xref: /src/sys/arch/m68k/fpsp/satan.sa

*	$NetBSD: satan.sa,v 1.3 1994/10/26 07:49:31 cgd Exp $

*	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
*	M68000 Hi-Performance Microprocessor Division
*	M68040 Software Package 
*
*	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
*	All rights reserved.
*
*	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
*	To the maximum extent permitted by applicable law,
*	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
*	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
*	PARTICULAR PURPOSE and any warranty against infringement with
*	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
*	and any accompanying written materials. 
*
*	To the maximum extent permitted by applicable law,
*	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
*	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
*	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
*	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
*	SOFTWARE.  Motorola assumes no responsibility for the maintenance
*	and support of the SOFTWARE.  
*
*	You are hereby granted a copyright license to use, modify, and
*	distribute the SOFTWARE so long as this entire notice is retained
*	without alteration in any modified and/or redistributed versions,
*	and that such modified versions are clearly identified as such.
*	No licenses are granted by implication, estoppel or otherwise
*	under any patents or trademarks of Motorola, Inc.

*
*	satan.sa 3.3 12/19/90
*
*	The entry point satan computes the arctagent 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.
*

satan	IDNT	2,1 Motorola 040 Floating Point Software Package

	section	8

	include fpsp.h
	
BOUNDS1	DC.L $3FFB8000,$4002FFFF

ONE	DC.L $3F800000

	DC.L $00000000

ATANA3	DC.L $BFF6687E,$314987D8
ATANA2	DC.L $4002AC69,$34A26DB3

ATANA1	DC.L $BFC2476F,$4E1DA28E
ATANB6	DC.L $3FB34444,$7F876989

ATANB5	DC.L $BFB744EE,$7FAF45DB
ATANB4	DC.L $3FBC71C6,$46940220

ATANB3	DC.L $BFC24924,$921872F9
ATANB2	DC.L $3FC99999,$99998FA9

ATANB1	DC.L $BFD55555,$55555555
ATANC5	DC.L $BFB70BF3,$98539E6A

ATANC4	DC.L $3FBC7187,$962D1D7D
ATANC3	DC.L $BFC24924,$827107B8

ATANC2	DC.L $3FC99999,$9996263E
ATANC1	DC.L $BFD55555,$55555536

PPIBY2	DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
NPIBY2	DC.L $BFFF0000,$C90FDAA2,$2168C235,$00000000
PTINY	DC.L $00010000,$80000000,$00000000,$00000000
NTINY	DC.L $80010000,$80000000,$00000000,$00000000

