CoCalc -- ssin.S

GitHub Repository: awilliam/linux-vfio
Path: blob/master/arch/m68k/fpsp040/ssin.S
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|
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|	ssin.sa 3.3 7/29/91
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|
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|	The entry point sSIN computes the sine of an input argument
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|	sCOS computes the cosine, and sSINCOS computes both. The
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|	corresponding entry points with a "d" computes the same
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|	corresponding function values for denormalized inputs.
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|
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|	Input: Double-extended number X in location pointed to
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|		by address register a0.
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|
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|	Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or
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|		COS is requested. Otherwise, for SINCOS, sin(X) is returned
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|		in Fp0, and cos(X) is returned in Fp1.
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|
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|	Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS.
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|
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|	Accuracy and Monotonicity: The returned result is within 1 ulp in
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|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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|		result is subsequently rounded to double precision. The
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|		result is provably monotonic in double precision.
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|
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|	Speed: The programs sSIN and sCOS take approximately 150 cycles for
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|		input argument X such that |X| < 15Pi, which is the usual
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|		situation. The speed for sSINCOS is approximately 190 cycles.
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|
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|	Algorithm:
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|
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|	SIN and COS:
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|	1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1.
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|
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|	2. If |X| >= 15Pi or |X| < 2**(-40), go to 7.
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|
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|	3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
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|		k = N mod 4, so in particular, k = 0,1,2,or 3. Overwrite
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|		k by k := k + AdjN.
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|
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|	4. If k is even, go to 6.
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|
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|	5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r)
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|		where cos(r) is approximated by an even polynomial in r,
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|		1 + r*r*(B1+s*(B2+ ... + s*B8)),	s = r*r.
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|		Exit.
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|
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|	6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r)
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|		where sin(r) is approximated by an odd polynomial in r
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|		r + r*s*(A1+s*(A2+ ... + s*A7)),	s = r*r.
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|		Exit.
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|
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|	7. If |X| > 1, go to 9.
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|
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|	8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1.
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|
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|	9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3.
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|
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|	SINCOS:
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|	1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
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|
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|	2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
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|		k = N mod 4, so in particular, k = 0,1,2,or 3.
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|
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|	3. If k is even, go to 5.
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|
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|	4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e.
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|		j1 exclusive or with the l.s.b. of k.
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|		sgn1 := (-1)**j1, sgn2 := (-1)**j2.
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|		SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where
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|		sin(r) and cos(r) are computed as odd and even polynomials
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|		in r, respectively. Exit
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|
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|	5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1.
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|		SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where
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|		sin(r) and cos(r) are computed as odd and even polynomials
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|		in r, respectively. Exit
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|
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|	6. If |X| > 1, go to 8.
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|
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|	7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit.
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|
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|	8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
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|
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|		Copyright (C) Motorola, Inc. 1990
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|			All Rights Reserved
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|
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|       For details on the license for this file, please see the
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|       file, README, in this same directory.
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|SSIN	idnt	2,1 | Motorola 040 Floating Point Software Package
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	|section	8
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#include "fpsp.h"
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BOUNDS1:	.long 0x3FD78000,0x4004BC7E
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TWOBYPI:	.long 0x3FE45F30,0x6DC9C883
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SINA7:	.long 0xBD6AAA77,0xCCC994F5
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SINA6:	.long 0x3DE61209,0x7AAE8DA1
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SINA5:	.long 0xBE5AE645,0x2A118AE4
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SINA4:	.long 0x3EC71DE3,0xA5341531
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SINA3:	.long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
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SINA2:	.long 0x3FF80000,0x88888888,0x888859AF,0x00000000
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SINA1:	.long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
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COSB8:	.long 0x3D2AC4D0,0xD6011EE3
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COSB7:	.long 0xBDA9396F,0x9F45AC19
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COSB6:	.long 0x3E21EED9,0x0612C972
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COSB5:	.long 0xBE927E4F,0xB79D9FCF
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COSB4:	.long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
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COSB3:	.long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
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COSB2:	.long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
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COSB1:	.long 0xBF000000
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INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A
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TWOPI1:	.long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
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TWOPI2:	.long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
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	|xref	PITBL
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	.set	INARG,FP_SCR4
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	.set	X,FP_SCR5
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	.set	XDCARE,X+2
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	.set	XFRAC,X+4
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	.set	RPRIME,FP_SCR1
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	.set	SPRIME,FP_SCR2
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	.set	POSNEG1,L_SCR1
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	.set	TWOTO63,L_SCR1
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	.set	ENDFLAG,L_SCR2
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	.set	N,L_SCR2
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	.set	ADJN,L_SCR3
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	| xref	t_frcinx
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	|xref	t_extdnrm
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	|xref	sto_cos
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	.global	ssind
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ssind:
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|--SIN(X) = X FOR DENORMALIZED X
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	bra		t_extdnrm
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	.global	scosd
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scosd:
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|--COS(X) = 1 FOR DENORMALIZED X
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	fmoves		#0x3F800000,%fp0
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|
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|	9D25B Fix: Sometimes the previous fmove.s sets fpsr bits
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|
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	fmovel		#0,%fpsr
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|
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	bra		t_frcinx
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	.global	ssin
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ssin:
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|--SET ADJN TO 0
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	movel		#0,ADJN(%a6)
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	bras		SINBGN
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	.global	scos
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scos:
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|--SET ADJN TO 1
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	movel		#1,ADJN(%a6)
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SINBGN:
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|--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
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	fmovex		(%a0),%fp0	| ...LOAD INPUT
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	movel		(%a0),%d0
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	movew		4(%a0),%d0
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	fmovex		%fp0,X(%a6)
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	andil		#0x7FFFFFFF,%d0		| ...COMPACTIFY X
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	cmpil		#0x3FD78000,%d0		| ...|X| >= 2**(-40)?
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	bges		SOK1
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	bra		SINSM
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SOK1:
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	cmpil		#0x4004BC7E,%d0		| ...|X| < 15 PI?
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	blts		SINMAIN
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	bra		REDUCEX
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SINMAIN:
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|--THIS IS THE USUAL CASE, |X| <= 15 PI.
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|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
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	fmovex		%fp0,%fp1
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	fmuld		TWOBYPI,%fp1	| ...X*2/PI
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|--HIDE THE NEXT THREE INSTRUCTIONS
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	lea		PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
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207

