path: root/sys/arch/m68k/fpsp/ssin.sa

*	$OpenBSD: ssin.sa,v 1.4 2007/11/25 16:40:04 jmc Exp $
*	$NetBSD: ssin.sa,v 1.3 1994/10/26 07:50:01 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.

*
*	ssin.sa 3.3 7/29/91
*
*	The entry point sSIN computes the sine of an input argument
*	sCOS computes the cosine, and sSINCOS computes both. The
*	corresponding entry points with a "d" computes the same
*	corresponding function values for denormalized inputs.
*
*	Input: Double-extended number X in location pointed to
*		by address register a0.
*
*	Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or
*		COS is requested. Otherwise, for SINCOS, sin(X) is returned
*		in Fp0, and cos(X) is returned in Fp1.
*
*	Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS.
*
*	Accuracy and Monotonicity: The returned result is within 1 ulp 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 programs sSIN and sCOS take approximately 150 cycles for
*		input argument X such that |X| < 15Pi, which is the usual
*		situation. The speed for sSINCOS is approximately 190 cycles.
*
*	Algorithm:
*
*	SIN and COS:
*	1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1.
*
*	2. If |X| >= 15Pi or |X| < 2**(-40), go to 7.
*
*	3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
*		k = N mod 4, so in particular, k = 0,1,2,or 3. Overwirte
*		k by k := k + AdjN.
*
*	4. If k is even, go to 6.
*
*	5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r)
*		where cos(r) is approximated by an even polynomial in r,
*		1 + r*r*(B1+s*(B2+ ... + s*B8)),	s = r*r.
*		Exit.
*
*	6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r)
*		where sin(r) is approximated by an odd polynomial in r
*		r + r*s*(A1+s*(A2+ ... + s*A7)),	s = r*r.
*		Exit.
*
*	7. If |X| > 1, go to 9.
*
*	8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1.
*
*	9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3.
*
*	SINCOS:
*	1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
*
*	2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
*		k = N mod 4, so in particular, k = 0,1,2,or 3.
*
*	3. If k is even, go to 5.
*
*	4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e.
*		j1 exclusive or with the l.s.b. of k.
*		sgn1 := (-1)**j1, sgn2 := (-1)**j2.
*		SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where
*		sin(r) and cos(r) are computed as odd and even polynomials
*		in r, respectively. Exit
*
*	5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1.
*		SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where
*		sin(r) and cos(r) are computed as odd and even polynomials
*		in r, respectively. Exit
*
*	6. If |X| > 1, go to 8.
*
*	7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit.
*
*	8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
*