ATANTBL:
	DC.L	$3FFB0000,$83D152C5,$060B7A51,$00000000
	DC.L	$3FFB0000,$8BC85445,$65498B8B,$00000000
	DC.L	$3FFB0000,$93BE4060,$17626B0D,$00000000
	DC.L	$3FFB0000,$9BB3078D,$35AEC202,$00000000
	DC.L	$3FFB0000,$A3A69A52,$5DDCE7DE,$00000000
	DC.L	$3FFB0000,$AB98E943,$62765619,$00000000
	DC.L	$3FFB0000,$B389E502,$F9C59862,$00000000
	DC.L	$3FFB0000,$BB797E43,$6B09E6FB,$00000000
	DC.L	$3FFB0000,$C367A5C7,$39E5F446,$00000000
	DC.L	$3FFB0000,$CB544C61,$CFF7D5C6,$00000000
	DC.L	$3FFB0000,$D33F62F8,$2488533E,$00000000
	DC.L	$3FFB0000,$DB28DA81,$62404C77,$00000000
	DC.L	$3FFB0000,$E310A407,$8AD34F18,$00000000
	DC.L	$3FFB0000,$EAF6B0A8,$188EE1EB,$00000000
	DC.L	$3FFB0000,$F2DAF194,$9DBE79D5,$00000000
	DC.L	$3FFB0000,$FABD5813,$61D47E3E,$00000000
	DC.L	$3FFC0000,$8346AC21,$0959ECC4,$00000000
	DC.L	$3FFC0000,$8B232A08,$304282D8,$00000000
	DC.L	$3FFC0000,$92FB70B8,$D29AE2F9,$00000000
	DC.L	$3FFC0000,$9ACF476F,$5CCD1CB4,$00000000
	DC.L	$3FFC0000,$A29E7630,$4954F23F,$00000000
	DC.L	$3FFC0000,$AA68C5D0,$8AB85230,$00000000
	DC.L	$3FFC0000,$B22DFFFD,$9D539F83,$00000000
	DC.L	$3FFC0000,$B9EDEF45,$3E900EA5,$00000000
	DC.L	$3FFC0000,$C1A85F1C,$C75E3EA5,$00000000
	DC.L	$3FFC0000,$C95D1BE8,$28138DE6,$00000000
	DC.L	$3FFC0000,$D10BF300,$840D2DE4,$00000000
	DC.L	$3FFC0000,$D8B4B2BA,$6BC05E7A,$00000000
	DC.L	$3FFC0000,$E0572A6B,$B42335F6,$00000000
	DC.L	$3FFC0000,$E7F32A70,$EA9CAA8F,$00000000
	DC.L	$3FFC0000,$EF888432,$64ECEFAA,$00000000
	DC.L	$3FFC0000,$F7170A28,$ECC06666,$00000000
	DC.L	$3FFD0000,$812FD288,$332DAD32,$00000000
	DC.L	$3FFD0000,$88A8D1B1,$218E4D64,$00000000
	DC.L	$3FFD0000,$9012AB3F,$23E4AEE8,$00000000
	DC.L	$3FFD0000,$976CC3D4,$11E7F1B9,$00000000
	DC.L	$3FFD0000,$9EB68949,$3889A227,$00000000
	DC.L	$3FFD0000,$A5EF72C3,$4487361B,$00000000
	DC.L	$3FFD0000,$AD1700BA,$F07A7227,$00000000
	DC.L	$3FFD0000,$B42CBCFA,$FD37EFB7,$00000000
	DC.L	$3FFD0000,$BB303A94,$0BA80F89,$00000000
	DC.L	$3FFD0000,$C22115C6,$FCAEBBAF,$00000000
	DC.L	$3FFD0000,$C8FEF3E6,$86331221,$00000000
	DC.L	$3FFD0000,$CFC98330,$B4000C70,$00000000
	DC.L	$3FFD0000,$D6807AA1,$102C5BF9,$00000000
	DC.L	$3FFD0000,$DD2399BC,$31252AA3,$00000000
	DC.L	$3FFD0000,$E3B2A855,$6B8FC517,$00000000
	DC.L	$3FFD0000,$EA2D764F,$64315989,$00000000
	DC.L	$3FFD0000,$F3BF5BF8,$BAD1A21D,$00000000
	DC.L	$3FFE0000,$801CE39E,$0D205C9A,$00000000
	DC.L	$3FFE0000,$8630A2DA,$DA1ED066,$00000000
	DC.L	$3FFE0000,$8C1AD445,$F3E09B8C,$00000000
	DC.L	$3FFE0000,$91DB8F16,$64F350E2,$00000000
	DC.L	$3FFE0000,$97731420,$365E538C,$00000000
	DC.L	$3FFE0000,$9CE1C8E6,$A0B8CDBA,$00000000
	DC.L	$3FFE0000,$A22832DB,$CADAAE09,$00000000
	DC.L	$3FFE0000,$A746F2DD,$B7602294,$00000000
	DC.L	$3FFE0000,$AC3EC0FB,$997DD6A2,$00000000
	DC.L	$3FFE0000,$B110688A,$EBDC6F6A,$00000000
	DC.L	$3FFE0000,$B5BCC490,$59ECC4B0,$00000000
	DC.L	$3FFE0000,$BA44BC7D,$D470782F,$00000000
	DC.L	$3FFE0000,$BEA94144,$FD049AAC,$00000000
	DC.L	$3FFE0000,$C2EB4ABB,$661628B6,$00000000
	DC.L	$3FFE0000,$C70BD54C,$E602EE14,$00000000