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|--FP1 IS NOW READY
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	fmovel		%fp1,N(%a6)		| ...CONVERT TO INTEGER
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	movel		N(%a6),%d0
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	asll		#4,%d0
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	addal		%d0,%a1	| ...A1 IS THE ADDRESS OF N*PIBY2
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|				...WHICH IS IN TWO PIECES Y1 & Y2
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	fsubx		(%a1)+,%fp0	| ...X-Y1
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|--HIDE THE NEXT ONE
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	fsubs		(%a1),%fp0	| ...FP0 IS R = (X-Y1)-Y2
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SINCONT:
221
|--continuation from REDUCEX
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|--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
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	movel		N(%a6),%d0
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	addl		ADJN(%a6),%d0	| ...SEE IF D0 IS ODD OR EVEN
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	rorl		#1,%d0	| ...D0 WAS ODD IFF D0 IS NEGATIVE
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	cmpil		#0,%d0
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	blt		COSPOLY
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SINPOLY:
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|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
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|--THEN WE RETURN	SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
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|--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
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|--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
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|--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
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|--WHERE T=S*S.
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|--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
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|--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
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	fmovex		%fp0,X(%a6)	| ...X IS R
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	fmulx		%fp0,%fp0	| ...FP0 IS S
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|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
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	fmoved		SINA7,%fp3
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	fmoved		SINA6,%fp2
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|--FP0 IS NOW READY
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	fmovex		%fp0,%fp1
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	fmulx		%fp1,%fp1	| ...FP1 IS T
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|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
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	rorl		#1,%d0
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	andil		#0x80000000,%d0
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|				...LEAST SIG. BIT OF D0 IN SIGN POSITION
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	eorl		%d0,X(%a6)	| ...X IS NOW R'= SGN*R
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	fmulx		%fp1,%fp3	| ...TA7
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	fmulx		%fp1,%fp2	| ...TA6
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	faddd		SINA5,%fp3 | ...A5+TA7
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	faddd		SINA4,%fp2 | ...A4+TA6
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	fmulx		%fp1,%fp3	| ...T(A5+TA7)
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	fmulx		%fp1,%fp2	| ...T(A4+TA6)
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	faddd		SINA3,%fp3 | ...A3+T(A5+TA7)
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	faddx		SINA2,%fp2 | ...A2+T(A4+TA6)
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	fmulx		%fp3,%fp1	| ...T(A3+T(A5+TA7))
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	fmulx		%fp0,%fp2	| ...S(A2+T(A4+TA6))
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	faddx		SINA1,%fp1 | ...A1+T(A3+T(A5+TA7))
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	fmulx		X(%a6),%fp0	| ...R'*S
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	faddx		%fp2,%fp1	| ...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
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|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
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|--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING
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	fmulx		%fp1,%fp0		| ...SIN(R')-R'
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|--FP1 RELEASED.
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	fmovel		%d1,%FPCR		|restore users exceptions
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	faddx		X(%a6),%fp0		|last inst - possible exception set
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	bra		t_frcinx
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COSPOLY:
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|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
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|--THEN WE RETURN	SGN*COS(R). SGN*COS(R) IS COMPUTED BY
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|--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
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|--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
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|--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
291
|--WHERE T=S*S.
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|--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
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|--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
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|--AND IS THEREFORE STORED AS SINGLE PRECISION.
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	fmulx		%fp0,%fp0	| ...FP0 IS S
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|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
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	fmoved		COSB8,%fp2
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	fmoved		COSB7,%fp3
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|--FP0 IS NOW READY
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	fmovex		%fp0,%fp1
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	fmulx		%fp1,%fp1	| ...FP1 IS T
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|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
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	fmovex		%fp0,X(%a6)	| ...X IS S
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	rorl		#1,%d0
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	andil		#0x80000000,%d0
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|			...LEAST SIG. BIT OF D0 IN SIGN POSITION
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	fmulx		%fp1,%fp2	| ...TB8
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|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
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	eorl		%d0,X(%a6)	| ...X IS NOW S'= SGN*S
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	andil		#0x80000000,%d0
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	fmulx		%fp1,%fp3	| ...TB7
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|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
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	oril		#0x3F800000,%d0	| ...D0 IS SGN IN SINGLE
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	movel		%d0,POSNEG1(%a6)
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	faddd		COSB6,%fp2 | ...B6+TB8
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	faddd		COSB5,%fp3 | ...B5+TB7
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	fmulx		%fp1,%fp2	| ...T(B6+TB8)
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	fmulx		%fp1,%fp3	| ...T(B5+TB7)
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	faddd		COSB4,%fp2 | ...B4+T(B6+TB8)
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	faddx		COSB3,%fp3 | ...B3+T(B5+TB7)
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328
	fmulx		%fp1,%fp2	| ...T(B4+T(B6+TB8))
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	fmulx		%fp3,%fp1	| ...T(B3+T(B5+TB7))
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	faddx		COSB2,%fp2 | ...B2+T(B4+T(B6+TB8))
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	fadds		COSB1,%fp1 | ...B1+T(B3+T(B5+TB7))
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	fmulx		%fp2,%fp0	| ...S(B2+T(B4+T(B6+TB8)))
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|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
336
|--FP2 RELEASED.
337