SSIN	IDNT	2,1 Motorola 040 Floating Point Software Package

	section	8

	include	fpsp.h

BOUNDS1	DC.L $3FD78000,$4004BC7E
TWOBYPI	DC.L $3FE45F30,$6DC9C883

SINA7	DC.L $BD6AAA77,$CCC994F5
SINA6	DC.L $3DE61209,$7AAE8DA1

SINA5	DC.L $BE5AE645,$2A118AE4
SINA4	DC.L $3EC71DE3,$A5341531

SINA3	DC.L $BF2A01A0,$1A018B59,$00000000,$00000000

SINA2	DC.L $3FF80000,$88888888,$888859AF,$00000000

SINA1	DC.L $BFFC0000,$AAAAAAAA,$AAAAAA99,$00000000

COSB8	DC.L $3D2AC4D0,$D6011EE3
COSB7	DC.L $BDA9396F,$9F45AC19

COSB6	DC.L $3E21EED9,$0612C972
COSB5	DC.L $BE927E4F,$B79D9FCF

COSB4	DC.L $3EFA01A0,$1A01D423,$00000000,$00000000

COSB3	DC.L $BFF50000,$B60B60B6,$0B61D438,$00000000

COSB2	DC.L $3FFA0000,$AAAAAAAA,$AAAAAB5E
COSB1	DC.L $BF000000

INVTWOPI DC.L $3FFC0000,$A2F9836E,$4E44152A

TWOPI1	DC.L $40010000,$C90FDAA2,$00000000,$00000000
TWOPI2	DC.L $3FDF0000,$85A308D4,$00000000,$00000000

	xref	PITBL

INARG	equ	FP_SCR4

X	equ	FP_SCR5
XDCARE	equ	X+2
XFRAC	equ	X+4

RPRIME	equ	FP_SCR1
SPRIME	equ	FP_SCR2

POSNEG1	equ	L_SCR1
TWOTO63	equ	L_SCR1

ENDFLAG	equ	L_SCR2
N	equ	L_SCR2

ADJN	equ	L_SCR3

	xref	t_frcinx
	xref	t_extdnrm
	xref	sto_cos

	xdef	ssind
ssind:
*--SIN(X) = X FOR DENORMALIZED X
	bra		t_extdnrm

	xdef	scosd
scosd:
*--COS(X) = 1 FOR DENORMALIZED X

	FMOVE.S		#:3F800000,FP0
*
*	9D25B Fix: Sometimes the previous fmove.s sets fpsr bits
*
	fmove.l		#0,fpsr
*
	bra		t_frcinx

	xdef	ssin
ssin:
*--SET ADJN TO 0
	CLR.L		ADJN(a6)
	BRA.B		SINBGN

	xdef	scos
scos:
*--SET ADJN TO 1
	MOVE.L		#1,ADJN(a6)

SINBGN:
*--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE

	FMOVE.X		(a0),FP0	...LOAD INPUT

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

	CMPI.L		#$3FD78000,D0		...|X| >= 2**(-40)?
	BGE.B		SOK1
	BRA.W		SINSM

SOK1:
	CMPI.L		#$4004BC7E,D0		...|X| < 15 PI?
	BLT.B		SINMAIN
	BRA.W		REDUCEX

SINMAIN:
*--THIS IS THE USUAL CASE, |X| <= 15 PI.
*--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
	FMOVE.X		FP0,FP1
	FMUL.D		TWOBYPI,FP1	...X*2/PI

*--HIDE THE NEXT THREE INSTRUCTIONS
	LEA		PITBL+$200,A1 ...TABLE OF N*PI/2, N = -32,...,32
	

*--FP1 IS NOW READY
	FMOVE.L		FP1,N(a6)		...CONVERT TO INTEGER

	MOVE.L		N(a6),D0
	ASL.L		#4,D0
	ADDA.L		D0,A1	...A1 IS THE ADDRESS OF N*PIBY2
*				...WHICH IS IN TWO PIECES Y1 & Y2

	FSUB.X		(A1)+,FP0	...X-Y1
*--HIDE THE NEXT ONE
	FSUB.S		(A1),FP0	...FP0 IS R = (X-Y1)-Y2

SINCONT:
*--continuation from REDUCEX

*--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
	MOVE.L		N(a6),D0
	ADD.L		ADJN(a6),D0	...SEE IF D0 IS ODD OR EVEN
	ROR.L		#1,D0	...D0 WAS ODD IFF D0 IS NEGATIVE
	TST.L		D0
	BLT.W		COSPOLY

SINPOLY:
*--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
*--THEN WE RETURN	SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
*--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
*--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
*--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
*--WHERE T=S*S.
*--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
*--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
	FMOVE.X		FP0,X(a6)	...X IS R
	FMUL.X		FP0,FP0	...FP0 IS S
*---HIDE THE NEXT TWO WHILE WAITING FOR FP0
	FMOVE.D		SINA7,FP3
	FMOVE.D		SINA6,FP2
*--FP0 IS NOW READY
	FMOVE.X		FP0,FP1
	FMUL.X		FP1,FP1	...FP1 IS T
*--HIDE THE NEXT TWO WHILE WAITING FOR FP1

	ROR.L		#1,D0
	ANDI.L		#$80000000,D0
*				...LEAST SIG. BIT OF D0 IN SIGN POSITION
	EOR.L		D0,X(a6)	...X IS NOW R'= SGN*R

	FMUL.X		FP1,FP3	...TA7
	FMUL.X		FP1,FP2	...TA6

	FADD.D		SINA5,FP3 ...A5+TA7
	FADD.D		SINA4,FP2 ...A4+TA6

	FMUL.X		FP1,FP3	...T(A5+TA7)
	FMUL.X		FP1,FP2	...T(A4+TA6)