	DC.L	$3FFE0000,$CD000549,$ADEC7159,$00000000
	DC.L	$3FFE0000,$D48457D2,$D8EA4EA3,$00000000
	DC.L	$3FFE0000,$DB948DA7,$12DECE3B,$00000000
	DC.L	$3FFE0000,$E23855F9,$69E8096A,$00000000
	DC.L	$3FFE0000,$E8771129,$C4353259,$00000000
	DC.L	$3FFE0000,$EE57C16E,$0D379C0D,$00000000
	DC.L	$3FFE0000,$F3E10211,$A87C3779,$00000000
	DC.L	$3FFE0000,$F919039D,$758B8D41,$00000000
	DC.L	$3FFE0000,$FE058B8F,$64935FB3,$00000000
	DC.L	$3FFF0000,$8155FB49,$7B685D04,$00000000
	DC.L	$3FFF0000,$83889E35,$49D108E1,$00000000
	DC.L	$3FFF0000,$859CFA76,$511D724B,$00000000
	DC.L	$3FFF0000,$87952ECF,$FF8131E7,$00000000
	DC.L	$3FFF0000,$89732FD1,$9557641B,$00000000
	DC.L	$3FFF0000,$8B38CAD1,$01932A35,$00000000
	DC.L	$3FFF0000,$8CE7A8D8,$301EE6B5,$00000000
	DC.L	$3FFF0000,$8F46A39E,$2EAE5281,$00000000
	DC.L	$3FFF0000,$922DA7D7,$91888487,$00000000
	DC.L	$3FFF0000,$94D19FCB,$DEDF5241,$00000000
	DC.L	$3FFF0000,$973AB944,$19D2A08B,$00000000
	DC.L	$3FFF0000,$996FF00E,$08E10B96,$00000000
	DC.L	$3FFF0000,$9B773F95,$12321DA7,$00000000
	DC.L	$3FFF0000,$9D55CC32,$0F935624,$00000000
	DC.L	$3FFF0000,$9F100575,$006CC571,$00000000
	DC.L	$3FFF0000,$A0A9C290,$D97CC06C,$00000000
	DC.L	$3FFF0000,$A22659EB,$EBC0630A,$00000000
	DC.L	$3FFF0000,$A388B4AF,$F6EF0EC9,$00000000
	DC.L	$3FFF0000,$A4D35F10,$61D292C4,$00000000
	DC.L	$3FFF0000,$A60895DC,$FBE3187E,$00000000
	DC.L	$3FFF0000,$A72A51DC,$7367BEAC,$00000000
	DC.L	$3FFF0000,$A83A5153,$0956168F,$00000000
	DC.L	$3FFF0000,$A93A2007,$7539546E,$00000000
	DC.L	$3FFF0000,$AA9E7245,$023B2605,$00000000
	DC.L	$3FFF0000,$AC4C84BA,$6FE4D58F,$00000000
	DC.L	$3FFF0000,$ADCE4A4A,$606B9712,$00000000
	DC.L	$3FFF0000,$AF2A2DCD,$8D263C9C,$00000000
	DC.L	$3FFF0000,$B0656F81,$F22265C7,$00000000
	DC.L	$3FFF0000,$B1846515,$0F71496A,$00000000
	DC.L	$3FFF0000,$B28AAA15,$6F9ADA35,$00000000
	DC.L	$3FFF0000,$B37B44FF,$3766B895,$00000000
	DC.L	$3FFF0000,$B458C3DC,$E9630433,$00000000
	DC.L	$3FFF0000,$B525529D,$562246BD,$00000000
	DC.L	$3FFF0000,$B5E2CCA9,$5F9D88CC,$00000000
	DC.L	$3FFF0000,$B692CADA,$7ACA1ADA,$00000000
	DC.L	$3FFF0000,$B736AEA7,$A6925838,$00000000
	DC.L	$3FFF0000,$B7CFAB28,$7E9F7B36,$00000000
	DC.L	$3FFF0000,$B85ECC66,$CB219835,$00000000
	DC.L	$3FFF0000,$B8E4FD5A,$20A593DA,$00000000
	DC.L	$3FFF0000,$B99F41F6,$4AFF9BB5,$00000000
	DC.L	$3FFF0000,$BA7F1E17,$842BBE7B,$00000000
	DC.L	$3FFF0000,$BB471285,$7637E17D,$00000000
	DC.L	$3FFF0000,$BBFABE8A,$4788DF6F,$00000000
	DC.L	$3FFF0000,$BC9D0FAD,$2B689D79,$00000000
	DC.L	$3FFF0000,$BD306A39,$471ECD86,$00000000
	DC.L	$3FFF0000,$BDB6C731,$856AF18A,$00000000
	DC.L	$3FFF0000,$BE31CAC5,$02E80D70,$00000000
	DC.L	$3FFF0000,$BEA2D55C,$E33194E2,$00000000
	DC.L	$3FFF0000,$BF0B10B7,$C03128F0,$00000000
	DC.L	$3FFF0000,$BF6B7A18,$DACB778D,$00000000
	DC.L	$3FFF0000,$BFC4EA46,$63FA18F6,$00000000
	DC.L	$3FFF0000,$C0181BDE,$8B89A454,$00000000
	DC.L	$3FFF0000,$C065B066,$CFBF6439,$00000000
	DC.L	$3FFF0000,$C0AE345F,$56340AE6,$00000000
	DC.L	$3FFF0000,$C0F22291,$9CB9E6A7,$00000000