338

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	faddx		%fp1,%fp0
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|--FP1 RELEASED
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	fmulx		X(%a6),%fp0
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	fmovel		%d1,%FPCR		|restore users exceptions
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	fadds		POSNEG1(%a6),%fp0	|last inst - possible exception set
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	bra		t_frcinx
347

348

349
SINBORS:
350
|--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
351
|--IF |X| < 2**(-40), RETURN X OR 1.
352
	cmpil		#0x3FFF8000,%d0
353
	bgts		REDUCEX
354

355

356
SINSM:
357
	movel		ADJN(%a6),%d0
358
	cmpil		#0,%d0
359
	bgts		COSTINY
360

361
SINTINY:
362
	movew		#0x0000,XDCARE(%a6)	| ...JUST IN CASE
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	fmovel		%d1,%FPCR		|restore users exceptions
364
	fmovex		X(%a6),%fp0		|last inst - possible exception set
365
	bra		t_frcinx
366

367

368
COSTINY:
369
	fmoves		#0x3F800000,%fp0
370

371
	fmovel		%d1,%FPCR		|restore users exceptions
372
	fsubs		#0x00800000,%fp0	|last inst - possible exception set
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	bra		t_frcinx
374

375

376
REDUCEX:
377
|--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
378
|--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
379
|--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
380