	FADD.D		SINA3,FP3 ...A3+T(A5+TA7)
	FADD.X		SINA2,FP2 ...A2+T(A4+TA6)

	FMUL.X		FP3,FP1	...T(A3+T(A5+TA7))

	FMUL.X		FP0,FP2	...S(A2+T(A4+TA6))
	FADD.X		SINA1,FP1 ...A1+T(A3+T(A5+TA7))
	FMUL.X		X(a6),FP0	...R'*S

	FADD.X		FP2,FP1	...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
*--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
*--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING
	

	FMUL.X		FP1,FP0		...SIN(R')-R'
*--FP1 RELEASED.

	FMOVE.L		d1,FPCR		;restore users exceptions
	FADD.X		X(a6),FP0		;last inst - possible exception set
	bra		t_frcinx


COSPOLY:
*--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
*--THEN WE RETURN	SGN*COS(R). SGN*COS(R) IS COMPUTED BY
*--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
*--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
*--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
*--WHERE T=S*S.
*--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
*--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
*--AND IS THEREFORE STORED AS SINGLE PRECISION.

	FMUL.X		FP0,FP0	...FP0 IS S
*---HIDE THE NEXT TWO WHILE WAITING FOR FP0
	FMOVE.D		COSB8,FP2
	FMOVE.D		COSB7,FP3
*--FP0 IS NOW READY
	FMOVE.X		FP0,FP1
	FMUL.X		FP1,FP1	...FP1 IS T
*--HIDE THE NEXT TWO WHILE WAITING FOR FP1
	FMOVE.X		FP0,X(a6)	...X IS S
	ROR.L		#1,D0
	ANDI.L		#$80000000,D0
*			...LEAST SIG. BIT OF D0 IN SIGN POSITION

	FMUL.X		FP1,FP2	...TB8
*--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
	EOR.L		D0,X(a6)	...X IS NOW S'= SGN*S
	ANDI.L		#$80000000,D0

	FMUL.X		FP1,FP3	...TB7
*--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
	ORI.L		#$3F800000,D0	...D0 IS SGN IN SINGLE
	MOVE.L		D0,POSNEG1(a6)

	FADD.D		COSB6,FP2 ...B6+TB8
	FADD.D		COSB5,FP3 ...B5+TB7

	FMUL.X		FP1,FP2	...T(B6+TB8)
	FMUL.X		FP1,FP3	...T(B5+TB7)

	FADD.D		COSB4,FP2 ...B4+T(B6+TB8)
	FADD.X		COSB3,FP3 ...B3+T(B5+TB7)

	FMUL.X		FP1,FP2	...T(B4+T(B6+TB8))
	FMUL.X		FP3,FP1	...T(B3+T(B5+TB7))

	FADD.X		COSB2,FP2 ...B2+T(B4+T(B6+TB8))
	FADD.S		COSB1,FP1 ...B1+T(B3+T(B5+TB7))

	FMUL.X		FP2,FP0	...S(B2+T(B4+T(B6+TB8)))
*--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
*--FP2 RELEASED.
	

	FADD.X		FP1,FP0
*--FP1 RELEASED

	FMUL.X		X(a6),FP0

	FMOVE.L		d1,FPCR		;restore users exceptions
	FADD.S		POSNEG1(a6),FP0	;last inst - possible exception set
	bra		t_frcinx


SINBORS:
*--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
*--IF |X| < 2**(-40), RETURN X OR 1.
	CMPI.L		#$3FFF8000,D0
	BGT.B		REDUCEX
        

SINSM:
	MOVE.L		ADJN(a6),D0
	TST.L		D0
	BGT.B		COSTINY

SINTINY:
	CLR.W		XDCARE(a6)	...JUST IN CASE
	FMOVE.L		d1,FPCR		;restore users exceptions
	FMOVE.X		X(a6),FP0		;last inst - possible exception set
	bra		t_frcinx


COSTINY:
	FMOVE.S		#:3F800000,FP0

	FMOVE.L		d1,FPCR		;restore users exceptions
	FSUB.S		#:00800000,FP0	;last inst - possible exception set
	bra		t_frcinx


REDUCEX:
*--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
*--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
*--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.

