patch-1.3.94 linux/arch/m68k/fpsp040/ssin.S

Next file: linux/arch/m68k/fpsp040/ssinh.S
Previous file: linux/arch/m68k/fpsp040/srem_mod.S
Back to the patch index
Back to the overall index

diff -u --recursive --new-file v1.3.93/linux/arch/m68k/fpsp040/ssin.S linux/arch/m68k/fpsp040/ssin.S
@@ -0,0 +1,746 @@
+|
+|	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 funtion 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 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.
+|
+
+|		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.
+
+|SSIN	idnt	2,1 | Motorola 040 Floating Point Software Package
+
+	|section	8
+
+	.include "fpsp.h"
+
+BOUNDS1:	.long 0x3FD78000,0x4004BC7E
+TWOBYPI:	.long 0x3FE45F30,0x6DC9C883
+
+SINA7:	.long 0xBD6AAA77,0xCCC994F5
+SINA6:	.long 0x3DE61209,0x7AAE8DA1
+
+SINA5:	.long 0xBE5AE645,0x2A118AE4
+SINA4:	.long 0x3EC71DE3,0xA5341531
+
+SINA3:	.long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
+
+SINA2:	.long 0x3FF80000,0x88888888,0x888859AF,0x00000000
+
+SINA1:	.long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
+
+COSB8:	.long 0x3D2AC4D0,0xD6011EE3
+COSB7:	.long 0xBDA9396F,0x9F45AC19
+
+COSB6:	.long 0x3E21EED9,0x0612C972
+COSB5:	.long 0xBE927E4F,0xB79D9FCF
+
+COSB4:	.long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
+
+COSB3:	.long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
+
+COSB2:	.long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
+COSB1:	.long 0xBF000000
+
+INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A
+
+TWOPI1:	.long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
+TWOPI2:	.long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
+
+	|xref	PITBL
+
+	.set	INARG,FP_SCR4
+
+	.set	X,FP_SCR5
+	.set	XDCARE,X+2
+	.set	XFRAC,X+4
+
+	.set	RPRIME,FP_SCR1
+	.set	SPRIME,FP_SCR2
+
+	.set	POSNEG1,L_SCR1
+	.set	TWOTO63,L_SCR1
+
+	.set	ENDFLAG,L_SCR2
+	.set	N,L_SCR2
+
+	.set	ADJN,L_SCR3
+
+	| xref	t_frcinx
+	|xref	t_extdnrm
+	|xref	sto_cos
+
+	.global	ssind
+ssind:
+|--SIN(X) = X FOR DENORMALIZED X
+	bra		t_extdnrm
+
+	.global	scosd
+scosd:
+|--COS(X) = 1 FOR DENORMALIZED X
+
+	fmoves		#0x3F800000,%fp0
+|
+|	9D25B Fix: Sometimes the previous fmove.s sets fpsr bits
+|
+	fmovel		#0,%fpsr
+|
+	bra		t_frcinx
+
+	.global	ssin
+ssin:
+|--SET ADJN TO 0
+	movel		#0,ADJN(%a6)
+	bras		SINBGN
+
+	.global	scos
+scos:
+|--SET ADJN TO 1
+	movel		#1,ADJN(%a6)
+
+SINBGN:
+|--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
+
+	fmovex		(%a0),%fp0	| ...LOAD INPUT
+
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	fmovex		%fp0,X(%a6)
+	andil		#0x7FFFFFFF,%d0		| ...COMPACTIFY X
+
+	cmpil		#0x3FD78000,%d0		| ...|X| >= 2**(-40)?
+	bges		SOK1
+	bra		SINSM
+
+SOK1:
+	cmpil		#0x4004BC7E,%d0		| ...|X| < 15 PI?
+	blts		SINMAIN
+	bra		REDUCEX
+
+SINMAIN:
+|--THIS IS THE USUAL CASE, |X| <= 15 PI.
