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

• Lines: 456
• Date: Sat Feb 24 22:58:44 1996
• Orig file: v1.3.93/linux/arch/m68k/fpsp040/stan.S
• Orig date: Thu Jan 1 02:00:00 1970

diff -u --recursive --new-file v1.3.93/linux/arch/m68k/fpsp040/stan.S linux/arch/m68k/fpsp040/stan.S
@@ -0,0 +1,455 @@
+|
+|	stan.sa 3.3 7/29/91
+|
+|	The entry point stan computes the tangent of
+|	an input argument;
+|	stand does the same except for denormalized input.
+|
+|	Input: Double-extended number X in location pointed to
+|		by address register a0.
+|
+|	Output: The value tan(X) returned in floating-point register Fp0.
+|
+|	Accuracy and Monotonicity: The returned result is within 3 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 program sTAN takes approximately 170 cycles for
+|		input argument X such that |X| < 15Pi, which is the the usual
+|		situation.
+|
+|	Algorithm:
+|
+|	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 2, so in particular, k = 0 or 1.
+|
+|	3. If k is odd, go to 5.
+|
+|	4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a
+|		rational function U/V where
+|		U = r + r*s*(P1 + s*(P2 + s*P3)), and
+|		V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))),  s = r*r.
+|		Exit.
+|
+|	4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a
+|		rational function U/V where
+|		U = r + r*s*(P1 + s*(P2 + s*P3)), and
+|		V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r,
+|		-Cot(r) = -V/U. Exit.
+|
+|	6. If |X| > 1, go to 8.
+|
+|	7. (|X|<2**(-40)) Tan(X) = X. 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+|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.
+
+|STAN	idnt	2,1 | Motorola 040 Floating Point Software Package
+
+	|section	8
+
+	.include "fpsp.h"
+
+BOUNDS1:	.long 0x3FD78000,0x4004BC7E
+TWOBYPI:	.long 0x3FE45F30,0x6DC9C883
+
+TANQ4:	.long 0x3EA0B759,0xF50F8688
+TANP3:	.long 0xBEF2BAA5,0xA8924F04
+
+TANQ3:	.long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000
+
+TANP2:	.long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000
+
+TANQ2:	.long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000
+
+TANP1:	.long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000
+
+TANQ1:	.long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000
+
+INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000
+
+TWOPI1:	.long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
+TWOPI2:	.long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
+
+|--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
+|--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
+|--MOST 69 BITS LONG.
+	.global	PITBL
+PITBL:
+  .long  0xC0040000,0xC90FDAA2,0x2168C235,0x21800000
+  .long  0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000
+  .long  0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000
+  .long  0xC0040000,0xB6365E22,0xEE46F000,0x21480000
+  .long  0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000
+  .long  0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000
+  .long  0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000
+  .long  0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000
+  .long  0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000
+  .long  0xC0040000,0x90836524,0x88034B96,0x20B00000
+  .long  0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000
+  .long  0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000
+  .long  0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000
+  .long  0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000
+  .long  0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000
+  .long  0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000
+  .long  0xC0030000,0xC90FDAA2,0x2168C235,0x21000000
+  .long  0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000
+  .long  0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000
+  .long  0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000
+  .long  0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000
+  .long  0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000
+  .long  0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000
+  .long  0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000
+  .long  0xC0020000,0xC90FDAA2,0x2168C235,0x20800000
+  .long  0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000
+  .long  0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000
+  .long  0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000
+  .long  0xC0010000,0xC90FDAA2,0x2168C235,0x20000000
+  .long  0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000
+  .long  0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000
+  .long  0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000
+  .long  0x00000000,0x00000000,0x00000000,0x00000000
+  .long  0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000
+  .long  0x40000000,0xC90FDAA2,0x2168C235,0x9F800000
+  .long  0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000
+  .long  0x40010000,0xC90FDAA2,0x2168C235,0xA0000000
+  .long  0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000
+  .long  0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000
+  .long  0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000
+  .long  0x40020000,0xC90FDAA2,0x2168C235,0xA0800000
+  .long  0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000
+  .long  0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000
+  .long  0x40030000,0x8A3AE64F,0x76F80584,0x21080000
+  .long  0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000
+  .long  0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000
+  .long  0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000
+  .long  0x40030000,0xBC7EDCF7,0xFF523611,0x21680000
+  .long  0x40030000,0xC90FDAA2,0x2168C235,0xA1000000
+  .long  0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000
+  .long  0x40030000,0xE231D5F6,0x6595DA7B,0x21300000
+  .long  0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000
+  .long  0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000
+  .long  0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000
+  .long  0x40040000,0x8A3AE64F,0x76F80584,0x21880000
+  .long  0x40040000,0x90836524,0x88034B96,0xA0B00000
+  .long  0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000
+  .long  0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000
+  .long  0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000
+  .long  0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000
+  .long  0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000
+  .long  0x40040000,0xB6365E22,0xEE46F000,0xA1480000
+  .long  0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000
+  .long  0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000
+  .long  0x40040000,0xC90FDAA2,0x2168C235,0xA1800000
+
+	.set	INARG,FP_SCR4
+
+	.set	TWOTO63,L_SCR1
+	.set	ENDFLAG,L_SCR2
+	.set	N,L_SCR3
+
+	| xref	t_frcinx
+	|xref	t_extdnrm
+
+	.global	stand
+stand:
+|--TAN(X) = X FOR DENORMALIZED X
+
+	bra		t_extdnrm
+
+	.global	stan
+stan:
+	fmovex		(%a0),%fp0	| ...LOAD INPUT
+
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	andil		#0x7FFFFFFF,%d0
+
+	cmpil		#0x3FD78000,%d0		| ...|X| >= 2**(-40)?