381
	fmovemx	%fp2-%fp5,-(%a7)	| ...save FP2 through FP5
382
	movel		%d2,-(%a7)
383
        fmoves         #0x00000000,%fp1
384
|--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
385
|--there is a danger of unwanted overflow in first LOOP iteration.  In this
386
|--case, reduce argument by one remainder step to make subsequent reduction
387
|--safe.
388
	cmpil	#0x7ffeffff,%d0		|is argument dangerously large?
389
	bnes	LOOP
390
	movel	#0x7ffe0000,FP_SCR2(%a6)	|yes
391
|					;create 2**16383*PI/2
392
	movel	#0xc90fdaa2,FP_SCR2+4(%a6)
393
	clrl	FP_SCR2+8(%a6)
394
	ftstx	%fp0			|test sign of argument
395
	movel	#0x7fdc0000,FP_SCR3(%a6)	|create low half of 2**16383*
396
|					;PI/2 at FP_SCR3
397
	movel	#0x85a308d3,FP_SCR3+4(%a6)
398
	clrl   FP_SCR3+8(%a6)
399
	fblt	red_neg
400
	orw	#0x8000,FP_SCR2(%a6)	|positive arg
401
	orw	#0x8000,FP_SCR3(%a6)
402
red_neg:
403
	faddx  FP_SCR2(%a6),%fp0		|high part of reduction is exact
404
	fmovex  %fp0,%fp1		|save high result in fp1
405
	faddx  FP_SCR3(%a6),%fp0		|low part of reduction
406
	fsubx  %fp0,%fp1			|determine low component of result
407
	faddx  FP_SCR3(%a6),%fp1		|fp0/fp1 are reduced argument.
408

409
|--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
410
|--integer quotient will be stored in N
411
|--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1)
412

413
LOOP:
414
	fmovex		%fp0,INARG(%a6)	| ...+-2**K * F, 1 <= F < 2
415
	movew		INARG(%a6),%d0
416
        movel          %d0,%a1		| ...save a copy of D0
417
	andil		#0x00007FFF,%d0
418
	subil		#0x00003FFF,%d0	| ...D0 IS K
419
	cmpil		#28,%d0
420
	bles		LASTLOOP
421
CONTLOOP:
422
	subil		#27,%d0	 | ...D0 IS L := K-27
423
	movel		#0,ENDFLAG(%a6)
424
	bras		WORK
425
LASTLOOP:
426
	clrl		%d0		| ...D0 IS L := 0
427
	movel		#1,ENDFLAG(%a6)
428

429
WORK:
430
|--FIND THE REMAINDER OF (R,r) W.R.T.	2**L * (PI/2). L IS SO CHOSEN
431
|--THAT	INT( X * (2/PI) / 2**(L) ) < 2**29.
432

433
|--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
434
|--2**L * (PIby2_1), 2**L * (PIby2_2)
435

436
	movel		#0x00003FFE,%d2	| ...BIASED EXPO OF 2/PI
437
	subl		%d0,%d2		| ...BIASED EXPO OF 2**(-L)*(2/PI)
438

439
	movel		#0xA2F9836E,FP_SCR1+4(%a6)
440
	movel		#0x4E44152A,FP_SCR1+8(%a6)
441
	movew		%d2,FP_SCR1(%a6)	| ...FP_SCR1 is 2**(-L)*(2/PI)
442

443
	fmovex		%fp0,%fp2
444
	fmulx		FP_SCR1(%a6),%fp2
445
|--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
446
|--FLOATING POINT FORMAT, THE TWO FMOVE'S	FMOVE.L FP <--> N
447
|--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
448
|--(SIGN(INARG)*2**63	+	FP2) - SIGN(INARG)*2**63 WILL GIVE
449
|--US THE DESIRED VALUE IN FLOATING POINT.
450

451
|--HIDE SIX CYCLES OF INSTRUCTION
452
        movel		%a1,%d2
453
        swap		%d2
454
	andil		#0x80000000,%d2
455
	oril		#0x5F000000,%d2	| ...D2 IS SIGN(INARG)*2**63 IN SGL
456
	movel		%d2,TWOTO63(%a6)
457

458
	movel		%d0,%d2
459
	addil		#0x00003FFF,%d2	| ...BIASED EXPO OF 2**L * (PI/2)
460

461
|--FP2 IS READY
462
	fadds		TWOTO63(%a6),%fp2	| ...THE FRACTIONAL PART OF FP1 IS ROUNDED
463

464
|--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1  and  2**(L)*Piby2_2
465
        movew		%d2,FP_SCR2(%a6)
466
	clrw           FP_SCR2+2(%a6)
467
	movel		#0xC90FDAA2,FP_SCR2+4(%a6)
468
	clrl		FP_SCR2+8(%a6)		| ...FP_SCR2 is  2**(L) * Piby2_1
469

