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Diffstat (limited to 'kernel/arch/m68k/fpsp040/decbin.S')
| -rw-r--r-- | kernel/arch/m68k/fpsp040/decbin.S | 505 |
1 files changed, 505 insertions, 0 deletions
diff --git a/kernel/arch/m68k/fpsp040/decbin.S b/kernel/arch/m68k/fpsp040/decbin.S new file mode 100644 index 000000000..16ed796ba --- /dev/null +++ b/kernel/arch/m68k/fpsp040/decbin.S @@ -0,0 +1,505 @@ +| +| decbin.sa 3.3 12/19/90 +| +| Description: Converts normalized packed bcd value pointed to by +| register A6 to extended-precision value in FP0. +| +| Input: Normalized packed bcd value in ETEMP(a6). +| +| Output: Exact floating-point representation of the packed bcd value. +| +| Saves and Modifies: D2-D5 +| +| Speed: The program decbin takes ??? cycles to execute. +| +| Object Size: +| +| External Reference(s): None. +| +| Algorithm: +| Expected is a normal bcd (i.e. non-exceptional; all inf, zero, +| and NaN operands are dispatched without entering this routine) +| value in 68881/882 format at location ETEMP(A6). +| +| A1. Convert the bcd exponent to binary by successive adds and muls. +| Set the sign according to SE. Subtract 16 to compensate +| for the mantissa which is to be interpreted as 17 integer +| digits, rather than 1 integer and 16 fraction digits. +| Note: this operation can never overflow. +| +| A2. Convert the bcd mantissa to binary by successive +| adds and muls in FP0. Set the sign according to SM. +| The mantissa digits will be converted with the decimal point +| assumed following the least-significant digit. +| Note: this operation can never overflow. +| +| A3. Count the number of leading/trailing zeros in the +| bcd string. If SE is positive, count the leading zeros; +| if negative, count the trailing zeros. Set the adjusted +| exponent equal to the exponent from A1 and the zero count +| added if SM = 1 and subtracted if SM = 0. Scale the +| mantissa the equivalent of forcing in the bcd value: +| +| SM = 0 a non-zero digit in the integer position +| SM = 1 a non-zero digit in Mant0, lsd of the fraction +| +| this will insure that any value, regardless of its +| representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted +| consistently. +| +| A4. Calculate the factor 10^exp in FP1 using a table of +| 10^(2^n) values. To reduce the error in forming factors +| greater than 10^27, a directed rounding scheme is used with +| tables rounded to RN, RM, and RP, according to the table +| in the comments of the pwrten section. +| +| A5. Form the final binary number by scaling the mantissa by +| the exponent factor. This is done by multiplying the +| mantissa in FP0 by the factor in FP1 if the adjusted +| exponent sign is positive, and dividing FP0 by FP1 if +| it is negative. +| +| Clean up and return. Check if the final mul or div resulted +| in an inex2 exception. If so, set inex1 in the fpsr and +| check if the inex1 exception is enabled. If so, set d7 upper +| word to $0100. This will signal unimp.sa that an enabled inex1 +| exception occurred. Unimp will fix the stack. +| + +| Copyright (C) Motorola, Inc. 1990 +| All Rights Reserved +| +| For details on the license for this file, please see the +| file, README, in this same directory. + +|DECBIN idnt 2,1 | Motorola 040 Floating Point