	FMOVEM.X	FP2-FP5,-(A7)	...save FP2 through FP5
	MOVE.L		D2,-(A7)
        FMOVE.S         #:00000000,FP1
*--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
*--there is a danger of unwanted overflow in first LOOP iteration.  In this
*--case, reduce argument by one remainder step to make subsequent reduction
*--safe.
	cmpi.l	#$7ffeffff,d0		;is argument dangerously large?
	bne.b	LOOP
	move.l	#$7ffe0000,FP_SCR2(a6)	;yes
*					;create 2**16383*PI/2
	move.l	#$c90fdaa2,FP_SCR2+4(a6)
	clr.l	FP_SCR2+8(a6)
	ftst.x	fp0			;test sign of argument
	move.l	#$7fdc0000,FP_SCR3(a6)	;create low half of 2**16383*
*					;PI/2 at FP_SCR3
	move.l	#$85a308d3,FP_SCR3+4(a6)
	clr.l   FP_SCR3+8(a6)
	fblt.w	red_neg
	or.w	#$8000,FP_SCR2(a6)	;positive arg
	or.w	#$8000,FP_SCR3(a6)
red_neg:
	fadd.x  FP_SCR2(a6),fp0		;high part of reduction is exact
	fmove.x  fp0,fp1		;save high result in fp1
	fadd.x  FP_SCR3(a6),fp0		;low part of reduction
	fsub.x  fp0,fp1			;determine low component of result
	fadd.x  FP_SCR3(a6),fp1		;fp0/fp1 are reduced argument.

*--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
*--integer quotient will be stored in N
*--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)

LOOP:
	FMOVE.X		FP0,INARG(a6)	...+-2**K * F, 1 <= F < 2
	MOVE.W		INARG(a6),D0
        MOVE.L          D0,A1		...save a copy of D0
	ANDI.L		#$00007FFF,D0
	SUBI.L		#$00003FFF,D0	...D0 IS K
	CMPI.L		#28,D0
	BLE.B		LASTLOOP
CONTLOOP:
	SUBI.L		#27,D0	 ...D0 IS L := K-27
	CLR.L		ENDFLAG(a6)
	BRA.B		WORK
LASTLOOP:
	CLR.L		D0		...D0 IS L := 0
	MOVE.L		#1,ENDFLAG(a6)

WORK:
*--FIND THE REMAINDER OF (R,r) W.R.T.	2**L * (PI/2). L IS SO CHOSEN
*--THAT	INT( X * (2/PI) / 2**(L) ) < 2**29.

*--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
*--2**L * (PIby2_1), 2**L * (PIby2_2)

	MOVE.L		#$00003FFE,D2	...BIASED EXPO OF 2/PI
	SUB.L		D0,D2		...BIASED EXPO OF 2**(-L)*(2/PI)

	MOVE.L		#$A2F9836E,FP_SCR1+4(a6)
	MOVE.L		#$4E44152A,FP_SCR1+8(a6)
	MOVE.W		D2,FP_SCR1(a6)	...FP_SCR1 is 2**(-L)*(2/PI)

	FMOVE.X		FP0,FP2
	FMUL.X		FP_SCR1(a6),FP2
*--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
*--FLOATING POINT FORMAT, THE TWO FMOVE'S	FMOVE.L FP <--> N
*--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
*--(SIGN(INARG)*2**63	+	FP2) - SIGN(INARG)*2**63 WILL GIVE
*--US THE DESIRED VALUE IN FLOATING POINT.

