l_ssin.s

VXWORKS源代码

SINTINY:
	movew		#0x0000,a6@(XDCARE)	|...JUST IN CASE
	fmovel		d1,fpcr			| restore users exceptions
	fmovex		a6@(X),fp0		| last inst - possible exception set
	jra 		__l_t_frcinx


COSTINY:
	.long 0xf23c4400,0x3f800000	 /*	fmoves	&0x3F800000,fp0 */


	fmovel		d1,fpcr		| restore users exceptions
	.long 0xf23c4428,0x00800000	 /*	fsubs	&0x00800000,fp0 */
	jra 		__l_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@-
	.long 0xf23c4480,0x00000000	/*	fmoves	&0x00000000,fp1 */

|--If compact form of abs(arg) in d0=0x7ffeffff, 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?
	jne 	LOOP
	movel	#0x7ffe0000,a6@(FP_SCR2)	| yes
|						| create 2**16383*PI/2
	movel	#0xc90fdaa2,a6@(FP_SCR2+4)
	clrl	a6@(FP_SCR2+8)
	ftstx	fp0				| test sign of argument
	movel	#0x7fdc0000,a6@(FP_SCR3)	| create low half of 2**16383*
|						| PI/2 at FP_SCR3
	movel	#0x85a308d3,a6@(FP_SCR3+4)
	clrl  	a6@(FP_SCR3+8)
	fblt	red_neg
	orw	#0x8000,a6@(FP_SCR2)		| positive arg
	orw	#0x8000,a6@(FP_SCR3)
red_neg:
	faddx 	a6@(FP_SCR2),fp0	| high part of reduction is exact
	fmovex  fp0,fp1			| save high result in fp1
	faddx 	a6@(FP_SCR3),fp0	| low part of reduction
	fsubx   fp0,fp1			| determine low component of result
	faddx 	a6@(FP_SCR3),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,a6@(INARG)	|...+-2**K * F, 1 <= F < 2
	movew		a6@(INARG),d0
        movel          d0,a1		|...save a copy of d0
	andil		#0x00007FFF,d0
	subil		#0x00003FFF,d0	|...D0 IS K
	cmpil		#28,d0
	jle 		LASTLOOP
CONTLOOP:
	subil		#27,d0	 |...D0 IS L := K-27
	movel		#0,a6@(ENDFLAG)
	jra 		WORK
LASTLOOP:
	clrl		d0		|...D0 IS L := 0
	movel		#1,a6@(ENDFLAG)

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,a6@(FP_SCR1+4)
	movel		#0x4E44152A,a6@(FP_SCR1+8)
	movew		d2,a6@(FP_SCR1)	|...FP_SCR1 is 2**(-L)*(2/PI)

	fmovex		fp0,fp2
	fmulx		a6@(FP_SCR1),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,a6@(TWOTO63)

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

|--FP2 IS READY
	fadds		a6@(TWOTO63),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,a6@(FP_SCR2)
	clrw          	a6@(FP_SCR2+2)
	movel		#0xC90FDAA2,a6@(FP_SCR2+4)
	clrl		a6@(FP_SCR2+8)		|...FP_SCR2 is  2**(L) * Piby2_1

|--FP2 IS READY
	fsubs		a6@(TWOTO63),fp2		|...FP2 is N

	addil		#0x00003FDD,d0
        movew		d0,a6@(FP_SCR3)
	clrw          	a6@(FP_SCR3+2)
	movel		#0x85A308D3,a6@(FP_SCR3+4)
	clrl		a6@(FP_SCR3+8)		|...FP_SCR3 is 2**(L) * Piby2_2

	movel		a6@(ENDFLAG),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		a6@(FP_SCR2),fp4		|...w = N*P1
	fmovex		fp2,fp5
	fmulx		a6@(FP_SCR3),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
	jgt 		RESTORE

|--Need to calculate r
	fsubx		fp0,fp3			|...A-R
	faddx		fp3,fp1			|...FP1 is r := (A-R)+a
	jra 		LOOP

RESTORE:
        fmovel		fp2,a6@(N)
	movel		A7@+,d2
	fmovemx	A7@+,fp2-fp5


	movel		a6@(ADJN),d0
	cmpil		#4,d0

	jlt 		SINCONT
	jra 		SCCONT

	.globl	__l_ssincosd
__l_ssincosd:
|--SIN AND COS OF X FOR DENORMALIZED X

	.long 0xf23c4480,0x3f800000	/*	fmoves	&0x3F800000,fp1 */
	bsrl		__l_sto_cos		| store cosine result
	jra 		__l_t_extdnrm