470
|--FP2 IS READY
471
	fsubs		TWOTO63(%a6),%fp2		| ...FP2 is N
472

473
	addil		#0x00003FDD,%d0
474
        movew		%d0,FP_SCR3(%a6)
475
	clrw           FP_SCR3+2(%a6)
476
	movel		#0x85A308D3,FP_SCR3+4(%a6)
477
	clrl		FP_SCR3+8(%a6)		| ...FP_SCR3 is 2**(L) * Piby2_2
478

479
	movel		ENDFLAG(%a6),%d0
480

481
|--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
482
|--P2 = 2**(L) * Piby2_2
483
	fmovex		%fp2,%fp4
484
	fmulx		FP_SCR2(%a6),%fp4		| ...W = N*P1
485
	fmovex		%fp2,%fp5
486
	fmulx		FP_SCR3(%a6),%fp5		| ...w = N*P2
487
	fmovex		%fp4,%fp3
488
|--we want P+p = W+w  but  |p| <= half ulp of P
489
|--Then, we need to compute  A := R-P   and  a := r-p
490
	faddx		%fp5,%fp3			| ...FP3 is P
491
	fsubx		%fp3,%fp4			| ...W-P
492

493
	fsubx		%fp3,%fp0			| ...FP0 is A := R - P
494
        faddx		%fp5,%fp4			| ...FP4 is p = (W-P)+w
495

496
	fmovex		%fp0,%fp3			| ...FP3 A
497
	fsubx		%fp4,%fp1			| ...FP1 is a := r - p
498

499
|--Now we need to normalize (A,a) to  "new (R,r)" where R+r = A+a but
500
|--|r| <= half ulp of R.
501
	faddx		%fp1,%fp0			| ...FP0 is R := A+a
502
|--No need to calculate r if this is the last loop
503
	cmpil		#0,%d0
504
	bgt		RESTORE
505

506
|--Need to calculate r
507
	fsubx		%fp0,%fp3			| ...A-R
508
	faddx		%fp3,%fp1			| ...FP1 is r := (A-R)+a
509
	bra		LOOP
510

511
RESTORE:
512
        fmovel		%fp2,N(%a6)
513
	movel		(%a7)+,%d2
514
	fmovemx	(%a7)+,%fp2-%fp5
515

516

517
	movel		ADJN(%a6),%d0
518
	cmpil		#4,%d0
519

520
	blt		SINCONT
521
	bras		SCCONT
522

523
	.global	ssincosd
524
ssincosd:
525
|--SIN AND COS OF X FOR DENORMALIZED X
526

527
	fmoves		#0x3F800000,%fp1
528
	bsr		sto_cos		|store cosine result
529
	bra		t_extdnrm
530

531
	.global	ssincos
532
ssincos:
533
|--SET ADJN TO 4
534
	movel		#4,ADJN(%a6)
535

536
	fmovex		(%a0),%fp0	| ...LOAD INPUT
537

538
	movel		(%a0),%d0
539
	movew		4(%a0),%d0
540
	fmovex		%fp0,X(%a6)
541
	andil		#0x7FFFFFFF,%d0		| ...COMPACTIFY X
542

543
	cmpil		#0x3FD78000,%d0		| ...|X| >= 2**(-40)?
544
	bges		SCOK1
545
	bra		SCSM
546

547
SCOK1:
548
	cmpil		#0x4004BC7E,%d0		| ...|X| < 15 PI?
549
	blts		SCMAIN
550
	bra		REDUCEX
551

552

553
SCMAIN:
554
|--THIS IS THE USUAL CASE, |X| <= 15 PI.
555
|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
556
	fmovex		%fp0,%fp1
557
	fmuld		TWOBYPI,%fp1	| ...X*2/PI
558

559
|--HIDE THE NEXT THREE INSTRUCTIONS
560
	lea		PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
561

562

563
|--FP1 IS NOW READY
564
	fmovel		%fp1,N(%a6)		| ...CONVERT TO INTEGER
565

566
	movel		N(%a6),%d0
567
	asll		#4,%d0
568
	addal		%d0,%a1		| ...ADDRESS OF N*PIBY2, IN Y1, Y2
569

