,0xCCC994F5 +SINA6: long 0x3DE61209,0x7AAE8DA1 +SINA5: long 0xBE5AE645,0x2A118AE4 +SINA4: long 0x3EC71DE3,0xA5341531 +SINA3: long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000 +SINA2: long 0x3FF80000,0x88888888,0x888859AF,0x00000000 +SINA1: long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000 + +COSB8: long 0x3D2AC4D0,0xD6011EE3 +COSB7: long 0xBDA9396F,0x9F45AC19 +COSB6: long 0x3E21EED9,0x0612C972 +COSB5: long 0xBE927E4F,0xB79D9FCF +COSB4: long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000 +COSB3: long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000 +COSB2: long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E +COSB1: long 0xBF000000 + + set INARG,FP_SCR0 + + set X,FP_SCR0 +# set XDCARE,X+2 + set XFRAC,X+4 + + set RPRIME,FP_SCR0 + set SPRIME,FP_SCR1 + + set POSNEG1,L_SCR1 + set TWOTO63,L_SCR1 + + set ENDFLAG,L_SCR2 + set INT,L_SCR2 + + set ADJN,L_SCR3 + +############################################ + global ssin +ssin: + mov.l &0,ADJN(%a6) # yes; SET ADJN TO 0 + bra.b SINBGN + +############################################ + global scos +scos: + mov.l &1,ADJN(%a6) # yes; SET ADJN TO 1 + +############################################ +SINBGN: +#--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE + + fmov.x (%a0),%fp0 # LOAD INPUT + fmov.x %fp0,X(%a6) # save input at X + +# "COMPACTIFY" X + mov.l (%a0),%d1 # put exp in hi word + mov.w 4(%a0),%d1 # fetch hi(man) + and.l &0x7FFFFFFF,%d1 # strip sign + + cmpi.l %d1,&0x3FD78000 # is |X| >= 2**(-40)? + bge.b SOK1 # no + bra.w SINSM # yes; input is very small + +SOK1: + cmp.l %d1,&0x4004BC7E # is |X| < 15 PI? + blt.b SINMAIN # no + bra.w SREDUCEX # yes; input is very large + +#--THIS IS THE USUAL CASE, |X| <= 15 PI. +#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. +SINMAIN: + fmov.x %fp0,%fp1 + fmul.d TWOBYPI(%pc),%fp1 # X*2/PI + + lea PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32 + + fmov.l %fp1,INT(%a6) # CONVERT TO INTEGER + + mov.l INT(%a6),%d1 # make a copy of N + asl.l &4,%d1 # N *= 16 + add.l %d1,%a1 # tbl_addr = a1 + (N*16) + +# A1 IS THE ADDRESS OF N*PIBY2 +# ...WHICH IS IN TWO PIECES Y1 & Y2 + fsub.x (%a1)+,%fp0 # X-Y1 + fsub.s (%a1),%fp0 # fp0 = R = (X-Y1)-Y2 + +SINCONT: +#--continuation from REDUCEX + +#--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED + mov.l INT(%a6),%d1 + add.l ADJN(%a6),%d1 # SEE IF D0 IS ODD OR EVEN + ror.l &1,%d1 # D0 WAS ODD IFF D0 IS NEGATIVE + cmp.l %d1,&0 + blt.w COSPOLY + +#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J. +#--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY +#--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE +#--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS +#--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))]) +#--WHERE T=S*S. +#--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION +#--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT. +SINPOLY: + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmov.x %fp0,X(%a6) # X IS R + fmul.x %fp0,%fp0 # FP0 IS S + + fmov.d SINA7(%pc),%fp3 + fmov.d SINA6(%pc),%fp2 + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS T + + ror.l &1,%d1 + and.l &0x80000000,%d1 +# ...LEAST SIG. BIT OF D0 IN SIGN POSITION + eor.l %d1,X(%a6) # X IS NOW R'= SGN*R + + fmul.x %fp1,%fp3 # TA7 + fmul.x %fp1,%fp2 # TA6 + + fadd.d SINA5(%pc),%fp3 # A5+TA7 + fadd.d SINA4(%pc),%fp2 # A4+TA6 + + fmul.x %fp1,%fp3 # T(A5+TA7) + fmul.x %fp1,%fp2 # T(A4+TA6) + + fadd.d SINA3(%pc),%fp3 # A3+T(A5+TA7) + fadd.x SINA2(%pc),%fp2 # A2+T(A4+TA6) + + fmul.x %fp3,%fp1 # T(A3+T(A5+TA7)) + + fmul.x %fp0,%fp2 # S(A2+T(A4+TA6)) + fadd.x SINA1(%pc),%fp1 # A1+T(A3+T(A5+TA7)) + fmul.x X(%a6),%fp0 # R'*S + + fadd.x %fp2,%fp1 # [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] + + fmul.x %fp1,%fp0 # SIN(R')-R' + + fmovm.x (%sp)+,&0x30 # restore fp2/fp3 + + fmov.l %d0,%fpcr # restore users round mode,prec + fadd.x X(%a6),%fp0 # last inst - possible exception set + bra t_inx2 + +#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J. +#--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY +#--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE +#--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS +#--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))]) +#--WHERE T=S*S. +#--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION +#--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2 +#--AND IS THEREFORE STORED AS SINGLE PRECISION. +COSPOLY: + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmul.x %fp0,%fp0 # FP0 IS S + + fmov.d COSB8(%pc),%fp2 + fmov.d COSB7(%pc),%fp3 + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS T + + fmov.x %fp0,X(%a6) # X IS S + ror.l &1,%d1 + and.l &0x80000000,%d1 +# ...LEAST SIG. BIT OF D0 IN SIGN POSITION + + fmul.x %fp1,%fp2 # TB8 + + eor.l %d1,X(%a6) # X IS NOW S'= SGN*S + and.l &0x80000000,%d1 + + fmul.x %fp1,%fp3 # TB7 + + or.l &0x3F800000,%d1 # D0 IS SGN IN SINGLE + mov.l %d1,POSNEG1(%a6) + + fadd.d COSB6(%pc),%fp2 # B6+TB8 + fadd.d COSB5(%pc),%fp3 # B5+TB7 + + fmul.x %fp1,%fp2 # T(B6+TB8) + fmul.x %fp1,%fp3 # T(B5+TB7) + + fadd.d COSB4(%pc),%fp2 # B4+T(B6+TB8) + fadd.x COSB3(%pc),%fp3 # B3+T(B5+TB7) + + fmul.x %fp1,%fp2 # T(B4+T(B6+TB8)) + fmul.x %fp3,%fp1 # T(B3+T(B5+TB7)) + + fadd.x COSB2(%pc),%fp2 # B2+T(B4+T(B6+TB8)) + fadd.s COSB1(%pc),%fp1 # B1+T(B3+T(B5+TB7)) + + fmul.x %fp2,%fp0 # S(B2+T(B4+T(B6+TB8))) + + fadd.x %fp1,%fp0 + + fmul.x X(%a6),%fp0 + + fmovm.x (%sp)+,&0x30 # restore fp2/fp3 + + fmov.l %d0,%fpcr # restore users round mode,prec + fadd.s POSNEG1(%a6),%fp0 # last inst - possible exception set + bra t_inx2 + +############################################## + +# SINe: Big OR Small? +#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. +#--IF |X| < 2**(-40), RETURN X OR 1. +SINBORS: + cmp.l %d1,&0x3FFF8000 + bgt.l SREDUCEX + +SINSM: + mov.l ADJN(%a6),%d1 + cmp.l %d1,&0 + bgt.b COSTINY + +# here, the operation may underflow iff the precision is sgl or dbl. +# extended denorms are handled through another entry point. +SINTINY: +# mov.w &0x0000,XDCARE(%a6) # JUST IN CASE + + fmov.l %d0,%fpcr # restore users round mode,prec + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x X(%a6),%fp0 # last inst - possible exception set + bra t_catch + +COSTINY: + fmov.s &0x3F800000,%fp0 # fp0 = 1.0 + fmov.l %d0,%fpcr # restore users round mode,prec + fadd.s &0x80800000,%fp0 # last inst - possible exception set + bra t_pinx2 + +################################################ + global ssind +#--SIN(X) = X FOR DENORMALIZED X +ssind: + bra t_extdnrm + +############################################ + global scosd +#--COS(X) = 1 FOR DENORMALIZED X +scosd: + fmov.s &0x3F800000,%fp0 # fp0 = 1.0 + bra t_pinx2 + +################################################## + + global ssincos +ssincos: +#--SET ADJN TO 4 + mov.l &4,ADJN(%a6) + + fmov.x (%a0),%fp0 # LOAD INPUT + fmov.x %fp0,X(%a6) + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 # COMPACTIFY X + + cmp.l %d1,&0x3FD78000 # |X| >= 2**(-40)? + bge.b SCOK1 + bra.w SCSM + +SCOK1: + cmp.l %d1,&0x4004BC7E # |X| < 15 PI? + blt.b SCMAIN + bra.w SREDUCEX + + +#--THIS IS THE USUAL CASE, |X| <= 15 PI. +#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. +SCMAIN: + fmov.x %fp0,%fp1 + + fmul.d TWOBYPI(%pc),%fp1 # X*2/PI + + lea PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32 + + fmov.l %fp1,INT(%a6) # CONVERT TO INTEGER + + mov.l INT(%a6),%d1 + asl.l &4,%d1 + add.l %d1,%a1 # ADDRESS OF N*PIBY2, IN Y1, Y2 + + fsub.x (%a1)+,%fp0 # X-Y1 + fsub.s (%a1),%fp0 # FP0 IS R = (X-Y1)-Y2 + +SCCONT: +#--continuation point from REDUCEX + + mov.l INT(%a6),%d1 + ror.l &1,%d1 + cmp.l %d1,&0 # D0 < 0 IFF N IS ODD + bge.w NEVEN + +SNODD: +#--REGISTERS SAVED SO FAR: D0, A0, FP2. + fmovm.x &0x04,-(%sp) # save fp2 + + fmov.x %fp0,RPRIME(%a6) + fmul.x %fp0,%fp0 # FP0 IS S = R*R + fmov.d SINA7(%pc),%fp1 # A7 + fmov.d COSB8(%pc),%fp2 # B8 + fmul.x %fp0,%fp1 # SA7 + fmul.x %fp0,%fp2 # SB8 + + mov.l %d2,-(%sp) + mov.l %d1,%d2 + ror.l &1,%d2 + and.l &0x80000000,%d2 + eor.l %d1,%d2 + and.l &0x80000000,%d2 + + fadd.d SINA6(%pc),%fp1 # A6+SA7 + fadd.d COSB7(%pc),%fp2 # B7+SB8 + + fmul.x %fp0,%fp1 # S(A6+SA7) + eor.l %d2,RPRIME(%a6) + mov.l (%sp)+,%d2 + fmul.x %fp0,%fp2 # S(B7+SB8) + ror.l &1,%d1 + and.l &0x80000000,%d1 + mov.l &0x3F800000,POSNEG1(%a6) + eor.l %d1,POSNEG1(%a6) + + fadd.d SINA5(%pc),%fp1 # A5+S(A6+SA7) + fadd.d COSB6(%pc),%fp2 # B6+S(B7+SB8) + + fmul.x %fp0,%fp1 # S(A5+S(A6+SA7)) + fmul.x %fp0,%fp2 # S(B6+S(B7+SB8)) + fmov.x %fp0,SPRIME(%a6) + + fadd.d SINA4(%pc),%fp1 # A4+S(A5+S(A6+SA7)) + eor.l %d1,SPRIME(%a6) + fadd.d COSB5(%pc),%fp2 # B5+S(B6+S(B7+SB8)) + + fmul.x %fp0,%fp1 # S(A4+...) + fmul.x %fp0,%fp2 # S(B5+...) + + fadd.d SINA3(%pc),%fp1 # A3+S(A4+...) + fadd.d COSB4(%pc),%fp2 # B4+S(B5+...) + + fmul.x %fp0,%fp1 # S(A3+...) + fmul.x %fp0,%fp2 # S(B4+...) + + fadd.x SINA2(%pc),%fp1 # A2+S(A3+...) + fadd.x COSB3(%pc),%fp2 # B3+S(B4+...) + + fmul.x %fp0,%fp1 # S(A2+...) + fmul.x %fp0,%fp2 # S(B3+...) + + fadd.x SINA1(%pc),%fp1 # A1+S(A2+...) + fadd.x COSB2(%pc),%fp2 # B2+S(B3+...) + + fmul.x %fp0,%fp1 # S(A1+...) + fmul.x %fp2,%fp0 # S(B2+...) + + fmul.x RPRIME(%a6),%fp1 # R'S(A1+...) + fadd.s COSB1(%pc),%fp0 # B1+S(B2...) + fmul.x SPRIME(%a6),%fp0 # S'(B1+S(B2+...)) + + fmovm.x (%sp)+,&0x20 # restore fp2 + + fmov.l %d0,%fpcr + fadd.x RPRIME(%a6),%fp1 # COS(X) + bsr sto_cos # store cosine result + fadd.s POSNEG1(%a6),%fp0 # SIN(X) + bra t_inx2 + +NEVEN: +#--REGISTERS SAVED SO FAR: FP2. + fmovm.x &0x04,-(%sp) # save fp2 + + fmov.x %fp0,RPRIME(%a6) + fmul.x %fp0,%fp0 # FP0 IS S = R*R + + fmov.d COSB8(%pc),%fp1 # B8 + fmov.d SINA7(%pc),%fp2 # A7 + + fmul.x %fp0,%fp1 # SB8 + fmov.x %fp0,SPRIME(%a6) + fmul.x %fp0,%fp2 # SA7 + + ror.l &1,%d1 + and.l &0x80000000,%d1 + + fadd.d COSB7(%pc),%fp1 # B7+SB8 + fadd.d SINA6(%pc),%fp2 # A6+SA7 + + eor.l %d1,RPRIME(%a6) + eor.l %d1,SPRIME(%a6) + + fmul.x %fp0,%fp1 # S(B7+SB8) + + or.l &0x3F800000,%d1 + mov.l %d1,POSNEG1(%a6) + + fmul.x %fp0,%fp2 # S(A6+SA7) + + fadd.d COSB6(%pc),%fp1 # B6+S(B7+SB8) + fadd.d SINA5(%pc),%fp2 # A5+S(A6+SA7) + + fmul.x %fp0,%fp1 # S(B6+S(B7+SB8)) + fmul.x %fp0,%fp2 # S(A5+S(A6+SA7)) + + fadd.d COSB5(%pc),%fp1 # B5+S(B6+S(B7+SB8)) + fadd.d SINA4(%pc),%fp2 # A4+S(A5+S(A6+SA7)) + + fmul.x %fp0,%fp1 # S(B5+...) + fmul.x %fp0,%fp2 # S(A4+...) + + fadd.d COSB4(%pc),%fp1 # B4+S(B5+...) + fadd.d SINA3(%pc),%fp2 # A3+S(A4+...) + + fmul.x %fp0,%fp1 # S(B4+...) + fmul.x %fp0,%fp2 # S(A3+...) + + fadd.x COSB3(%pc),%fp1 # B3+S(B4+...) + fadd.x SINA2(%pc),%fp2 # A2+S(A3+...) + + fmul.x %fp0,%fp1 # S(B3+...) + fmul.x %fp0,%fp2 # S(A2+...) + + fadd.x COSB2(%pc),%fp1 # B2+S(B3+...) + fadd.x SINA1(%pc),%fp2 # A1+S(A2+...) + + fmul.x %fp0,%fp1 # S(B2+...) + fmul.x %fp2,%fp0 # s(a1+...) + + + fadd.s COSB1(%pc),%fp1 # B1+S(B2...) + fmul.x RPRIME(%a6),%fp0 # R'S(A1+...) + fmul.x SPRIME(%a6),%fp1 # S'(B1+S(B2+...)) + + fmovm.x (%sp)+,&0x20 # restore fp2 + + fmov.l %d0,%fpcr + fadd.s POSNEG1(%a6),%fp1 # COS(X) + bsr sto_cos # store cosine result + fadd.x RPRIME(%a6),%fp0 # SIN(X) + bra t_inx2 + +################################################ + +SCBORS: + cmp.l %d1,&0x3FFF8000 + bgt.w SREDUCEX + +################################################ + +SCSM: +# mov.w &0x0000,XDCARE(%a6) + fmov.s &0x3F800000,%fp1 + + fmov.l %d0,%fpcr + fsub.s &0x00800000,%fp1 + bsr sto_cos # store cosine result + fmov.l %fpcr,%d0 # d0 must have fpcr,too + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x X(%a6),%fp0 + bra t_catch + +############################################## + + global ssincosd +#--SIN AND COS OF X FOR DENORMALIZED X +ssincosd: + mov.l %d0,-(%sp) # save d0 + fmov.s &0x3F800000,%fp1 + bsr sto_cos # store cosine result + mov.l (%sp)+,%d0 # restore d0 + bra t_extdnrm + +############################################ + +#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW. +#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING +#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE. +SREDUCEX: + fmovm.x &0x3c,-(%sp) # save {fp2-fp5} + mov.l %d2,-(%sp) # save d2 + fmov.s &0x00000000,%fp1 # fp1 = 0 + +#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that +#--there is a danger of unwanted overflow in first LOOP iteration. In this +#--case, reduce argument by one remainder step to make subsequent reduction +#--safe. + cmp.l %d1,&0x7ffeffff # is arg dangerously large? + bne.b SLOOP # no + +# yes; create 2**16383*PI/2 + mov.w &0x7ffe,FP_SCR0_EX(%a6) + mov.l &0xc90fdaa2,FP_SCR0_HI(%a6) + clr.l FP_SCR0_LO(%a6) + +# create low half of 2**16383*PI/2 at FP_SCR1 + mov.w &0x7fdc,FP_SCR1_EX(%a6) + mov.l &0x85a308d3,FP_SCR1_HI(%a6) + clr.l FP_SCR1_LO(%a6) + + ftest.x %fp0 # test sign of argument + fblt.w sred_neg + + or.b &0x80,FP_SCR0_EX(%a6) # positive arg + or.b &0x80,FP_SCR1_EX(%a6) +sred_neg: + fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact + fmov.x %fp0,%fp1 # save high result in fp1 + fadd.x FP_SCR1(%a6),%fp0 # low part of reduction + fsub.x %fp0,%fp1 # determine low component of result + fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument. + +#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4. +#--integer quotient will be stored in N +#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1) +SLOOP: + fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2 + mov.w INARG(%a6),%d1 + mov.l %d1,%a1 # save a copy of D0 + and.l &0x00007FFF,%d1 + sub.l &0x00003FFF,%d1 # d0 = K + cmp.l %d1,&28 + ble.b SLASTLOOP +SCONTLOOP: + sub.l &27,%d1 # d0 = L := K-27 + mov.b &0,ENDFLAG(%a6) + bra.b SWORK +SLASTLOOP: + clr.l %d1 # d0 = L := 0 + mov.b &1,ENDFLAG(%a6) + +SWORK: +#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN +#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29. + +#--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63), +#--2**L * (PIby2_1), 2**L * (PIby2_2) + + mov.l &0x00003FFE,%d2 # BIASED EXP OF 2/PI + sub.l %d1,%d2 # BIASED EXP OF 2**(-L)*(2/PI) + + mov.l &0xA2F9836E,FP_SCR0_HI(%a6) + mov.l &0x4E44152A,FP_SCR0_LO(%a6) + mov.w %d2,FP_SCR0_EX(%a6) # FP_SCR0 = 2**(-L)*(2/PI) + + fmov.x %fp0,%fp2 + fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI) + +#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN +#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N +#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT +#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE +#--US THE DESIRED VALUE IN FLOATING POINT. + mov.l %a1,%d2 + swap %d2 + and.l &0x80000000,%d2 + or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL + mov.l %d2,TWOTO63(%a6) + fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED + fsub.s TWOTO63(%a6),%fp2 # fp2 = N +# fint.x %fp2 + +#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2 + mov.l %d1,%d2 # d2 = L + + add.l &0x00003FFF,%d2 # BIASED EXP OF 2**L * (PI/2) + mov.w %d2,FP_SCR0_EX(%a6) + mov.l &0xC90FDAA2,FP_SCR0_HI(%a6) + clr.l FP_SCR0_LO(%a6) # FP_SCR0 = 2**(L) * Piby2_1 + + add.l &0x00003FDD,%d1 + mov.w %d1,FP_SCR1_EX(%a6) + mov.l &0x85A308D3,FP_SCR1_HI(%a6) + clr.l FP_SCR1_LO(%a6) # FP_SCR1 = 2**(L) * Piby2_2 + + mov.b ENDFLAG(%a6),%d1 + +#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and +#--P2 = 2**(L) * Piby2_2 + fmov.x %fp2,%fp4 # fp4 = N + fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1 + fmov.x %fp2,%fp5 # fp5 = N + fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2 + fmov.x %fp4,%fp3 # fp3 = W = N*P1 + +#--we want P+p = W+w but |p| <= half ulp of P +#--Then, we need to compute A := R-P and a := r-p + fadd.x %fp5,%fp3 # fp3 = P + fsub.x %fp3,%fp4 # fp4 = W-P + + fsub.x %fp3,%fp0 # fp0 = A := R - P + fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w + + fmov.x %fp0,%fp3 # fp3 = A + fsub.x %fp4,%fp1 # fp1 = a := r - p + +#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but +#--|r| <= half ulp of R. + fadd.x %fp1,%fp0 # fp0 = R := A+a +#--No need to calculate r if this is the last loop + cmp.b %d1,&0 + bgt.w SRESTORE + +#--Need to calculate r + fsub.x %fp0,%fp3 # fp3 = A-R + fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a + bra.w SLOOP + +SRESTORE: + fmov.l %fp2,INT(%a6) + mov.l (%sp)+,%d2 # restore d2 + fmovm.x (%sp)+,&0x3c # restore {fp2-fp5} + + mov.l ADJN(%a6),%d1 + cmp.l %d1,&4 + + blt.w SINCONT + bra.w SCCONT + +######################################################################### +# stan(): computes the tangent of a normalized input # +# stand(): computes the tangent of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = tan(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulp in 64 significant bit, i.e. # +# within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. # +# # +# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let # +# k = N mod 2, so in particular, k = 0 or 1. # +# # +# 3. If k is odd, go to 5. # +# # +# 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a # +# rational function U/V where # +# U = r + r*s*(P1 + s*(P2 + s*P3)), and # +# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r. # +# Exit. # +# # +# 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by # +# a rational function U/V where # +# U = r + r*s*(P1 + s*(P2 + s*P3)), and # +# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r, # +# -Cot(r) = -V/U. Exit. # +# # +# 6. If |X| > 1, go to 8. # +# # +# 7. (|X|<2**(-40)) Tan(X) = X. Exit. # +# # +# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back # +# to 2. # +# # +######################################################################### + +TANQ4: + long 0x3EA0B759,0xF50F8688 +TANP3: + long 0xBEF2BAA5,0xA8924F04 + +TANQ3: + long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000 + +TANP2: + long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000 + +TANQ2: + long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000 + +TANP1: + long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000 + +TANQ1: + long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000 + +INVTWOPI: + long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000 + +TWOPI1: + long 0x40010000,0xC90FDAA2,0x00000000,0x00000000 +TWOPI2: + long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000 + +#--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING +#--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT +#--MOST 69 BITS LONG. +# global PITBL +PITBL: + long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000 + long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000 + long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000 + long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000 + long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000 + long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000 + long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000 + long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000 + long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000 + long 0xC0040000,0x90836524,0x88034B96,0x20B00000 + long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000 + long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000 + long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000 + long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000 + long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000 + long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000 + long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000 + long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000 + long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000 + long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000 + long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000 + long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000 + long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000 + long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000 + long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000 + long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000 + long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000 + long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000 + long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000 + long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000 + long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000 + long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000 + long 0x00000000,0x00000000,0x00000000,0x00000000 + long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000 + long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000 + long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000 + long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000 + long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000 + long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000 + long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000 + long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000 + long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000 + long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000 + long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000 + long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000 + long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000 + long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000 + long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000 + long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000 + long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000 + long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000 + long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000 + long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000 + long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000 + long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000 + long 0x40040000,0x90836524,0x88034B96,0xA0B00000 + long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000 + long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000 + long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000 + long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000 + long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000 + long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000 + long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000 + long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000 + long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000 + + set INARG,FP_SCR0 + + set TWOTO63,L_SCR1 + set INT,L_SCR1 + set ENDFLAG,L_SCR2 + + global stan +stan: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + + cmp.l %d1,&0x3FD78000 # |X| >= 2**(-40)? + bge.b TANOK1 + bra.w TANSM +TANOK1: + cmp.l %d1,&0x4004BC7E # |X| < 15 PI? + blt.b TANMAIN + bra.w REDUCEX + +TANMAIN: +#--THIS IS THE USUAL CASE, |X| <= 15 PI. +#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. + fmov.x %fp0,%fp1 + fmul.d TWOBYPI(%pc),%fp1 # X*2/PI + + lea.l PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32 + + fmov.l %fp1,%d1 # CONVERT TO INTEGER + + asl.l &4,%d1 + add.l %d1,%a1 # ADDRESS N*PIBY2 IN Y1, Y2 + + fsub.x (%a1)+,%fp0 # X-Y1 + + fsub.s (%a1),%fp0 # FP0 IS R = (X-Y1)-Y2 + + ror.l &5,%d1 + and.l &0x80000000,%d1 # D0 WAS ODD IFF D0 < 0 + +TANCONT: + fmovm.x &0x0c,-(%sp) # save fp2,fp3 + + cmp.l %d1,&0 + blt.w NODD + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # S = R*R + + fmov.d TANQ4(%pc),%fp3 + fmov.d TANP3(%pc),%fp2 + + fmul.x %fp1,%fp3 # SQ4 + fmul.x %fp1,%fp2 # SP3 + + fadd.d TANQ3(%pc),%fp3 # Q3+SQ4 + fadd.x TANP2(%pc),%fp2 # P2+SP3 + + fmul.x %fp1,%fp3 # S(Q3+SQ4) + fmul.x %fp1,%fp2 # S(P2+SP3) + + fadd.x TANQ2(%pc),%fp3 # Q2+S(Q3+SQ4) + fadd.x TANP1(%pc),%fp2 # P1+S(P2+SP3) + + fmul.x %fp1,%fp3 # S(Q2+S(Q3+SQ4)) + fmul.x %fp1,%fp2 # S(P1+S(P2+SP3)) + + fadd.x TANQ1(%pc),%fp3 # Q1+S(Q2+S(Q3+SQ4)) + fmul.x %fp0,%fp2 # RS(P1+S(P2+SP3)) + + fmul.x %fp3,%fp1 # S(Q1+S(Q2+S(Q3+SQ4))) + + fadd.x %fp2,%fp0 # R+RS(P1+S(P2+SP3)) + + fadd.s &0x3F800000,%fp1 # 1+S(Q1+...) + + fmovm.x (%sp)+,&0x30 # restore fp2,fp3 + + fmov.l %d0,%fpcr # restore users round mode,prec + fdiv.x %fp1,%fp0 # last inst - possible exception set + bra t_inx2 + +NODD: + fmov.x %fp0,%fp1 + fmul.x %fp0,%fp0 # S = R*R + + fmov.d TANQ4(%pc),%fp3 + fmov.d TANP3(%pc),%fp2 + + fmul.x %fp0,%fp3 # SQ4 + fmul.x %fp0,%fp2 # SP3 + + fadd.d TANQ3(%pc),%fp3 # Q3+SQ4 + fadd.x TANP2(%pc),%fp2 # P2+SP3 + + fmul.x %fp0,%fp3 # S(Q3+SQ4) + fmul.x %fp0,%fp2 # S(P2+SP3) + + fadd.x TANQ2(%pc),%fp3 # Q2+S(Q3+SQ4) + fadd.x TANP1(%pc),%fp2 # P1+S(P2+SP3) + + fmul.x %fp0,%fp3 # S(Q2+S(Q3+SQ4)) + fmul.x %fp0,%fp2 # S(P1+S(P2+SP3)) + + fadd.x TANQ1(%pc),%fp3 # Q1+S(Q2+S(Q3+SQ4)) + fmul.x %fp1,%fp2 # RS(P1+S(P2+SP3)) + + fmul.x %fp3,%fp0 # S(Q1+S(Q2+S(Q3+SQ4))) + + fadd.x %fp2,%fp1 # R+RS(P1+S(P2+SP3)) + fadd.s &0x3F800000,%fp0 # 1+S(Q1+...) + + fmovm.x (%sp)+,&0x30 # restore fp2,fp3 + + fmov.x %fp1,-(%sp) + eor.l &0x80000000,(%sp) + + fmov.l %d0,%fpcr # restore users round mode,prec + fdiv.x (%sp)+,%fp0 # last inst - possible exception set + bra t_inx2 + +TANBORS: +#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. +#--IF |X| < 2**(-40), RETURN X OR 1. + cmp.l %d1,&0x3FFF8000 + bgt.b REDUCEX + +TANSM: + fmov.x %fp0,-(%sp) + fmov.l %d0,%fpcr # restore users round mode,prec + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x (%sp)+,%fp0 # last inst - posibble exception set + bra t_catch + + global stand +#--TAN(X) = X FOR DENORMALIZED X +stand: + bra t_extdnrm + +#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW. +#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING +#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE. +REDUCEX: + fmovm.x &0x3c,-(%sp) # save {fp2-fp5} + mov.l %d2,-(%sp) # save d2 + fmov.s &0x00000000,%fp1 # fp1 = 0 + +#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that +#--there is a danger of unwanted overflow in first LOOP iteration. In this +#--case, reduce argument by one remainder step to make subsequent reduction +#--safe. + cmp.l %d1,&0x7ffeffff # is arg dangerously large? + bne.b LOOP # no + +# yes; create 2**16383*PI/2 + mov.w &0x7ffe,FP_SCR0_EX(%a6) + mov.l &0xc90fdaa2,FP_SCR0_HI(%a6) + clr.l FP_SCR0_LO(%a6) + +# create low half of 2**16383*PI/2 at FP_SCR1 + mov.w &0x7fdc,FP_SCR1_EX(%a6) + mov.l &0x85a308d3,FP_SCR1_HI(%a6) + clr.l FP_SCR1_LO(%a6) + + ftest.x %fp0 # test sign of argument + fblt.w red_neg + + or.b &0x80,FP_SCR0_EX(%a6) # positive arg + or.b &0x80,FP_SCR1_EX(%a6) +red_neg: + fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact + fmov.x %fp0,%fp1 # save high result in fp1 + fadd.x FP_SCR1(%a6),%fp0 # low part of reduction + fsub.x %fp0,%fp1 # determine low component of result + fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument. + +#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4. +#--integer quotient will be stored in N +#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1) +LOOP: + fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2 + mov.w INARG(%a6),%d1 + mov.l %d1,%a1 # save a copy of D0 + and.l &0x00007FFF,%d1 + sub.l &0x00003FFF,%d1 # d0 = K + cmp.l %d1,&28 + ble.b LASTLOOP +CONTLOOP: + sub.l &27,%d1 # d0 = L := K-27 + mov.b &0,ENDFLAG(%a6) + bra.b WORK +LASTLOOP: + clr.l %d1 # d0 = L := 0 + mov.b &1,ENDFLAG(%a6) + +WORK: +#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN +#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29. + +#--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63), +#--2**L * (PIby2_1), 2**L * (PIby2_2) + + mov.l &0x00003FFE,%d2 # BIASED EXP OF 2/PI + sub.l %d1,%d2 # BIASED EXP OF 2**(-L)*(2/PI) + + mov.l &0xA2F9836E,FP_SCR0_HI(%a6) + mov.l &0x4E44152A,FP_SCR0_LO(%a6) + mov.w %d2,FP_SCR0_EX(%a6) # FP_SCR0 = 2**(-L)*(2/PI) + + fmov.x %fp0,%fp2 + fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI) + +#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN +#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N +#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT +#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE +#--US THE DESIRED VALUE IN FLOATING POINT. + mov.l %a1,%d2 + swap %d2 + and.l &0x80000000,%d2 + or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL + mov.l %d2,TWOTO63(%a6) + fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED + fsub.s TWOTO63(%a6),%fp2 # fp2 = N +# fintrz.x %fp2,%fp2 + +#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2 + mov.l %d1,%d2 # d2 = L + + add.l &0x00003FFF,%d2 # BIASED EXP OF 2**L * (PI/2) + mov.w %d2,FP_SCR0_EX(%a6) + mov.l &0xC90FDAA2,FP_SCR0_HI(%a6) + clr.l FP_SCR0_LO(%a6) # FP_SCR0 = 2**(L) * Piby2_1 + + add.l &0x00003FDD,%d1 + mov.w %d1,FP_SCR1_EX(%a6) + mov.l &0x85A308D3,FP_SCR1_HI(%a6) + clr.l FP_SCR1_LO(%a6) # FP_SCR1 = 2**(L) * Piby2_2 + + mov.b ENDFLAG(%a6),%d1 + +#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and +#--P2 = 2**(L) * Piby2_2 + fmov.x %fp2,%fp4 # fp4 = N + fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1 + fmov.x %fp2,%fp5 # fp5 = N + fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2 + fmov.x %fp4,%fp3 # fp3 = W = N*P1 + +#--we want P+p = W+w but |p| <= half ulp of P +#--Then, we need to compute A := R-P and a := r-p + fadd.x %fp5,%fp3 # fp3 = P + fsub.x %fp3,%fp4 # fp4 = W-P + + fsub.x %fp3,%fp0 # fp0 = A := R - P + fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w + + fmov.x %fp0,%fp3 # fp3 = A + fsub.x %fp4,%fp1 # fp1 = a := r - p + +#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but +#--|r| <= half ulp of R. + fadd.x %fp1,%fp0 # fp0 = R := A+a +#--No need to calculate r if this is the last loop + cmp.b %d1,&0 + bgt.w RESTORE + +#--Need to calculate r + fsub.x %fp0,%fp3 # fp3 = A-R + fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a + bra.w LOOP + +RESTORE: + fmov.l %fp2,INT(%a6) + mov.l (%sp)+,%d2 # restore d2 + fmovm.x (%sp)+,&0x3c # restore {fp2-fp5} + + mov.l INT(%a6),%d1 + ror.l &1,%d1 + + bra.w TANCONT + +######################################################################### +# satan(): computes the arctangent of a normalized number # +# satand(): computes the arctangent of a denormalized number # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = arctan(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 2 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5. # +# # +# Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. # +# Note that k = -4, -3,..., or 3. # +# Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 # +# significant bits of X with a bit-1 attached at the 6-th # +# bit position. Define u to be u = (X-F) / (1 + X*F). # +# # +# Step 3. Approximate arctan(u) by a polynomial poly. # +# # +# Step 4. Return arctan(F) + poly, arctan(F) is fetched from a # +# table of values calculated beforehand. Exit. # +# # +# Step 5. If |X| >= 16, go to Step 7. # +# # +# Step 6. Approximate arctan(X) by an odd polynomial in X. Exit. # +# # +# Step 7. Define X' = -1/X. Approximate arctan(X') by an odd # +# polynomial in X'. # +# Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit. # +# # +######################################################################### + +ATANA3: long 0xBFF6687E,0x314987D8 +ATANA2: long 0x4002AC69,0x34A26DB3 +ATANA1: long 0xBFC2476F,0x4E1DA28E + +ATANB6: long 0x3FB34444,0x7F876989 +ATANB5: long 0xBFB744EE,0x7FAF45DB +ATANB4: long 0x3FBC71C6,0x46940220 +ATANB3: long 0xBFC24924,0x921872F9 +ATANB2: long 0x3FC99999,0x99998FA9 +ATANB1: long 0xBFD55555,0x55555555 + +ATANC5: long 0xBFB70BF3,0x98539E6A +ATANC4: long 0x3FBC7187,0x962D1D7D +ATANC3: long 0xBFC24924,0x827107B8 +ATANC2: long 0x3FC99999,0x9996263E +ATANC1: long 0xBFD55555,0x55555536 + +PPIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 +NPIBY2: long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000 + +PTINY: long 0x00010000,0x80000000,0x00000000,0x00000000 +NTINY: long 0x80010000,0x80000000,0x00000000,0x00000000 + +ATANTBL: + long 0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000 + long 0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000 + long 0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000 + long 0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000 + long 0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000 + long 0x3FFB0000,0xAB98E943,0x62765619,0x00000000 + long 0x3FFB0000,0xB389E502,0xF9C59862,0x00000000 + long 0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000 + long 0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000 + long 0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000 + long 0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000 + long 0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000 + long 0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000 + long 0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000 + long 0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000 + long 0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000 + long 0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000 + long 0x3FFC0000,0x8B232A08,0x304282D8,0x00000000 + long 0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000 + long 0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000 + long 0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000 + long 0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000 + long 0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000 + long 0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000 + long 0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000 + long 0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000 + long 0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000 + long 0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000 + long 0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000 + long 0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000 + long 0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000 + long 0x3FFC0000,0xF7170A28,0xECC06666,0x00000000 + long 0x3FFD0000,0x812FD288,0x332DAD32,0x00000000 + long 0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000 + long 0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000 + long 0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000 + long 0x3FFD0000,0x9EB68949,0x3889A227,0x00000000 + long 0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000 + long 0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000 + long 0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000 + long 0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000 + long 0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000 + long 0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000 + long 0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000 + long 0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000 + long 0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000 + long 0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000 + long 0x3FFD0000,0xEA2D764F,0x64315989,0x00000000 + long 0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000 + long 0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000 + long 0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000 + long 0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000 + long 0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000 + long 0x3FFE0000,0x97731420,0x365E538C,0x00000000 + long 0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000 + long 0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000 + long 0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000 + long 0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000 + long 0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000 + long 0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000 + long 0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000 + long 0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000 + long 0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000 + long 0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000 + long 0x3FFE0000,0xCD000549,0xADEC7159,0x00000000 + long 0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000 + long 0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000 + long 0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000 + long 0x3FFE0000,0xE8771129,0xC4353259,0x00000000 + long 0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000 + long 0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000 + long 0x3FFE0000,0xF919039D,0x758B8D41,0x00000000 + long 0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000 + long 0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000 + long 0x3FFF0000,0x83889E35,0x49D108E1,0x00000000 + long 0x3FFF0000,0x859CFA76,0x511D724B,0x00000000 + long 0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000 + long 0x3FFF0000,0x89732FD1,0x9557641B,0x00000000 + long 0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000 + long 0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000 + long 0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000 + long 0x3FFF0000,0x922DA7D7,0x91888487,0x00000000 + long 0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000 + long 0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000 + long 0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000 + long 0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000 + long 0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000 + long 0x3FFF0000,0x9F100575,0x006CC571,0x00000000 + long 0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000 + long 0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000 + long 0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000 + long 0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000 + long 0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000 + long 0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000 + long 0x3FFF0000,0xA83A5153,0x0956168F,0x00000000 + long 0x3FFF0000,0xA93A2007,0x7539546E,0x00000000 + long 0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000 + long 0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000 + long 0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000 + long 0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000 + long 0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000 + long 0x3FFF0000,0xB1846515,0x0F71496A,0x00000000 + long 0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000 + long 0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000 + long 0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000 + long 0x3FFF0000,0xB525529D,0x562246BD,0x00000000 + long 0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000 + long 0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000 + long 0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000 + long 0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000 + long 0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000 + long 0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000 + long 0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000 + long 0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000 + long 0x3FFF0000,0xBB471285,0x7637E17D,0x00000000 + long 0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000 + long 0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000 + long 0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000 + long 0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000 + long 0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000 + long 0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000 + long 0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000 + long 0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000 + long 0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000 + long 0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000 + long 0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000 + long 0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000 + long 0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000 + + set X,FP_SCR0 + set XDCARE,X+2 + set XFRAC,X+4 + set XFRACLO,X+8 + + set ATANF,FP_SCR1 + set ATANFHI,ATANF+4 + set ATANFLO,ATANF+8 + + global satan +#--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S +satan: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + fmov.x %fp0,X(%a6) + and.l &0x7FFFFFFF,%d1 + + cmp.l %d1,&0x3FFB8000 # |X| >= 1/16? + bge.b ATANOK1 + bra.w ATANSM + +ATANOK1: + cmp.l %d1,&0x4002FFFF # |X| < 16 ? + ble.b ATANMAIN + bra.w ATANBIG + +#--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE +#--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ). +#--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN +#--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE +#--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS +#--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR +#--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO +#--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE +#--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL +#--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE +#--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION +#--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION +#--WILL INVOLVE A VERY LONG POLYNOMIAL. + +#--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS +#--WE CHOSE F TO BE +-2^K * 1.BBBB1 +#--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE +#--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE +#--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS +#-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|). + +ATANMAIN: + + and.l &0xF8000000,XFRAC(%a6) # FIRST 5 BITS + or.l &0x04000000,XFRAC(%a6) # SET 6-TH BIT TO 1 + mov.l &0x00000000,XFRACLO(%a6) # LOCATION OF X IS NOW F + + fmov.x %fp0,%fp1 # FP1 IS X + fmul.x X(%a6),%fp1 # FP1 IS X*F, NOTE THAT X*F > 0 + fsub.x X(%a6),%fp0 # FP0 IS X-F + fadd.s &0x3F800000,%fp1 # FP1 IS 1 + X*F + fdiv.x %fp1,%fp0 # FP0 IS U = (X-F)/(1+X*F) + +#--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|) +#--CREATE ATAN(F) AND STORE IT IN ATANF, AND +#--SAVE REGISTERS FP2. + + mov.l %d2,-(%sp) # SAVE d2 TEMPORARILY + mov.l %d1,%d2 # THE EXP AND 16 BITS OF X + and.l &0x00007800,%d1 # 4 VARYING BITS OF F'S FRACTION + and.l &0x7FFF0000,%d2 # EXPONENT OF F + sub.l &0x3FFB0000,%d2 # K+4 + asr.l &1,%d2 + add.l %d2,%d1 # THE 7 BITS IDENTIFYING F + asr.l &7,%d1 # INDEX INTO TBL OF ATAN(|F|) + lea ATANTBL(%pc),%a1 + add.l %d1,%a1 # ADDRESS OF ATAN(|F|) + mov.l (%a1)+,ATANF(%a6) + mov.l (%a1)+,ATANFHI(%a6) + mov.l (%a1)+,ATANFLO(%a6) # ATANF IS NOW ATAN(|F|) + mov.l X(%a6),%d1 # LOAD SIGN AND EXPO. AGAIN + and.l &0x80000000,%d1 # SIGN(F) + or.l %d1,ATANF(%a6) # ATANF IS NOW SIGN(F)*ATAN(|F|) + mov.l (%sp)+,%d2 # RESTORE d2 + +#--THAT'S ALL I HAVE TO DO FOR NOW, +#--BUT ALAS, THE DIVIDE IS STILL CRANKING! + +#--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS +#--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U +#--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT. +#--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3)) +#--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3. +#--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT +#--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED + + fmovm.x &0x04,-(%sp) # save fp2 + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 + fmov.d ATANA3(%pc),%fp2 + fadd.x %fp1,%fp2 # A3+V + fmul.x %fp1,%fp2 # V*(A3+V) + fmul.x %fp0,%fp1 # U*V + fadd.d ATANA2(%pc),%fp2 # A2+V*(A3+V) + fmul.d ATANA1(%pc),%fp1 # A1*U*V + fmul.x %fp2,%fp1 # A1*U*V*(A2+V*(A3+V)) + fadd.x %fp1,%fp0 # ATAN(U), FP1 RELEASED + + fmovm.x (%sp)+,&0x20 # restore fp2 + + fmov.l %d0,%fpcr # restore users rnd mode,prec + fadd.x ATANF(%a6),%fp0 # ATAN(X) + bra t_inx2 + +ATANBORS: +#--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED. +#--FP0 