X	equ	FP_SCR1
XDCARE	equ	X+2
XFRAC	equ	X+4
XFRACLO	equ	X+8

ATANF	equ	FP_SCR2
ATANFHI	equ	ATANF+4
ATANFLO	equ	ATANF+8


	xref	t_frcinx
	xref	t_extdnrm

	xdef	satand
satand:
*--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT

	bra		t_extdnrm

	xdef	satan
satan:
*--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S

	FMOVE.X		(A0),FP0	...LOAD INPUT

	MOVE.L		(A0),D0
	MOVE.W		4(A0),D0
	FMOVE.X		FP0,X(a6)
	ANDI.L		#$7FFFFFFF,D0

	CMPI.L		#$3FFB8000,D0		...|X| >= 1/16?
	BGE.B		ATANOK1
	BRA.W		ATANSM

ATANOK1:
	CMPI.L		#$4002FFFF,D0		...|X| < 16 ?
	BLE.B		ATANMAIN
	BRA.W		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:

	CLR.W		XDCARE(a6)		...CLEAN UP X JUST IN CASE
	ANDI.L		#$F8000000,XFRAC(a6)	...FIRST 5 BITS
	ORI.L		#$04000000,XFRAC(a6)	...SET 6-TH BIT TO 1
	CLR.L		XFRACLO(a6)		...LOCATION OF X IS NOW F

	FMOVE.X		FP0,FP1			...FP1 IS X
	FMUL.X		X(a6),FP1		...FP1 IS X*F, NOTE THAT X*F > 0
	FSUB.X		X(a6),FP0		...FP0 IS X-F
	FADD.S		#:3F800000,FP1		...FP1 IS 1 + X*F
	FDIV.X		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.

	MOVE.L		d2,-(a7)	...SAVE d2 TEMPORARILY
	MOVE.L		d0,d2		...THE EXPO AND 16 BITS OF X
	ANDI.L		#$00007800,d0	...4 VARYING BITS OF F'S FRACTION
	ANDI.L		#$7FFF0000,d2	...EXPONENT OF F
	SUBI.L		#$3FFB0000,d2	...K+4
	ASR.L		#1,d2
	ADD.L		d2,d0		...THE 7 BITS IDENTIFYING F
	ASR.L		#7,d0		...INDEX INTO TBL OF ATAN(|F|)
	LEA		ATANTBL,a1
	ADDA.L		d0,a1		...ADDRESS OF ATAN(|F|)
	MOVE.L		(a1)+,ATANF(a6)
	MOVE.L		(a1)+,ATANFHI(a6)
	MOVE.L		(a1)+,ATANFLO(a6)	...ATANF IS NOW ATAN(|F|)
	MOVE.L		X(a6),d0		...LOAD SIGN AND EXPO. AGAIN
	ANDI.L		#$80000000,d0	...SIGN(F)
	OR.L		d0,ATANF(a6)	...ATANF IS NOW SIGN(F)*ATAN(|F|)
	MOVE.L		(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

	
	FMOVE.X		FP0,FP1
	FMUL.X		FP1,FP1
	FMOVE.D		ATANA3,FP2
	FADD.X		FP1,FP2		...A3+V
	FMUL.X		FP1,FP2		...V*(A3+V)
	FMUL.X		FP0,FP1		...U*V
	FADD.D		ATANA2,FP2	...A2+V*(A3+V)
	FMUL.D		ATANA1,FP1	...A1*U*V
	FMUL.X		FP2,FP1		...A1*U*V*(A2+V*(A3+V))
	
	FADD.X		FP1,FP0		...ATAN(U), FP1 RELEASED
	FMOVE.L		d1,FPCR		;restore users exceptions
	FADD.X		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.
	CMPI.L		#$3FFF8000,d0
	BGT.W		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.