+	bges		TANOK1
+	bra		TANSM
+TANOK1:
+	cmpil		#0x4004BC7E,%d0		| ...|X| < 15 PI?
+	blts		TANMAIN
+	bra		REDUCEX
+
+
+TANMAIN:
+|--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 TWO INSTRUCTIONS
+	leal		PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
+
+|--FP1 IS NOW READY
+	fmovel		%fp1,%d0		| ...CONVERT TO INTEGER
+
+	asll		#4,%d0
+	addal		%d0,%a1		| ...ADDRESS N*PIBY2 IN Y1, Y2
+
+	fsubx		(%a1)+,%fp0	| ...X-Y1
+|--HIDE THE NEXT ONE
+
+	fsubs		(%a1),%fp0	| ...FP0 IS R = (X-Y1)-Y2
+
+	rorl		#5,%d0
+	andil		#0x80000000,%d0	| ...D0 WAS ODD IFF D0 < 0
+
+TANCONT:
+
+	cmpil		#0,%d0
+	blt		NODD
+
+	fmovex		%fp0,%fp1
+	fmulx		%fp1,%fp1	 	| ...S = R*R
+
+	fmoved		TANQ4,%fp3
+	fmoved		TANP3,%fp2
+
+	fmulx		%fp1,%fp3	 	| ...SQ4
+	fmulx		%fp1,%fp2	 	| ...SP3
+
+	faddd		TANQ3,%fp3	| ...Q3+SQ4
+	faddx		TANP2,%fp2	| ...P2+SP3
+
+	fmulx		%fp1,%fp3	 	| ...S(Q3+SQ4)
+	fmulx		%fp1,%fp2	 	| ...S(P2+SP3)
+
+	faddx		TANQ2,%fp3	| ...Q2+S(Q3+SQ4)
+	faddx		TANP1,%fp2	| ...P1+S(P2+SP3)
+
+	fmulx		%fp1,%fp3	 	| ...S(Q2+S(Q3+SQ4))
+	fmulx		%fp1,%fp2	 	| ...S(P1+S(P2+SP3))
+
+	faddx		TANQ1,%fp3	| ...Q1+S(Q2+S(Q3+SQ4))
+	fmulx		%fp0,%fp2	 	| ...RS(P1+S(P2+SP3))
+
+	fmulx		%fp3,%fp1	 	| ...S(Q1+S(Q2+S(Q3+SQ4)))
+	
+
+	faddx		%fp2,%fp0	 	| ...R+RS(P1+S(P2+SP3))
+	
+
+	fadds		#0x3F800000,%fp1	| ...1+S(Q1+...)
+
+	fmovel		%d1,%fpcr		|restore users exceptions
+	fdivx		%fp1,%fp0		|last inst - possible exception set
+
+	bra		t_frcinx
+
+NODD:
+	fmovex		%fp0,%fp1
+	fmulx		%fp0,%fp0	 	| ...S = R*R
+
+	fmoved		TANQ4,%fp3
+	fmoved		TANP3,%fp2
+
+	fmulx		%fp0,%fp3	 	| ...SQ4
+	fmulx		%fp0,%fp2	 	| ...SP3
+
+	faddd		TANQ3,%fp3	| ...Q3+SQ4
+	faddx		TANP2,%fp2	| ...P2+SP3
+
+	fmulx		%fp0,%fp3	 	| ...S(Q3+SQ4)
+	fmulx		%fp0,%fp2	 	| ...S(P2+SP3)
+
+	faddx		TANQ2,%fp3	| ...Q2+S(Q3+SQ4)
+	faddx		TANP1,%fp2	| ...P1+S(P2+SP3)
+
+	fmulx		%fp0,%fp3	 	| ...S(Q2+S(Q3+SQ4))
+	fmulx		%fp0,%fp2	 	| ...S(P1+S(P2+SP3))
+
+	faddx		TANQ1,%fp3	| ...Q1+S(Q2+S(Q3+SQ4))
+	fmulx		%fp1,%fp2	 	| ...RS(P1+S(P2+SP3))
+
+	fmulx		%fp3,%fp0	 	| ...S(Q1+S(Q2+S(Q3+SQ4)))
+	
+
+	faddx		%fp2,%fp1	 	| ...R+RS(P1+S(P2+SP3))
+	fadds		#0x3F800000,%fp0	| ...1+S(Q1+...)
+	
+
+	fmovex		%fp1,-(%sp)
+	eoril		#0x80000000,(%sp)
+
+	fmovel		%d1,%fpcr	 	|restore users exceptions
+	fdivx		(%sp)+,%fp0	|last inst - possible exception set
+
+	bra		t_frcinx
+
+TANBORS:
+|--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
+|--IF |X| < 2**(-40), RETURN X OR 1.
+	cmpil		#0x3FFF8000,%d0
+	bgts		REDUCEX
+
+TANSM:
+
+	fmovex		%fp0,-(%sp)
+	fmovel		%d1,%fpcr		 |restore users exceptions
+	fmovex		(%sp)+,%fp0	|last inst - posibble 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		N(%a6),%d0
+        rorl		#1,%d0
+
+
+	bra		TANCONT
+
+	|end