IS X AND |X| <= 1/16 OR |X| >= 16. + cmp.l %d1,&0x3FFF8000 + bgt.w ATANBIG # I.E. |X| >= 16 + +ATANSM: +#--|X| <= 1/16 +#--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE +#--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6))))) +#--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] ) +#--WHERE Y = X*X, AND Z = Y*Y. + + cmp.l %d1,&0x3FD78000 + blt.w ATANTINY + +#--COMPUTE POLYNOMIAL + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmul.x %fp0,%fp0 # FPO IS Y = X*X + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS Z = Y*Y + + fmov.d ATANB6(%pc),%fp2 + fmov.d ATANB5(%pc),%fp3 + + fmul.x %fp1,%fp2 # Z*B6 + fmul.x %fp1,%fp3 # Z*B5 + + fadd.d ATANB4(%pc),%fp2 # B4+Z*B6 + fadd.d ATANB3(%pc),%fp3 # B3+Z*B5 + + fmul.x %fp1,%fp2 # Z*(B4+Z*B6) + fmul.x %fp3,%fp1 # Z*(B3+Z*B5) + + fadd.d ATANB2(%pc),%fp2 # B2+Z*(B4+Z*B6) + fadd.d ATANB1(%pc),%fp1 # B1+Z*(B3+Z*B5) + + fmul.x %fp0,%fp2 # Y*(B2+Z*(B4+Z*B6)) + fmul.x X(%a6),%fp0 # X*Y + + fadd.x %fp2,%fp1 # [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] + + fmul.x %fp1,%fp0 # X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) + + fmovm.x (%sp)+,&0x30 # restore fp2/fp3 + + fmov.l %d0,%fpcr # restore users rnd mode,prec + fadd.x X(%a6),%fp0 + bra t_inx2 + +ATANTINY: +#--|X| < 2^(-40), ATAN(X) = X + + fmov.l %d0,%fpcr # restore users rnd mode,prec + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x X(%a6),%fp0 # last inst - possible exception set + + bra t_catch + +ATANBIG: +#--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE, +#--RETURN SIGN(X)*PI/2 + ATAN(-1/X). + cmp.l %d1,&0x40638000 + bgt.w ATANHUGE + +#--APPROXIMATE ATAN(-1/X) BY +#--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X' +#--THIS CAN BE RE-WRITTEN AS +#--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y. + + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmov.s &0xBF800000,%fp1 # LOAD -1 + fdiv.x %fp0,%fp1 # FP1 IS -1/X + +#--DIVIDE IS STILL CRANKING + + fmov.x %fp1,%fp0 # FP0 IS X' + fmul.x %fp0,%fp0 # FP0 IS Y = X'*X' + fmov.x %fp1,X(%a6) # X IS REALLY X' + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS Z = Y*Y + + fmov.d ATANC5(%pc),%fp3 + fmov.d ATANC4(%pc),%fp2 + + fmul.x %fp1,%fp3 # Z*C5 + fmul.x %fp1,%fp2 # Z*B4 + + fadd.d ATANC3(%pc),%fp3 # C3+Z*C5 + fadd.d ATANC2(%pc),%fp2 # C2+Z*C4 + + fmul.x %fp3,%fp1 # Z*(C3+Z*C5), FP3 RELEASED + fmul.x %fp0,%fp2 # Y*(C2+Z*C4) + + fadd.d ATANC1(%pc),%fp1 # C1+Z*(C3+Z*C5) + fmul.x X(%a6),%fp0 # X'*Y + + fadd.x %fp2,%fp1 # [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] + + fmul.x %fp1,%fp0 # X'*Y*([B1+Z*(B3+Z*B5)] +# ... +[Y*(B2+Z*(B4+Z*B6))]) + fadd.x X(%a6),%fp0 + + fmovm.x (%sp)+,&0x30 # restore fp2/fp3 + + fmov.l %d0,%fpcr # restore users rnd mode,prec + tst.b (%a0) + bpl.b pos_big + +neg_big: + fadd.x NPIBY2(%pc),%fp0 + bra t_minx2 + +pos_big: + fadd.x PPIBY2(%pc),%fp0 + bra t_pinx2 + +ATANHUGE: +#--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY + tst.b (%a0) + bpl.b pos_huge + +neg_huge: + fmov.x NPIBY2(%pc),%fp0 + fmov.l %d0,%fpcr + fadd.x PTINY(%pc),%fp0 + bra t_minx2 + +pos_huge: + fmov.x PPIBY2(%pc),%fp0 + fmov.l %d0,%fpcr + fadd.x NTINY(%pc),%fp0 + bra t_pinx2 + + global satand +#--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT +satand: + bra t_extdnrm + +######################################################################### +# sasin(): computes the inverse sine of a normalized input # +# sasind(): computes the inverse sine of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = arcsin(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# ASIN # +# 1. If |X| >= 1, go to 3. # +# # +# 2. (|X| < 1) Calculate asin(X) by # +# z := sqrt( [1-X][1+X] ) # +# asin(X) = atan( x / z ). # +# Exit. # +# # +# 3. If |X| > 1, go to 5. # +# # +# 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.# +# # +# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. # +# Exit. # +# # +######################################################################### + + global sasin +sasin: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + cmp.l %d1,&0x3FFF8000 + bge.b ASINBIG + +# This catch is added here for the '060 QSP. Originally, the call to +# satan() would handle this case by causing the exception which would +# not be caught until gen_except(). Now, with the exceptions being +# detected inside of satan(), the exception would have been handled there +# instead of inside sasin() as expected. + cmp.l %d1,&0x3FD78000 + blt.w ASINTINY + +#--THIS IS THE USUAL CASE, |X| < 1 +#--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) ) + +ASINMAIN: + fmov.s &0x3F800000,%fp1 + fsub.x %fp0,%fp1 # 1-X + fmovm.x &0x4,-(%sp) # {fp2} + fmov.s &0x3F800000,%fp2 + fadd.x %fp0,%fp2 # 1+X + fmul.x %fp2,%fp1 # (1+X)(1-X) + fmovm.x (%sp)+,&0x20 # {fp2} + fsqrt.x %fp1 # SQRT([1-X][1+X]) + fdiv.x %fp1,%fp0 # X/SQRT([1-X][1+X]) + fmovm.x &0x01,-(%sp) # save X/SQRT(...) + lea (%sp),%a0 # pass ptr to X/SQRT(...) + bsr satan + add.l &0xc,%sp # clear X/SQRT(...) from stack + bra t_inx2 + +ASINBIG: + fabs.x %fp0 # |X| + fcmp.s %fp0,&0x3F800000 + fbgt t_operr # cause an operr exception + +#--|X| = 1, ASIN(X) = +- PI/2. +ASINONE: + fmov.x PIBY2(%pc),%fp0 + mov.l (%a0),%d1 + and.l &0x80000000,%d1 # SIGN BIT OF X + or.l &0x3F800000,%d1 # +-1 IN SGL FORMAT + mov.l %d1,-(%sp) # push SIGN(X) IN SGL-FMT + fmov.l %d0,%fpcr + fmul.s (%sp)+,%fp0 + bra t_inx2 + +#--|X| < 2^(-40), ATAN(X) = X +ASINTINY: + fmov.l %d0,%fpcr # restore users rnd mode,prec + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x (%a0),%fp0 # last inst - possible exception + bra t_catch + + global sasind +#--ASIN(X) = X FOR DENORMALIZED X +sasind: + bra t_extdnrm + +######################################################################### +# sacos(): computes the inverse cosine of a normalized input # +# sacosd(): computes the inverse cosine of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = arccos(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# ACOS # +# 1. If |X| >= 1, go to 3. # +# # +# 2. (|X| < 1) Calculate acos(X) by # +# z := (1-X) / (1+X) # +# acos(X) = 2 * atan( sqrt(z) ). # +# Exit. # +# # +# 3. If |X| > 1, go to 5. # +# # +# 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit. # +# # +# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. # +# Exit. # +# # +######################################################################### + + global sacos +sacos: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 # pack exp w/ upper 16 fraction + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + cmp.l %d1,&0x3FFF8000 + bge.b ACOSBIG + +#--THIS IS THE USUAL CASE, |X| < 1 +#--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) ) + +ACOSMAIN: + fmov.s &0x3F800000,%fp1 + fadd.x %fp0,%fp1 # 1+X + fneg.x %fp0 # -X + fadd.s &0x3F800000,%fp0 # 1-X + fdiv.x %fp1,%fp0 # (1-X)/(1+X) + fsqrt.x %fp0 # SQRT((1-X)/(1+X)) + mov.l %d0,-(%sp) # save original users fpcr + clr.l %d0 + fmovm.x &0x01,-(%sp) # save SQRT(...) to stack + lea (%sp),%a0 # pass ptr to sqrt + bsr satan # ATAN(SQRT([1-X]/[1+X])) + add.l &0xc,%sp # clear SQRT(...) from stack + + fmov.l (%sp)+,%fpcr # restore users round prec,mode + fadd.x %fp0,%fp0 # 2 * ATAN( STUFF ) + bra t_pinx2 + +ACOSBIG: + fabs.x %fp0 + fcmp.s %fp0,&0x3F800000 + fbgt t_operr # cause an operr exception + +#--|X| = 1, ACOS(X) = 0 OR PI + tst.b (%a0) # is X positive or negative? + bpl.b ACOSP1 + +#--X = -1 +#Returns PI and inexact exception +ACOSM1: + fmov.x PI(%pc),%fp0 # load PI + fmov.l %d0,%fpcr # load round mode,prec + fadd.s &0x00800000,%fp0 # add a small value + bra t_pinx2 + +ACOSP1: + bra ld_pzero # answer is positive zero + + global sacosd +#--ACOS(X) = PI/2 FOR DENORMALIZED X +sacosd: + fmov.l %d0,%fpcr # load user's rnd mode/prec + fmov.x PIBY2(%pc),%fp0 + bra t_pinx2 + +######################################################################### +# setox(): computes the exponential for a normalized input # +# setoxd(): computes the exponential for a denormalized input # +# setoxm1(): computes the exponential minus 1 for a normalized input # +# setoxm1d(): computes the exponential minus 1 for a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = exp(X) or exp(X)-1 # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 0.85 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM and IMPLEMENTATION **************************************** # +# # +# setoxd # +# ------ # +# Step 1. Set ans := 1.0 # +# # +# Step 2. Return ans := ans + sign(X)*2^(-126). Exit. # +# Notes: This will always generate one exception -- inexact. # +# # +# # +# setox # +# ----- # +# # +# Step 1. Filter out extreme cases of input argument. # +# 1.1 If |X| >= 2^(-65), go to Step 1.3. # +# 1.2 Go to Step 7. # +# 1.3 If |X| < 16380 log(2), go to Step 2. # +# 1.4 Go to Step 8. # +# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.# +# To avoid the use of floating-point comparisons, a # +# compact representation of |X| is used. This format is a # +# 32-bit integer, the upper (more significant) 16 bits # +# are the sign and biased exponent field of |X|; the # +# lower 16 bits are the 16 most significant fraction # +# (including the explicit bit) bits of |X|. Consequently, # +# the comparisons in Steps 1.1 and 1.3 can be performed # +# by integer comparison. Note also that the constant # +# 16380 log(2) used in Step 1.3 is also in the compact # +# form. Thus taking the branch to Step 2 guarantees # +# |X| < 16380 log(2). There is no harm to have a small # +# number of cases where |X| is less than, but close to, # +# 16380 log(2) and the branch to Step 9 is taken. # +# # +# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). # +# 2.1 Set AdjFlag := 0 (indicates the branch 1.3 -> 2 # +# was taken) # +# 2.2 N := round-to-nearest-integer( X * 64/log2 ). # +# 2.3 Calculate J = N mod 64; so J = 0,1,2,..., # +# or 63. # +# 2.4 Calculate M = (N - J)/64; so N = 64M + J. # +# 2.5 Calculate the address of the stored value of # +# 2^(J/64). # +# 2.6 Create the value Scale = 2^M. # +# Notes: The calculation in 2.2 is really performed by # +# Z := X * constant # +# N := round-to-nearest-integer(Z) # +# where # +# constant := single-precision( 64/log 2 ). # +# # +# Using a single-precision constant avoids memory # +# access. Another effect of using a single-precision # +# "constant" is that the calculated value Z is # +# # +# Z = X*(64/log2)*(1+eps), |eps| <= 2^(-24). # +# # +# This error has to be considered later in Steps 3 and 4. # +# # +# Step 3. Calculate X - N*log2/64. # +# 3.1 R := X + N*L1, # +# where L1 := single-precision(-log2/64). # +# 3.2 R := R + N*L2, # +# L2 := extended-precision(-log2/64 - L1).# +# Notes: a) The way L1 and L2 are chosen ensures L1+L2 # +# approximate the value -log2/64 to 88 bits of accuracy. # +# b) N*L1 is exact because N is no longer than 22 bits # +# and L1 is no longer than 24 bits. # +# c) The calculation X+N*L1 is also exact due to # +# cancellation. Thus, R is practically X+N(L1+L2) to full # +# 64 bits. # +# d) It is important to estimate how large can |R| be # +# after Step 3.2. # +# # +# N = rnd-to-int( X*64/log2 (1+eps) ), |eps|<=2^(-24) # +# X*64/log2 (1+eps) = N + f, |f| <= 0.5 # +# X*64/log2 - N = f - eps*X 64/log2 # +# X - N*log2/64 = f*log2/64 - eps*X # +# # +# # +# Now |X| <= 16446 log2, thus # +# # +# |X - N*log2/64| <= (0.5 + 16446/2^(18))*log2/64 # +# <= 0.57 log2/64. # +# This bound will be used in Step 4. # +# # +# Step 4. Approximate exp(R)-1 by a polynomial # +# p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) # +# Notes: a) In order to reduce memory access, the coefficients # +# are made as "short" as possible: A1 (which is 1/2), A4 # +# and A5 are single precision; A2 and A3 are double # +# precision. # +# b) Even with the restrictions above, # +# |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062. # +# Note that 0.0062 is slightly bigger than 0.57 log2/64. # +# c) To fully utilize the pipeline, p is separated into # +# two independent pieces of roughly equal complexities # +# p = [ R + R*S*(A2 + S*A4) ] + # +# [ S*(A1 + S*(A3 + S*A5)) ] # +# where S = R*R. # +# # +# Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by # +# ans := T + ( T*p + t) # +# where T and t are the stored values for 2^(J/64). # +# Notes: 2^(J/64) is stored as T and t where T+t approximates # +# 2^(J/64) to roughly 85 bits; T is in extended precision # +# and t is in single precision. Note also that T is # +# rounded to 62 bits so that the last two bits of T are # +# zero. The reason for such a special form is that T-1, # +# T-2, and T-8 will all be exact --- a property that will # +# give much more accurate computation of the function # +# EXPM1. # +# # +# Step 6. Reconstruction of exp(X) # +# exp(X) = 2^M * 2^(J/64) * exp(R). # +# 6.1 If AdjFlag = 0, go to 6.3 # +# 6.2 ans := ans * AdjScale # +# 6.3 Restore the user FPCR # +# 6.4 Return ans := ans * Scale. Exit. # +# Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R, # +# |M| <= 16380, and Scale = 2^M. Moreover, exp(X) will # +# neither overflow nor underflow. If AdjFlag = 1, that # +# means that # +# X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380. # +# Hence, exp(X) may overflow or underflow or neither. # +# When that is the case, AdjScale = 2^(M1) where M1 is # +# approximately M. Thus 6.2 will never cause # +# over/underflow. Possible exception in 6.4 is overflow # +# or underflow. The inexact exception is not generated in # +# 6.4. Although one can argue that the inexact flag # +# should always be raised, to simulate that exception # +# cost to much than the flag is worth in practical uses. # +# # +# Step 7. Return 1 + X. # +# 7.1 ans := X # +# 7.2 Restore user FPCR. # +# 7.3 Return ans := 1 + ans. Exit # +# Notes: For non-zero X, the inexact exception will always be # +# raised by 7.3. That is the only exception raised by 7.3.# +# Note also that we use the FMOVEM instruction to move X # +# in Step 7.1 to avoid unnecessary trapping. (Although # +# the FMOVEM may not seem relevant since X is normalized, # +# the precaution will be useful in the library version of # +# this code where the separate entry for denormalized # +# inputs will be done away with.) # +# # +# Step 8. Handle exp(X) where |X| >= 16380log2. # +# 8.1 If |X| > 16480 log2, go to Step 9. # +# (mimic 2.2 - 2.6) # +# 8.2 N := round-to-integer( X * 64/log2 ) # +# 8.3 Calculate J = N mod 64, J = 0,1,...,63 # +# 8.4 K := (N-J)/64, M1 := truncate(K/2), M = K-M1, # +# AdjFlag := 1. # +# 8.5 Calculate the address of the stored value # +# 2^(J/64). # +# 8.6 Create the values Scale = 2^M, AdjScale = 2^M1. # +# 8.7 Go to Step 3. # +# Notes: Refer to notes for 2.2 - 2.6. # +# # +# Step 9. Handle exp(X), |X| > 16480 log2. # +# 9.1 If X < 0, go to 9.3 # +# 9.2 ans := Huge, go to 9.4 # +# 9.3 ans := Tiny. # +# 9.4 Restore user FPCR. # +# 9.5 Return ans := ans * ans. Exit. # +# Notes: Exp(X) will surely overflow or underflow, depending on # +# X's sign. "Huge" and "Tiny" are respectively large/tiny # +# extended-precision numbers whose square over/underflow # +# with an inexact result. Thus, 9.5 always raises the # +# inexact together with either overflow or underflow. # +# # +# setoxm1d # +# -------- # +# # +# Step 1. Set ans := 0 # +# # +# Step 2. Return ans := X + ans. Exit. # +# Notes: This will return X with the appropriate rounding # +# precision prescribed by the user FPCR. # +# # +# setoxm1 # +# ------- # +# # +# Step 1. Check |X| # +# 1.1 If |X| >= 1/4, go to Step 1.3. # +# 1.2 Go to Step 7. # +# 1.3 If |X| < 70 log(2), go to Step 2. # +# 1.4 Go to Step 10. # +# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.# +# However, it is conceivable |X| can be small very often # +# because EXPM1 is intended to evaluate exp(X)-1 # +# accurately when |X| is small. For further details on # +# the comparisons, see the notes on Step 1 of setox. # +# # +# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). # +# 2.1 N := round-to-nearest-integer( X * 64/log2 ). # +# 2.2 Calculate J = N mod 64; so J = 0,1,2,..., # +# or 63. # +# 2.3 Calculate M = (N - J)/64; so N = 64M + J. # +# 2.4 Calculate the address of the stored value of # +# 2^(J/64). # +# 2.5 Create the values Sc = 2^M and # +# OnebySc := -2^(-M). # +# Notes: See the notes on Step 2 of setox. # +# # +# Step 3. Calculate X - N*log2/64. # +# 3.1 R := X + N*L1, # +# where L1 := single-precision(-log2/64). # +# 3.2 R := R + N*L2, # +# L2 := extended-precision(-log2/64 - L1).# +# Notes: Applying the analysis of Step 3 of setox in this case # +# shows that |R| <= 0.0055 (note that |X| <= 70 log2 in # +# this case). # +# # +# Step 4. Approximate exp(R)-1 by a polynomial # +# p = R+R*R*(A1+R*(A2+R*(A3+R*(A4+R*(A5+R*A6))))) # +# Notes: a) In order to reduce memory access, the coefficients # +# are made as "short" as possible: A1 (which is 1/2), A5 # +# and A6 are single precision; A2, A3 and A4 are double # +# precision. # +# b) Even with the restriction above, # +# |p - (exp(R)-1)| < |R| * 2^(-72.7) # +# for all |R| <= 0.0055. # +# c) To fully utilize the pipeline, p is separated into # +# two independent pieces of roughly equal complexity # +# p = [ R*S*(A2 + S*(A4 + S*A6)) ] + # +# [ R + S*(A1 + S*(A3 + S*A5)) ] # +# where S = R*R. # +# # +# Step 5. Compute 2^(J/64)*p by # +# p := T*p # +# where T and t are the stored values for 2^(J/64). # +# Notes: 2^(J/64) is stored as T and t where T+t approximates # +# 2^(J/64) to roughly 85 bits; T is in extended precision # +# and t is in single precision. Note also that T is # +# rounded to 62 bits so that the last two bits of T are # +# zero. The reason for such a special form is that T-1, # +# T-2, and T-8 will all be exact --- a property that will # +# be exploited in Step 6 below. The total relative error # +# in p is no bigger than 2^(-67.7) compared to the final # +# result. # +# # +# Step 6. Reconstruction of exp(X)-1 # +# exp(X)-1 = 2^M * ( 2^(J/64) + p - 2^(-M) ). # +# 6.1 If M <= 63, go to Step 6.3. # +# 6.2 ans := T + (p + (t + OnebySc)). Go to 6.6 # +# 6.3 If M >= -3, go to 6.5. # +# 6.4 ans := (T + (p + t)) + OnebySc. Go to 6.6 # +# 6.5 ans := (T + OnebySc) + (p + t). # +# 6.6 Restore user FPCR. # +# 6.7 Return ans := Sc * ans. Exit. # +# Notes: The various arrangements of the expressions give # +# accurate evaluations. # +# # +# Step 7. exp(X)-1 for |X| < 1/4. # +# 7.1 If |X| >= 2^(-65), go to Step 9. # +# 7.2 Go to Step 8. # +# # +# Step 8. Calculate exp(X)-1, |X| < 2^(-65). # +# 8.1 If |X| < 2^(-16312), goto 8.3 # +# 8.2 Restore FPCR; return ans := X - 2^(-16382). # +# Exit. # +# 8.3 X := X * 2^(140). # +# 8.4 Restore FPCR; ans := ans - 2^(-16382). # +# Return ans := ans*2^(140). Exit # +# Notes: The idea is to return "X - tiny" under the user # +# precision and rounding modes. To avoid unnecessary # +# inefficiency, we stay away from denormalized numbers # +# the best we can. For |X| >= 2^(-16312), the # +# straightforward 8.2 generates the inexact exception as # +# the case warrants. # +# # +# Step 9. Calculate exp(X)-1, |X| < 1/4, by a polynomial # +# p = X + X*X*(B1 + X*(B2 + ... + X*B12)) # +# Notes: a) In order to reduce memory access, the coefficients # +# are made as "short" as possible: B1 (which is 1/2), B9 # +# to B12 are single precision; B3 to B8 are double # +# precision; and B2 is double extended. # +# b) Even with the restriction above, # +# |p - (exp(X)-1)| < |X| 2^(-70.6) # +# for all |X| <= 0.251. # +# Note that 0.251 is slightly bigger than 1/4. # +# c) To fully preserve accuracy, the polynomial is # +# computed as # +# X + ( S*B1 + Q ) where S = X*X and # +# Q = X*S*(B2 + X*(B3 + ... + X*B12)) # +# d) To fully utilize the pipeline, Q is separated into # +# two independent pieces of roughly equal complexity # +# Q = [ X*S*(B2 + S*(B4 + ... + S*B12)) ] + # +# [ S*S*(B3 + S*(B5 + ... + S*B11)) ] # +# # +# Step 10. Calculate exp(X)-1 for |X| >= 70 log 2. # +# 10.1 If X >= 70log2 , exp(X) - 1 = exp(X) for all # +# practical purposes. Therefore, go to Step 1 of setox. # +# 10.2 If X <= -70log2, exp(X) - 1 = -1 for all practical # +# purposes. # +# ans := -1 # +# Restore user FPCR # +# Return ans := ans + 2^(-126). Exit. # +# Notes: 10.2 will always create an inexact and return -1 + tiny # +# in the user rounding precision and mode. # +# # +######################################################################### + +L2: long 0x3FDC0000,0x82E30865,0x4361C4C6,0x00000000 + +EEXPA3: long 0x3FA55555,0x55554CC1 +EEXPA2: long 0x3FC55555,0x55554A54 + +EM1A4: long 0x3F811111,0x11174385 +EM1A3: long 0x3FA55555,0x55554F5A + +EM1A2: long 0x3FC55555,0x55555555,0x00000000,0x00000000 + +EM1B8: long 0x3EC71DE3,0xA5774682 +EM1B7: long 0x3EFA01A0,0x19D7CB68 + +EM1B6: long 0x3F2A01A0,0x1A019DF3 +EM1B5: long 0x3F56C16C,0x16C170E2 + +EM1B4: long 0x3F811111,0x11111111 +EM1B3: long 0x3FA55555,0x55555555 + +EM1B2: long 0x3FFC0000,0xAAAAAAAA,0xAAAAAAAB + long 0x00000000 + +TWO140: long 0x48B00000,0x00000000 +TWON140: + long 0x37300000,0x00000000 + +EEXPTBL: + long 0x3FFF0000,0x80000000,0x00000000,0x00000000 + long 0x3FFF0000,0x8164D1F3,0xBC030774,0x9F841A9B + long 0x3FFF0000,0x82CD8698,0xAC2BA1D8,0x9FC1D5B9 + long 0x3FFF0000,0x843A28C3,0xACDE4048,0xA0728369 + long 0x3FFF0000,0x85AAC367,0xCC487B14,0x1FC5C95C + long 0x3FFF0000,0x871F6196,0x9E8D1010,0x1EE85C9F + long 0x3FFF0000,0x88980E80,0x92DA8528,0x9FA20729 + long 0x3FFF0000,0x8A14D575,0x496EFD9C,0xA07BF9AF + long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E8,0xA0020DCF + long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E4,0x205A63DA + long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x1EB70051 + long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x1F6EB029 + long 0x3FFF0000,0x91C3D373,0xAB11C338,0xA0781494 + long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0x9EB319B0 + long 0x3FFF0000,0x94F4EFA8,0xFEF70960,0x2017457D + long 0x3FFF0000,0x96942D37,0x20185A00,0x1F11D537 + long 0x3FFF0000,0x9837F051,0x8DB8A970,0x9FB952DD + long 0x3FFF0000,0x99E04593,0x20B7FA64,0x1FE43087 + long 0x3FFF0000,0x9B8D39B9,0xD54E5538,0x1FA2A818 + long 0x3FFF0000,0x9D3ED9A7,0x2CFFB750,0x1FDE494D + long 0x3FFF0000,0x9EF53260,0x91A111AC,0x20504890 + long 0x3FFF0000,0xA0B0510F,0xB9714FC4,0xA073691C + long 0x3FFF0000,0xA2704303,0x0C496818,0x1F9B7A05 + long 0x3FFF0000,0xA43515AE,0x09E680A0,0xA0797126 + long 0x3FFF0000,0xA5FED6A9,0xB15138EC,0xA071A140 + long 0x3FFF0000,0xA7CD93B4,0xE9653568,0x204F62DA + long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x1F283C4A + long 0x3FFF0000,0xAB7A39B5,0xA93ED338,0x9F9A7FDC + long 0x3FFF0000,0xAD583EEA,0x42A14AC8,0xA05B3FAC + long 0x3FFF0000,0xAF3B78AD,0x690A4374,0x1FDF2610 + long 0x3FFF0000,0xB123F581,0xD2AC2590,0x9F705F90 + long 0x3FFF0000,0xB311C412,0xA9112488,0x201F678A + long 0x3FFF0000,0xB504F333,0xF9DE6484,0x1F32FB13 + long 0x3FFF0000,0xB6FD91E3,0x28D17790,0x20038B30 + long 0x3FFF0000,0xB8FBAF47,0x62FB9EE8,0x200DC3CC + long 0x3FFF0000,0xBAFF5AB2,0x133E45FC,0x9F8B2AE6 + long 0x3FFF0000,0xBD08A39F,0x580C36C0,0xA02BBF70 + long 0x3FFF0000,0xBF1799B6,0x7A731084,0xA00BF518 + long 0x3FFF0000,0xC12C4CCA,0x66709458,0xA041DD41 + long 0x3FFF0000,0xC346CCDA,0x24976408,0x9FDF137B + long 0x3FFF0000,0xC5672A11,0x5506DADC,0x201F1568 + long 0x3FFF0000,0xC78D74C8,0xABB9B15C,0x1FC13A2E + long 0x3FFF0000,0xC9B9BD86,0x6E2F27A4,0xA03F8F03 + long 0x3FFF0000,0xCBEC14FE,0xF2727C5C,0x1FF4907D + long 0x3FFF0000,0xCE248C15,0x1F8480E4,0x9E6E53E4 + long 0x3FFF0000,0xD06333DA,0xEF2B2594,0x1FD6D45C + long 0x3FFF0000,0xD2A81D91,0xF12AE45C,0xA076EDB9 + long 0x3FFF0000,0xD4F35AAB,0xCFEDFA20,0x9FA6DE21 + long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x1EE69A2F + long 0x3FFF0000,0xD99D15C2,0x78AFD7B4,0x207F439F + long 0x3FFF0000,0xDBFBB797,0xDAF23754,0x201EC207 + long 0x3FFF0000,0xDE60F482,0x5E0E9124,0x9E8BE175 + long 0x3FFF0000,0xE0CCDEEC,0x2A94E110,0x20032C4B + long 0x3FFF0000,0xE33F8972,0xBE8A5A50,0x2004DFF5 + long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x1E72F47A + long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x1F722F22 + long 0x3FFF0000,0xEAC0C6E7,0xDD243930,0xA017E945 + long 0x3FFF0000,0xED4F301E,0xD9942B84,0x1F401A5B + long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CC,0x9FB9A9E3 + long 0x3FFF0000,0xF281773C,0x59FFB138,0x20744C05 + long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x1F773A19 + long 0x3FFF0000,0xF7D0DF73,0x0AD13BB8,0x1FFE90D5 + long 0x3FFF0000,0xFA83B2DB,0x722A033C,0xA041ED22 + long 0x3FFF0000,0xFD3E0C0C,0xF486C174,0x1F853F3A + + set ADJFLAG,L_SCR2 + set SCALE,FP_SCR0 + set ADJSCALE,FP_SCR1 + set SC,FP_SCR0 + set ONEBYSC,FP_SCR1 + + global setox +setox: +#--entry point for EXP(X), here X is finite, non-zero, and not NaN's + +#--Step 1. + mov.l (%a0),%d1 # load part of input X + and.l &0x7FFF0000,%d1 # biased expo. of X + cmp.l %d1,&0x3FBE0000 # 2^(-65) + bge.b EXPC1 # normal case + bra EXPSM + +EXPC1: +#--The case |X| >= 2^(-65) + mov.w 4(%a0),%d1 # expo. and partial sig. of |X| + cmp.l %d1,&0x400CB167 # 16380 log2 trunc. 