*--HIDE SIX CYCLES OF INSTRUCTION
        MOVE.L		A1,D2
        SWAP		D2
	ANDI.L		#$80000000,D2
	ORI.L		#$5F000000,D2	...D2 IS SIGN(INARG)*2**63 IN SGL
	MOVE.L		D2,TWOTO63(a6)

	MOVE.L		D0,D2
	ADDI.L		#$00003FFF,D2	...BIASED EXPO OF 2**L * (PI/2)

*--FP2 IS READY
	FADD.S		TWOTO63(a6),FP2	...THE FRACTIONAL PART OF FP1 IS ROUNDED

*--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1  and  2**(L)*Piby2_2
        MOVE.W		D2,FP_SCR2(a6)
	CLR.W           FP_SCR2+2(a6)
	MOVE.L		#$C90FDAA2,FP_SCR2+4(a6)
	CLR.L		FP_SCR2+8(a6)		...FP_SCR2 is  2**(L) * Piby2_1	

*--FP2 IS READY
	FSUB.S		TWOTO63(a6),FP2		...FP2 is N

	ADDI.L		#$00003FDD,D0
        MOVE.W		D0,FP_SCR3(a6)
	CLR.W           FP_SCR3+2(a6)
	MOVE.L		#$85A308D3,FP_SCR3+4(a6)
	CLR.L		FP_SCR3+8(a6)		...FP_SCR3 is 2**(L) * Piby2_2

	MOVE.L		ENDFLAG(a6),D0

*--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
*--P2 = 2**(L) * Piby2_2
	FMOVE.X		FP2,FP4
	FMul.X		FP_SCR2(a6),FP4		...W = N*P1
	FMove.X		FP2,FP5
	FMul.X		FP_SCR3(a6),FP5		...w = N*P2
	FMove.X		FP4,FP3
*--we want P+p = W+w  but  |p| <= half ulp of P
*--Then, we need to compute  A := R-P   and  a := r-p
	FAdd.X		FP5,FP3			...FP3 is P
	FSub.X		FP3,FP4			...W-P

	FSub.X		FP3,FP0			...FP0 is A := R - P
        FAdd.X		FP5,FP4			...FP4 is p = (W-P)+w

	FMove.X		FP0,FP3			...FP3 A
	FSub.X		FP4,FP1			...FP1 is a := r - p

*--Now we need to normalize (A,a) to  "new (R,r)" where R+r = A+a but
*--|r| <= half ulp of R.
	FAdd.X		FP1,FP0			...FP0 is R := A+a
*--No need to calculate r if this is the last loop
	TST.L		D0
	BGT.W		RESTORE

*--Need to calculate r
	FSub.X		FP0,FP3			...A-R
	FAdd.X		FP3,FP1			...FP1 is r := (A-R)+a
	BRA.W		LOOP

RESTORE:
        FMOVE.L		FP2,N(a6)
	MOVE.L		(A7)+,D2
	FMOVEM.X	(A7)+,FP2-FP5

	
	MOVE.L		ADJN(a6),D0
	CMPI.L		#4,D0

	BLT.W		SINCONT
	BRA.B		SCCONT

	xdef	ssincosd
ssincosd:
*--SIN AND COS OF X FOR DENORMALIZED X

	FMOVE.S		#:3F800000,FP1
	bsr		sto_cos		;store cosine result
	bra		t_extdnrm

	xdef	ssincos
ssincos:
*--SET ADJN TO 4
	MOVE.L		#4,ADJN(a6)

	FMOVE.X		(a0),FP0	...LOAD INPUT

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

	CMPI.L		#$3FD78000,D0		...|X| >= 2**(-40)?
	BGE.B		SCOK1
	BRA.W		SCSM

SCOK1:
	CMPI.L		#$4004BC7E,D0		...|X| < 15 PI?
	BLT.B		SCMAIN
	BRA.W		REDUCEX


SCMAIN:
*--THIS IS THE USUAL CASE, |X| <= 15 PI.
*--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
	FMOVE.X		FP0,FP1
	FMUL.D		TWOBYPI,FP1	...X*2/PI