+|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
+	fmovex		%fp0,%fp1
+	fmuld		TWOBYPI,%fp1	| ...X*2/PI
+
+|--HIDE THE NEXT THREE INSTRUCTIONS
+	lea		PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
+	
+
+|--FP1 IS NOW READY
+	fmovel		%fp1,N(%a6)		| ...CONVERT TO INTEGER
+
+	movel		N(%a6),%d0
+	asll		#4,%d0
+	addal		%d0,%a1	| ...A1 IS THE ADDRESS OF N*PIBY2
+|				...WHICH IS IN TWO PIECES Y1 & Y2
+
+	fsubx		(%a1)+,%fp0	| ...X-Y1
+|--HIDE THE NEXT ONE
+	fsubs		(%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
+	movel		N(%a6),%d0
+	addl		ADJN(%a6),%d0	| ...SEE IF D0 IS ODD OR EVEN
+	rorl		#1,%d0	| ...D0 WAS ODD IFF D0 IS NEGATIVE
+	cmpil		#0,%d0
+	blt		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.
+	fmovex		%fp0,X(%a6)	| ...X IS R
+	fmulx		%fp0,%fp0	| ...FP0 IS S
+|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
+	fmoved		SINA7,%fp3
+	fmoved		SINA6,%fp2
+|--FP0 IS NOW READY
+	fmovex		%fp0,%fp1
+	fmulx		%fp1,%fp1	| ...FP1 IS T
+|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
+
+	rorl		#1,%d0
+	andil		#0x80000000,%d0
+|				...LEAST SIG. BIT OF D0 IN SIGN POSITION
+	eorl		%d0,X(%a6)	| ...X IS NOW R'= SGN*R
+
+	fmulx		%fp1,%fp3	| ...TA7
+	fmulx		%fp1,%fp2	| ...TA6
+
+	faddd		SINA5,%fp3 | ...A5+TA7
+	faddd		SINA4,%fp2 | ...A4+TA6
+
+	fmulx		%fp1,%fp3	| ...T(A5+TA7)
+	fmulx		%fp1,%fp2	| ...T(A4+TA6)
+
+	faddd		SINA3,%fp3 | ...A3+T(A5+TA7)
+	faddx		SINA2,%fp2 | ...A2+T(A4+TA6)
+
+	fmulx		%fp3,%fp1	| ...T(A3+T(A5+TA7))
+
+	fmulx		%fp0,%fp2	| ...S(A2+T(A4+TA6))
+	faddx		SINA1,%fp1 | ...A1+T(A3+T(A5+TA7))
+	fmulx		X(%a6),%fp0	| ...R'*S
+
+	faddx		%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
+	
+
+	fmulx		%fp1,%fp0		| ...SIN(R')-R'
+|--FP1 RELEASED.
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	faddx		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.
+
+	fmulx		%fp0,%fp0	| ...FP0 IS S
+|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
+	fmoved		COSB8,%fp2
+	fmoved		COSB7,%fp3
+|--FP0 IS NOW READY
+	fmovex		%fp0,%fp1
+	fmulx		%fp1,%fp1	| ...FP1 IS T
+|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
+	fmovex		%fp0,X(%a6)	| ...X IS S
+	rorl		#1,%d0
+	andil		#0x80000000,%d0
+|			...LEAST SIG. BIT OF D0 IN SIGN POSITION
+
+	fmulx		%fp1,%fp2	| ...TB8
+|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
+	eorl		%d0,X(%a6)	| ...X IS NOW S'= SGN*S
+	andil		#0x80000000,%d0
+
+	fmulx		%fp1,%fp3	| ...TB7
+|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
+	oril		#0x3F800000,%d0	| ...D0 IS SGN IN SINGLE
+	movel		%d0,POSNEG1(%a6)
+
+	faddd		COSB6,%fp2 | ...B6+TB8
+	faddd		COSB5,%fp3 | ...B5+TB7
+
+	fmulx		%fp1,%fp2	| ...T(B6+TB8)
+	fmulx		%fp1,%fp3	| ...T(B5+TB7)
+
+	faddd		COSB4,%fp2 | ...B4+T(B6+TB8)
+	faddx		COSB3,%fp3 | ...B3+T(B5+TB7)
+
+	fmulx		%fp1,%fp2	| ...T(B4+T(B6+TB8))
+	fmulx		%fp3,%fp1	| ...T(B3+T(B5+TB7))
+
+	faddx		COSB2,%fp2 | ...B2+T(B4+T(B6+TB8))
+	fadds		COSB1,%fp1 | ...B1+T(B3+T(B5+TB7))
+
+	fmulx		%fp2,%fp0	| ...S(B2+T(B4+T(B6+TB8)))
+|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
+|--FP2 RELEASED.