Software Package + + |section 8 + +#include "fpsp.h" + +| +| PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded +| to nearest, minus, and plus, respectively. The tables include +| 10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}. No rounding +| is required until the power is greater than 27, however, all +| tables include the first 5 for ease of indexing. +| + |xref PTENRN + |xref PTENRM + |xref PTENRP + +RTABLE: .byte 0,0,0,0 + .byte 2,3,2,3 + .byte 2,3,3,2 + .byte 3,2,2,3 + + .global decbin + .global calc_e + .global pwrten + .global calc_m + .global norm + .global ap_st_z + .global ap_st_n +| + .set FNIBS,7 + .set FSTRT,0 +| + .set ESTRT,4 + .set EDIGITS,2 | +| +| Constants in single precision +FZERO: .long 0x00000000 +FONE: .long 0x3F800000 +FTEN: .long 0x41200000 + + .set TEN,10 + +| +decbin: + | fmovel #0,FPCR ;clr real fpcr + moveml %d2-%d5,-(%a7) +| +| Calculate exponent: +| 1. Copy bcd value in memory for use as a working copy. +| 2. Calculate absolute value of exponent in d1 by mul and add. +| 3. Correct for exponent sign. +| 4. Subtract 16 to compensate for interpreting the mant as all integer digits. +| (i.e., all digits assumed left of the decimal point.) +| +| Register usage: +| +| calc_e: +| (*) d0: temp digit storage +| (*) d1: accumulator for binary exponent +| (*) d2: digit count +| (*) d3: offset pointer +| ( ) d4: first word of bcd +| ( ) a0: pointer to working bcd value +| ( ) a6: pointer to original bcd value +| (*) FP_SCR1: working copy of original bcd value +| (*) L_SCR1: copy of original exponent word +| +calc_e: + movel #EDIGITS,%d2 |# of nibbles (digits) in fraction part + moveql #ESTRT,%d3 |counter to pick up digits + leal FP_SCR1(%a6),%a0 |load tmp bcd storage address + movel ETEMP(%a6),(%a0) |save input bcd value + movel ETEMP_HI(%a6),4(%a0) |save words 2 and 3 + movel ETEMP_LO(%a6),8(%a0) |and work with these + movel (%a0),%d4 |get first word of bcd + clrl %d1 |zero d1 for accumulator +e_gd: + mulul #TEN,%d1 |mul partial product by one digit place + bfextu %d4{%d3:#4},%d0 |get the digit and zero extend into d0 + addl %d0,%d1 |d1 = d1 + d0 + addqb #4,%d3 |advance d3 to the next digit + dbf %d2,e_gd |if we have used all 3 digits, exit loop + btst #30,%d4 |get SE + beqs e_pos |don't negate if pos + negl %d1 |negate before subtracting +e_pos: + subl #16,%d1 |sub to compensate for shift of mant + bges e_save |if still pos, do not neg + negl %d1 |now negative, make pos and set SE + orl #0x40000000,%d4 |set SE in d4, + orl #0x40000000,(%a0) |and in working bcd +e_save: + movel %d1,L_SCR1(%a6) |save exp in memory +| +| +| Calculate mantissa: +| 1. Calculate absolute value of mantissa in fp0 by mul and add. +| 2. Correct for mantissa sign. +| (i.e., all digits assumed left of the decimal point.) +| +| Register usage: +| +| calc_m: +| (*) d0: temp digit storage +| (*) d1: lword counter +| (*) d2: digit count +| (*) d3: offset pointer +| ( ) d4: words 2 and 3 of bcd +| ( ) a0: pointer to working bcd value +| ( ) a6: pointer to original bcd value +| (*) fp0: mantissa accumulator +| ( ) FP_SCR1: working copy of original bcd value +| ( ) L_SCR1: copy of original exponent word +| +calc_m: + moveql #1,%d1 |word counter, init to 1 + fmoves FZERO,%fp0 |accumulator +| +| +| Since the packed