16 bits + blt.b EXPMAIN # normal case + bra EEXPBIG + +EXPMAIN: +#--Step 2. +#--This is the normal branch: 2^(-65) <= |X| < 16380 log2. + fmov.x (%a0),%fp0 # load input from (a0) + + fmov.x %fp0,%fp1 + fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X + fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3} + mov.l &0,ADJFLAG(%a6) + fmov.l %fp0,%d1 # N = int( X * 64/log2 ) + lea EEXPTBL(%pc),%a1 + fmov.l %d1,%fp0 # convert to floating-format + + mov.l %d1,L_SCR1(%a6) # save N temporarily + and.l &0x3F,%d1 # D0 is J = N mod 64 + lsl.l &4,%d1 + add.l %d1,%a1 # address of 2^(J/64) + mov.l L_SCR1(%a6),%d1 + asr.l &6,%d1 # D0 is M + add.w &0x3FFF,%d1 # biased expo. of 2^(M) + mov.w L2(%pc),L_SCR1(%a6) # prefetch L2, no need in CB + +EXPCONT1: +#--Step 3. +#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X, +#--a0 points to 2^(J/64), D0 is biased expo. of 2^(M) + fmov.x %fp0,%fp2 + fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64) + fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64 + fadd.x %fp1,%fp0 # X + N*L1 + fadd.x %fp2,%fp0 # fp0 is R, reduced arg. + +#--Step 4. +#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL +#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) +#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R +#--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))] + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # fp1 IS S = R*R + + fmov.s &0x3AB60B70,%fp2 # fp2 IS A5 + + fmul.x %fp1,%fp2 # fp2 IS S*A5 + fmov.x %fp1,%fp3 + fmul.s &0x3C088895,%fp3 # fp3 IS S*A4 + + fadd.d EEXPA3(%pc),%fp2 # fp2 IS A3+S*A5 + fadd.d EEXPA2(%pc),%fp3 # fp3 IS A2+S*A4 + + fmul.x %fp1,%fp2 # fp2 IS S*(A3+S*A5) + mov.w %d1,SCALE(%a6) # SCALE is 2^(M) in extended + mov.l &0x80000000,SCALE+4(%a6) + clr.l SCALE+8(%a6) + + fmul.x %fp1,%fp3 # fp3 IS S*(A2+S*A4) + + fadd.s &0x3F000000,%fp2 # fp2 IS A1+S*(A3+S*A5) + fmul.x %fp0,%fp3 # fp3 IS R*S*(A2+S*A4) + + fmul.x %fp1,%fp2 # fp2 IS S*(A1+S*(A3+S*A5)) + fadd.x %fp3,%fp0 # fp0 IS R+R*S*(A2+S*A4), + + fmov.x (%a1)+,%fp1 # fp1 is lead. pt. of 2^(J/64) + fadd.x %fp2,%fp0 # fp0 is EXP(R) - 1 + +#--Step 5 +#--final reconstruction process +#--EXP(X) = 2^M * ( 2^(J/64) + 2^(J/64)*(EXP(R)-1) ) + + fmul.x %fp1,%fp0 # 2^(J/64)*(Exp(R)-1) + fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3} + fadd.s (%a1),%fp0 # accurate 2^(J/64) + + fadd.x %fp1,%fp0 # 2^(J/64) + 2^(J/64)*... + mov.l ADJFLAG(%a6),%d1 + +#--Step 6 + tst.l %d1 + beq.b NORMAL +ADJUST: + fmul.x ADJSCALE(%a6),%fp0 +NORMAL: + fmov.l %d0,%fpcr # restore user FPCR + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x SCALE(%a6),%fp0 # multiply 2^(M) + bra t_catch + +EXPSM: +#--Step 7 + fmovm.x (%a0),&0x80 # load X + fmov.l %d0,%fpcr + fadd.s &0x3F800000,%fp0 # 1+X in user mode + bra t_pinx2 + +EEXPBIG: +#--Step 8 + cmp.l %d1,&0x400CB27C # 16480 log2 + bgt.b EXP2BIG +#--Steps 8.2 -- 8.6 + fmov.x (%a0),%fp0 # load input from (a0) + + fmov.x %fp0,%fp1 + fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X + fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3} + mov.l &1,ADJFLAG(%a6) + fmov.l %fp0,%d1 # N = int( X * 64/log2 ) + lea EEXPTBL(%pc),%a1 + fmov.l %d1,%fp0 # convert to floating-format + mov.l %d1,L_SCR1(%a6) # save N temporarily + and.l &0x3F,%d1 # D0 is J = N mod 64 + lsl.l &4,%d1 + add.l %d1,%a1 # address of 2^(J/64) + mov.l L_SCR1(%a6),%d1 + asr.l &6,%d1 # D0 is K + mov.l %d1,L_SCR1(%a6) # save K temporarily + asr.l &1,%d1 # D0 is M1 + sub.l %d1,L_SCR1(%a6) # a1 is M + add.w &0x3FFF,%d1 # biased expo. of 2^(M1) + mov.w %d1,ADJSCALE(%a6) # ADJSCALE := 2^(M1) + mov.l &0x80000000,ADJSCALE+4(%a6) + clr.l ADJSCALE+8(%a6) + mov.l L_SCR1(%a6),%d1 # D0 is M + add.w &0x3FFF,%d1 # biased expo. of 2^(M) + bra.w EXPCONT1 # go back to Step 3 + +EXP2BIG: +#--Step 9 + tst.b (%a0) # is X positive or negative? + bmi t_unfl2 + bra t_ovfl2 + + global setoxd +setoxd: +#--entry point for EXP(X), X is denormalized + mov.l (%a0),-(%sp) + andi.l &0x80000000,(%sp) + ori.l &0x00800000,(%sp) # sign(X)*2^(-126) + + fmov.s &0x3F800000,%fp0 + + fmov.l %d0,%fpcr + fadd.s (%sp)+,%fp0 + bra t_pinx2 + + global setoxm1 +setoxm1: +#--entry point for EXPM1(X), here X is finite, non-zero, non-NaN + +#--Step 1. +#--Step 1.1 + mov.l (%a0),%d1 # load part of input X + and.l &0x7FFF0000,%d1 # biased expo. of X + cmp.l %d1,&0x3FFD0000 # 1/4 + bge.b EM1CON1 # |X| >= 1/4 + bra EM1SM + +EM1CON1: +#--Step 1.3 +#--The case |X| >= 1/4 + mov.w 4(%a0),%d1 # expo. and partial sig. of |X| + cmp.l %d1,&0x4004C215 # 70log2 rounded up to 16 bits + ble.b EM1MAIN # 1/4 <= |X| <= 70log2 + bra EM1BIG + +EM1MAIN: +#--Step 2. +#--This is the case: 1/4 <= |X| <= 70 log2. + fmov.x (%a0),%fp0 # load input from (a0) + + fmov.x %fp0,%fp1 + fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X + fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3} + fmov.l %fp0,%d1 # N = int( X * 64/log2 ) + lea EEXPTBL(%pc),%a1 + fmov.l %d1,%fp0 # convert to floating-format + + mov.l %d1,L_SCR1(%a6) # save N temporarily + and.l &0x3F,%d1 # D0 is J = N mod 64 + lsl.l &4,%d1 + add.l %d1,%a1 # address of 2^(J/64) + mov.l L_SCR1(%a6),%d1 + asr.l &6,%d1 # D0 is M + mov.l %d1,L_SCR1(%a6) # save a copy of M + +#--Step 3. +#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X, +#--a0 points to 2^(J/64), D0 and a1 both contain M + fmov.x %fp0,%fp2 + fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64) + fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64 + fadd.x %fp1,%fp0 # X + N*L1 + fadd.x %fp2,%fp0 # fp0 is R, reduced arg. + add.w &0x3FFF,%d1 # D0 is biased expo. of 2^M + +#--Step 4. +#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL +#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6))))) +#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R +#--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))] + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # fp1 IS S = R*R + + fmov.s &0x3950097B,%fp2 # fp2 IS a6 + + fmul.x %fp1,%fp2 # fp2 IS S*A6 + fmov.x %fp1,%fp3 + fmul.s &0x3AB60B6A,%fp3 # fp3 IS S*A5 + + fadd.d EM1A4(%pc),%fp2 # fp2 IS A4+S*A6 + fadd.d EM1A3(%pc),%fp3 # fp3 IS A3+S*A5 + mov.w %d1,SC(%a6) # SC is 2^(M) in extended + mov.l &0x80000000,SC+4(%a6) + clr.l SC+8(%a6) + + fmul.x %fp1,%fp2 # fp2 IS S*(A4+S*A6) + mov.l L_SCR1(%a6),%d1 # D0 is M + neg.w %d1 # D0 is -M + fmul.x %fp1,%fp3 # fp3 IS S*(A3+S*A5) + add.w &0x3FFF,%d1 # biased expo. of 2^(-M) + fadd.d EM1A2(%pc),%fp2 # fp2 IS A2+S*(A4+S*A6) + fadd.s &0x3F000000,%fp3 # fp3 IS A1+S*(A3+S*A5) + + fmul.x %fp1,%fp2 # fp2 IS S*(A2+S*(A4+S*A6)) + or.w &0x8000,%d1 # signed/expo. of -2^(-M) + mov.w %d1,ONEBYSC(%a6) # OnebySc is -2^(-M) + mov.l &0x80000000,ONEBYSC+4(%a6) + clr.l ONEBYSC+8(%a6) + fmul.x %fp3,%fp1 # fp1 IS S*(A1+S*(A3+S*A5)) + + fmul.x %fp0,%fp2 # fp2 IS R*S*(A2+S*(A4+S*A6)) + fadd.x %fp1,%fp0 # fp0 IS R+S*(A1+S*(A3+S*A5)) + + fadd.x %fp2,%fp0 # fp0 IS EXP(R)-1 + + fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3} + +#--Step 5 +#--Compute 2^(J/64)*p + + fmul.x (%a1),%fp0 # 2^(J/64)*(Exp(R)-1) + +#--Step 6 +#--Step 6.1 + mov.l L_SCR1(%a6),%d1 # retrieve M + cmp.l %d1,&63 + ble.b MLE63 +#--Step 6.2 M >= 64 + fmov.s 12(%a1),%fp1 # fp1 is t + fadd.x ONEBYSC(%a6),%fp1 # fp1 is t+OnebySc + fadd.x %fp1,%fp0 # p+(t+OnebySc), fp1 released + fadd.x (%a1),%fp0 # T+(p+(t+OnebySc)) + bra EM1SCALE +MLE63: +#--Step 6.3 M <= 63 + cmp.l %d1,&-3 + bge.b MGEN3 +MLTN3: +#--Step 6.4 M <= -4 + fadd.s 12(%a1),%fp0 # p+t + fadd.x (%a1),%fp0 # T+(p+t) + fadd.x ONEBYSC(%a6),%fp0 # OnebySc + (T+(p+t)) + bra EM1SCALE +MGEN3: +#--Step 6.5 -3 <= M <= 63 + fmov.x (%a1)+,%fp1 # fp1 is T + fadd.s (%a1),%fp0 # fp0 is p+t + fadd.x ONEBYSC(%a6),%fp1 # fp1 is T+OnebySc + fadd.x %fp1,%fp0 # (T+OnebySc)+(p+t) + +EM1SCALE: +#--Step 6.6 + fmov.l %d0,%fpcr + fmul.x SC(%a6),%fp0 + bra t_inx2 + +EM1SM: +#--Step 7 |X| < 1/4. + cmp.l %d1,&0x3FBE0000 # 2^(-65) + bge.b EM1POLY + +EM1TINY: +#--Step 8 |X| < 2^(-65) + cmp.l %d1,&0x00330000 # 2^(-16312) + blt.b EM12TINY +#--Step 8.2 + mov.l &0x80010000,SC(%a6) # SC is -2^(-16382) + mov.l &0x80000000,SC+4(%a6) + clr.l SC+8(%a6) + fmov.x (%a0),%fp0 + fmov.l %d0,%fpcr + mov.b &FADD_OP,%d1 # last inst is ADD + fadd.x SC(%a6),%fp0 + bra t_catch + +EM12TINY: +#--Step 8.3 + fmov.x (%a0),%fp0 + fmul.d TWO140(%pc),%fp0 + mov.l &0x80010000,SC(%a6) + mov.l &0x80000000,SC+4(%a6) + clr.l SC+8(%a6) + fadd.x SC(%a6),%fp0 + fmov.l %d0,%fpcr + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.d TWON140(%pc),%fp0 + bra t_catch + +EM1POLY: +#--Step 9 exp(X)-1 by a simple polynomial + fmov.x (%a0),%fp0 # fp0 is X + fmul.x %fp0,%fp0 # fp0 is S := X*X + fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3} + fmov.s &0x2F30CAA8,%fp1 # fp1 is B12 + fmul.x %fp0,%fp1 # fp1 is S*B12 + fmov.s &0x310F8290,%fp2 # fp2 is B11 + fadd.s &0x32D73220,%fp1 # fp1 is B10+S*B12 + + fmul.x %fp0,%fp2 # fp2 is S*B11 + fmul.x %fp0,%fp1 # fp1 is S*(B10 + ... + + fadd.s &0x3493F281,%fp2 # fp2 is B9+S*... + fadd.d EM1B8(%pc),%fp1 # fp1 is B8+S*... + + fmul.x %fp0,%fp2 # fp2 is S*(B9+... + fmul.x %fp0,%fp1 # fp1 is S*(B8+... + + fadd.d EM1B7(%pc),%fp2 # fp2 is B7+S*... + fadd.d EM1B6(%pc),%fp1 # fp1 is B6+S*... + + fmul.x %fp0,%fp2 # fp2 is S*(B7+... + fmul.x %fp0,%fp1 # fp1 is S*(B6+... + + fadd.d EM1B5(%pc),%fp2 # fp2 is B5+S*... + fadd.d EM1B4(%pc),%fp1 # fp1 is B4+S*... + + fmul.x %fp0,%fp2 # fp2 is S*(B5+... + fmul.x %fp0,%fp1 # fp1 is S*(B4+... + + fadd.d EM1B3(%pc),%fp2 # fp2 is B3+S*... + fadd.x EM1B2(%pc),%fp1 # fp1 is B2+S*... + + fmul.x %fp0,%fp2 # fp2 is S*(B3+... + fmul.x %fp0,%fp1 # fp1 is S*(B2+... + + fmul.x %fp0,%fp2 # fp2 is S*S*(B3+...) + fmul.x (%a0),%fp1 # fp1 is X*S*(B2... + + fmul.s &0x3F000000,%fp0 # fp0 is S*B1 + fadd.x %fp2,%fp1 # fp1 is Q + + fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3} + + fadd.x %fp1,%fp0 # fp0 is S*B1+Q + + fmov.l %d0,%fpcr + fadd.x (%a0),%fp0 + bra t_inx2 + +EM1BIG: +#--Step 10 |X| > 70 log2 + mov.l (%a0),%d1 + cmp.l %d1,&0 + bgt.w EXPC1 +#--Step 10.2 + fmov.s &0xBF800000,%fp0 # fp0 is -1 + fmov.l %d0,%fpcr + fadd.s &0x00800000,%fp0 # -1 + 2^(-126) + bra t_minx2 + + global setoxm1d +setoxm1d: +#--entry point for EXPM1(X), here X is denormalized +#--Step 0. + bra t_extdnrm + +######################################################################### +# sgetexp(): returns the exponent portion of the input argument. # +# The exponent bias is removed and the exponent value is # +# returned as an extended precision number in fp0. # +# sgetexpd(): handles denormalized numbers. # +# # +# sgetman(): extracts the mantissa of the input argument. The # +# mantissa is converted to an extended precision number w/ # +# an exponent of $3fff and is returned in fp0. The range of # +# the result is [1.0 - 2.0). # +# sgetmand(): handles denormalized numbers. # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# # +# OUTPUT ************************************************************** # +# fp0 = exponent(X) or mantissa(X) # +# # +######################################################################### + + global sgetexp +sgetexp: + mov.w SRC_EX(%a0),%d0 # get the exponent + bclr &0xf,%d0 # clear the sign bit + subi.w &0x3fff,%d0 # subtract off the bias + fmov.w %d0,%fp0 # return exp in fp0 + blt.b sgetexpn # it's negative + rts + +sgetexpn: + mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit + rts + + global sgetexpd +sgetexpd: + bsr.l norm # normalize + neg.w %d0 # new exp = -(shft amt) + subi.w &0x3fff,%d0 # subtract off the bias + fmov.w %d0,%fp0 # return exp in fp0 + mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit + rts + + global sgetman +sgetman: + mov.w SRC_EX(%a0),%d0 # get the exp + ori.w &0x7fff,%d0 # clear old exp + bclr &0xe,%d0 # make it the new exp +-3fff + +# here, we build the result in a tmp location so as not to disturb the input + mov.l SRC_HI(%a0),FP_SCR0_HI(%a6) # copy to tmp loc + mov.l SRC_LO(%a0),FP_SCR0_LO(%a6) # copy to tmp loc + mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent + fmov.x FP_SCR0(%a6),%fp0 # put new value back in fp0 + bmi.b sgetmann # it's negative + rts + +sgetmann: + mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit + rts + +# +# For denormalized numbers, shift the mantissa until the j-bit = 1, +# then load the exponent with +/1 $3fff. +# + global sgetmand +sgetmand: + bsr.l norm # normalize exponent + bra.b sgetman + +######################################################################### +# scosh(): computes the hyperbolic cosine of a normalized input # +# scoshd(): computes the hyperbolic cosine of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = cosh(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# COSH # +# 1. If |X| > 16380 log2, go to 3. # +# # +# 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae # +# y = |X|, z = exp(Y), and # +# cosh(X) = (1/2)*( z + 1/z ). # +# Exit. # +# # +# 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. # +# # +# 4. (16380 log2 < |X| <= 16480 log2) # +# cosh(X) = sign(X) * exp(|X|)/2. # +# However, invoking exp(|X|) may cause premature # +# overflow. Thus, we calculate sinh(X) as follows: # +# Y := |X| # +# Fact := 2**(16380) # +# Y' := Y - 16381 log2 # +# cosh(X) := Fact * exp(Y'). # +# Exit. # +# # +# 5. (|X| > 16480 log2) sinh(X) must overflow. Return # +# Huge*Huge to generate overflow and an infinity with # +# the appropriate sign. Huge is the largest finite number # +# in extended format. Exit. # +# # +######################################################################### + +TWO16380: + long 0x7FFB0000,0x80000000,0x00000000,0x00000000 + + global scosh +scosh: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + cmp.l %d1,&0x400CB167 + bgt.b COSHBIG + +#--THIS IS THE USUAL CASE, |X| < 16380 LOG2 +#--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) + + fabs.x %fp0 # |X| + + mov.l %d0,-(%sp) + clr.l %d0 + fmovm.x &0x01,-(%sp) # save |X| to stack + lea (%sp),%a0 # pass ptr to |X| + bsr setox # FP0 IS EXP(|X|) + add.l &0xc,%sp # erase |X| from stack + fmul.s &0x3F000000,%fp0 # (1/2)EXP(|X|) + mov.l (%sp)+,%d0 + + fmov.s &0x3E800000,%fp1 # (1/4) + fdiv.x %fp0,%fp1 # 1/(2 EXP(|X|)) + + fmov.l %d0,%fpcr + mov.b &FADD_OP,%d1 # last inst is ADD + fadd.x %fp1,%fp0 + bra t_catch + +COSHBIG: + cmp.l %d1,&0x400CB2B3 + bgt.b COSHHUGE + + fabs.x %fp0 + fsub.d T1(%pc),%fp0 # (|X|-16381LOG2_LEAD) + fsub.d T2(%pc),%fp0 # |X| - 16381 LOG2, ACCURATE + + mov.l %d0,-(%sp) + clr.l %d0 + fmovm.x &0x01,-(%sp) # save fp0 to stack + lea (%sp),%a0 # pass ptr to fp0 + bsr setox + add.l &0xc,%sp # clear fp0 from stack + mov.l (%sp)+,%d0 + + fmov.l %d0,%fpcr + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x TWO16380(%pc),%fp0 + bra t_catch + +COSHHUGE: + bra t_ovfl2 + + global scoshd +#--COSH(X) = 1 FOR DENORMALIZED X +scoshd: + fmov.s &0x3F800000,%fp0 + + fmov.l %d0,%fpcr + fadd.s &0x00800000,%fp0 + bra t_pinx2 + +######################################################################### +# ssinh(): computes the hyperbolic sine of a normalized input # +# ssinhd(): computes the hyperbolic sine of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = sinh(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# SINH # +# 1. If |X| > 16380 log2, go to 3. # +# # +# 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formula # +# y = |X|, sgn = sign(X), and z = expm1(Y), # +# sinh(X) = sgn*(1/2)*( z + z/(1+z) ). # +# Exit. # +# # +# 3. If |X| > 16480 log2, go to 5. # +# # +# 4. (16380 log2 < |X| <= 16480 log2) # +# sinh(X) = sign(X) * exp(|X|)/2. # +# However, invoking exp(|X|) may cause premature overflow. # +# Thus, we calculate sinh(X) as follows: # +# Y := |X| # +# sgn := sign(X) # +# sgnFact := sgn * 2**(16380) # +# Y' := Y - 16381 log2 # +# sinh(X) := sgnFact * exp(Y'). # +# Exit. # +# # +# 5. (|X| > 16480 log2) sinh(X) must overflow. Return # +# sign(X)*Huge*Huge to generate overflow and an infinity with # +# the appropriate sign. Huge is the largest finite number in # +# extended format. Exit. # +# # +######################################################################### + + global ssinh +ssinh: + fmov.x (%a0),%fp0 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + mov.l %d1,%a1 # save (compacted) operand + and.l &0x7FFFFFFF,%d1 + cmp.l %d1,&0x400CB167 + bgt.b SINHBIG + +#--THIS IS THE USUAL CASE, |X| < 16380 LOG2 +#--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) ) + + fabs.x %fp0 # Y = |X| + + movm.l &0x8040,-(%sp) # {a1/d0} + fmovm.x &0x01,-(%sp) # save Y on stack + lea (%sp),%a0 # pass ptr to Y + clr.l %d0 + bsr setoxm1 # FP0 IS Z = EXPM1(Y) + add.l &0xc,%sp # clear Y from stack + fmov.l &0,%fpcr + movm.l (%sp)+,&0x0201 # {a1/d0} + + fmov.x %fp0,%fp1 + fadd.s &0x3F800000,%fp1 # 1+Z + fmov.x %fp0,-(%sp) + fdiv.x %fp1,%fp0 # Z/(1+Z) + mov.l %a1,%d1 + and.l &0x80000000,%d1 + or.l &0x3F000000,%d1 + fadd.x (%sp)+,%fp0 + mov.l %d1,-(%sp) + + fmov.l %d0,%fpcr + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.s (%sp)+,%fp0 # last fp inst - possible exceptions set + bra t_catch + +SINHBIG: + cmp.l %d1,&0x400CB2B3 + bgt t_ovfl + fabs.x %fp0 + fsub.d T1(%pc),%fp0 # (|X|-16381LOG2_LEAD) + mov.l &0,-(%sp) + mov.l &0x80000000,-(%sp) + mov.l %a1,%d1 + and.l &0x80000000,%d1 + or.l &0x7FFB0000,%d1 + mov.l %d1,-(%sp) # EXTENDED FMT + fsub.d T2(%pc),%fp0 # |X| - 16381 LOG2, ACCURATE + + mov.l %d0,-(%sp) + clr.l %d0 + fmovm.x &0x01,-(%sp) # save fp0 on stack + lea (%sp),%a0 # pass ptr to fp0 + bsr setox + add.l &0xc,%sp # clear fp0 from stack + + mov.l (%sp)+,%d0 + fmov.l %d0,%fpcr + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x (%sp)+,%fp0 # possible exception + bra t_catch + + global ssinhd +#--SINH(X) = X FOR DENORMALIZED X +ssinhd: + bra t_extdnrm + +######################################################################### +# stanh(): computes the hyperbolic tangent of a normalized input # +# stanhd(): computes the hyperbolic tangent of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = tanh(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# TANH # +# 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. # +# # +# 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by # +# sgn := sign(X), y := 2|X|, z := expm1(Y), and # +# tanh(X) = sgn*( z/(2+z) ). # +# Exit. # +# # +# 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, # +# go to 7. # +# # +# 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. # +# # +# 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by # +# sgn := sign(X), y := 2|X|, z := exp(Y), # +# tanh(X) = sgn - [ sgn*2/(1+z) ]. # +# Exit. # +# # +# 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we # +# calculate Tanh(X) by # +# sgn := sign(X), Tiny := 2**(-126), # +# tanh(X) := sgn - sgn*Tiny. # +# Exit. # +# # +# 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. # +# # +######################################################################### + + set X,FP_SCR0 + set XFRAC,X+4 + + set SGN,L_SCR3 + + set V,FP_SCR0 + + global stanh +stanh: + fmov.x (%a0),%fp0 # LOAD INPUT + + fmov.x %fp0,X(%a6) + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + mov.l %d1,X(%a6) + and.l &0x7FFFFFFF,%d1 + cmp.l %d1, &0x3fd78000 # is |X| < 2^(-40)? + blt.w TANHBORS # yes + cmp.l %d1, &0x3fffddce # is |X| > (5/2)LOG2? + bgt.w TANHBORS # yes + +#--THIS IS THE USUAL CASE +#--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). + + mov.l X(%a6),%d1 + mov.l %d1,SGN(%a6) + and.l &0x7FFF0000,%d1 + add.l &0x00010000,%d1 # EXPONENT OF 2|X| + mov.l %d1,X(%a6) + and.l &0x80000000,SGN(%a6) + fmov.x X(%a6),%fp0 # FP0 IS Y = 2|X| + + mov.l %d0,-(%sp) + clr.l %d0 + fmovm.x &0x1,-(%sp) # save Y on stack + lea (%sp),%a0 # pass ptr to Y + bsr setoxm1 # FP0 IS Z = EXPM1(Y) + add.l &0xc,%sp # clear Y from stack + mov.l (%sp)+,%d0 + + fmov.x %fp0,%fp1 + fadd.s &0x40000000,%fp1 # Z+2 + mov.l SGN(%a6),%d1 + fmov.x %fp1,V(%a6) + eor.l %d1,V(%a6) + + fmov.l %d0,%fpcr # restore users round prec,mode + fdiv.x V(%a6),%fp0 + bra t_inx2 + +TANHBORS: + cmp.l %d1,&0x3FFF8000 + blt.w TANHSM + + cmp.l %d1,&0x40048AA1 + bgt.w TANHHUGE + +#-- (5/2) LOG2 < |X| < 50 LOG2, +#--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), +#--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. + + mov.l X(%a6),%d1 + mov.l %d1,SGN(%a6) + and.l &0x7FFF0000,%d1 + add.l &0x00010000,%d1 # EXPO OF 2|X| + mov.l %d1,X(%a6) # Y = 2|X| + and.l &0x80000000,SGN(%a6) + mov.l SGN(%a6),%d1 + fmov.x X(%a6),%fp0 # Y = 2|X| + + mov.l %d0,-(%sp) + clr.l %d0 + fmovm.x &0x01,-(%sp) # save Y on stack + lea (%sp),%a0 # pass ptr to Y + bsr setox # FP0 IS EXP(Y) + add.l &0xc,%sp # clear Y from stack + mov.l (%sp)+,%d0 + mov.l SGN(%a6),%d1 + fadd.s &0x3F800000,%fp0 # EXP(Y)+1 + + eor.l &0xC0000000,%d1 # -SIGN(X)*2 + fmov.s %d1,%fp1 # -SIGN(X)*2 IN SGL FMT + fdiv.x %fp0,%fp1 # -SIGN(X)2 / [EXP(Y)+1 ] + + mov.l SGN(%a6),%d1 + or.l &0x3F800000,%d1 # SGN + fmov.s %d1,%fp0 # SGN IN SGL FMT + + fmov.l %d0,%fpcr # restore users round prec,mode + mov.b &FADD_OP,%d1 # last inst is ADD + fadd.x %fp1,%fp0 + bra t_inx2 + +TANHSM: + fmov.l %d0,%fpcr # restore users round prec,mode + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x X(%a6),%fp0 # last inst - possible exception set + bra t_catch + +#---RETURN SGN(X) - SGN(X)EPS +TANHHUGE: + mov.l X(%a6),%d1 + and.l &0x80000000,%d1 + or.l &0x3F800000,%d1 + fmov.s %d1,%fp0 + and.l &0x80000000,%d1 + eor.l &0x80800000,%d1 # -SIGN(X)*EPS + + fmov.l %d0,%fpcr # restore users round prec,mode + fadd.s %d1,%fp0 + bra t_inx2 + + global stanhd +#--TANH(X) = X FOR DENORMALIZED X +stanhd: + bra t_extdnrm + +######################################################################### +# slogn(): computes the natural logarithm of a normalized input # +# slognd(): computes the natural logarithm of a denormalized input # +# slognp1(): computes the log(1+X) of a normalized input # +# slognp1d(): computes the log(1+X) of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = log(X) or log(1+X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 2 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# LOGN: # +# Step 1. If |X-1| < 1/16, approximate log(X) by an odd # +# polynomial in u, where u = 2(X-1)/(X+1). Otherwise, # +# move on to Step 2. # +# # +# Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first # +# seven significant bits of Y plus 2**(-7), i.e. # +# F = 1.xxxxxx1 in base 2 where the six "x" match those # +# of Y. Note that |Y-F| <= 2**(-7). # +# # +# Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a # +# polynomial in u, log(1+u) = poly. # +# # +# Step 4. Reconstruct # +# log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u) # +# by k*log(2) + (log(F) + poly). The values of log(F) are # +# calculated beforehand and stored in the program. # +# # +# lognp1: # +# Step 1: If |X| < 1/16, approximate log(1+X) by an odd # +# polynomial in u where u = 2X/(2+X). Otherwise, move on # +# to Step 2. # +# # +# Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done # +# in Step 2 of the algorithm for LOGN and compute # +# log(1+X) as k*log(2) + log(F) + poly where poly # +# approximates log(1+u), u = (Y-F)/F. # +# # +# Implementation Notes: # +# Note 1. There are 64 different possible values for F, thus 64 # +# log(F)'s need to be tabulated. Moreover, the values of # +# 1/F are also tabulated so that the division in (Y-F)/F # +# can be performed by a multiplication. # +# # +# Note 2. In Step 2 of lognp1, in order to preserved accuracy, # +# the value Y-F has to be calculated carefully when # +# 1/2 <= X < 3/2. # +# # +# Note 3. To fully exploit the pipeline, polynomials are usually # +# separated into two parts evaluated independently before # +# being added up. # +# # +######################################################################### +LOGOF2: + long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000 + +one: + long 0x3F800000 +zero: + long 0x00000000 +infty: + long 0x7F800000 +negone: + long 0xBF800000 + +LOGA6: + long 0x3FC2499A,0xB5E4040B +LOGA5: + long 0xBFC555B5,0x848CB7DB + +LOGA4: + long 0x3FC99999,0x987D8730 +LOGA3: + long 0xBFCFFFFF,0xFF6F7E97 + +LOGA2: + long 0x3FD55555,0x555555A4 +LOGA1: + long 0xBFE00000,0x00000008 + +LOGB5: + long 0x3F175496,0xADD7DAD6 +LOGB4: + long 0x3F3C71C2,0xFE80C7E0 + +LOGB3: + long 0x3F624924,0x928BCCFF +LOGB2: + long 0x3F899999,0x999995EC + +LOGB1: + long 0x3FB55555,0x55555555 +TWO: + long 0x40000000,0x00000000 + +LTHOLD: + long 0x3f990000,0x80000000,0x00000000,0x00000000 + +LOGTBL: + long 0x3FFE0000,0xFE03F80F,0xE03F80FE,0x00000000 + long 0x3FF70000,0xFF015358,0x833C47E2,0x00000000 + long 0x3FFE0000,0xFA232CF2,0x52138AC0,0x00000000 + long 0x3FF90000,0xBDC8D83E,0xAD88D549,0x00000000 + long 0x3FFE0000,0xF6603D98,0x0F6603DA,0x00000000 + long 0x3FFA0000,0x9CF43DCF,0xF5EAFD48,0x00000000 + long 0x3FFE0000,0xF2B9D648,0x0F2B9D65,0x00000000 + long 0x3FFA0000,0xDA16EB88,0xCB8DF614,0x00000000 + long 0x3FFE0000,0xEF2EB71F,0xC4345238,0x00000000 + long 0x3FFB0000,0x8B29B775,0x1BD70743,0x00000000 + long 0x3FFE0000,0xEBBDB2A5,0xC1619C8C,0x00000000 + long 0x3FFB0000,0xA8D839F8,0x30C1FB49,0x00000000 + long 0x3FFE0000,0xE865AC7B,0x7603A197,0x00000000 + long 0x3FFB0000,0xC61A2EB1,0x8CD907AD,0x00000000 + long 0x3FFE0000,0xE525982A,0xF70C880E,0x00000000 + long 0x3FFB0000,0xE2F2A47A,0xDE3A18AF,0x00000000 + long 0x3FFE0000,0xE1FC780E,0x1FC780E2,0x00000000 + long 0x3FFB0000,0xFF64898E,0xDF55D551,0x00000000 + long 0x3FFE0000,0xDEE95C4C,0xA037BA57,0x00000000 + long 0x3FFC0000,0x8DB956A9,0x7B3D0148,0x00000000 + long 0x3FFE0000,0xDBEB61EE,0xD19C5958,0x00000000 + long 0x3FFC0000,0x9B8FE100,0xF47BA1DE,0x00000000 + long 0x3FFE0000,0xD901B203,0x6406C80E,0x00000000 + long 0x3FFC0000,0xA9372F1D,0x0DA1BD17,0x00000000 + long 0x3FFE0000,0xD62B80D6,0x2B80D62C,0x00000000 + long 0x3FFC0000,0xB6B07F38,0xCE90E46B,0x00000000 + long 0x3FFE0000,0xD3680D36,0x80D3680D,0x00000000 + long 0x3FFC0000,0xC3FD0329,0x06488481,0x00000000 + long 0x3FFE0000,0xD0B69FCB,0xD2580D0B,0x00000000 + long 0x3FFC0000,0xD11DE0FF,0x15AB18CA,0x00000000 + long 0x3FFE0000,0xCE168A77,0x25080CE1,0x00000000 + long 0x3FFC0000,0xDE1433A1,0x6C66B150,0x00000000 + long 0x3FFE0000,0xCB8727C0,0x65C393E0,0x00000000 + long 0x3FFC0000,0xEAE10B5A,0x7DDC8ADD,0x00000000 + long 0x3FFE0000,0xC907DA4E,0x871146AD,0x00000000 + long 0x3FFC0000,0xF7856E5E,0xE2C9B291,0x00000000 + long 0x3FFE0000,0xC6980C69,0x80C6980C,0x00000000 + long 0x3FFD0000,0x82012CA5,0xA68206D7,0x00000000 + long 0x3FFE0000,0xC4372F85,0x5D824CA6,0x00000000 + long 0x3FFD0000,0x882C5FCD,0x7256A8C5,0x00000000 + long 0x3FFE0000,0xC1E4BBD5,0x95F6E947,0x00000000 + long 0x3FFD0000,0x8E44C60B,0x4CCFD7DE,0x00000000 + long 0x3FFE0000,0xBFA02FE8,0x0BFA02FF,0x00000000 + long 0x3FFD0000,0x944AD09E,0xF4351AF6,0x00000000 + long 0x3FFE0000,0xBD691047,0x07661AA3,0x00000000 + long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B2,0x00000000 + long 0x3FFE0000,0xBB3EE721,0xA54D880C,0x00000000 + long 0x3FFD0000,0xA0218434,0x353F1DE8,0x00000000 + long 0x3FFE0000,0xB92143FA,0x36F5E02E,0x00000000 + long 0x3FFD0000,0xA5F2FCAB,0xBBC506DA,0x00000000 + long 0x3FFE0000,0xB70FBB5A,0x19BE3659,0x00000000 + long 0x3FFD0000,0xABB3B8BA,0x2AD362A5,0x00000000 + long 0x3FFE0000,0xB509E68A,0x9B94821F,0x00000000 + long 0x3FFD0000,0xB1641795,0xCE3CA97B,0x00000000 + long 0x3FFE0000,0xB30F6352,0x8917C80B,0x00000000 + long 0x3FFD0000,0xB7047551,0x5D0F1C61,0x00000000 + long 0x3FFE0000,0xB11FD3B8,0x0B11FD3C,0x00000000 + long 0x3FFD0000,0xBC952AFE,0xEA3D13E1,0x00000000 + long 0x3FFE0000,0xAF3ADDC6,0x80AF3ADE,0x00000000 + long 0x3FFD0000,0xC2168ED0,0xF458BA4A,0x00000000 + long 0x3FFE0000,0xAD602B58,0x0AD602B6,0x00000000 + long 0x3FFD0000,0xC788F439,0xB3163BF1,0x00000000 + long 0x3FFE0000,0xAB8F69E2,0x8359CD11,0x00000000 + long 0x3FFD0000,0xCCECAC08,0xBF04565D,0x00000000 + long 0x3FFE0000,0xA9C84A47,0xA07F5638,0x00000000 + long 0x3FFD0000,0xD2420487,0x2DD85160,0x00000000 + long 0x3FFE0000,0xA80A80A8,0x0A80A80B,0x00000000 + long 0x3FFD0000,0xD7894992,0x3BC3588A,0x00000000 + long 0x3FFE0000,0xA655C439,0x2D7B73A8,0x00000000 + long 0x3FFD0000,0xDCC2C4B4,0x9887DACC,0x00000000 + long 0x3FFE0000,0xA4A9CF1D,0x96833751,0x00000000 + long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9E,0x00000000 + long 0x3FFE0000,0xA3065E3F,0xAE7CD0E0,0x00000000 + long 0x3FFD0000,0xE70D785C,0x2F9F5BDC,0x00000000 + long 0x3FFE0000,0xA16B312E,0xA8FC377D,0x00000000 + long 0x3FFD0000,0xEC1F392C,0x5179F283,0x00000000 + long 0x3FFE0000,0x9FD809FD,0x809FD80A,0x00000000 + long 0x3FFD0000,0xF12440D3,0xE36130E6,0x00000000 + long 0x3FFE0000,0x9E4CAD23,0xDD5F3A20,0x00000000 + long 0x3FFD0000,0xF61CCE92,0x346600BB,0x00000000 + long 0x3FFE0000,0x9CC8E160,0xC3FB19B9,0x00000000 + long 0x3FFD0000,0xFB091FD3,0x8145630A,0x00000000 + long 0x3FFE0000,0x9B4C6F9E,0xF03A3CAA,0x00000000 + long 0x3FFD0000,0xFFE97042,0xBFA4C2AD,0x00000000 + long 0x3FFE0000,0x99D722DA,0xBDE58F06,0x00000000 + long 0x3FFE0000,0x825EFCED,0x49369330,0x00000000 + long 0x3FFE0000,0x9868C809,0x868C8098,0x00000000 + long 0x3FFE0000,0x84C37A7A,0xB9A905C9,0x00000000 + long 0x3FFE0000,0x97012E02,0x5C04B809,0x00000000 + long 0x3FFE0000,0x87224C2E,0x8E645FB7,0x00000000 + long 0x3FFE0000,0x95A02568,0x095A0257,0x00000000 + long 0x3FFE0000,0x897B8CAC,0x9F7DE298,0x00000000 + long 0x3FFE0000,0x94458094,0x45809446,0x00000000 + long 0x3FFE0000,0x8BCF55DE,0xC4CD05FE,0x00000000 + long 0x3FFE0000,0x92F11384,0x0497889C,0x00000000 + long 0x3FFE0000,0x8E1DC0FB,0x89E125E5,0x00000000 + long 0x3FFE0000,0x91A2B3C4,0xD5E6F809,0x00000000 + long 0x3FFE0000,0x9066E68C,0x955B6C9B,0x00000000 + long 0x3FFE0000,0x905A3863,0x3E06C43B,0x00000000 + long 0x3FFE0000,0x92AADE74,0xC7BE59E0,0x00000000 + long 0x3FFE0000,0x8F1779D9,0xFDC3A219,0x00000000 + long 0x3FFE0000,0x94E9BFF6,0x15845643,0x00000000 + long 0x3FFE0000,0x8DDA5202,0x37694809,0x00000000 + long 0x3FFE0000,0x9723A1B7,0x20134203,0x00000000 + long 0x3FFE0000,0x8CA29C04,0x6514E023,0x00000000 + long 0x3FFE0000,0x995899C8,0x90EB8990,0x00000000 + long 0x3FFE0000,0x8B70344A,0x139BC75A,0x00000000 + long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2F,0x00000000 + long 0x3FFE0000,0x8A42F870,0x5669DB46,0x00000000 + long 0x3FFE0000,0x9DB4224F,0xFFE1157C,0x00000000 + long 0x3FFE0000,0x891AC73A,0xE9819B50,0x00000000 + long 0x3FFE0000,0x9FDADC26,0x8B7A12DA,0x00000000 + long 0x3FFE0000,0x87F78087,0xF78087F8,0x00000000 + long 0x3FFE0000,0xA1FCFF17,0xCE733BD4,0x00000000 + long 0x3FFE0000,0x86D90544,0x7A34ACC6,0x00000000 + long 0x3FFE0000,0xA41A9E8F,0x5446FB9F,0x00000000 + long 0x3FFE0000,0x85BF3761,0x2CEE3C9B,0x00000000 + long 0x3FFE0000,0xA633CD7E,0x6771CD8B,0x00000000 + long 0x3FFE0000,0x84A9F9C8,0x084A9F9D,0x00000000 + long 0x3FFE0000,0xA8489E60,0x0B435A5E,0x00000000 + long 0x3FFE0000,0x83993052,0x3FBE3368,0x00000000 + long 0x3FFE0000,0xAA59233C,0xCCA4BD49,0x00000000 + long 0x3FFE0000,0x828CBFBE,0xB9A020A3,0x00000000 + long 0x3FFE0000,0xAC656DAE,0x6BCC4985,0x00000000 + long 0x3FFE0000,0x81848DA8,0xFAF0D277,0x00000000 + long 0x3FFE0000,0xAE6D8EE3,0x60BB2468,0x00000000 + long 0x3FFE0000,0x80808080,0x80808081,0x00000000 + long 0x3FFE0000,0xB07197A2,0x3C46C654,0x00000000 + + set ADJK,L_SCR1 + + set X,FP_SCR0 + set XDCARE,X+2 + set XFRAC,X+4 + + set F,FP_SCR1 + set FFRAC,F+4 + + set KLOG2,FP_SCR0 + + set SAVEU,FP_SCR0 + + global slogn +#--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S +slogn: + fmov.x (%a0),%fp0 # LOAD INPUT + mov.l &0x00000000,ADJK(%a6) + +LOGBGN: +#--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS +#--A FINITE, NON-ZERO, NORMALIZED NUMBER. + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + + mov.l (%a0),X(%a6) + mov.l 4(%a0),X+4(%a6) + mov.l 8(%a0),X+8(%a6) + + cmp.l %d1,&0 # CHECK IF X IS NEGATIVE + blt.w LOGNEG # LOG OF NEGATIVE ARGUMENT IS INVALID +# X IS POSITIVE, CHECK IF X IS NEAR 1 + cmp.l %d1,&0x3ffef07d # IS X < 15/16? + blt.b LOGMAIN # YES + cmp.l %d1,&0x3fff8841 # IS X > 17/16? + ble.w LOGNEAR1 # NO + +LOGMAIN: +#--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1 + +#--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY. +#--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1. +#--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y) +#-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F). +#--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING +#--LOG(1+U) CAN BE VERY EFFICIENT. +#--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO +#--DIVISION IS NEEDED TO CALCULATE (Y-F)/F. + +#--GET K, Y, F, AND ADDRESS OF 1/F. + asr.l &8,%d1 + asr.l &8,%d1 # SHIFTED 16 BITS, BIASED EXPO. OF X + sub.l &0x3FFF,%d1 # THIS IS K + add.l ADJK(%a6),%d1 # ADJUST K, ORIGINAL INPUT MAY BE DENORM. + lea LOGTBL(%pc),%a0 # BASE ADDRESS OF 1/F AND LOG(F) + fmov.l %d1,%fp1 # CONVERT K TO FLOATING-POINT FORMAT + +#--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F + mov.l &0x3FFF0000,X(%a6) # X IS NOW Y, I.E. 2^(-K)*X + mov.l XFRAC(%a6),FFRAC(%a6) + and.l &0xFE000000,FFRAC(%a6) # FIRST 7 BITS OF Y + or.l &0x01000000,FFRAC(%a6) # GET F: ATTACH A 1 AT THE EIGHTH BIT + mov.l FFRAC(%a6),%d1 # READY TO GET ADDRESS OF 1/F + and.l &0x7E000000,%d1 + asr.l &8,%d1 + asr.l &8,%d1 + asr.l &4,%d1 # SHIFTED 20, D0 IS THE DISPLACEMENT + add.l %d1,%a0 # A0 IS THE ADDRESS FOR 1/F + + fmov.x X(%a6),%fp0 + mov.l &0x3fff0000,F(%a6) + clr.l F+8(%a6) + fsub.x F(%a6),%fp0 # Y-F + fmovm.x &0xc,-(%sp) # SAVE FP2-3 WHILE FP0 IS NOT READY +#--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K +#--REGISTERS SAVED: FPCR, FP1, FP2 + +LP1CONT1: +#--AN RE-ENTRY POINT FOR LOGNP1 + fmul.x (%a0),%fp0 # FP0 IS U = (Y-F)/F + fmul.x LOGOF2(%pc),%fp1 # GET K*LOG2 WHILE FP0 IS NOT READY + fmov.x %fp0,%fp2 + fmul.x %fp2,%fp2 # FP2 IS V=U*U + fmov.x %fp1,KLOG2(%a6) # PUT K*LOG2 IN MEMEORY, FREE FP1 + +#--LOG(1+U) IS APPROXIMATED BY +#--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS +#--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))] + + fmov.x %fp2,%fp3 + fmov.x %fp2,%fp1 + + fmul.d LOGA6(%pc),%fp1 # V*A6 + fmul.d LOGA5(%pc),%fp2 # V*A5 + + fadd.d LOGA4(%pc),%fp1 # A4+V*A6 + fadd.d LOGA3(%pc),%fp2 # A3+V*A5 + + fmul.x %fp3,%fp1 # V*(A4+V*A6) + fmul.x %fp3,%fp2 # V*(A3+V*A5) + + fadd.d LOGA2(%pc),%fp1 # A2+V*(A4+V*A6) + fadd.d LOGA1(%pc),%fp2 # A1+V*(A3+V*A5) + + fmul.x %fp3,%fp1 # V*(A2+V*(A4+V*A6)) + add.l &16,%a0 # ADDRESS OF LOG(F) + fmul.x %fp3,%fp2 # V*(A1+V*(A3+V*A5)) + + fmul.x %fp0,%fp1 # U*V*(A2+V*(A4+V*A6)) + fadd.x %fp2,%fp0 # U+V*(A1+V*(A3+V*A5)) + + fadd.x (%a0),%fp1 # LOG(F)+U*V*(A2+V*(A4+V*A6)) + fmovm.x (%sp)+,&0x30 # RESTORE FP2-3 + fadd.x %fp1,%fp0 # FP0 IS LOG(F) + LOG(1+U) + + fmov.l %d0,%fpcr + fadd.x KLOG2(%a6),%fp0 # FINAL ADD + bra t_inx2 + + +LOGNEAR1: + +# if the input is exactly equal to one, then exit through ld_pzero. +# if these 2 lines weren't here, the correct answer would be returned +# but the INEX2 bit would be set. + fcmp.b %fp0,&0x1 # is it equal to one? + fbeq.l ld_pzero # yes + +#--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT. + fmov.x %fp0,%fp1 + fsub.s one(%pc),%fp1 # FP1 IS X-1 + fadd.s one(%pc),%fp0 # FP0 IS X+1 + fadd.x %fp1,%fp1 # FP1 IS 2(X-1) +#--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL +#--IN U, U = 2(X-1)/(X+1) = FP1/FP0 + +LP1CONT2: +#--THIS IS AN RE-ENTRY POINT FOR LOGNP1 + fdiv.x %fp0,%fp1 # FP1 IS U + fmovm.x &0xc,-(%sp) # SAVE FP2-3 +#--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3 +#--LET V=U*U, W=V*V, CALCULATE +#--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY +#--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] ) + fmov.x %fp1,%fp0 + fmul.x %fp0,%fp0 # FP0 IS V + fmov.x %fp1,SAVEU(%a6) # STORE U IN MEMORY, FREE FP1 + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS W + + fmov.d LOGB5(%pc),%fp3 + fmov.d LOGB4(%pc),%fp2 + + fmul.x %fp1,%fp3 # W*B5 + fmul.x %fp1,%fp2 # W*B4 + + fadd.d LOGB3(%pc),%fp3 # B3+W*B5 + fadd.d LOGB2(%pc),%fp2 # B2+W*B4 + + fmul.x %fp3,%fp1 # W*(B3+W*B5), FP3 RELEASED + + fmul.x %fp0,%fp2 # V*(B2+W*B4) + + fadd.d LOGB1(%pc),%fp1 # B1+W*(B3+W*B5) + fmul.x SAVEU(%a6),%fp0 # FP0 IS U*V + + fadd.x %fp2,%fp1 # B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED + fmovm.x (%sp)+,&0x30 # FP2-3 RESTORED + + fmul.x %fp1,%fp0 # U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] ) + + fmov.l %d0,%fpcr + fadd.x SAVEU(%a6),%fp0 + bra t_inx2 + +#--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID +LOGNEG: + bra t_operr + + global slognd +slognd: +#--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT + + mov.l &-100,ADJK(%a6) # INPUT = 2^(ADJK) * FP0 + +#----normalize the input value by left shifting k bits (k to be determined +#----below), adjusting exponent and storing -k to ADJK +#----the value TWOTO100 is no longer needed. +#----Note that this code assumes the denormalized input is NON-ZERO. + + movm.l &0x3f00,-(%sp) # save some registers {d2-d7} + mov.l (%a0),%d3 # D3 is exponent of smallest norm. # + mov.l 4(%a0),%d4 + mov.l 8(%a0),%d5 # (D4,D5) is (Hi_X,Lo_X) + clr.l %d2 # D2 used for holding K + + tst.l %d4 + bne.b Hi_not0 + +Hi_0: + mov.l %d5,%d4 + clr.l %d5 + mov.l &32,%d2 + clr.l %d6 + bfffo %d4{&0:&32},%d6 + lsl.l %d6,%d4 + add.l %d6,%d2 # (D3,D4,D5) is normalized + + mov.l %d3,X(%a6) + mov.l %d4,XFRAC(%a6) + mov.l %d5,XFRAC+4(%a6) + neg.l %d2 + mov.l %d2,ADJK(%a6) + fmov.x X(%a6),%fp0 + movm.l (%sp)+,&0xfc # restore registers {d2-d7} + lea X(%a6),%a0 + bra.w LOGBGN # begin regular log(X) + +Hi_not0: + clr.l %d6 + bfffo %d4{&0:&32},%d6 # find first 1 + mov.l %d6,%d2 # get k + lsl.l %d6,%d4 + mov.l %d5,%d7 # a copy of D5 + lsl.l %d6,%d5 + neg.l %d6 + add.l &32,%d6 + lsr.l %d6,%d7 + or.l %d7,%d4 # (D3,D4,D5) normalized + + mov.l %d3,X(%a6) + mov.l %d4,XFRAC(%a6) + mov.l %d5,XFRAC+4(%a6) + neg.l %d2 + mov.l %d2,ADJK(%a6) + fmov.x X(%a6),%fp0 + movm.l (%sp)+,&0xfc # restore registers {d2-d7} + lea X(%a6),%a0 + bra.w LOGBGN # begin regular log(X) + + global slognp1 +#--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S +slognp1: + fmov.x (%a0),%fp0 # LOAD INPUT + fabs.x %fp0 # test magnitude + fcmp.x %fp0,LTHOLD(%pc) # compare with min threshold + fbgt.w LP1REAL # if greater, continue + fmov.l %d0,%fpcr + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x (%a0),%fp0 # return signed argument + bra t_catch + +LP1REAL: + fmov.x (%a0),%fp0 # LOAD INPUT + mov.l &0x00000000,ADJK(%a6) + fmov.x %fp0,%fp1 # FP1 IS INPUT Z + fadd.s one(%pc),%fp0 # X := ROUND(1+Z) + fmov.x %fp0,X(%a6) + mov.w XFRAC(%a6),XDCARE(%a6) + mov.l X(%a6),%d1 + cmp.l %d1,&0 + ble.w LP1NEG0 # LOG OF ZERO OR -VE + cmp.l %d1,&0x3ffe8000 # IS BOUNDS [1/2,3/2]? + blt.w LOGMAIN + cmp.l %d1,&0x3fffc000 + bgt.w LOGMAIN +#--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z, +#--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE, +#--SIMPLY INVOKE LOG(X) FOR LOG(1+Z). + +LP1NEAR1: +#--NEXT SEE IF EXP(-1/16) < X < EXP(1/16) + cmp.l %d1,&0x3ffef07d + blt.w LP1CARE + cmp.l %d1,&0x3fff8841 + bgt.w LP1CARE + +LP1ONE16: +#--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2) +#--WHERE U = 2Z/(2+Z) = 2Z/(1+X). + fadd.x %fp1,%fp1 # FP1 IS 2Z + fadd.s one(%pc),%fp0 # FP0 IS 1+X +#--U = FP1/FP0 + bra.w LP1CONT2 + +LP1CARE: +#--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE +#--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST +#--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2], +#--THERE ARE ONLY TWO CASES. +#--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z +#--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z +#--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF +#--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED. + + mov.l XFRAC(%a6),FFRAC(%a6) + and.l &0xFE000000,FFRAC(%a6) + or.l &0x01000000,FFRAC(%a6) # F OBTAINED + cmp.l %d1,&0x3FFF8000 # SEE IF 1+Z > 1 + bge.b KISZERO + +KISNEG1: + fmov.s TWO(%pc),%fp0 + mov.l &0x3fff0000,F(%a6) + clr.l F+8(%a6) + fsub.x F(%a6),%fp0 # 2-F + mov.l FFRAC(%a6),%d1 + and.l &0x7E000000,%d1 + asr.l &8,%d1 + asr.l &8,%d1 + asr.l &4,%d1 # D0 CONTAINS DISPLACEMENT FOR 1/F + fadd.x %fp1,%fp1 # GET 2Z + fmovm.x &0xc,-(%sp) # SAVE FP2 {%fp2/%fp3} + fadd.x %fp1,%fp0 # FP0 IS Y-F = (2-F)+2Z + lea LOGTBL(%pc),%a0 # A0 IS ADDRESS OF 1/F + add.l %d1,%a0 + fmov.s negone(%pc),%fp1 # FP1 IS K = -1 + bra.w LP1CONT1 + +KISZERO: + fmov.s one(%pc),%fp0 + mov.l &0x3fff0000,F(%a6) + clr.l F+8(%a6) + fsub.x F(%a6),%fp0 # 1-F + mov.l FFRAC(%a6),%d1 + and.l &0x7E000000,%d1 + asr.l &8,%d1 + asr.l &8,%d1 + asr.l &4,%d1 + fadd.x %fp1,%fp0 # FP0 IS Y-F + fmovm.x &0xc,-(%sp) # FP2 SAVED {%fp2/%fp3} + lea LOGTBL(%pc),%a0 + add.l %d1,%a0 # A0 IS ADDRESS OF 1/F + fmov.s zero(%pc),%fp1 # FP1 IS K = 0 + bra.w LP1CONT1 + +LP1NEG0: +#--FPCR