diff options
Diffstat (limited to 'kernel/arch/m68k/fpsp040/satan.S')
| -rw-r--r-- | kernel/arch/m68k/fpsp040/satan.S | 477 |
1 files changed, 477 insertions, 0 deletions
diff --git a/kernel/arch/m68k/fpsp040/satan.S b/kernel/arch/m68k/fpsp040/satan.S new file mode 100644 index 000000000..c8a664998 --- /dev/null +++ b/kernel/arch/m68k/fpsp040/satan.S @@ -0,0 +1,477 @@ +| +| satan.sa 3.3 12/19/90 +| +| The entry point satan computes the arctangent of an +| input value. satand does the same except the input value is a +| denormalized number. +| +| Input: Double-extended value in memory location pointed to by address +| register a0. +| +| Output: Arctan(X) returned in floating-point register Fp0. +| +| 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. +| +| Speed: The program satan takes approximately 160 cycles for input +| argument X such that 1/16 < |X| < 16. For the other arguments, +| the program will run no worse than 10% slower. +| +| 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. +| + +| 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. + +|satan idnt 2,1 | Motorola 040 Floating Point Software Package + + |section 8 + +#include "fpsp.h" + +BOUNDS1: .long 0x3FFB8000,0x4002FFFF + +ONE: .long 0x3F800000 + + .long 0x00000000 + +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_SCR1 + .set XDCARE,X+2 + .set XFRAC,X+4 + .set XFRACLO,X+8 + + .set ATANF,FP_SCR2 + .set ATANFHI,ATANF+4 + .set ATANFLO,ATANF+8 + + + | xref t_frcinx + |xref t_extdnrm + + .global satand +satand: +|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT + + bra t_extdnrm + + .global satan +satan: +|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S + + fmovex (%a0),%fp0 | ...LOAD INPUT + + movel (%a0),%d0 + movew 4(%a0),%d0 + fmovex %fp0,X(%a6) + andil #0x7FFFFFFF,%d0 + + cmpil #0x3FFB8000,%d0 | ...|X| >= 1/16? + bges ATANOK1 + bra ATANSM + +ATANOK1: + cmpil #0x4002FFFF,%d0 | ...|X| < 16 ? + bles ATANMAIN + bra 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: + + movew #0x0000,XDCARE(%a6) | ...CLEAN UP X JUST IN CASE + andil #0xF8000000,XFRAC(%a6) | ...FIRST 5 BITS + oril #0x04000000,XFRAC(%a6) | ...SET 6-TH BIT TO 1 + movel #0x00000000,XFRACLO(%a6) | ...LOCATION OF X IS NOW F + + fmovex %fp0,%fp1 | ...FP1 IS X + fmulx X(%a6),%fp1 | ...FP1 IS X*F, NOTE THAT X*F > 0 + fsubx X(%a6),%fp0 | ...FP0 IS X-F + fadds #0x3F800000,%fp1 | ...FP1 IS 1 + X*F + fdivx %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. + + movel %d2,-(%a7) | ...SAVE d2 TEMPORARILY + movel %d0,%d2 | ...THE EXPO AND 16 BITS OF X + andil #0x00007800,%d0 | ...4 VARYING BITS OF F'S FRACTION + andil #0x7FFF0000,%d2 | ...EXPONENT OF F + subil #0x3FFB0000,%d2 | ...K+4 + asrl #1,%d2 + addl %d2,%d0 | ...THE 7 BITS IDENTIFYING F + asrl #7,%d0 | ...INDEX INTO TBL OF ATAN(|F|) + lea ATANTBL,%a1 + addal %d0,%a1 | ...ADDRESS OF ATAN(|F|) + movel (%a1)+,ATANF(%a6) + movel (%a1)+,ATANFHI(%a6) + movel (%a1)+,ATANFLO(%a6) | ...ATANF IS NOW ATAN(|F|) + movel X(%a6),%d0 | ...LOAD SIGN AND EXPO. AGAIN + andil #0x80000000,%d0 | ...SIGN(F) + orl %d0,ATANF(%a6) | ...ATANF IS NOW SIGN(F)*ATAN(|F|) + movel (%a7)+,%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 + + + fmovex %fp0,%fp1 + fmulx %fp1,%fp1 + fmoved ATANA3,%fp2 + faddx %fp1,%fp2 | ...A3+V + fmulx %fp1,%fp2 | ...V*(A3+V) + fmulx %fp0,%fp1 | ...U*V + faddd ATANA2,%fp2 | ...A2+V*(A3+V) + fmuld ATANA1,%fp1 | ...A1*U*V + fmulx %fp2,%fp1 | ...A1*U*V*(A2+V*(A3+V)) + + faddx %fp1,%fp0 | ...ATAN(U), FP1 RELEASED + fmovel %d1,%FPCR |restore users exceptions + faddx ATANF(%a6),%fp0 | ...ATAN(X) + bra t_frcinx + +ATANBORS: +|--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED. +|--FP0 IS X AND |X| <= 1/16 OR |X| >= 16. + cmpil #0x3FFF8000,%d0 + bgt 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. + + cmpil #0x3FD78000,%d0 + blt ATANTINY +|--COMPUTE POLYNOMIAL + fmulx %fp0,%fp0 | ...FP0 IS Y = X*X + + + movew #0x0000,XDCARE(%a6) + + fmovex %fp0,%fp1 + fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y + + fmoved ATANB6,%fp2 + fmoved ATANB5,%fp3 + + fmulx %fp1,%fp2 | ...Z*B6 + fmulx %fp1,%fp3 | ...Z*B5 + + faddd ATANB4,%fp2 | ...B4+Z*B6 + faddd ATANB3,%fp3 | ...B3+Z*B5 + + fmulx %fp1,%fp2 | ...Z*(B4+Z*B6) + fmulx %fp3,%fp1 | ...Z*(B3+Z*B5) + + faddd ATANB2,%fp2 | ...B2+Z*(B4+Z*B6) + faddd ATANB1,%fp1 | ...B1+Z*(B3+Z*B5) + + fmulx %fp0,%fp2 | ...Y*(B2+Z*(B4+Z*B6)) + fmulx X(%a6),%fp0 | ...X*Y + + faddx %fp2,%fp1 | ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] + + + fmulx %fp1,%fp0 | ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) + + fmovel %d1,%FPCR |restore users exceptions + faddx X(%a6),%fp0 + + bra t_frcinx + +ATANTINY: +|--|X| < 2^(-40), ATAN(X) = X + movew #0x0000,XDCARE(%a6) + + fmovel %d1,%FPCR |restore users exceptions + fmovex X(%a6),%fp0 |last inst - possible exception set + + bra t_frcinx + +ATANBIG: +|--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE, +|--RETURN SIGN(X)*PI/2 + ATAN(-1/X). + cmpil #0x40638000,%d0 + bgt 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. + + fmoves #0xBF800000,%fp1 | ...LOAD -1 + fdivx %fp0,%fp1 | ...FP1 IS -1/X + + +|--DIVIDE IS STILL CRANKING + + fmovex %fp1,%fp0 | ...FP0 IS X' + fmulx %fp0,%fp0 | ...FP0 IS Y = X'*X' + fmovex %fp1,X(%a6) | ...X IS REALLY X' + + fmovex %fp0,%fp1 + fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y + + fmoved ATANC5,%fp3 + fmoved ATANC4,%fp2 + + fmulx %fp1,%fp3 | ...Z*C5 + fmulx %fp1,%fp2 | ...Z*B4 + + faddd ATANC3,%fp3 | ...C3+Z*C5 + faddd ATANC2,%fp2 | ...C2+Z*C4 + + fmulx %fp3,%fp1 | ...Z*(C3+Z*C5), FP3 RELEASED + fmulx %fp0,%fp2 | ...Y*(C2+Z*C4) + + faddd ATANC1,%fp1 | ...C1+Z*(C3+Z*C5) + fmulx X(%a6),%fp0 | ...X'*Y + + faddx %fp2,%fp1 | ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] + + + fmulx %fp1,%fp0 | ...X'*Y*([B1+Z*(B3+Z*B5)] +| ... +[Y*(B2+Z*(B4+Z*B6))]) + faddx X(%a6),%fp0 + + fmovel %d1,%FPCR |restore users exceptions + + btstb #7,(%a0) + beqs pos_big + +neg_big: + faddx NPIBY2,%fp0 + bra t_frcinx + +pos_big: + faddx PPIBY2,%fp0 + bra t_frcinx + +ATANHUGE: +|--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY + btstb #7,(%a0) + beqs pos_huge + +neg_huge: + fmovex NPIBY2,%fp0 + fmovel %d1,%fpcr + fsubx NTINY,%fp0 + bra t_frcinx + +pos_huge: + fmovex PPIBY2,%fp0 + fmovel %d1,%fpcr + fsubx PTINY,%fp0 + bra t_frcinx + + |end |