ssin.s

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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
|--Intermediate 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