+	
+
+	faddx		%fp1,%fp0
+|--FP1 RELEASED
+
+	fmulx		X(%a6),%fp0
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fadds		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.
+	cmpil		#0x3FFF8000,%d0
+	bgts		REDUCEX
+        
+
+SINSM:
+	movel		ADJN(%a6),%d0
+	cmpil		#0,%d0
+	bgts		COSTINY
+
+SINTINY:
+	movew		#0x0000,XDCARE(%a6)	| ...JUST IN CASE
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fmovex		X(%a6),%fp0		|last inst - possible exception set
+	bra		t_frcinx
+
+
+COSTINY:
+	fmoves		#0x3F800000,%fp0
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fsubs		#0x00800000,%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.
+
+	fmovemx	%fp2-%fp5,-(%a7)	| ...save FP2 through FP5
+	movel		%d2,-(%a7)
+        fmoves         #0x00000000,%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.
+	cmpil	#0x7ffeffff,%d0		|is argument dangerously large?
+	bnes	LOOP
+	movel	#0x7ffe0000,FP_SCR2(%a6)	|yes
+|					;create 2**16383*PI/2
+	movel	#0xc90fdaa2,FP_SCR2+4(%a6)
+	clrl	FP_SCR2+8(%a6)
+	ftstx	%fp0			|test sign of argument
+	movel	#0x7fdc0000,FP_SCR3(%a6)	|create low half of 2**16383*
+|					;PI/2 at FP_SCR3
+	movel	#0x85a308d3,FP_SCR3+4(%a6)
+	clrl   FP_SCR3+8(%a6)
+	fblt	red_neg
+	orw	#0x8000,FP_SCR2(%a6)	|positive arg
+	orw	#0x8000,FP_SCR3(%a6)
+red_neg:
+	faddx  FP_SCR2(%a6),%fp0		|high part of reduction is exact
+	fmovex  %fp0,%fp1		|save high result in fp1
+	faddx  FP_SCR3(%a6),%fp0		|low part of reduction
+	fsubx  %fp0,%fp1			|determine low component of result
+	faddx  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:
+	fmovex		%fp0,INARG(%a6)	| ...+-2**K * F, 1 <= F < 2
+	movew		INARG(%a6),%d0
+        movel          %d0,%a1		| ...save a copy of D0
+	andil		#0x00007FFF,%d0
+	subil		#0x00003FFF,%d0	| ...D0 IS K
+	cmpil		#28,%d0
+	bles		LASTLOOP
+CONTLOOP:
+	subil		#27,%d0	 | ...D0 IS L := K-27
+	movel		#0,ENDFLAG(%a6)
+	bras		WORK
+LASTLOOP:
+	clrl		%d0		| ...D0 IS L := 0
+	movel		#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)
+
+	movel		#0x00003FFE,%d2	| ...BIASED EXPO OF 2/PI
+	subl		%d0,%d2		| ...BIASED EXPO OF 2**(-L)*(2/PI)
+
+	movel		#0xA2F9836E,FP_SCR1+4(%a6)
+	movel		#0x4E44152A,FP_SCR1+8(%a6)
+	movew		%d2,FP_SCR1(%a6)	| ...FP_SCR1 is 2**(-L)*(2/PI)
+
+	fmovex		%fp0,%fp2
+	fmulx		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
+        movel		%a1,%d2
+        swap		%d2
+	andil		#0x80000000,%d2
+	oril		#0x5F000000,%d2	| ...D2 IS SIGN(INARG)*2**63 IN SGL
+	movel		%d2,TWOTO63(%a6)
+
+	movel		%d0,%d2
+	addil		#0x00003FFF,%d2	| ...BIASED EXPO OF 2**L * (PI/2)
+
+|--FP2 IS READY
+	fadds		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
