arch/m68k/fpsp040/satan.S

|
|	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
|
|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|	The copyright notice above does not evidence any
|	actual or intended publication of such source code.

|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