Quelle  satan.S   Sprache: Sparc

|
| 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