+        movew		%d2,FP_SCR2(%a6)
+	clrw           FP_SCR2+2(%a6)
+	movel		#0xC90FDAA2,FP_SCR2+4(%a6)
+	clrl		FP_SCR2+8(%a6)		| ...FP_SCR2 is  2**(L) * Piby2_1	
+
+|--FP2 IS READY
+	fsubs		TWOTO63(%a6),%fp2		| ...FP2 is N
+
+	addil		#0x00003FDD,%d0
+        movew		%d0,FP_SCR3(%a6)
+	clrw           FP_SCR3+2(%a6)
+	movel		#0x85A308D3,FP_SCR3+4(%a6)
+	clrl		FP_SCR3+8(%a6)		| ...FP_SCR3 is 2**(L) * Piby2_2
+
+	movel		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
+	fmovex		%fp2,%fp4
+	fmulx		FP_SCR2(%a6),%fp4		| ...W = N*P1
+	fmovex		%fp2,%fp5
+	fmulx		FP_SCR3(%a6),%fp5		| ...w = N*P2
+	fmovex		%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
+	faddx		%fp5,%fp3			| ...FP3 is P
+	fsubx		%fp3,%fp4			| ...W-P
+
+	fsubx		%fp3,%fp0			| ...FP0 is A := R - P
+        faddx		%fp5,%fp4			| ...FP4 is p = (W-P)+w
+
+	fmovex		%fp0,%fp3			| ...FP3 A
+	fsubx		%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.
+	faddx		%fp1,%fp0			| ...FP0 is R := A+a
+|--No need to calculate r if this is the last loop
+	cmpil		#0,%d0
+	bgt		RESTORE
+
+|--Need to calculate r
+	fsubx		%fp0,%fp3			| ...A-R
+	faddx		%fp3,%fp1			| ...FP1 is r := (A-R)+a
+	bra		LOOP
+
+RESTORE:
+        fmovel		%fp2,N(%a6)
+	movel		(%a7)+,%d2
+	fmovemx	(%a7)+,%fp2-%fp5
+
+	
+	movel		ADJN(%a6),%d0
+	cmpil		#4,%d0
+
+	blt		SINCONT
+	bras		SCCONT
+
+	.global	ssincosd
+ssincosd:
+|--SIN AND COS OF X FOR DENORMALIZED X
+
+	fmoves		#0x3F800000,%fp1
+	bsr		sto_cos		|store cosine result
+	bra		t_extdnrm
+
+	.global	ssincos
+ssincos:
+|--SET ADJN TO 4
+	movel		#4,ADJN(%a6)
+
+	fmovex		(%a0),%fp0	| ...LOAD INPUT
+
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	fmovex		%fp0,X(%a6)
+	andil		#0x7FFFFFFF,%d0		| ...COMPACTIFY X
+
+	cmpil		#0x3FD78000,%d0		| ...|X| >= 2**(-40)?
+	bges		SCOK1
+	bra		SCSM
+
+SCOK1:
+	cmpil		#0x4004BC7E,%d0		| ...|X| < 15 PI?
+	blts		SCMAIN
+	bra		REDUCEX
+
+
+SCMAIN:
+|--THIS IS THE USUAL CASE, |X| <= 15 PI.
+|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
+	fmovex		%fp0,%fp1
+	fmuld		TWOBYPI,%fp1	| ...X*2/PI
+
+|--HIDE THE NEXT THREE INSTRUCTIONS
+	lea		PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
+	
+
+|--FP1 IS NOW READY
+	fmovel		%fp1,N(%a6)		| ...CONVERT TO INTEGER
+
+	movel		N(%a6),%d0
+	asll		#4,%d0
+	addal		%d0,%a1		| ...ADDRESS OF N*PIBY2, IN Y1, Y2
+
+	fsubx		(%a1)+,%fp0	| ...X-Y1
+        fsubs		(%a1),%fp0	| ...FP0 IS R = (X-Y1)-Y2
+
+SCCONT:
+|--continuation point from REDUCEX
+
+|--HIDE THE NEXT TWO
+	movel		N(%a6),%d0
+	rorl		#1,%d0
+	
+	cmpil		#0,%d0		| ...D0 < 0 IFF N IS ODD
+	bge		NEVEN
+
+NODD:
+|--REGISTERS SAVED SO FAR: D0, A0, FP2.