	CMPI.L		#$3FD78000,d0
	BLT.W		ATANTINY
*--COMPUTE POLYNOMIAL
	FMUL.X		FP0,FP0	...FP0 IS Y = X*X

	
	CLR.W		XDCARE(a6)

	FMOVE.X		FP0,FP1
	FMUL.X		FP1,FP1		...FP1 IS Z = Y*Y

	FMOVE.D		ATANB6,FP2
	FMOVE.D		ATANB5,FP3

	FMUL.X		FP1,FP2		...Z*B6
	FMUL.X		FP1,FP3		...Z*B5

	FADD.D		ATANB4,FP2	...B4+Z*B6
	FADD.D		ATANB3,FP3	...B3+Z*B5

	FMUL.X		FP1,FP2		...Z*(B4+Z*B6)
	FMUL.X		FP3,FP1		...Z*(B3+Z*B5)

	FADD.D		ATANB2,FP2	...B2+Z*(B4+Z*B6)
	FADD.D		ATANB1,FP1	...B1+Z*(B3+Z*B5)

	FMUL.X		FP0,FP2		...Y*(B2+Z*(B4+Z*B6))
	FMUL.X		X(a6),FP0		...X*Y

	FADD.X		FP2,FP1		...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
	

	FMUL.X		FP1,FP0	...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])

	FMOVE.L		d1,FPCR		;restore users exceptions
	FADD.X		X(a6),FP0

	bra		t_frcinx

ATANTINY:
*--|X| < 2^(-40), ATAN(X) = X
	CLR.W		XDCARE(a6)

	FMOVE.L		d1,FPCR		;restore users exceptions
	FMOVE.X		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).
	CMPI.L		#$40638000,d0
	BGT.W		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.

	FMOVE.S		#:BF800000,FP1	...LOAD -1
	FDIV.X		FP0,FP1		...FP1 IS -1/X

	
*--DIVIDE IS STILL CRANKING

	FMOVE.X		FP1,FP0		...FP0 IS X'
	FMUL.X		FP0,FP0		...FP0 IS Y = X'*X'
	FMOVE.X		FP1,X(a6)		...X IS REALLY X'

	FMOVE.X		FP0,FP1
	FMUL.X		FP1,FP1		...FP1 IS Z = Y*Y

	FMOVE.D		ATANC5,FP3
	FMOVE.D		ATANC4,FP2

	FMUL.X		FP1,FP3		...Z*C5
	FMUL.X		FP1,FP2		...Z*B4

	FADD.D		ATANC3,FP3	...C3+Z*C5
	FADD.D		ATANC2,FP2	...C2+Z*C4

	FMUL.X		FP3,FP1		...Z*(C3+Z*C5), FP3 RELEASED
	FMUL.X		FP0,FP2		...Y*(C2+Z*C4)

	FADD.D		ATANC1,FP1	...C1+Z*(C3+Z*C5)
	FMUL.X		X(a6),FP0		...X'*Y

	FADD.X		FP2,FP1		...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
	

	FMUL.X		FP1,FP0		...X'*Y*([B1+Z*(B3+Z*B5)]
*					...	+[Y*(B2+Z*(B4+Z*B6))])
	FADD.X		X(a6),FP0

	FMOVE.L		d1,FPCR		;restore users exceptions
	
	btst.b		#7,(a0)
	beq.b		pos_big

neg_big:
	FADD.X		NPIBY2,FP0
	bra		t_frcinx

pos_big:
	FADD.X		PPIBY2,FP0
	bra		t_frcinx

ATANHUGE:
*--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
	btst.b		#7,(a0)
	beq.b		pos_huge

neg_huge:
	FMOVE.X		NPIBY2,fp0
	fmove.l		d1,fpcr
	fsub.x		NTINY,fp0
	bra		t_frcinx

pos_huge:
	FMOVE.X		PPIBY2,fp0
	fmove.l		d1,fpcr
	fsub.x		PTINY,fp0
	bra		t_frcinx
	
	end