*--HIDE THE NEXT THREE INSTRUCTIONS
	LEA		PITBL+$200,A1 ...TABLE OF N*PI/2, N = -32,...,32
	

*--FP1 IS NOW READY
	FMOVE.L		FP1,N(a6)		...CONVERT TO INTEGER

	MOVE.L		N(a6),D0
	ASL.L		#4,D0
	ADDA.L		D0,A1		...ADDRESS OF N*PIBY2, IN Y1, Y2

	FSUB.X		(A1)+,FP0	...X-Y1
        FSUB.S		(A1),FP0	...FP0 IS R = (X-Y1)-Y2

SCCONT:
*--continuation point from REDUCEX

*--HIDE THE NEXT TWO
	MOVE.L		N(a6),D0
	ROR.L		#1,D0
	
	TST.L		D0		...D0 < 0 IFF N IS ODD
	BGE.W		NEVEN

NODD:
*--REGISTERS SAVED SO FAR: D0, A0, FP2.

	FMOVE.X		FP0,RPRIME(a6)
	FMUL.X		FP0,FP0	 ...FP0 IS S = R*R
	FMOVE.D		SINA7,FP1	...A7
	FMOVE.D		COSB8,FP2	...B8
	FMUL.X		FP0,FP1	 ...SA7
	MOVE.L		d2,-(A7)
	MOVE.L		D0,d2
	FMUL.X		FP0,FP2	 ...SB8
	ROR.L		#1,d2
	ANDI.L		#$80000000,d2

	FADD.D		SINA6,FP1	...A6+SA7
	EOR.L		D0,d2
	ANDI.L		#$80000000,d2
	FADD.D		COSB7,FP2	...B7+SB8

	FMUL.X		FP0,FP1	 ...S(A6+SA7)
	EOR.L		d2,RPRIME(a6)
	MOVE.L		(A7)+,d2
	FMUL.X		FP0,FP2	 ...S(B7+SB8)
	ROR.L		#1,D0
	ANDI.L		#$80000000,D0

	FADD.D		SINA5,FP1	...A5+S(A6+SA7)
	MOVE.L		#$3F800000,POSNEG1(a6)
	EOR.L		D0,POSNEG1(a6)
	FADD.D		COSB6,FP2	...B6+S(B7+SB8)

	FMUL.X		FP0,FP1	 ...S(A5+S(A6+SA7))
	FMUL.X		FP0,FP2	 ...S(B6+S(B7+SB8))
	FMOVE.X		FP0,SPRIME(a6)

	FADD.D		SINA4,FP1	...A4+S(A5+S(A6+SA7))
	EOR.L		D0,SPRIME(a6)
	FADD.D		COSB5,FP2	...B5+S(B6+S(B7+SB8))

	FMUL.X		FP0,FP1	 ...S(A4+...)
	FMUL.X		FP0,FP2	 ...S(B5+...)

	FADD.D		SINA3,FP1	...A3+S(A4+...)
	FADD.D		COSB4,FP2	...B4+S(B5+...)

	FMUL.X		FP0,FP1	 ...S(A3+...)
	FMUL.X		FP0,FP2	 ...S(B4+...)

	FADD.X		SINA2,FP1	...A2+S(A3+...)
	FADD.X		COSB3,FP2	...B3+S(B4+...)

	FMUL.X		FP0,FP1	 ...S(A2+...)
	FMUL.X		FP0,FP2	 ...S(B3+...)

	FADD.X		SINA1,FP1	...A1+S(A2+...)
	FADD.X		COSB2,FP2	...B2+S(B3+...)

	FMUL.X		FP0,FP1	 ...S(A1+...)
	FMUL.X		FP2,FP0	 ...S(B2+...)

	

	FMUL.X		RPRIME(a6),FP1	...R'S(A1+...)
	FADD.S		COSB1,FP0	...B1+S(B2...)
	FMUL.X		SPRIME(a6),FP0	...S'(B1+S(B2+...))

	move.l		d1,-(sp)	;restore users mode & precision
	andi.l		#$ff,d1		;mask off all exceptions
	fmove.l		d1,FPCR
	FADD.X		RPRIME(a6),FP1	...COS(X)
	bsr		sto_cos		;store cosine result
	FMOVE.L		(sp)+,FPCR	;restore users exceptions
	FADD.S		POSNEG1(a6),FP0	...SIN(X)

	bra		t_frcinx


NEVEN:
*--REGISTERS SAVED SO FAR: FP2.

