| | 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