+
+	fmovex		%fp0,RPRIME(%a6)
+	fmulx		%fp0,%fp0	 | ...FP0 IS S = R*R
+	fmoved		SINA7,%fp1	| ...A7
+	fmoved		COSB8,%fp2	| ...B8
+	fmulx		%fp0,%fp1	 | ...SA7
+	movel		%d2,-(%a7)
+	movel		%d0,%d2
+	fmulx		%fp0,%fp2	 | ...SB8
+	rorl		#1,%d2
+	andil		#0x80000000,%d2
+
+	faddd		SINA6,%fp1	| ...A6+SA7
+	eorl		%d0,%d2
+	andil		#0x80000000,%d2
+	faddd		COSB7,%fp2	| ...B7+SB8
+
+	fmulx		%fp0,%fp1	 | ...S(A6+SA7)
+	eorl		%d2,RPRIME(%a6)
+	movel		(%a7)+,%d2
+	fmulx		%fp0,%fp2	 | ...S(B7+SB8)
+	rorl		#1,%d0
+	andil		#0x80000000,%d0
+
+	faddd		SINA5,%fp1	| ...A5+S(A6+SA7)
+	movel		#0x3F800000,POSNEG1(%a6)
+	eorl		%d0,POSNEG1(%a6)
+	faddd		COSB6,%fp2	| ...B6+S(B7+SB8)
+
+	fmulx		%fp0,%fp1	 | ...S(A5+S(A6+SA7))
+	fmulx		%fp0,%fp2	 | ...S(B6+S(B7+SB8))
+	fmovex		%fp0,SPRIME(%a6)
+
+	faddd		SINA4,%fp1	| ...A4+S(A5+S(A6+SA7))
+	eorl		%d0,SPRIME(%a6)
+	faddd		COSB5,%fp2	| ...B5+S(B6+S(B7+SB8))
+
+	fmulx		%fp0,%fp1	 | ...S(A4+...)
+	fmulx		%fp0,%fp2	 | ...S(B5+...)
+
+	faddd		SINA3,%fp1	| ...A3+S(A4+...)
+	faddd		COSB4,%fp2	| ...B4+S(B5+...)
+
+	fmulx		%fp0,%fp1	 | ...S(A3+...)
+	fmulx		%fp0,%fp2	 | ...S(B4+...)
+
+	faddx		SINA2,%fp1	| ...A2+S(A3+...)
+	faddx		COSB3,%fp2	| ...B3+S(B4+...)
+
+	fmulx		%fp0,%fp1	 | ...S(A2+...)
+	fmulx		%fp0,%fp2	 | ...S(B3+...)
+
+	faddx		SINA1,%fp1	| ...A1+S(A2+...)
+	faddx		COSB2,%fp2	| ...B2+S(B3+...)
+
+	fmulx		%fp0,%fp1	 | ...S(A1+...)
+	fmulx		%fp2,%fp0	 | ...S(B2+...)
+
+	
+
+	fmulx		RPRIME(%a6),%fp1	| ...R'S(A1+...)
+	fadds		COSB1,%fp0	| ...B1+S(B2...)
+	fmulx		SPRIME(%a6),%fp0	| ...S'(B1+S(B2+...))
+
+	movel		%d1,-(%sp)	|restore users mode & precision
+	andil		#0xff,%d1		|mask off all exceptions
+	fmovel		%d1,%FPCR
+	faddx		RPRIME(%a6),%fp1	| ...COS(X)
+	bsr		sto_cos		|store cosine result
+	fmovel		(%sp)+,%FPCR	|restore users exceptions
+	fadds		POSNEG1(%a6),%fp0	| ...SIN(X)
+
+	bra		t_frcinx
+
+
+NEVEN:
+|--REGISTERS SAVED SO FAR: FP2.