SAVED. D0 IS X IN COMPACT FORM. + cmp.l %d1,&0 + blt.b LP1NEG +LP1ZERO: + fmov.s negone(%pc),%fp0 + + fmov.l %d0,%fpcr + bra t_dz + +LP1NEG: + fmov.s zero(%pc),%fp0 + + fmov.l %d0,%fpcr + bra t_operr + + global slognp1d +#--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT +# Simply return the denorm +slognp1d: + bra t_extdnrm + +######################################################################### +# satanh(): computes the inverse hyperbolic tangent of a norm input # +# satanhd(): computes the inverse hyperbolic tangent of a denorm input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = arctanh(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 3 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# ATANH # +# 1. If |X| >= 1, go to 3. # +# # +# 2. (|X| < 1) Calculate atanh(X) by # +# sgn := sign(X) # +# y := |X| # +# z := 2y/(1-y) # +# atanh(X) := sgn * (1/2) * logp1(z) # +# Exit. # +# # +# 3. If |X| > 1, go to 5. # +# # +# 4. (|X| = 1) Generate infinity with an appropriate sign and # +# divide-by-zero by # +# sgn := sign(X) # +# atan(X) := sgn / (+0). # +# Exit. # +# # +# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. # +# Exit. # +# # +######################################################################### + + global satanh +satanh: + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + cmp.l %d1,&0x3FFF8000 + bge.b ATANHBIG + +#--THIS IS THE USUAL CASE, |X| < 1 +#--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z). + + fabs.x (%a0),%fp0 # Y = |X| + fmov.x %fp0,%fp1 + fneg.x %fp1 # -Y + fadd.x %fp0,%fp0 # 2Y + fadd.s &0x3F800000,%fp1 # 1-Y + fdiv.x %fp1,%fp0 # 2Y/(1-Y) + mov.l (%a0),%d1 + and.l &0x80000000,%d1 + or.l &0x3F000000,%d1 # SIGN(X)*HALF + mov.l %d1,-(%sp) + + mov.l %d0,-(%sp) # save rnd prec,mode + clr.l %d0 # pass ext prec,RN + fmovm.x &0x01,-(%sp) # save Z on stack + lea (%sp),%a0 # pass ptr to Z + bsr slognp1 # LOG1P(Z) + add.l &0xc,%sp # clear Z from stack + + mov.l (%sp)+,%d0 # fetch old prec,mode + fmov.l %d0,%fpcr # load it + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.s (%sp)+,%fp0 + bra t_catch + +ATANHBIG: + fabs.x (%a0),%fp0 # |X| + fcmp.s %fp0,&0x3F800000 + fbgt t_operr + bra t_dz + + global satanhd +#--ATANH(X) = X FOR DENORMALIZED X +satanhd: + bra t_extdnrm + +######################################################################### +# slog10(): computes the base-10 logarithm of a normalized input # +# slog10d(): computes the base-10 logarithm of a denormalized input # +# slog2(): computes the base-2 logarithm of a normalized input # +# slog2d(): computes the base-2 logarithm of a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = log_10(X) or log_2(X) # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 1.7 ulps in 64 significant bit, # +# i.e. within 0.5003 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# slog10d: # +# # +# Step 0. If X < 0, create a NaN and raise the invalid operation # +# flag. Otherwise, save FPCR in D1; set FpCR to default. # +# Notes: Default means round-to-nearest mode, no floating-point # +# traps, and precision control = double extended. # +# # +# Step 1. Call slognd to obtain Y = log(X), the natural log of X. # +# Notes: Even if X is denormalized, log(X) is always normalized. # +# # +# Step 2. Compute log_10(X) = log(X) * (1/log(10)). # +# 2.1 Restore the user FPCR # +# 2.2 Return ans := Y * INV_L10. # +# # +# slog10: # +# # +# Step 0. If X < 0, create a NaN and raise the invalid operation # +# flag. Otherwise, save FPCR in D1; set FpCR to default. # +# Notes: Default means round-to-nearest mode, no floating-point # +# traps, and precision control = double extended. # +# # +# Step 1. Call sLogN to obtain Y = log(X), the natural log of X. # +# # +# Step 2. Compute log_10(X) = log(X) * (1/log(10)). # +# 2.1 Restore the user FPCR # +# 2.2 Return ans := Y * INV_L10. # +# # +# sLog2d: # +# # +# Step 0. If X < 0, create a NaN and raise the invalid operation # +# flag. Otherwise, save FPCR in D1; set FpCR to default. # +# Notes: Default means round-to-nearest mode, no floating-point # +# traps, and precision control = double extended. # +# # +# Step 1. Call slognd to obtain Y = log(X), the natural log of X. # +# Notes: Even if X is denormalized, log(X) is always normalized. # +# # +# Step 2. Compute log_10(X) = log(X) * (1/log(2)). # +# 2.1 Restore the user FPCR # +# 2.2 Return ans := Y * INV_L2. # +# # +# sLog2: # +# # +# Step 0. If X < 0, create a NaN and raise the invalid operation # +# flag. Otherwise, save FPCR in D1; set FpCR to default. # +# Notes: Default means round-to-nearest mode, no floating-point # +# traps, and precision control = double extended. # +# # +# Step 1. If X is not an integer power of two, i.e., X != 2^k, # +# go to Step 3. # +# # +# Step 2. Return k. # +# 2.1 Get integer k, X = 2^k. # +# 2.2 Restore the user FPCR. # +# 2.3 Return ans := convert-to-double-extended(k). # +# # +# Step 3. Call sLogN to obtain Y = log(X), the natural log of X. # +# # +# Step 4. Compute log_2(X) = log(X) * (1/log(2)). # +# 4.1 Restore the user FPCR # +# 4.2 Return ans := Y * INV_L2. # +# # +######################################################################### + +INV_L10: + long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 + +INV_L2: + long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 + + global slog10 +#--entry point for Log10(X), X is normalized +slog10: + fmov.b &0x1,%fp0 + fcmp.x %fp0,(%a0) # if operand == 1, + fbeq.l ld_pzero # return an EXACT zero + + mov.l (%a0),%d1 + blt.w invalid + mov.l %d0,-(%sp) + clr.l %d0 + bsr slogn # log(X), X normal. + fmov.l (%sp)+,%fpcr + fmul.x INV_L10(%pc),%fp0 + bra t_inx2 + + global slog10d +#--entry point for Log10(X), X is denormalized +slog10d: + mov.l (%a0),%d1 + blt.w invalid + mov.l %d0,-(%sp) + clr.l %d0 + bsr slognd # log(X), X denorm. + fmov.l (%sp)+,%fpcr + fmul.x INV_L10(%pc),%fp0 + bra t_minx2 + + global slog2 +#--entry point for Log2(X), X is normalized +slog2: + mov.l (%a0),%d1 + blt.w invalid + + mov.l 8(%a0),%d1 + bne.b continue # X is not 2^k + + mov.l 4(%a0),%d1 + and.l &0x7FFFFFFF,%d1 + bne.b continue + +#--X = 2^k. + mov.w (%a0),%d1 + and.l &0x00007FFF,%d1 + sub.l &0x3FFF,%d1 + beq.l ld_pzero + fmov.l %d0,%fpcr + fmov.l %d1,%fp0 + bra t_inx2 + +continue: + mov.l %d0,-(%sp) + clr.l %d0 + bsr slogn # log(X), X normal. + fmov.l (%sp)+,%fpcr + fmul.x INV_L2(%pc),%fp0 + bra t_inx2 + +invalid: + bra t_operr + + global slog2d +#--entry point for Log2(X), X is denormalized +slog2d: + mov.l (%a0),%d1 + blt.w invalid + mov.l %d0,-(%sp) + clr.l %d0 + bsr slognd # log(X), X denorm. + fmov.l (%sp)+,%fpcr + fmul.x INV_L2(%pc),%fp0 + bra t_minx2 + +######################################################################### +# stwotox(): computes 2**X for a normalized input # +# stwotoxd(): computes 2**X for a denormalized input # +# stentox(): computes 10**X for a normalized input # +# stentoxd(): computes 10**X for a denormalized input # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input # +# d0 = round precision,mode # +# # +# OUTPUT ************************************************************** # +# fp0 = 2**X or 10**X # +# # +# ACCURACY and MONOTONICITY ******************************************* # +# The returned result is within 2 ulps in 64 significant bit, # +# i.e. within 0.5001 ulp to 53 bits if the result is subsequently # +# rounded to double precision. The result is provably monotonic # +# in double precision. # +# # +# ALGORITHM *********************************************************** # +# # +# twotox # +# 1. If |X| > 16480, go to ExpBig. # +# # +# 2. If |X| < 2**(-70), go to ExpSm. # +# # +# 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore # +# decompose N as # +# N = 64(M + M') + j, j = 0,1,2,...,63. # +# # +# 4. Overwrite r := r * log2. Then # +# 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). # +# Go to expr to compute that expression. # +# # +# tentox # +# 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig. # +# # +# 2. If |X| < 2**(-70), go to ExpSm. # +# # +# 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set # +# N := round-to-int(y). Decompose N as # +# N = 64(M + M') + j, j = 0,1,2,...,63. # +# # +# 4. Define r as # +# r := ((X - N*L1)-N*L2) * L10 # +# where L1, L2 are the leading and trailing parts of # +# log_10(2)/64 and L10 is the natural log of 10. Then # +# 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). # +# Go to expr to compute that expression. # +# # +# expr # +# 1. Fetch 2**(j/64) from table as Fact1 and Fact2. # +# # +# 2. Overwrite Fact1 and Fact2 by # +# Fact1 := 2**(M) * Fact1 # +# Fact2 := 2**(M) * Fact2 # +# Thus Fact1 + Fact2 = 2**(M) * 2**(j/64). # +# # +# 3. Calculate P where 1 + P approximates exp(r): # +# P = r + r*r*(A1+r*(A2+...+r*A5)). # +# # +# 4. Let AdjFact := 2**(M'). Return # +# AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ). # +# Exit. # +# # +# ExpBig # +# 1. Generate overflow by Huge * Huge if X > 0; otherwise, # +# generate underflow by Tiny * Tiny. # +# # +# ExpSm # +# 1. Return 1 + X. # +# # +######################################################################### + +L2TEN64: + long 0x406A934F,0x0979A371 # 64LOG10/LOG2 +L10TWO1: + long 0x3F734413,0x509F8000 # LOG2/64LOG10 + +L10TWO2: + long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000 + +LOG10: long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000 + +LOG2: long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000 + +EXPA5: long 0x3F56C16D,0x6F7BD0B2 +EXPA4: long 0x3F811112,0x302C712C +EXPA3: long 0x3FA55555,0x55554CC1 +EXPA2: long 0x3FC55555,0x55554A54 +EXPA1: long 0x3FE00000,0x00000000,0x00000000,0x00000000 + +TEXPTBL: + long 0x3FFF0000,0x80000000,0x00000000,0x3F738000 + long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA + long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9 + long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9 + long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA + long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C + long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1 + long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA + long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373 + long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670 + long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700 + long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0 + long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D + long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319 + long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B + long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5 + long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A + long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B + long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF + long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA + long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD + long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E + long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B + long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB + long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB + long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274 + long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C + long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00 + long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301 + long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367 + long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F + long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C + long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB + long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB + long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C + long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA + long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD + long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51 + long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A + long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2 + long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB + long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17 + long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C + long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8 + long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53 + long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE + long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124 + long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243 + long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A + long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61 + long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610 + long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1 + long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12 + long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE + long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4 + long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F + long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A + long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A + long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC + long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F + long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A + long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795 + long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B + long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581 + + set INT,L_SCR1 + + set X,FP_SCR0 + set XDCARE,X+2 + set XFRAC,X+4 + + set ADJFACT,FP_SCR0 + + set FACT1,FP_SCR0 + set FACT1HI,FACT1+4 + set FACT1LOW,FACT1+8 + + set FACT2,FP_SCR1 + set FACT2HI,FACT2+4 + set FACT2LOW,FACT2+8 + + global stwotox +#--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S +stwotox: + fmovm.x (%a0),&0x80 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + fmov.x %fp0,X(%a6) + and.l &0x7FFFFFFF,%d1 + + cmp.l %d1,&0x3FB98000 # |X| >= 2**(-70)? + bge.b TWOOK1 + bra.w EXPBORS + +TWOOK1: + cmp.l %d1,&0x400D80C0 # |X| > 16480? + ble.b TWOMAIN + bra.w EXPBORS + +TWOMAIN: +#--USUAL CASE, 2^(-70) <= |X| <= 16480 + + fmov.x %fp0,%fp1 + fmul.s &0x42800000,%fp1 # 64 * X + fmov.l %fp1,INT(%a6) # N = ROUND-TO-INT(64 X) + mov.l %d2,-(%sp) + lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64) + fmov.l INT(%a6),%fp1 # N --> FLOATING FMT + mov.l INT(%a6),%d1 + mov.l %d1,%d2 + and.l &0x3F,%d1 # D0 IS J + asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64) + add.l %d1,%a1 # ADDRESS FOR 2^(J/64) + asr.l &6,%d2 # d2 IS L, N = 64L + J + mov.l %d2,%d1 + asr.l &1,%d1 # D0 IS M + sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J + add.l &0x3FFF,%d2 + +#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64), +#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN. +#--ADJFACT = 2^(M'). +#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2. + + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmul.s &0x3C800000,%fp1 # (1/64)*N + mov.l (%a1)+,FACT1(%a6) + mov.l (%a1)+,FACT1HI(%a6) + mov.l (%a1)+,FACT1LOW(%a6) + mov.w (%a1)+,FACT2(%a6) + + fsub.x %fp1,%fp0 # X - (1/64)*INT(64 X) + + mov.w (%a1)+,FACT2HI(%a6) + clr.w FACT2HI+2(%a6) + clr.l FACT2LOW(%a6) + add.w %d1,FACT1(%a6) + fmul.x LOG2(%pc),%fp0 # FP0 IS R + add.w %d1,FACT2(%a6) + + bra.w expr + +EXPBORS: +#--FPCR, D0 SAVED + cmp.l %d1,&0x3FFF8000 + bgt.b TEXPBIG + +#--|X| IS SMALL, RETURN 1 + X + + fmov.l %d0,%fpcr # restore users round prec,mode + fadd.s &0x3F800000,%fp0 # RETURN 1 + X + bra t_pinx2 + +TEXPBIG: +#--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW +#--REGISTERS SAVE SO FAR ARE FPCR AND D0 + mov.l X(%a6),%d1 + cmp.l %d1,&0 + blt.b EXPNEG + + bra t_ovfl2 # t_ovfl expects positive value + +EXPNEG: + bra t_unfl2 # t_unfl expects positive value + + global stwotoxd +stwotoxd: +#--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT + + fmov.l %d0,%fpcr # set user's rounding mode/precision + fmov.s &0x3F800000,%fp0 # RETURN 1 + X + mov.l (%a0),%d1 + or.l &0x00800001,%d1 + fadd.s %d1,%fp0 + bra t_pinx2 + + global stentox +#--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S +stentox: + fmovm.x (%a0),&0x80 # LOAD INPUT + + mov.l (%a0),%d1 + mov.w 4(%a0),%d1 + fmov.x %fp0,X(%a6) + and.l &0x7FFFFFFF,%d1 + + cmp.l %d1,&0x3FB98000 # |X| >= 2**(-70)? + bge.b TENOK1 + bra.w EXPBORS + +TENOK1: + cmp.l %d1,&0x400B9B07 # |X| <= 16480*log2/log10 ? + ble.b TENMAIN + bra.w EXPBORS + +TENMAIN: +#--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 + + fmov.x %fp0,%fp1 + fmul.d L2TEN64(%pc),%fp1 # X*64*LOG10/LOG2 + fmov.l %fp1,INT(%a6) # N=INT(X*64*LOG10/LOG2) + mov.l %d2,-(%sp) + lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64) + fmov.l INT(%a6),%fp1 # N --> FLOATING FMT + mov.l INT(%a6),%d1 + mov.l %d1,%d2 + and.l &0x3F,%d1 # D0 IS J + asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64) + add.l %d1,%a1 # ADDRESS FOR 2^(J/64) + asr.l &6,%d2 # d2 IS L, N = 64L + J + mov.l %d2,%d1 + asr.l &1,%d1 # D0 IS M + sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J + add.l &0x3FFF,%d2 + +#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64), +#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN. +#--ADJFACT = 2^(M'). +#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2. + fmovm.x &0x0c,-(%sp) # save fp2/fp3 + + fmov.x %fp1,%fp2 + + fmul.d L10TWO1(%pc),%fp1 # N*(LOG2/64LOG10)_LEAD + mov.l (%a1)+,FACT1(%a6) + + fmul.x L10TWO2(%pc),%fp2 # N*(LOG2/64LOG10)_TRAIL + + mov.l (%a1)+,FACT1HI(%a6) + mov.l (%a1)+,FACT1LOW(%a6) + fsub.x %fp1,%fp0 # X - N L_LEAD + mov.w (%a1)+,FACT2(%a6) + + fsub.x %fp2,%fp0 # X - N L_TRAIL + + mov.w (%a1)+,FACT2HI(%a6) + clr.w FACT2HI+2(%a6) + clr.l FACT2LOW(%a6) + + fmul.x LOG10(%pc),%fp0 # FP0 IS R + add.w %d1,FACT1(%a6) + add.w %d1,FACT2(%a6) + +expr: +#--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN. +#--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64). +#--FP0 IS R. THE FOLLOWING CODE COMPUTES +#-- 2**(M'+M) * 2**(J/64) * EXP(R) + + fmov.x %fp0,%fp1 + fmul.x %fp1,%fp1 # FP1 IS S = R*R + + fmov.d EXPA5(%pc),%fp2 # FP2 IS A5 + fmov.d EXPA4(%pc),%fp3 # FP3 IS A4 + + fmul.x %fp1,%fp2 # FP2 IS S*A5 + fmul.x %fp1,%fp3 # FP3 IS S*A4 + + fadd.d EXPA3(%pc),%fp2 # FP2 IS A3+S*A5 + fadd.d EXPA2(%pc),%fp3 # FP3 IS A2+S*A4 + + fmul.x %fp1,%fp2 # FP2 IS S*(A3+S*A5) + fmul.x %fp1,%fp3 # FP3 IS S*(A2+S*A4) + + fadd.d EXPA1(%pc),%fp2 # FP2 IS A1+S*(A3+S*A5) + fmul.x %fp0,%fp3 # FP3 IS R*S*(A2+S*A4) + + fmul.x %fp1,%fp2 # FP2 IS S*(A1+S*(A3+S*A5)) + fadd.x %fp3,%fp0 # FP0 IS R+R*S*(A2+S*A4) + fadd.x %fp2,%fp0 # FP0 IS EXP(R) - 1 + + fmovm.x (%sp)+,&0x30 # restore fp2/fp3 + +#--FINAL RECONSTRUCTION PROCESS +#--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0) + + fmul.x FACT1(%a6),%fp0 + fadd.x FACT2(%a6),%fp0 + fadd.x FACT1(%a6),%fp0 + + fmov.l %d0,%fpcr # restore users round prec,mode + mov.w %d2,ADJFACT(%a6) # INSERT EXPONENT + mov.l (%sp)+,%d2 + mov.l &0x80000000,ADJFACT+4(%a6) + clr.l ADJFACT+8(%a6) + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x ADJFACT(%a6),%fp0 # FINAL ADJUSTMENT + bra t_catch + + global stentoxd +stentoxd: +#--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT + + fmov.l %d0,%fpcr # set user's rounding mode/precision + fmov.s &0x3F800000,%fp0 # RETURN 1 + X + mov.l (%a0),%d1 + or.l &0x00800001,%d1 + fadd.s %d1,%fp0 + bra t_pinx2 + +######################################################################### +# sscale(): computes the destination operand scaled by the source # +# operand. If the absoulute value of the source operand is # +# >= 2^14, an overflow or underflow is returned. # +# # +# INPUT *************************************************************** # +# a0 = pointer to double-extended source operand X # +# a1 = pointer to double-extended destination operand Y # +# # +# OUTPUT ************************************************************** # +# fp0 = scale(X,Y) # +# # +######################################################################### + +set SIGN, L_SCR1 + + global sscale +sscale: + mov.l %d0,-(%sp) # store off ctrl bits for now + + mov.w DST_EX(%a1),%d1 # get dst exponent + smi.b SIGN(%a6) # use SIGN to hold dst sign + andi.l &0x00007fff,%d1 # strip sign from dst exp + + mov.w SRC_EX(%a0),%d0 # check src bounds + andi.w &0x7fff,%d0 # clr src sign bit + cmpi.w %d0,&0x3fff # is src ~ ZERO? + blt.w src_small # yes + cmpi.w %d0,&0x400c # no; is src too big? + bgt.w src_out # yes + +# +# Source is within 2^14 range. +# +src_ok: + fintrz.x SRC(%a0),%fp0 # calc int of src + fmov.l %fp0,%d0 # int src to d0 +# don't want any accrued bits from the fintrz showing up later since +# we may need to read the fpsr for the last fp op in t_catch2(). + fmov.l &0x0,%fpsr + + tst.b DST_HI(%a1) # is dst denormalized? + bmi.b sok_norm + +# the dst is a DENORM. normalize the DENORM and add the adjustment to +# the src value. then, jump to the norm part of the routine. +sok_dnrm: + mov.l %d0,-(%sp) # save src for now + + mov.w DST_EX(%a1),FP_SCR0_EX(%a6) # make a copy + mov.l DST_HI(%a1),FP_SCR0_HI(%a6) + mov.l DST_LO(%a1),FP_SCR0_LO(%a6) + + lea FP_SCR0(%a6),%a0 # pass ptr to DENORM + bsr.l norm # normalize the DENORM + neg.l %d0 + add.l (%sp)+,%d0 # add adjustment to src + + fmovm.x FP_SCR0(%a6),&0x80 # load normalized DENORM + + cmpi.w %d0,&-0x3fff # is the shft amt really low? + bge.b sok_norm2 # thank goodness no + +# the multiply factor that we're trying to create should be a denorm +# for the multiply to work. therefore, we're going to actually do a +# multiply with a denorm which will cause an unimplemented data type +# exception to be put into the machine which will be caught and corrected +# later. we don't do this with