570
	fsubx		(%a1)+,%fp0	| ...X-Y1
571
        fsubs		(%a1),%fp0	| ...FP0 IS R = (X-Y1)-Y2
572

573
SCCONT:
574
|--continuation point from REDUCEX
575

576
|--HIDE THE NEXT TWO
577
	movel		N(%a6),%d0
578
	rorl		#1,%d0
579

580
	cmpil		#0,%d0		| ...D0 < 0 IFF N IS ODD
581
	bge		NEVEN
582

583
NODD:
584
|--REGISTERS SAVED SO FAR: D0, A0, FP2.
585

586
	fmovex		%fp0,RPRIME(%a6)
587
	fmulx		%fp0,%fp0	 | ...FP0 IS S = R*R
588
	fmoved		SINA7,%fp1	| ...A7
589
	fmoved		COSB8,%fp2	| ...B8
590
	fmulx		%fp0,%fp1	 | ...SA7
591
	movel		%d2,-(%a7)
592
	movel		%d0,%d2
593
	fmulx		%fp0,%fp2	 | ...SB8
594
	rorl		#1,%d2
595
	andil		#0x80000000,%d2
596

597
	faddd		SINA6,%fp1	| ...A6+SA7
598
	eorl		%d0,%d2
599
	andil		#0x80000000,%d2
600
	faddd		COSB7,%fp2	| ...B7+SB8
601

602
	fmulx		%fp0,%fp1	 | ...S(A6+SA7)
603
	eorl		%d2,RPRIME(%a6)
604
	movel		(%a7)+,%d2
605
	fmulx		%fp0,%fp2	 | ...S(B7+SB8)
606
	rorl		#1,%d0
607
	andil		#0x80000000,%d0
608

609
	faddd		SINA5,%fp1	| ...A5+S(A6+SA7)
610
	movel		#0x3F800000,POSNEG1(%a6)
611
	eorl		%d0,POSNEG1(%a6)
612
	faddd		COSB6,%fp2	| ...B6+S(B7+SB8)
613

614
	fmulx		%fp0,%fp1	 | ...S(A5+S(A6+SA7))
615
	fmulx		%fp0,%fp2	 | ...S(B6+S(B7+SB8))
616
	fmovex		%fp0,SPRIME(%a6)
617

618
	faddd		SINA4,%fp1	| ...A4+S(A5+S(A6+SA7))
619
	eorl		%d0,SPRIME(%a6)
620
	faddd		COSB5,%fp2	| ...B5+S(B6+S(B7+SB8))
621

622
	fmulx		%fp0,%fp1	 | ...S(A4+...)
623
	fmulx		%fp0,%fp2	 | ...S(B5+...)
624

625
	faddd		SINA3,%fp1	| ...A3+S(A4+...)
626
	faddd		COSB4,%fp2	| ...B4+S(B5+...)
627

628
	fmulx		%fp0,%fp1	 | ...S(A3+...)
629
	fmulx		%fp0,%fp2	 | ...S(B4+...)
630

631
	faddx		SINA2,%fp1	| ...A2+S(A3+...)
632
	faddx		COSB3,%fp2	| ...B3+S(B4+...)
633

634
	fmulx		%fp0,%fp1	 | ...S(A2+...)
635
	fmulx		%fp0,%fp2	 | ...S(B3+...)
636

637
	faddx		SINA1,%fp1	| ...A1+S(A2+...)
638
	faddx		COSB2,%fp2	| ...B2+S(B3+...)
639

640
	fmulx		%fp0,%fp1	 | ...S(A1+...)
641
	fmulx		%fp2,%fp0	 | ...S(B2+...)
642

643

644

645
	fmulx		RPRIME(%a6),%fp1	| ...R'S(A1+...)
646
	fadds		COSB1,%fp0	| ...B1+S(B2...)
647
	fmulx		SPRIME(%a6),%fp0	| ...S'(B1+S(B2+...))
648

649
	movel		%d1,-(%sp)	|restore users mode & precision
650
	andil		#0xff,%d1		|mask off all exceptions
651
	fmovel		%d1,%FPCR
652
	faddx		RPRIME(%a6),%fp1	| ...COS(X)
653
	bsr		sto_cos		|store cosine result
654
	fmovel		(%sp)+,%FPCR	|restore users exceptions
655
	fadds		POSNEG1(%a6),%fp0	| ...SIN(X)
656