+
+	fmovex		%fp0,RPRIME(%a6)
+	fmulx		%fp0,%fp0	 | ...FP0 IS S = R*R
+	fmoved		COSB8,%fp1			| ...B8
+	fmoved		SINA7,%fp2			| ...A7
+	fmulx		%fp0,%fp1	 | ...SB8
+	fmovex		%fp0,SPRIME(%a6)
+	fmulx		%fp0,%fp2	 | ...SA7
+	rorl		#1,%d0
+	andil		#0x80000000,%d0
+	faddd		COSB7,%fp1	| ...B7+SB8
+	faddd		SINA6,%fp2	| ...A6+SA7
+	eorl		%d0,RPRIME(%a6)
+	eorl		%d0,SPRIME(%a6)
+	fmulx		%fp0,%fp1	 | ...S(B7+SB8)
+	oril		#0x3F800000,%d0
+	movel		%d0,POSNEG1(%a6)
+	fmulx		%fp0,%fp2	 | ...S(A6+SA7)
+
+	faddd		COSB6,%fp1	| ...B6+S(B7+SB8)
+	faddd		SINA5,%fp2	| ...A5+S(A6+SA7)
+
+	fmulx		%fp0,%fp1	 | ...S(B6+S(B7+SB8))
+	fmulx		%fp0,%fp2	 | ...S(A5+S(A6+SA7))
+
+	faddd		COSB5,%fp1	| ...B5+S(B6+S(B7+SB8))
+	faddd		SINA4,%fp2	| ...A4+S(A5+S(A6+SA7))
+
+	fmulx		%fp0,%fp1	 | ...S(B5+...)
+	fmulx		%fp0,%fp2	 | ...S(A4+...)
+
+	faddd		COSB4,%fp1	| ...B4+S(B5+...)
+	faddd		SINA3,%fp2	| ...A3+S(A4+...)
+
+	fmulx		%fp0,%fp1	 | ...S(B4+...)
+	fmulx		%fp0,%fp2	 | ...S(A3+...)
+
+	faddx		COSB3,%fp1	| ...B3+S(B4+...)
+	faddx		SINA2,%fp2	| ...A2+S(A3+...)
+
+	fmulx		%fp0,%fp1	 | ...S(B3+...)
+	fmulx		%fp0,%fp2	 | ...S(A2+...)
+
+	faddx		COSB2,%fp1	| ...B2+S(B3+...)
+	faddx		SINA1,%fp2	| ...A1+S(A2+...)
+
+	fmulx		%fp0,%fp1	 | ...S(B2+...)
+	fmulx		%fp2,%fp0	 | ...s(a1+...)
+
+	
+
+	fadds		COSB1,%fp1	| ...B1+S(B2...)
+	fmulx		RPRIME(%a6),%fp0	| ...R'S(A1+...)
+	fmulx		SPRIME(%a6),%fp1	| ...S'(B1+S(B2+...))
+
+	movel		%d1,-(%sp)	|save users mode & precision
+	andil		#0xff,%d1		|mask off all exceptions
+	fmovel		%d1,%FPCR
+	fadds		POSNEG1(%a6),%fp1	| ...COS(X)
+	bsr		sto_cos		|store cosine result
+	fmovel		(%sp)+,%FPCR	|restore users exceptions
+	faddx		RPRIME(%a6),%fp0	| ...SIN(X)
+
+	bra		t_frcinx
+
+SCBORS:
+	cmpil		#0x3FFF8000,%d0
+	bgt		REDUCEX
+        
+
+SCSM:
+	movew		#0x0000,XDCARE(%a6)
+	fmoves		#0x3F800000,%fp1
+
+	movel		%d1,-(%sp)	|save users mode & precision
+	andil		#0xff,%d1		|mask off all exceptions
+	fmovel		%d1,%FPCR
+	fsubs		#0x00800000,%fp1
+	bsr		sto_cos		|store cosine result
+	fmovel		(%sp)+,%FPCR	|restore users exceptions
+	fmovex		X(%a6),%fp0
+	bra		t_frcinx
+
+	|end
FUNET's LINUX-ADM group, linux-adm@nic.funet.fi
TCL-scripts by Sam Shen, slshen@lbl.gov with Sam's (original) version
of this