	FMOVE.X		FP0,RPRIME(a6)
	FMUL.X		FP0,FP0	 ...FP0 IS S = R*R
	FMOVE.D		COSB8,FP1			...B8
	FMOVE.D		SINA7,FP2			...A7
	FMUL.X		FP0,FP1	 ...SB8
	FMOVE.X		FP0,SPRIME(a6)
	FMUL.X		FP0,FP2	 ...SA7
	ROR.L		#1,D0
	ANDI.L		#$80000000,D0
	FADD.D		COSB7,FP1	...B7+SB8
	FADD.D		SINA6,FP2	...A6+SA7
	EOR.L		D0,RPRIME(a6)
	EOR.L		D0,SPRIME(a6)
	FMUL.X		FP0,FP1	 ...S(B7+SB8)
	ORI.L		#$3F800000,D0
	MOVE.L		D0,POSNEG1(a6)
	FMUL.X		FP0,FP2	 ...S(A6+SA7)

	FADD.D		COSB6,FP1	...B6+S(B7+SB8)
	FADD.D		SINA5,FP2	...A5+S(A6+SA7)

	FMUL.X		FP0,FP1	 ...S(B6+S(B7+SB8))
	FMUL.X		FP0,FP2	 ...S(A5+S(A6+SA7))

	FADD.D		COSB5,FP1	...B5+S(B6+S(B7+SB8))
	FADD.D		SINA4,FP2	...A4+S(A5+S(A6+SA7))

	FMUL.X		FP0,FP1	 ...S(B5+...)
	FMUL.X		FP0,FP2	 ...S(A4+...)

	FADD.D		COSB4,FP1	...B4+S(B5+...)
	FADD.D		SINA3,FP2	...A3+S(A4+...)

	FMUL.X		FP0,FP1	 ...S(B4+...)
	FMUL.X		FP0,FP2	 ...S(A3+...)

	FADD.X		COSB3,FP1	...B3+S(B4+...)
	FADD.X		SINA2,FP2	...A2+S(A3+...)

	FMUL.X		FP0,FP1	 ...S(B3+...)
	FMUL.X		FP0,FP2	 ...S(A2+...)

	FADD.X		COSB2,FP1	...B2+S(B3+...)
	FADD.X		SINA1,FP2	...A1+S(A2+...)

	FMUL.X		FP0,FP1	 ...S(B2+...)
	fmul.x		fp2,fp0	 ...s(a1+...)

	

	FADD.S		COSB1,FP1	...B1+S(B2...)
	FMUL.X		RPRIME(a6),FP0	...R'S(A1+...)
	FMUL.X		SPRIME(a6),FP1	...S'(B1+S(B2+...))

	move.l		d1,-(sp)	;save users mode & precision
	andi.l		#$ff,d1		;mask off all exceptions
	fmove.l		d1,FPCR
	FADD.S		POSNEG1(a6),FP1	...COS(X)
	bsr		sto_cos		;store cosine result
	FMOVE.L		(sp)+,FPCR	;restore users exceptions
	FADD.X		RPRIME(a6),FP0	...SIN(X)

	bra		t_frcinx

SCBORS:
	CMPI.L		#$3FFF8000,D0
	BGT.W		REDUCEX
        

SCSM:
	CLR.W		XDCARE(a6)
	FMOVE.S		#:3F800000,FP1

	move.l		d1,-(sp)	;save users mode & precision
	andi.l		#$ff,d1		;mask off all exceptions
	fmove.l		d1,FPCR
	FSUB.S		#:00800000,FP1
	bsr		sto_cos		;store cosine result
	FMOVE.L		(sp)+,FPCR	;restore users exceptions
	FMOVE.X		X(a6),FP0
	bra		t_frcinx

	end