657
	bra		t_frcinx
658

659

660
NEVEN:
661
|--REGISTERS SAVED SO FAR: FP2.
662

663
	fmovex		%fp0,RPRIME(%a6)
664
	fmulx		%fp0,%fp0	 | ...FP0 IS S = R*R
665
	fmoved		COSB8,%fp1			| ...B8
666
	fmoved		SINA7,%fp2			| ...A7
667
	fmulx		%fp0,%fp1	 | ...SB8
668
	fmovex		%fp0,SPRIME(%a6)
669
	fmulx		%fp0,%fp2	 | ...SA7
670
	rorl		#1,%d0
671
	andil		#0x80000000,%d0
672
	faddd		COSB7,%fp1	| ...B7+SB8
673
	faddd		SINA6,%fp2	| ...A6+SA7
674
	eorl		%d0,RPRIME(%a6)
675
	eorl		%d0,SPRIME(%a6)
676
	fmulx		%fp0,%fp1	 | ...S(B7+SB8)
677
	oril		#0x3F800000,%d0
678
	movel		%d0,POSNEG1(%a6)
679
	fmulx		%fp0,%fp2	 | ...S(A6+SA7)
680

681
	faddd		COSB6,%fp1	| ...B6+S(B7+SB8)
682
	faddd		SINA5,%fp2	| ...A5+S(A6+SA7)
683

684
	fmulx		%fp0,%fp1	 | ...S(B6+S(B7+SB8))
685
	fmulx		%fp0,%fp2	 | ...S(A5+S(A6+SA7))
686

687
	faddd		COSB5,%fp1	| ...B5+S(B6+S(B7+SB8))
688
	faddd		SINA4,%fp2	| ...A4+S(A5+S(A6+SA7))
689

690
	fmulx		%fp0,%fp1	 | ...S(B5+...)
691
	fmulx		%fp0,%fp2	 | ...S(A4+...)
692

693
	faddd		COSB4,%fp1	| ...B4+S(B5+...)
694
	faddd		SINA3,%fp2	| ...A3+S(A4+...)
695

696
	fmulx		%fp0,%fp1	 | ...S(B4+...)
697
	fmulx		%fp0,%fp2	 | ...S(A3+...)
698

699
	faddx		COSB3,%fp1	| ...B3+S(B4+...)
700
	faddx		SINA2,%fp2	| ...A2+S(A3+...)
701

702
	fmulx		%fp0,%fp1	 | ...S(B3+...)
703
	fmulx		%fp0,%fp2	 | ...S(A2+...)
704

705
	faddx		COSB2,%fp1	| ...B2+S(B3+...)
706
	faddx		SINA1,%fp2	| ...A1+S(A2+...)
707

708
	fmulx		%fp0,%fp1	 | ...S(B2+...)
709
	fmulx		%fp2,%fp0	 | ...s(a1+...)
710

711

712

713
	fadds		COSB1,%fp1	| ...B1+S(B2...)
714
	fmulx		RPRIME(%a6),%fp0	| ...R'S(A1+...)
715
	fmulx		SPRIME(%a6),%fp1	| ...S'(B1+S(B2+...))
716

717
	movel		%d1,-(%sp)	|save users mode & precision
718
	andil		#0xff,%d1		|mask off all exceptions
719
	fmovel		%d1,%FPCR
720
	fadds		POSNEG1(%a6),%fp1	| ...COS(X)
721
	bsr		sto_cos		|store cosine result
722
	fmovel		(%sp)+,%FPCR	|restore users exceptions
723
	faddx		RPRIME(%a6),%fp0	| ...SIN(X)
724

725
	bra		t_frcinx
726

727
SCBORS:
728
	cmpil		#0x3FFF8000,%d0
729
	bgt		REDUCEX
730

731

732
SCSM:
733
	movew		#0x0000,XDCARE(%a6)
734
	fmoves		#0x3F800000,%fp1
735

736
	movel		%d1,-(%sp)	|save users mode & precision
737
	andil		#0xff,%d1		|mask off all exceptions
738
	fmovel		%d1,%FPCR
739
	fsubs		#0x00800000,%fp1
740
	bsr		sto_cos		|store cosine result
741
	fmovel		(%sp)+,%FPCR	|restore users exceptions
742
	fmovex		X(%a6),%fp0
743
	bra		t_frcinx
744

745
	|end
746

747
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