|
| 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