	.globl	__l_ssincos
__l_ssincos:
|--SET ADJN TO 4
	movel		#4,a6@(ADJN)

	fmovex		a0@,fp0			|...lOAD INPUT

	movel		A0@,d0
	movew		A0@(4),d0
	fmovex		fp0,a6@(X)
	andil		#0x7FFFFFFF,d0		|...COMPACTIFY X

	cmpil		#0x3FD78000,d0		|...|X| >= 2**(-40)?
	jge 		SCOK1
	jra 		SCSM

SCOK1:
	cmpil		#0x4004BC7E,d0		|...|X| < 15 PI?
	jlt 		SCMAIN
	jra 		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		__l_PITBL+0x200,a1 |...TABLE OF N*PI/2, N = -32,...,32


|--FP1 IS NOW READY
	fmovel		fp1,a6@(N)	|...CONVERT TO INTEGER

	movel		a6@(N),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		a6@(N),d0
	rorl		#1,d0

	cmpil		#0,d0		|...D0 < 0 IFF N IS ODD
	jge 		NEVEN

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

	fmovex		fp0,a6@(RPRIME)
	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,a6@(RPRIME)
	movel		A7@+,d2
	fmulx		fp0,fp2	 	|...S(B7+SB8)
	rorl		#1,d0
	andil		#0x80000000,d0

	faddd		SINA5,fp1	|...A5+S(A6+SA7)
	movel		#0x3F800000,a6@(POSNEG1)
	eorl		d0,a6@(POSNEG1)
	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,a6@(SPRIME)

	faddd		SINA4,fp1	|...A4+S(A5+S(A6+SA7))
	eorl		d0,a6@(SPRIME)
	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		a6@(RPRIME),fp1	/* |...R'S(A1+...) */
	fadds		COSB1,fp0	|...B1+S(B2...)
	fmulx		a6@(SPRIME),fp0	/* |...S'(B1+S(B2+...)) */

	movel		d1,a7@-		| restore users mode # precision
	andil		#0xff,d1	| mask off all exceptions
	fmovel		d1,fpcr
	faddx		a6@(RPRIME),fp1	|...COS(X)
	bsrl		__l_sto_cos	| store cosine result
	fmovel		a7@+,fpcr	| restore users exceptions
	fadds		a6@(POSNEG1),fp0	|...SIN(X)

	jra 		__l_t_frcinx


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

	fmovex		fp0,a6@(RPRIME)
	fmulx		fp0,fp0	 		|...FP0 IS S = R*R
	fmoved		COSB8,fp1		|...B8
	fmoved		SINA7,fp2		|...A7
	fmulx		fp0,fp1	 		|...SB8
	fmovex		fp0,a6@(SPRIME)
	fmulx		fp0,fp2	 		|...SA7
	rorl		#1,d0
	andil		#0x80000000,d0
	faddd		COSB7,fp1		|...B7+SB8
	faddd		SINA6,fp2		|...A6+SA7
	eorl		d0,a6@(RPRIME)
	eorl		d0,a6@(SPRIME)
	fmulx		fp0,fp1	 		|...S(B7+SB8)
	oril		#0x3F800000,d0
	movel		d0,a6@(POSNEG1)
	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		a6@(RPRIME),fp0	/* 	|...R'S(A1+...) */
	fmulx		a6@(SPRIME),fp1	/* 	|...S'(B1+S(B2+...)) */

	movel		d1,a7@-			| save users mode # precision
	andil		#0xff,d1		| mask off all exceptions
	fmovel		d1,fpcr
	fadds		a6@(POSNEG1),fp1	|...COS(X)
	bsrl		__l_sto_cos		| store cosine result
	fmovel		a7@+,fpcr		| restore users exceptions
	faddx		a6@(RPRIME),fp0		|...SIN(X)

	jra 		__l_t_frcinx

SCBORS:
	cmpil		#0x3FFF8000,d0
	jgt 		REDUCEX


SCSM:
	movew		#0x0000,a6@(XDCARE)
	.long 0xf23c4480,0x3f800000	/*	fmoves	&0x3F800000,fp1 */

	movel		d1,a7@-			| save users mode # precision
	andil		#0xff,d1		| mask off all exceptions
	fmovel		d1,fpcr
	.long 0xf23c44a8,0x00800000	/*	fsubs	&0x00800000,fp1 */
	bsrl		__l_sto_cos		| store cosine result
	fmovel		a7@+,fpcr		| restore users exceptions
	fmovex		a6@(X),fp0
	jra 		__l_t_frcinx

|	end