number has a long word between the first & second parts, +| get the integer digit then skip down & get the rest of the +| mantissa. We will unroll the loop once. +| + bfextu (%a0){#28:#4},%d0 |integer part is ls digit in long word + faddb %d0,%fp0 |add digit to sum in fp0 +| +| +| Get the rest of the mantissa. +| +loadlw: + movel (%a0,%d1.L*4),%d4 |load mantissa longword into d4 + moveql #FSTRT,%d3 |counter to pick up digits + moveql #FNIBS,%d2 |reset number of digits per a0 ptr +md2b: + fmuls FTEN,%fp0 |fp0 = fp0 * 10 + bfextu %d4{%d3:#4},%d0 |get the digit and zero extend + faddb %d0,%fp0 |fp0 = fp0 + digit +| +| +| If all the digits (8) in that long word have been converted (d2=0), +| then inc d1 (=2) to point to the next long word and reset d3 to 0 +| to initialize the digit offset, and set d2 to 7 for the digit count; +| else continue with this long word. +| + addqb #4,%d3 |advance d3 to the next digit + dbf %d2,md2b |check for last digit in this lw +nextlw: + addql #1,%d1 |inc lw pointer in mantissa + cmpl #2,%d1 |test for last lw + ble loadlw |if not, get last one + +| +| Check the sign of the mant and make the value in fp0 the same sign. +| +m_sign: + btst #31,(%a0) |test sign of the mantissa + beq ap_st_z |if clear, go to append/strip zeros + fnegx %fp0 |if set, negate fp0 + +| +| Append/strip zeros: +| +| For adjusted exponents which have an absolute value greater than 27*, +| this routine calculates the amount needed to normalize the mantissa +| for the adjusted exponent. That number is subtracted from the exp +| if the exp was positive, and added if it was negative. The purpose +| of this is to reduce the value of the exponent and the possibility +| of error in calculation of pwrten. +| +| 1. Branch on the sign of the adjusted exponent. +| 2p.(positive exp) +| 2. Check M16 and the digits in lwords 2 and 3 in descending order. +| 3. Add one for each zero encountered until a non-zero digit. +| 4. Subtract the count from the exp. +| 5. Check if the exp has crossed zero in #3 above; make the exp abs +| and set SE. +| 6. Multiply the mantissa by 10**count. +| 2n.(negative exp) +| 2. Check the digits in lwords 3 and 2 in descending order. +| 3. Add one for each zero encountered until a non-zero digit. +| 4. Add the count to the exp. +| 5. Check if the exp has crossed zero in #3 above; clear SE. +| 6. Divide the mantissa by 10**count. +| +| *Why 27? If the adjusted exponent is within -28 < expA < 28, than +| any adjustment due to append/strip zeros will drive the resultant +| exponent towards zero. Since all pwrten constants with a power +| of 27 or less are exact, there is no need to use this routine to +| attempt to lessen the resultant exponent. +| +| Register usage: +| +| ap_st_z: +| (*) d0: temp digit storage +| (*) d1: zero count +| (*) d2: digit count +| (*) d3: offset pointer +| ( ) d4: first word of bcd +| (*) d5: lword counter +| ( ) a0: pointer to working bcd value +| ( ) FP_SCR1: working copy of original bcd value +| ( ) L_SCR1: copy of original exponent word +| +| +| First check the absolute value of the exponent to see if this +| routine is necessary. If so, then check the sign of the exponent +| and do append (+) or strip (-) zeros accordingly. +| This section handles a positive adjusted exponent. +| +ap_st_z: + movel L_SCR1(%a6),%d1 |load expA for range test + cmpl #27,%d1 |test is with 27 + ble pwrten |if abs(expA) <28, skip ap/st zeros + btst #30,(%a0) |check sign of exp + bne ap_st_n |if neg, go to neg side + clrl %d1 |zero count reg + movel (%a0),%d4 |load lword 1 to d4 + bfextu %d4{#28:#4},%d0 |get M16 in d0 + bnes ap_p_fx |if M16 is non-zero, go fix exp + addql #1,%d1 |inc zero count + moveql #1,%d5 |init lword counter + movel (%a0,%d5.L*4),%d4 |get lword 2 to d4 + bnes ap_p_cl |if lw 2 is zero, skip it + addql #8,%d1 |and inc count by 8 + addql #1,%d5 |inc lword counter + movel (%a0,%d5.L*4),%d4 |get lword 3 to d4 +ap_p_cl: + clrl %d3 |init offset reg + moveql #7,%d2 |init digit counter +ap_p_gd: + bfextu %d4{%d3:#4},%d0 |get digit + bnes ap_p_fx |if non-zero, go to fix exp + addql #4,%d3 |point to next digit + addql #1,%d1 |inc digit counter + dbf %d2,ap_p_gd |get next digit +ap_p_fx: + movel %d1,%d0 |copy counter to d2 + movel L_SCR1(%a6),%d1 |get adjusted exp from memory + subl %d0,%d1 |subtract count from exp + bges ap_p_fm |if still pos, go to pwrten + negl %d1 |now its neg; get abs + movel (%a0),%d4 |load lword 1 to d4 + orl #0x40000000,%d4 | and set SE in d4 + orl #0x40000000,(%a0) | and in memory +| +| Calculate the mantissa multiplier to compensate for the striping of +| zeros from the mantissa. +| +ap_p_fm: + movel #PTENRN,%a1 |get address of power-of-ten table + clrl %d3 |init table index + fmoves FONE,%fp1 |init fp1 to 1 + moveql #3,%d2 |init d2 to count bits in counter +ap_p_el: + asrl #1,%d0 |shift lsb into carry + bccs ap_p_en |if 1, mul fp1 by pwrten factor + fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) +ap_p_en: + addl #12,%d3 |inc d3 to next rtable entry + tstl %d0 |check if d0 is zero + bnes ap_p_el |if not, get next bit + fmulx %fp1,%fp0 |mul mantissa by 10**(no_bits_shifted) + bra pwrten |go calc pwrten +| +| This section handles a negative adjusted exponent. +| +ap_st_n: + clrl %d1 |clr counter + moveql #2,%d5 |set up d5 to point to lword 3 + movel (%a0,%d5.L*4),%d4 |get lword 3 + bnes ap_n_cl |if not zero, check digits + subl #1,%d5 |dec d5 to point to lword 2 + addql #8,%d1 |inc counter by 8 + movel (%a0,%d5.L*4),%d4 |get lword 2 +ap_n_cl: + movel #28,%d3 |point to last digit + moveql #7,%d2 |init digit counter +ap_n_gd: + bfextu %d4{%d3:#4},%d0 |get digit + bnes ap_n_fx |if non-zero, go to exp fix + subql #4,%d3 |point to previous digit + addql #1,%d1 |inc digit counter + dbf %d2,ap_n_gd |get next digit +ap_n_fx: + movel %d1,%d0 |copy counter to d0 + movel L_SCR1(%a6),%d1 |get adjusted exp from memory + subl %d0,%d1 |subtract count from exp + bgts ap_n_fm |if still pos, go fix mantissa + negl %d1 |take abs of exp and clr SE + movel (%a0),%d4 |load lword 1 to d4 + andl #0xbfffffff,%d4 | and clr SE in d4 + andl #0xbfffffff,(%a0) | and in memory +| +| Calculate the mantissa multiplier to compensate for the appending of +| zeros to the mantissa. +| +ap_n_fm: + movel #PTENRN,%a1 |get address of power-of-ten table + clrl %d3 |init table index + fmoves FONE,%fp1 |init fp1 to 1 + moveql #3,%d2 |init d2 to count bits in counter +ap_n_el: + asrl #1,%d0 |shift lsb into carry + bccs ap_n_en |if 1, mul fp1 by pwrten factor + fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) +ap_n_en: + addl #12,%d3 |inc d3 to next rtable entry + tstl %d0 |check if d0 is zero + bnes ap_n_el |if not, get next bit + fdivx %fp1,%fp0 |div mantissa by 10**(no_bits_shifted) +| +| +| Calculate power-of-ten factor from adjusted and shifted exponent. +| +| Register usage: +| +| pwrten: +| (*) d0: temp +| ( ) d1: exponent +| (*) d2: {FPCR[6:5],SM,SE} as index in RTABLE; temp +| (*) d3: FPCR work copy +| ( ) d4: first word of bcd +| (*) a1: RTABLE pointer +| calc_p: +| (*) d0: temp +| ( ) d1: exponent +| (*) d3: PWRTxx table index +| ( ) a0: pointer to working copy of bcd +| (*) a1: PWRTxx pointer +| (*) fp1: power-of-ten accumulator +| +| Pwrten calculates the exponent factor in the selected rounding mode +| according to the following table: +| +| Sign of Mant Sign of Exp Rounding Mode PWRTEN Rounding Mode +| +| ANY ANY RN RN +| +| + + RP RP +| - + RP RM +| + - RP RM +| - - RP RP +| +| + + RM RM +| - + RM RP +| + - RM RP +| - - RM RM +| +| + + RZ RM +| - + RZ RM +| + - RZ RP +| - - RZ RP +| +| +pwrten: + movel USER_FPCR(%a6),%d3 |get user's FPCR + bfextu %d3{#26:#2},%d2 |isolate rounding mode bits + movel (%a0),%d4 |reload 1st bcd word to d4 + asll #2,%d2 |format d2 to be + bfextu %d4{#0:#2},%d0 | {FPCR[6],FPCR[5],SM,SE} + addl %d0,%d2 |in d2 as index into RTABLE + leal RTABLE,%a1 |load rtable base + moveb (%a1,%d2),%d0 |load new rounding bits from table + clrl %d3 |clear d3 to force no exc and extended + bfins %d0,%d3{#26:#2} |stuff new rounding bits in FPCR + fmovel %d3,%FPCR |write new FPCR + asrl #1,%d0 |write correct PTENxx table + bccs not_rp |to a1 + leal PTENRP,%a1 |it is RP + bras calc_p |go to init section +not_rp: + asrl #1,%d0 |keep checking + bccs not_rm + leal PTENRM,%a1 |it is RM + bras calc_p |go to init section +not_rm: + leal PTENRN,%a1 |it is RN +calc_p: + movel %d1,%d0 |copy exp to d0;use d0 + bpls no_neg |if exp is negative, + negl %d0 |invert it + orl #0x40000000,(%a0) |and set SE bit +no_neg: + clrl %d3 |table index + fmoves FONE,%fp1 |init fp1 to 1 +e_loop: + asrl #1,%d0 |shift next bit into carry + bccs e_next |if zero, skip the mul + fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) +e_next: + addl #12,%d3 |inc d3 to next rtable entry + tstl %d0 |check if d0 is zero + bnes e_loop |not zero, continue shifting +| +| +| Check the sign of the adjusted exp and make the value in fp0 the +| same sign. If the exp was pos then multiply fp1*fp0; +| else divide fp0/fp1. +| +| Register Usage: +| norm: +| ( ) a0: pointer to working bcd value +| (*) fp0: mantissa accumulator +| ( ) fp1: scaling factor - 10**(abs(exp)) +| +norm: + btst #30,(%a0) |test the sign of the exponent + beqs mul |if clear, go to multiply +div: + fdivx %fp1,%fp0 |exp is negative, so divide mant by exp + bras end_dec +mul: + fmulx %fp1,%fp0 |exp is positive, so multiply by exp +| +| +| Clean up and return with result in fp0. +| +| If the final mul/div in decbin incurred an inex exception, +| it will be inex2, but will be reported as inex1 by get_op. +| +end_dec: + fmovel %FPSR,%d0 |get status register + bclrl #inex2_bit+8,%d0 |test for inex2 and clear it + fmovel %d0,%FPSR |return status reg w/o inex2 + beqs no_exc |skip this if no exc + orl #inx1a_mask,USER_FPSR(%a6) |set inex1/ainex +no_exc: + moveml (%a7)+,%d2-%d5 + rts + |end |