the DENORMs above because this method +# is slower. but, don't fret, I don't see it being used much either. + fmov.l (%sp)+,%fpcr # restore user fpcr + mov.l &0x80000000,%d1 # load normalized mantissa + subi.l &-0x3fff,%d0 # how many should we shift? + neg.l %d0 # make it positive + cmpi.b %d0,&0x20 # is it > 32? + bge.b sok_dnrm_32 # yes + lsr.l %d0,%d1 # no; bit stays in upper lw + clr.l -(%sp) # insert zero low mantissa + mov.l %d1,-(%sp) # insert new high mantissa + clr.l -(%sp) # make zero exponent + bra.b sok_norm_cont +sok_dnrm_32: + subi.b &0x20,%d0 # get shift count + lsr.l %d0,%d1 # make low mantissa longword + mov.l %d1,-(%sp) # insert new low mantissa + clr.l -(%sp) # insert zero high mantissa + clr.l -(%sp) # make zero exponent + bra.b sok_norm_cont + +# the src will force the dst to a DENORM value or worse. so, let's +# create an fp multiply that will create the result. +sok_norm: + fmovm.x DST(%a1),&0x80 # load fp0 with normalized src +sok_norm2: + fmov.l (%sp)+,%fpcr # restore user fpcr + + addi.w &0x3fff,%d0 # turn src amt into exp value + swap %d0 # put exponent in high word + clr.l -(%sp) # insert new exponent + mov.l &0x80000000,-(%sp) # insert new high mantissa + mov.l %d0,-(%sp) # insert new lo mantissa + +sok_norm_cont: + fmov.l %fpcr,%d0 # d0 needs fpcr for t_catch2 + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x (%sp)+,%fp0 # do the multiply + bra t_catch2 # catch any exceptions + +# +# Source is outside of 2^14 range. Test the sign and branch +# to the appropriate exception handler. +# +src_out: + mov.l (%sp)+,%d0 # restore ctrl bits + exg %a0,%a1 # swap src,dst ptrs + tst.b SRC_EX(%a1) # is src negative? + bmi t_unfl # yes; underflow + bra t_ovfl_sc # no; overflow + +# +# The source input is below 1, so we check for denormalized numbers +# and set unfl. +# +src_small: + tst.b DST_HI(%a1) # is dst denormalized? + bpl.b ssmall_done # yes + + mov.l (%sp)+,%d0 + fmov.l %d0,%fpcr # no; load control bits + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x DST(%a1),%fp0 # simply return dest + bra t_catch2 +ssmall_done: + mov.l (%sp)+,%d0 # load control bits into d1 + mov.l %a1,%a0 # pass ptr to dst + bra t_resdnrm + +######################################################################### +# smod(): computes the fp MOD of the input values X,Y. # +# srem(): computes the fp (IEEE) REM of the input values X,Y. # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input X # +# a1 = pointer to extended precision input Y # +# d0 = round precision,mode # +# # +# The input operands X and Y can be either normalized or # +# denormalized. # +# # +# OUTPUT ************************************************************** # +# fp0 = FREM(X,Y) or FMOD(X,Y) # +# # +# ALGORITHM *********************************************************** # +# # +# Step 1. Save and strip signs of X and Y: signX := sign(X), # +# signY := sign(Y), X := |X|, Y := |Y|, # +# signQ := signX EOR signY. Record whether MOD or REM # +# is requested. # +# # +# Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0. # +# If (L < 0) then # +# R := X, go to Step 4. # +# else # +# R := 2^(-L)X, j := L. # +# endif # +# # +# Step 3. Perform MOD(X,Y) # +# 3.1 If R = Y, go to Step 9. # +# 3.2 If R > Y, then { R := R - Y, Q := Q + 1} # +# 3.3 If j = 0, go to Step 4. # +# 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to # +# Step 3.1. # +# # +# Step 4. At this point, R = X - QY = MOD(X,Y). Set # +# Last_Subtract := false (used in Step 7 below). If # +# MOD is requested, go to Step 6. # +# # +# Step 5. R = MOD(X,Y), but REM(X,Y) is requested. # +# 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to # +# Step 6. # +# 5.2 If R > Y/2, then { set Last_Subtract := true, # +# Q := Q + 1, Y := signY*Y }. Go to Step 6. # +# 5.3 This is the tricky case of R = Y/2. If Q is odd, # +# then { Q := Q + 1, signX := -signX }. # +# # +# Step 6. R := signX*R. # +# # +# Step 7. If Last_Subtract = true, R := R - Y. # +# # +# Step 8. Return signQ, last 7 bits of Q, and R as required. # +# # +# Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, # +# X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1), # +# R := 0. Return signQ, last 7 bits of Q, and R. # +# # +######################################################################### + + set Mod_Flag,L_SCR3 + set Sc_Flag,L_SCR3+1 + + set SignY,L_SCR2 + set SignX,L_SCR2+2 + set SignQ,L_SCR3+2 + + set Y,FP_SCR0 + set Y_Hi,Y+4 + set Y_Lo,Y+8 + + set R,FP_SCR1 + set R_Hi,R+4 + set R_Lo,R+8 + +Scale: + long 0x00010000,0x80000000,0x00000000,0x00000000 + + global smod +smod: + clr.b FPSR_QBYTE(%a6) + mov.l %d0,-(%sp) # save ctrl bits + clr.b Mod_Flag(%a6) + bra.b Mod_Rem + + global srem +srem: + clr.b FPSR_QBYTE(%a6) + mov.l %d0,-(%sp) # save ctrl bits + mov.b &0x1,Mod_Flag(%a6) + +Mod_Rem: +#..Save sign of X and Y + movm.l &0x3f00,-(%sp) # save data registers + mov.w SRC_EX(%a0),%d3 + mov.w %d3,SignY(%a6) + and.l &0x00007FFF,%d3 # Y := |Y| + +# + mov.l SRC_HI(%a0),%d4 + mov.l SRC_LO(%a0),%d5 # (D3,D4,D5) is |Y| + + tst.l %d3 + bne.b Y_Normal + + mov.l &0x00003FFE,%d3 # $3FFD + 1 + tst.l %d4 + bne.b HiY_not0 + +HiY_0: + mov.l %d5,%d4 + clr.l %d5 + sub.l &32,%d3 + clr.l %d6 + bfffo %d4{&0:&32},%d6 + lsl.l %d6,%d4 + sub.l %d6,%d3 # (D3,D4,D5) is normalized +# ...with bias $7FFD + bra.b Chk_X + +HiY_not0: + clr.l %d6 + bfffo %d4{&0:&32},%d6 + sub.l %d6,%d3 + lsl.l %d6,%d4 + mov.l %d5,%d7 # a copy of D5 + lsl.l %d6,%d5 + neg.l %d6 + add.l &32,%d6 + lsr.l %d6,%d7 + or.l %d7,%d4 # (D3,D4,D5) normalized +# ...with bias $7FFD + bra.b Chk_X + +Y_Normal: + add.l &0x00003FFE,%d3 # (D3,D4,D5) normalized +# ...with bias $7FFD + +Chk_X: + mov.w DST_EX(%a1),%d0 + mov.w %d0,SignX(%a6) + mov.w SignY(%a6),%d1 + eor.l %d0,%d1 + and.l &0x00008000,%d1 + mov.w %d1,SignQ(%a6) # sign(Q) obtained + and.l &0x00007FFF,%d0 + mov.l DST_HI(%a1),%d1 + mov.l DST_LO(%a1),%d2 # (D0,D1,D2) is |X| + tst.l %d0 + bne.b X_Normal + mov.l &0x00003FFE,%d0 + tst.l %d1 + bne.b HiX_not0 + +HiX_0: + mov.l %d2,%d1 + clr.l %d2 + sub.l &32,%d0 + clr.l %d6 + bfffo %d1{&0:&32},%d6 + lsl.l %d6,%d1 + sub.l %d6,%d0 # (D0,D1,D2) is normalized +# ...with bias $7FFD + bra.b Init + +HiX_not0: + clr.l %d6 + bfffo %d1{&0:&32},%d6 + sub.l %d6,%d0 + lsl.l %d6,%d1 + mov.l %d2,%d7 # a copy of D2 + lsl.l %d6,%d2 + neg.l %d6 + add.l &32,%d6 + lsr.l %d6,%d7 + or.l %d7,%d1 # (D0,D1,D2) normalized +# ...with bias $7FFD + bra.b Init + +X_Normal: + add.l &0x00003FFE,%d0 # (D0,D1,D2) normalized +# ...with bias $7FFD + +Init: +# + mov.l %d3,L_SCR1(%a6) # save biased exp(Y) + mov.l %d0,-(%sp) # save biased exp(X) + sub.l %d3,%d0 # L := expo(X)-expo(Y) + + clr.l %d6 # D6 := carry <- 0 + clr.l %d3 # D3 is Q + mov.l &0,%a1 # A1 is k; j+k=L, Q=0 + +#..(Carry,D1,D2) is R + tst.l %d0 + bge.b Mod_Loop_pre + +#..expo(X) < expo(Y). Thus X = mod(X,Y) +# + mov.l (%sp)+,%d0 # restore d0 + bra.w Get_Mod + +Mod_Loop_pre: + addq.l &0x4,%sp # erase exp(X) +#..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L +Mod_Loop: + tst.l %d6 # test carry bit + bgt.b R_GT_Y + +#..At this point carry = 0, R = (D1,D2), Y = (D4,D5) + cmp.l %d1,%d4 # compare hi(R) and hi(Y) + bne.b R_NE_Y + cmp.l %d2,%d5 # compare lo(R) and lo(Y) + bne.b R_NE_Y + +#..At this point, R = Y + bra.w Rem_is_0 + +R_NE_Y: +#..use the borrow of the previous compare + bcs.b R_LT_Y # borrow is set iff R < Y + +R_GT_Y: +#..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0 +#..and Y < (D1,D2) < 2Y. Either way, perform R - Y + sub.l %d5,%d2 # lo(R) - lo(Y) + subx.l %d4,%d1 # hi(R) - hi(Y) + clr.l %d6 # clear carry + addq.l &1,%d3 # Q := Q + 1 + +R_LT_Y: +#..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0. + tst.l %d0 # see if j = 0. + beq.b PostLoop + + add.l %d3,%d3 # Q := 2Q + add.l %d2,%d2 # lo(R) = 2lo(R) + roxl.l &1,%d1 # hi(R) = 2hi(R) + carry + scs %d6 # set Carry if 2(R) overflows + addq.l &1,%a1 # k := k+1 + subq.l &1,%d0 # j := j - 1 +#..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y. + + bra.b Mod_Loop + +PostLoop: +#..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y. + +#..normalize R. + mov.l L_SCR1(%a6),%d0 # new biased expo of R + tst.l %d1 + bne.b HiR_not0 + +HiR_0: + mov.l %d2,%d1 + clr.l %d2 + sub.l &32,%d0 + clr.l %d6 + bfffo %d1{&0:&32},%d6 + lsl.l %d6,%d1 + sub.l %d6,%d0 # (D0,D1,D2) is normalized +# ...with bias $7FFD + bra.b Get_Mod + +HiR_not0: + clr.l %d6 + bfffo %d1{&0:&32},%d6 + bmi.b Get_Mod # already normalized + sub.l %d6,%d0 + lsl.l %d6,%d1 + mov.l %d2,%d7 # a copy of D2 + lsl.l %d6,%d2 + neg.l %d6 + add.l &32,%d6 + lsr.l %d6,%d7 + or.l %d7,%d1 # (D0,D1,D2) normalized + +# +Get_Mod: + cmp.l %d0,&0x000041FE + bge.b No_Scale +Do_Scale: + mov.w %d0,R(%a6) + mov.l %d1,R_Hi(%a6) + mov.l %d2,R_Lo(%a6) + mov.l L_SCR1(%a6),%d6 + mov.w %d6,Y(%a6) + mov.l %d4,Y_Hi(%a6) + mov.l %d5,Y_Lo(%a6) + fmov.x R(%a6),%fp0 # no exception + mov.b &1,Sc_Flag(%a6) + bra.b ModOrRem +No_Scale: + mov.l %d1,R_Hi(%a6) + mov.l %d2,R_Lo(%a6) + sub.l &0x3FFE,%d0 + mov.w %d0,R(%a6) + mov.l L_SCR1(%a6),%d6 + sub.l &0x3FFE,%d6 + mov.l %d6,L_SCR1(%a6) + fmov.x R(%a6),%fp0 + mov.w %d6,Y(%a6) + mov.l %d4,Y_Hi(%a6) + mov.l %d5,Y_Lo(%a6) + clr.b Sc_Flag(%a6) + +# +ModOrRem: + tst.b Mod_Flag(%a6) + beq.b Fix_Sign + + mov.l L_SCR1(%a6),%d6 # new biased expo(Y) + subq.l &1,%d6 # biased expo(Y/2) + cmp.l %d0,%d6 + blt.b Fix_Sign + bgt.b Last_Sub + + cmp.l %d1,%d4 + bne.b Not_EQ + cmp.l %d2,%d5 + bne.b Not_EQ + bra.w Tie_Case + +Not_EQ: + bcs.b Fix_Sign + +Last_Sub: +# + fsub.x Y(%a6),%fp0 # no exceptions + addq.l &1,%d3 # Q := Q + 1 + +# +Fix_Sign: +#..Get sign of X + mov.w SignX(%a6),%d6 + bge.b Get_Q + fneg.x %fp0 + +#..Get Q +# +Get_Q: + clr.l %d6 + mov.w SignQ(%a6),%d6 # D6 is sign(Q) + mov.l &8,%d7 + lsr.l %d7,%d6 + and.l &0x0000007F,%d3 # 7 bits of Q + or.l %d6,%d3 # sign and bits of Q +# swap %d3 +# fmov.l %fpsr,%d6 +# and.l &0xFF00FFFF,%d6 +# or.l %d3,%d6 +# fmov.l %d6,%fpsr # put Q in fpsr + mov.b %d3,FPSR_QBYTE(%a6) # put Q in fpsr + +# +Restore: + movm.l (%sp)+,&0xfc # {%d2-%d7} + mov.l (%sp)+,%d0 + fmov.l %d0,%fpcr + tst.b Sc_Flag(%a6) + beq.b Finish + mov.b &FMUL_OP,%d1 # last inst is MUL + fmul.x Scale(%pc),%fp0 # may cause underflow + bra t_catch2 +# the '040 package did this apparently to see if the dst operand for the +# preceding fmul was a denorm. but, it better not have been since the +# algorithm just got done playing with fp0 and expected no exceptions +# as a result. trust me... +# bra t_avoid_unsupp # check for denorm as a +# ;result of the scaling + +Finish: + mov.b &FMOV_OP,%d1 # last inst is MOVE + fmov.x %fp0,%fp0 # capture exceptions & round + bra t_catch2 + +Rem_is_0: +#..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1) + addq.l &1,%d3 + cmp.l %d0,&8 # D0 is j + bge.b Q_Big + + lsl.l %d0,%d3 + bra.b Set_R_0 + +Q_Big: + clr.l %d3 + +Set_R_0: + fmov.s &0x00000000,%fp0 + clr.b Sc_Flag(%a6) + bra.w Fix_Sign + +Tie_Case: +#..Check parity of Q + mov.l %d3,%d6 + and.l &0x00000001,%d6 + tst.l %d6 + beq.w Fix_Sign # Q is even + +#..Q is odd, Q := Q + 1, signX := -signX + addq.l &1,%d3 + mov.w SignX(%a6),%d6 + eor.l &0x00008000,%d6 + mov.w %d6,SignX(%a6) + bra.w Fix_Sign + +######################################################################### +# XDEF **************************************************************** # +# tag(): return the optype of the input ext fp number # +# # +# This routine is used by the 060FPLSP. # +# # +# XREF **************************************************************** # +# None # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision operand # +# # +# OUTPUT ************************************************************** # +# d0 = value of type tag # +# one of: NORM, INF, QNAN, SNAN, DENORM, ZERO # +# # +# ALGORITHM *********************************************************** # +# Simply test the exponent, j-bit, and mantissa values to # +# determine the type of operand. # +# If it's an unnormalized zero, alter the operand and force it # +# to be a normal zero. # +# # +######################################################################### + + global tag +tag: + mov.w FTEMP_EX(%a0), %d0 # extract exponent + andi.w &0x7fff, %d0 # strip off sign + cmpi.w %d0, &0x7fff # is (EXP == MAX)? + beq.b inf_or_nan_x +not_inf_or_nan_x: + btst &0x7,FTEMP_HI(%a0) + beq.b not_norm_x +is_norm_x: + mov.b &NORM, %d0 + rts +not_norm_x: + tst.w %d0 # is exponent = 0? + bne.b is_unnorm_x +not_unnorm_x: + tst.l FTEMP_HI(%a0) + bne.b is_denorm_x + tst.l FTEMP_LO(%a0) + bne.b is_denorm_x +is_zero_x: + mov.b &ZERO, %d0 + rts +is_denorm_x: + mov.b &DENORM, %d0 + rts +is_unnorm_x: + bsr.l unnorm_fix # convert to norm,denorm,or zero + rts +is_unnorm_reg_x: + mov.b &UNNORM, %d0 + rts +inf_or_nan_x: + tst.l FTEMP_LO(%a0) + bne.b is_nan_x + mov.l FTEMP_HI(%a0), %d0 + and.l &0x7fffffff, %d0 # msb is a don't care! + bne.b is_nan_x +is_inf_x: + mov.b &INF, %d0 + rts +is_nan_x: + mov.b &QNAN, %d0 + rts + +############################################################# + +qnan: long 0x7fff0000, 0xffffffff, 0xffffffff + +######################################################################### +# XDEF **************************************************************** # +# t_dz(): Handle 060FPLSP dz exception for "flogn" emulation. # +# t_dz2(): Handle 060FPLSP dz exception for "fatanh" emulation. # +# # +# These rouitnes are used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision source operand. # +# # +# OUTPUT ************************************************************** # +# fp0 = default DZ result. # +# # +# ALGORITHM *********************************************************** # +# Transcendental emulation for the 060FPLSP has detected that # +# a DZ exception should occur for the instruction. If DZ is disabled, # +# return the default result. # +# If DZ is enabled, the dst operand should be returned unscathed # +# in fp0 while fp1 is used to create a DZ exception so that the # +# operating system can log that such an event occurred. # +# # +######################################################################### + + global t_dz +t_dz: + tst.b SRC_EX(%a0) # check sign for neg or pos + bpl.b dz_pinf # branch if pos sign + + global t_dz2 +t_dz2: + ori.l &dzinf_mask+neg_mask,USER_FPSR(%a6) # set N/I/DZ/ADZ + + btst &dz_bit,FPCR_ENABLE(%a6) + bne.b dz_minf_ena + +# dz is disabled. return a -INF. + fmov.s &0xff800000,%fp0 # return -INF + rts + +# dz is enabled. create a dz exception so the user can record it +# but use fp1 instead. return the dst operand unscathed in fp0. +dz_minf_ena: + fmovm.x EXC_FP0(%a6),&0x80 # return fp0 unscathed + fmov.l USER_FPCR(%a6),%fpcr + fmov.s &0xbf800000,%fp1 # load -1 + fdiv.s &0x00000000,%fp1 # -1 / 0 + rts + +dz_pinf: + ori.l &dzinf_mask,USER_FPSR(%a6) # set I/DZ/ADZ + + btst &dz_bit,FPCR_ENABLE(%a6) + bne.b dz_pinf_ena + +# dz is disabled. return a +INF. + fmov.s &0x7f800000,%fp0 # return +INF + rts + +# dz is enabled. create a dz exception so the user can record it +# but use fp1 instead. return the dst operand unscathed in fp0. +dz_pinf_ena: + fmovm.x EXC_FP0(%a6),&0x80 # return fp0 unscathed + fmov.l USER_FPCR(%a6),%fpcr + fmov.s &0x3f800000,%fp1 # load +1 + fdiv.s &0x00000000,%fp1 # +1 / 0 + rts + +######################################################################### +# XDEF **************************************************************** # +# t_operr(): Handle 060FPLSP OPERR exception during emulation. # +# # +# This routine is used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# fp1 = source operand # +# # +# OUTPUT ************************************************************** # +# fp0 = default result # +# fp1 = unchanged # +# # +# ALGORITHM *********************************************************** # +# An operand error should occur as the result of transcendental # +# emulation in the 060FPLSP. If OPERR is disabled, just return a NAN # +# in fp0. If OPERR is enabled, return the dst operand unscathed in fp0 # +# and the source operand in fp1. Use fp2 to create an OPERR exception # +# so that the operating system can log the event. # +# # +######################################################################### + + global t_operr +t_operr: + ori.l &opnan_mask,USER_FPSR(%a6) # set NAN/OPERR/AIOP + + btst &operr_bit,FPCR_ENABLE(%a6) + bne.b operr_ena + +# operr is disabled. return a QNAN in fp0 + fmovm.x qnan(%pc),&0x80 # return QNAN + rts + +# operr is enabled. create an operr exception so the user can record it +# but use fp2 instead. return the dst operand unscathed in fp0. +operr_ena: + fmovm.x EXC_FP0(%a6),&0x80 # return fp0 unscathed + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x &0x04,-(%sp) # save fp2 + fmov.s &0x7f800000,%fp2 # load +INF + fmul.s &0x00000000,%fp2 # +INF x 0 + fmovm.x (%sp)+,&0x20 # restore fp2 + rts + +pls_huge: + long 0x7ffe0000,0xffffffff,0xffffffff +mns_huge: + long 0xfffe0000,0xffffffff,0xffffffff +pls_tiny: + long 0x00000000,0x80000000,0x00000000 +mns_tiny: + long 0x80000000,0x80000000,0x00000000 + +######################################################################### +# XDEF **************************************************************** # +# t_unfl(): Handle 060FPLSP underflow exception during emulation. # +# t_unfl2(): Handle 060FPLSP underflow exception during # +# emulation. result always positive. # +# # +# This routine is used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision source operand # +# # +# OUTPUT ************************************************************** # +# fp0 = default underflow result # +# # +# ALGORITHM *********************************************************** # +# An underflow should occur as the result of transcendental # +# emulation in the 060FPLSP. Create an underflow by using "fmul" # +# and two very small numbers of appropriate sign so the operating # +# system can log the event. # +# # +######################################################################### + + global t_unfl +t_unfl: + tst.b SRC_EX(%a0) + bpl.b unf_pos + + global t_unfl2 +t_unfl2: + ori.l &unfinx_mask+neg_mask,USER_FPSR(%a6) # set N/UNFL/INEX2/AUNFL/AINEX + + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x mns_tiny(%pc),&0x80 + fmul.x pls_tiny(%pc),%fp0 + + fmov.l %fpsr,%d0 + rol.l &0x8,%d0 + mov.b %d0,FPSR_CC(%a6) + rts +unf_pos: + ori.w &unfinx_mask,FPSR_EXCEPT(%a6) # set UNFL/INEX2/AUNFL/AINEX + + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x pls_tiny(%pc),&0x80 + fmul.x %fp0,%fp0 + + fmov.l %fpsr,%d0 + rol.l &0x8,%d0 + mov.b %d0,FPSR_CC(%a6) + rts + +######################################################################### +# XDEF **************************************************************** # +# t_ovfl(): Handle 060FPLSP overflow exception during emulation. # +# (monadic) # +# t_ovfl2(): Handle 060FPLSP overflow exception during # +# emulation. result always positive. (dyadic) # +# t_ovfl_sc(): Handle 060FPLSP overflow exception during # +# emulation for "fscale". # +# # +# This routine is used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision source operand # +# # +# OUTPUT ************************************************************** # +# fp0 = default underflow result # +# # +# ALGORITHM *********************************************************** # +# An overflow should occur as the result of transcendental # +# emulation in the 060FPLSP. Create an overflow by using "fmul" # +# and two very lareg numbers of appropriate sign so the operating # +# system can log the event. # +# For t_ovfl_sc() we take special care not to lose the INEX2 bit. # +# # +######################################################################### + + global t_ovfl_sc +t_ovfl_sc: + ori.l &ovfl_inx_mask,USER_FPSR(%a6) # set OVFL/AOVFL/AINEX + + mov.b %d0,%d1 # fetch rnd prec,mode + andi.b &0xc0,%d1 # extract prec + beq.w ovfl_work + +# dst op is a DENORM. we have to normalize the mantissa to see if the +# result would be inexact for the given precision. make a copy of the +# dst so we don't screw up the version passed to us. + mov.w LOCAL_EX(%a0),FP_SCR0_EX(%a6) + mov.l LOCAL_HI(%a0),FP_SCR0_HI(%a6) + mov.l LOCAL_LO(%a0),FP_SCR0_LO(%a6) + lea FP_SCR0(%a6),%a0 # pass ptr to FP_SCR0 + movm.l &0xc080,-(%sp) # save d0-d1/a0 + bsr.l norm # normalize mantissa + movm.l (%sp)+,&0x0103 # restore d0-d1/a0 + + cmpi.b %d1,&0x40 # is precision sgl? + bne.b ovfl_sc_dbl # no; dbl +ovfl_sc_sgl: + tst.l LOCAL_LO(%a0) # is lo lw of sgl set? + bne.b ovfl_sc_inx # yes + tst.b 3+LOCAL_HI(%a0) # is lo byte of hi lw set? + bne.b ovfl_sc_inx # yes + bra.w ovfl_work # don't set INEX2 +ovfl_sc_dbl: + mov.l LOCAL_LO(%a0),%d1 # are any of lo 11 bits of + andi.l &0x7ff,%d1 # dbl mantissa set? + beq.w ovfl_work # no; don't set INEX2 +ovfl_sc_inx: + ori.l &inex2_mask,USER_FPSR(%a6) # set INEX2 + bra.b ovfl_work # continue + + global t_ovfl +t_ovfl: + ori.w &ovfinx_mask,FPSR_EXCEPT(%a6) # set OVFL/INEX2/AOVFL/AINEX +ovfl_work: + tst.b SRC_EX(%a0) + bpl.b ovfl_p +ovfl_m: + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x mns_huge(%pc),&0x80 + fmul.x pls_huge(%pc),%fp0 + + fmov.l %fpsr,%d0 + rol.l &0x8,%d0 + ori.b &neg_mask,%d0 + mov.b %d0,FPSR_CC(%a6) + rts +ovfl_p: + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x pls_huge(%pc),&0x80 + fmul.x pls_huge(%pc),%fp0 + + fmov.l %fpsr,%d0 + rol.l &0x8,%d0 + mov.b %d0,FPSR_CC(%a6) + rts + + global t_ovfl2 +t_ovfl2: + ori.w &ovfinx_mask,FPSR_EXCEPT(%a6) # set OVFL/INEX2/AOVFL/AINEX + fmov.l USER_FPCR(%a6),%fpcr + fmovm.x pls_huge(%pc),&0x80 + fmul.x pls_huge(%pc),%fp0 + + fmov.l %fpsr,%d0 + rol.l &0x8,%d0 + mov.b %d0,FPSR_CC(%a6) + rts + +######################################################################### +# XDEF **************************************************************** # +# t_catch(): Handle 060FPLSP OVFL,UNFL,or INEX2 exception during # +# emulation. # +# t_catch2(): Handle 060FPLSP OVFL,UNFL,or INEX2 exception during # +# emulation. # +# # +# These routines are used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# fp0 = default underflow or overflow result # +# # +# OUTPUT ************************************************************** # +# fp0 = default result # +# # +# ALGORITHM *********************************************************** # +# If an overflow or underflow occurred during the last # +# instruction of transcendental 060FPLSP emulation, then it has already # +# occurred and has been logged. Now we need to see if an inexact # +# exception should occur. # +# # +######################################################################### + + global t_catch2 +t_catch2: + fmov.l %fpsr,%d0 + or.l %d0,USER_FPSR(%a6) + bra.b inx2_work + + global t_catch +t_catch: + fmov.l %fpsr,%d0 + or.l %d0,USER_FPSR(%a6) + +######################################################################### +# XDEF **************************************************************** # +# t_inx2(): Handle inexact 060FPLSP exception during emulation. # +# t_pinx2(): Handle inexact 060FPLSP exception for "+" results. # +# t_minx2(): Handle inexact 060FPLSP exception for "-" results. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# fp0 = default result # +# # +# OUTPUT ************************************************************** # +# fp0 = default result # +# # +# ALGORITHM *********************************************************** # +# The last instruction of transcendental emulation for the # +# 060FPLSP should be inexact. So, if inexact is enabled, then we create # +# the event here by adding a large and very small number together # +# so that the operating system can log the event. # +# Must check, too, if the result was zero, in which case we just # +# set the FPSR bits and return. # +# # +######################################################################### + + global t_inx2 +t_inx2: + fblt.w t_minx2 + fbeq.w inx2_zero + + global t_pinx2 +t_pinx2: + ori.w &inx2a_mask,FPSR_EXCEPT(%a6) # set INEX2/AINEX + bra.b inx2_work + + global t_minx2 +t_minx2: + ori.l &inx2a_mask+neg_mask,USER_FPSR(%a6) + +inx2_work: + btst &inex2_bit,FPCR_ENABLE(%a6) # is inexact enabled? + bne.b inx2_work_ena # yes + rts +inx2_work_ena: + fmov.l USER_FPCR(%a6),%fpcr # insert user's exceptions + fmov.s &0x3f800000,%fp1 # load +1 + fadd.x pls_tiny(%pc),%fp1 # cause exception + rts + +inx2_zero: + mov.b &z_bmask,FPSR_CC(%a6) + ori.w &inx2a_mask,2+USER_FPSR(%a6) # set INEX/AINEX + rts + +######################################################################### +# XDEF **************************************************************** # +# t_extdnrm(): Handle DENORM inputs in 060FPLSP. # +# t_resdnrm(): Handle DENORM inputs in 060FPLSP for "fscale". # +# # +# This routine is used by the 060FPLSP package. # +# # +# XREF **************************************************************** # +# None. # +# # +# INPUT *************************************************************** # +# a0 = pointer to extended precision input operand # +# # +# OUTPUT ************************************************************** # +# fp0 = default result # +# # +# ALGORITHM *********************************************************** # +# For all functions that have a denormalized input and that # +# f(x)=x, this is the entry point. # +# DENORM value is moved using "fmove" which triggers an exception # +# if enabled so the operating system can log the event. # +# # +######################################################################### + + global t_extdnrm +t_extdnrm: + fmov.l USER_FPCR(%a6),%fpcr + fmov.x SRC_EX(%a0),%fp0 + fmov.l %fpsr,%d0 + ori.l &unfinx_mask,%d0 + or.l %d0,USER_FPSR(%a6) + rts + + global t_resdnrm +t_resdnrm: + fmov.l USER_FPCR(%a6),%fpcr + fmov.x SRC_EX(%a0),%fp0 + fmov.l %fpsr,%d0 + or.l %d0,USER_FPSR(%a6) + rts + +########################################## + +# +# sto_cos: +# This is used by fsincos library emulation. The correct +# values are already in fp0 and fp1 so we do nothing here. +# + global sto_cos +sto_cos: + rts + +########################################## + +# +# dst_qnan --- force result when destination is a NaN +# + global dst_qnan +dst_qnan: + fmov.x DST(%a1),%fp0 + tst.b DST_EX(%a1) + bmi.b dst_qnan_m +dst_qnan_p: + mov.b &nan_bmask,FPSR_CC(%a6) + rts +dst_qnan_m: + mov.b &nan_bmask+neg_bmask,FPSR_CC(%a6) + rts + +# +# src_qnan --- force result when source is a NaN +# + global src_qnan +src_qnan: + fmov.x SRC(%a0),%fp0 + tst.b SRC_EX(%a0) + bmi.b src_qnan_m +src_qnan_p: + mov.b &nan_bmask,FPSR_CC(%a6) + rts +src_qnan_m: + mov.b &nan_bmask+neg_bmask,FPSR_CC(%a6) + rts + +########################################## + +# +# Native instruction support +# +# Some systems may need entry points even for 68060 native +# instructions. These routines are provided for +# convenience. +# + global _fadds_ +_fadds_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.s 0x8(%sp),%fp0 # load sgl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fadd.s 0x8(%sp),%fp0 # fadd w/ sgl src + rts + + global _faddd_ +_faddd_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.d 0x8(%sp),%fp0 # load dbl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fadd.d 0xc(%sp),%fp0 # fadd w/ dbl src + rts + + global _faddx_ +_faddx_: + fmovm.x 0x4(%sp),&0x80 # load ext dst + fadd.x 0x10(%sp),%fp0 # fadd w/ ext src + rts + + global _fsubs_ +_fsubs_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.s 0x8(%sp),%fp0 # load sgl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fsub.s 0x8(%sp),%fp0 # fsub w/ sgl src + rts + + global _fsubd_ +_fsubd_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.d 0x8(%sp),%fp0 # load dbl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fsub.d 0xc(%sp),%fp0 # fsub w/ dbl src + rts + + global _fsubx_ +_fsubx_: + fmovm.x 0x4(%sp),&0x80 # load ext dst + fsub.x 0x10(%sp),%fp0 # fsub w/ ext src + rts + + global _fmuls_ +_fmuls_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.s 0x8(%sp),%fp0 # load sgl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fmul.s 0x8(%sp),%fp0 # fmul w/ sgl src + rts + + global _fmuld_ +_fmuld_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.d 0x8(%sp),%fp0 # load dbl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fmul.d 0xc(%sp),%fp0 # fmul w/ dbl src + rts + + global _fmulx_ +_fmulx_: + fmovm.x 0x4(%sp),&0x80 # load ext dst + fmul.x 0x10(%sp),%fp0 # fmul w/ ext src + rts + + global _fdivs_ +_fdivs_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.s 0x8(%sp),%fp0 # load sgl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fdiv.s 0x8(%sp),%fp0 # fdiv w/ sgl src + rts + + global _fdivd_ +_fdivd_: + fmov.l %fpcr,-(%sp) # save fpcr + fmov.l &0x00000000,%fpcr # clear fpcr for load + fmov.d 0x8(%sp),%fp0 # load dbl dst + fmov.l (%sp)+,%fpcr # restore fpcr + fdiv.d 0xc(%sp),%fp0 # fdiv w/ dbl src + rts + + global _fdivx_ +_fdivx_: + fmovm.x 0x4(%sp),&0x80 # load ext dst + fdiv.x 0x10(%sp),%fp0 # fdiv w/ ext src + rts + + global _fabss_ +_fabss_: + fabs.s 0x4(%sp),%fp0 # fabs w/ sgl src + rts + + global _fabsd_ +_fabsd_: + fabs.d 0x4(%sp),%fp0 # fabs w/ dbl src + rts + + global _fabsx_ +_fabsx_: + fabs.x 0x4(%sp),%fp0 # fabs w/ ext src + rts + + global _fnegs_ +_fnegs_: + fneg.s 0x4(%sp),%fp0 # fneg w/ sgl src + rts + + global _fnegd_ +_fnegd_: + fneg.d 0x4(%sp),%fp0 # fneg w/ dbl src + rts + + global _fnegx_ +_fnegx_: + fneg.x 0x4(%sp),%fp0 # fneg w/ ext src + rts + + global _fsqrts_ +_fsqrts_: + fsqrt.s 0x4(%sp),%fp0 # fsqrt w/ sgl src + rts + + global _fsqrtd_ +_fsqrtd_: + fsqrt.d 0x4(%sp),%fp0 # fsqrt w/ dbl src + rts + + global _fsqrtx_ +_fsqrtx_: + fsqrt.x 0x4(%sp),%fp0 # fsqrt w/ ext src + rts + + global _fints_ +_fints_: + fint.s 0x4(%sp),%fp0 # fint w/ sgl src + rts + + global _fintd_ +_fintd_: + fint.d 0x4(%sp),%fp0 # fint w/ dbl src + rts + + global _fintx_ +_fintx_: + fint.x 0x4(%sp),%fp0 # fint w/ ext src + rts + + global _fintrzs_ +_fintrzs_: + fintrz.s 0x4(%sp),%fp0 # fintrz w/ sgl src + rts + + global _fintrzd_ +_fintrzd_: + fintrz.d 0x4(%sp),%fp0 # fintrx w/ dbl src + rts + + global _fintrzx_ +_fintrzx_: + fintrz.x 0x4(%sp),%fp0 # fintrz w/ ext src + rts + +######################################################################## + +######################################################################### +# src_zero(): Return signed zero according to sign of src operand. # +######################################################################### + global src_zero +src_zero: + tst.b SRC_EX(%a0) # get sign of src operand + bmi.b ld_mzero # if neg, load neg zero + +# +# ld_pzero(): return a positive zero. +# + global ld_pzero +ld_pzero: + fmov.s &0x00000000,%fp0 # load +0 + mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit + rts + +# ld_mzero(): return a negative zero. + global ld_mzero +ld_mzero: + fmov.s &0x80000000,%fp0 # load -0 + mov.b &neg_bmask+z_bmask,FPSR_CC(%a6) # set 'N','Z' ccode bits + rts + +######################################################################### +# dst_zero(): Return signed zero according to sign of dst operand. # +######################################################################### + global dst_zero +dst_zero: + tst.b DST_EX(%a1) # get sign of dst operand + bmi.b ld_mzero # if neg, load neg zero + bra.b ld_pzero # load positive zero + +######################################################################### +# src_inf(): Return signed inf according to sign of src operand. # +######################################################################### + global src_inf +src_inf: + tst.b SRC_EX(%a0) # get sign of src operand + bmi.b ld_minf # if negative branch + +# +# ld_pinf(): return a positive infinity. +# + global ld_pinf +ld_pinf: + fmov.s &0x7f800000,%fp0 # load +INF + mov.b &inf_bmask,FPSR_CC(%a6) # set 'INF' ccode bit + rts + +# +# ld_minf():return a negative infinity. +# + global ld_minf +ld_minf: + fmov.s &0xff800000,%fp0 # load -INF + mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set 'N','I' ccode bits + rts + +######################################################################### +# dst_inf(): Return signed inf according to sign of dst operand. # +######################################################################### + global dst_inf +dst_inf: + tst.b DST_EX(%a1) # get sign of dst operand + bmi.b ld_minf # if negative branch + bra.b ld_pinf + + global szr_inf +################################################################# +# szr_inf(): Return +ZERO for a negative src operand or # +# +INF for a positive src operand. # +# Routine used for fetox, ftwotox, and ftentox. # +################################################################# +szr_inf: + tst.b SRC_EX(%a0) # check sign of source + bmi.b ld_pzero + bra.b ld_pinf + +######################################################################### +# sopr_inf(): Return +INF for a positive src operand or # +# jump to operand error routine for a negative src operand. # +# Routine used for flogn, flognp1, flog10, and flog2. # +######################################################################### + global sopr_inf +sopr_inf: + tst.b SRC_EX(%a0) # check sign of source + bmi.w t_operr + bra.b ld_pinf + +################################################################# +# setoxm1i(): Return minus one for a negative src operand or # +# positive infinity for a positive src operand. # +# Routine used for fetoxm1. # +################################################################# + global setoxm1i +setoxm1i: + tst.b SRC_EX(%a0) # check sign of source + bmi.b ld_mone + bra.b ld_pinf + +######################################################################### +# src_one(): Return signed one according to sign of src operand. # +######################################################################### + global src_one +src_one: + tst.b SRC_EX(%a0) # check sign of source + bmi.b ld_mone + +# +# ld_pone(): return positive one. +# + global ld_pone +ld_pone: + fmov.s &0x3f800000,%fp0 # load +1 + clr.b FPSR_CC(%a6) + rts + +# +# ld_mone(): return negative one. +# + global ld_mone +ld_mone: + fmov.s &0xbf800000,%fp0 # load -1 + mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit + rts + +ppiby2: long 0x3fff0000, 0xc90fdaa2, 0x2168c235 +mpiby2: long 0xbfff0000, 0xc90fdaa2, 0x2168c235 + +################################################################# +# spi_2(): Return signed PI/2 according to sign of src operand. # +################################################################# + global spi_2 +spi_2: + tst.b SRC_EX(%a0) # check sign of source + bmi.b ld_mpi2 + +# +# ld_ppi2(): return positive PI/2. +# + global ld_ppi2 +ld_ppi2: + fmov.l %d0,%fpcr + fmov.x ppiby2(%pc),%fp0 # load +pi/2 + bra.w t_pinx2 # set INEX2 + +# +# ld_mpi2(): return negative PI/2. +# + global ld_mpi2 +ld_mpi2: + fmov.l %d0,%fpcr + fmov.x mpiby2(%pc),%fp0 # load -pi/2 + bra.w t_minx2 # set INEX2 + +#################################################### +# The following routines give support for fsincos. # +#################################################### + +# +# ssincosz(): When the src operand is ZERO, store a one in the +# cosine register and return a ZERO in fp0 w/ the same sign +# as the src operand. +# + global ssincosz +ssincosz: + fmov.s &0x3f800000,%fp1 + tst.b SRC_EX(%a0) # test sign + bpl.b sincoszp + fmov.s &0x80000000,%fp0 # return sin result in fp0 + mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) + rts +sincoszp: + fmov.s &0x00000000,%fp0 # return sin result in fp0 + mov.b &z_bmask,FPSR_CC(%a6) + rts + +# +# ssincosi(): When the src operand is INF, store a QNAN in the cosine +# register and jump to the operand error routine for negative +# src operands. +# + global ssincosi +ssincosi: + fmov.x qnan(%pc),%fp1 # load NAN + bra.w t_operr + +# +# ssincosqnan(): When the src operand is a QNAN, store the QNAN in the cosine +# register and branch to the src QNAN routine. +# + global ssincosqnan +ssincosqnan: + fmov.x LOCAL_EX(%a0),%fp1 + bra.w src_qnan + +######################################################################## + + global smod_sdnrm + global smod_snorm +smod_sdnrm: +smod_snorm: + mov.b DTAG(%a6),%d1 + beq.l smod + cmpi.b %d1,&ZERO + beq.w smod_zro + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l smod + bra.l dst_qnan + + global smod_szero +smod_szero: + mov.b DTAG(%a6),%d1 + beq.l t_operr + cmpi.b %d1,&ZERO + beq.l t_operr + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l t_operr + bra.l dst_qnan + + global smod_sinf +smod_sinf: + mov.b DTAG(%a6),%d1 + beq.l smod_fpn + cmpi.b %d1,&ZERO + beq.l smod_zro + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l smod_fpn + bra.l dst_qnan + +smod_zro: +srem_zro: + mov.b SRC_EX(%a0),%d1 # get src sign + mov.b DST_EX(%a1),%d0 # get dst sign + eor.b %d0,%d1 # get qbyte sign + andi.b &0x80,%d1 + mov.b %d1,FPSR_QBYTE(%a6) + tst.b %d0 + bpl.w ld_pzero + bra.w ld_mzero + +smod_fpn: +srem_fpn: + clr.b FPSR_QBYTE(%a6) + mov.l %d0,-(%sp) + mov.b SRC_EX(%a0),%d1 # get src sign + mov.b DST_EX(%a1),%d0 # get dst sign + eor.b %d0,%d1 # get qbyte sign + andi.b &0x80,%d1 + mov.b %d1,FPSR_QBYTE(%a6) + cmpi.b DTAG(%a6),&DENORM + bne.b smod_nrm + lea DST(%a1),%a0 + mov.l (%sp)+,%d0 + bra t_resdnrm +smod_nrm: + fmov.l (%sp)+,%fpcr + fmov.x DST(%a1),%fp0 + tst.b DST_EX(%a1) + bmi.b smod_nrm_neg + rts + +smod_nrm_neg: + mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' code + rts + +######################################################################### + global srem_snorm + global srem_sdnrm +srem_sdnrm: +srem_snorm: + mov.b DTAG(%a6),%d1 + beq.l srem + cmpi.b %d1,&ZERO + beq.w srem_zro + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l srem + bra.l dst_qnan + + global srem_szero +srem_szero: + mov.b DTAG(%a6),%d1 + beq.l t_operr + cmpi.b %d1,&ZERO + beq.l t_operr + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l t_operr + bra.l dst_qnan + + global srem_sinf +srem_sinf: + mov.b DTAG(%a6),%d1 + beq.w srem_fpn + cmpi.b %d1,&ZERO + beq.w srem_zro + cmpi.b %d1,&INF + beq.l t_operr + cmpi.b %d1,&DENORM + beq.l srem_fpn + bra.l dst_qnan + +######################################################################### + + global sscale_snorm + global sscale_sdnrm +sscale_snorm: +sscale_sdnrm: + mov.b DTAG(%a6),%d1 + beq.l sscale + cmpi.b %d1,&ZERO + beq.l dst_zero + cmpi.b %d1,&INF + beq.l dst_inf + cmpi.b %d1,&DENORM + beq.l sscale + bra.l dst_qnan + + global sscale_szero +sscale_szero: + mov.b DTAG(%a6),%d1 + beq.l sscale + cmpi.b %d1,&ZERO + beq.l dst_zero + cmpi.b %d1,&INF + beq.l dst_inf + cmpi.b %d1,&DENORM + beq.l sscale + bra.l dst_qnan + + global sscale_sinf +sscale_sinf: + mov.b DTAG(%a6),%d1 + beq.l t_operr + cmpi.b %d1,&QNAN + beq.l dst_qnan + bra.l t_operr + +######################################################################## + + global sop_sqnan +sop_sqnan: + mov.b DTAG(%a6),%d1 + cmpi.b %d1,&QNAN + beq.l dst_qnan + bra.l src_qnan + +######################################################################### +# norm(): normalize the mantissa of an extended precision input. the # +# input operand should not be normalized already. # +# # +# XDEF **************************************************************** # +# norm() # +# # +# XREF **************************************************************** # +# none # +# # +# INPUT *************************************************************** # +# a0 = pointer fp extended precision operand to normalize # +# # +# OUTPUT ************************************************************** # +# d0 = number of bit positions the mantissa was shifted # +# a0 = the input operand's mantissa is normalized; the exponent # +# is unchanged. # +# # +######################################################################### + global norm +norm: + mov.l %d2, -(%sp) # create some temp regs + mov.l %d3, -(%sp) + + mov.l FTEMP_HI(%a0), %d0 # load hi(mantissa) + mov.l FTEMP_LO(%a0), %d1 # load lo(mantissa) + + bfffo %d0{&0:&32}, %d2 # how many places to shift? + beq.b norm_lo # hi(man) is all zeroes! + +norm_hi: + lsl.l %d2, %d0 # left shift hi(man) + bfextu %d1{&0:%d2}, %d3 # extract lo bits + + or.l %d3, %d0 # create hi(man) + lsl.l %d2, %d1 # create lo(man) + + mov.l %d0, FTEMP_HI(%a0) # store new hi(man) + mov.l %d1, FTEMP_LO(%a0) # store new lo(man) + + mov.l %d2, %d0 # return shift amount + + mov.l (%sp)+, %d3 # restore temp regs + mov.l (%sp)+, %d2 + + rts + +norm_lo: + bfffo %d1{&0:&32}, %d2 # how many places to shift? + lsl.l %d2, %d1 # shift lo(man) + add.l &32, %d2 # add 32 to shft amount + + mov.l %d1, FTEMP_HI(%a0) # store hi(man) + clr.l FTEMP_LO(%a0) # lo(man) is now zero + + mov.l %d2, %d0 # return shift amount + + mov.l (%sp)+, %d3 # restore temp regs + mov.l (%sp)+, %d2 + + rts + +######################################################################### +# unnorm_fix(): - changes an UNNORM to one of NORM, DENORM, or ZERO # +# - returns corresponding optype tag # +# # +# XDEF **************************************************************** # +# unnorm_fix() # +# # +# XREF **************************************************************** # +# norm() - normalize the mantissa # +# # +# INPUT *************************************************************** # +# a0 = pointer to unnormalized extended precision number # +# # +# OUTPUT ************************************************************** # +# d0 = optype tag - is corrected to one of NORM, DENORM, or ZERO # +# a0 = input operand has been converted to a norm, denorm, or # +# zero; both the exponent and mantissa are changed. # +# # +######################################################################### + + global unnorm_fix +unnorm_fix: + bfffo FTEMP_HI(%a0){&0:&32}, %d0 # how many shifts are needed? + bne.b unnorm_shift # hi(man) is not all zeroes + +# +# hi(man) is all zeroes so see if any bits in lo(man) are set +# +unnorm_chk_lo: + bfffo FTEMP_LO(%a0){&0:&32}, %d0 # is operand really a zero? + beq.w unnorm_zero # yes + + add.w &32, %d0 # no; fix shift distance + +# +# d0 = # shifts needed for complete normalization +# +unnorm_shift: + clr.l %d1 # clear top word + mov.w FTEMP_EX(%a0), %d1 # extract exponent + and.w &0x7fff, %d1 # strip off sgn + + cmp.w %d0, %d1 # will denorm push exp < 0? + bgt.b unnorm_nrm_zero # yes; denorm only until exp = 0 + +# +# exponent would not go < 0. therefore, number stays normalized +# + sub.w %d0, %d1 # shift exponent value + mov.w FTEMP_EX(%a0), %d0 # load old exponent + and.w &0x8000, %d0 # save old sign + or.w %d0, %d1 # {sgn,new exp} + mov.w %d1, FTEMP_EX(%a0) # insert new exponent + + bsr.l norm # normalize UNNORM + + mov.b &NORM, %d0 # return new optype tag + rts + +# +# exponent would go < 0, so only denormalize until exp = 0 +# +unnorm_nrm_zero: + cmp.b %d1, &32 # is exp <= 32? + bgt.b unnorm_nrm_zero_lrg # no; go handle large exponent + + bfextu FTEMP_HI(%a0){%d1:&32}, %d0 # extract new hi(man) + mov.l %d0, FTEMP_HI(%a0) # save new hi(man) + + mov.l FTEMP_LO(%a0), %d0 # fetch old lo(man) + lsl.l %d1, %d0 # extract new lo(man) + mov.l %d0, FTEMP_LO(%a0) # save new lo(man) + + and.w &0x8000, FTEMP_EX(%a0) # set exp = 0 + + mov.b &DENORM, %d0 # return new optype tag + rts + +# +# only mantissa bits set are in lo(man) +# +unnorm_nrm_zero_lrg: + sub.w &32, %d1 # adjust shft amt by 32 + + mov.l FTEMP_LO(%a0), %d0 # fetch old lo(man) + lsl.l %d1, %d0 # left shift lo(man) + + mov.l %d0, FTEMP_HI(%a0) # store new hi(man) + clr.l FTEMP_LO(%a0) # lo(man) = 0 + + and.w &0x8000, FTEMP_EX(%a0) # set exp = 0 + + mov.b &DENORM, %d0 # return new optype tag + rts + +# +# whole mantissa is zero so this UNNORM is actually a zero +# +unnorm_zero: + and.w &0x8000, FTEMP_EX(%a0) # force exponent to zero + + mov.b &ZERO, %d0 # fix optype tag + rts |