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

• Lines: 428
• Date: Sat Feb 24 22:58:44 1996
• Orig file: v1.3.93/linux/arch/m68k/fpsp040/stwotox.S
• Orig date: Thu Jan 1 02:00:00 1970

diff -u --recursive --new-file v1.3.93/linux/arch/m68k/fpsp040/stwotox.S linux/arch/m68k/fpsp040/stwotox.S
@@ -0,0 +1,427 @@
+|
+|	stwotox.sa 3.1 12/10/90
+|
+|	stwotox  --- 2**X
+|	stwotoxd --- 2**X for denormalized X
+|	stentox  --- 10**X
+|	stentoxd --- 10**X for denormalized X
+|
+|	Input: Double-extended number X in location pointed to
+|		by address register a0.
+|
+|	Output: The function values are returned in Fp0.
+|
+|	Accuracy and Monotonicity: The returned result is within 2 ulps 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 stwotox takes approximately 190 cycles and the
+|		program stentox takes approximately 200 cycles.
+|
+|	Algorithm:
+|
+|	twotox
+|	1. If |X| > 16480, go to ExpBig.
+|
+|	2. If |X| < 2**(-70), go to ExpSm.
+|
+|	3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore
+|		decompose N as
+|		 N = 64(M + M') + j,  j = 0,1,2,...,63.
+|
+|	4. Overwrite r := r * log2. Then
+|		2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
+|		Go to expr to compute that expression.
+|
+|	tentox
+|	1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig.
+|
+|	2. If |X| < 2**(-70), go to ExpSm.
+|
+|	3. Set y := X*log_2(10)*64 (base 2 log of 10). Set
+|		N := round-to-int(y). Decompose N as
+|		 N = 64(M + M') + j,  j = 0,1,2,...,63.
+|
+|	4. Define r as
+|		r := ((X - N*L1)-N*L2) * L10
+|		where L1, L2 are the leading and trailing parts of log_10(2)/64
+|		and L10 is the natural log of 10. Then
+|		10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
+|		Go to expr to compute that expression.
+|
+|	expr
+|	1. Fetch 2**(j/64) from table as Fact1 and Fact2.
+|
+|	2. Overwrite Fact1 and Fact2 by
+|		Fact1 := 2**(M) * Fact1
+|		Fact2 := 2**(M) * Fact2
+|		Thus Fact1 + Fact2 = 2**(M) * 2**(j/64).
+|
+|	3. Calculate P where 1 + P approximates exp(r):
+|		P = r + r*r*(A1+r*(A2+...+r*A5)).
+|
+|	4. Let AdjFact := 2**(M'). Return
+|		AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ).
+|		Exit.
+|
+|	ExpBig
+|	1. Generate overflow by Huge * Huge if X > 0; otherwise, generate
+|		underflow by Tiny * Tiny.
+|
+|	ExpSm
+|	1. Return 1 + X.
+|
+
+|		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+|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.
+
+|STWOTOX	idnt	2,1 | Motorola 040 Floating Point Software Package
+
+	|section	8
+
+	.include "fpsp.h"
+
+BOUNDS1:	.long 0x3FB98000,0x400D80C0 | ... 2^(-70),16480
+BOUNDS2:	.long 0x3FB98000,0x400B9B07 | ... 2^(-70),16480 LOG2/LOG10
+
+L2TEN64:	.long 0x406A934F,0x0979A371 | ... 64LOG10/LOG2
+L10TWO1:	.long 0x3F734413,0x509F8000 | ... LOG2/64LOG10
+
+L10TWO2:	.long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
+
+LOG10:	.long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
+
+LOG2:	.long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
+
+EXPA5:	.long 0x3F56C16D,0x6F7BD0B2
+EXPA4:	.long 0x3F811112,0x302C712C
+EXPA3:	.long 0x3FA55555,0x55554CC1
+EXPA2:	.long 0x3FC55555,0x55554A54
+EXPA1:	.long 0x3FE00000,0x00000000,0x00000000,0x00000000
+
+HUGE:	.long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
+TINY:	.long 0x00010000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
+
+EXPTBL:
+	.long  0x3FFF0000,0x80000000,0x00000000,0x3F738000
+	.long  0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
+	.long  0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
+	.long  0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
+	.long  0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
+	.long  0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
+	.long  0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
+	.long  0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
+	.long  0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
+	.long  0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
+	.long  0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
+	.long  0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
+	.long  0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
+	.long  0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
+	.long  0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
+	.long  0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
+	.long  0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
+	.long  0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
+	.long  0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
+	.long  0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
+	.long  0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
+	.long  0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
+	.long  0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
+	.long  0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
+	.long  0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
+	.long  0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
+	.long  0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
+	.long  0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
+	.long  0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
+	.long  0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
+	.long  0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
+	.long  0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
+	.long  0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
+	.long  0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
+	.long  0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
+	.long  0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
+	.long  0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
+	.long  0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
+	.long  0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
+	.long  0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
+	.long  0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
+	.long  0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
+	.long  0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
+	.long  0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
+	.long  0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
+	.long  0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
+	.long  0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
+	.long  0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
+	.long  0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
+	.long  0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
+	.long  0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
+	.long  0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
+	.long  0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
+	.long  0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
+	.long  0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
+	.long  0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
+	.long  0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
+	.long  0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
+	.long  0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
+	.long  0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
+	.long  0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
+	.long  0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
+	.long  0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
+	.long  0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
+
+	.set	N,L_SCR1
+
+	.set	X,FP_SCR1
+	.set	XDCARE,X+2
+	.set	XFRAC,X+4
+
+	.set	ADJFACT,FP_SCR2
+
+	.set	FACT1,FP_SCR3
+	.set	FACT1HI,FACT1+4
+	.set	FACT1LOW,FACT1+8
+
+	.set	FACT2,FP_SCR4
+	.set	FACT2HI,FACT2+4
+	.set	FACT2LOW,FACT2+8
+
+	| xref	t_unfl
+	|xref	t_ovfl
+	|xref	t_frcinx
+
+	.global	stwotoxd
+stwotoxd:
+|--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
+
+	fmovel		%d1,%fpcr		| ...set user's rounding mode/precision
+	fmoves		#0x3F800000,%fp0  | ...RETURN 1 + X
+	movel		(%a0),%d0
+	orl		#0x00800001,%d0
+	fadds		%d0,%fp0
+	bra		t_frcinx
+
+	.global	stwotox
+stwotox:
+|--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
+	fmovemx	(%a0),%fp0-%fp0	| ...LOAD INPUT, do not set cc's
+
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	fmovex		%fp0,X(%a6)
+	andil		#0x7FFFFFFF,%d0
+
+	cmpil		#0x3FB98000,%d0		| ...|X| >= 2**(-70)?
+	bges		TWOOK1
+	bra		EXPBORS
+
+TWOOK1:
+	cmpil		#0x400D80C0,%d0		| ...|X| > 16480?
+	bles		TWOMAIN
+	bra		EXPBORS
+	
+
+TWOMAIN:
+|--USUAL CASE, 2^(-70) <= |X| <= 16480
+
+	fmovex		%fp0,%fp1
+	fmuls		#0x42800000,%fp1  | ...64 * X
+	
+	fmovel		%fp1,N(%a6)		| ...N = ROUND-TO-INT(64 X)
+	movel		%d2,-(%sp)
+	lea		EXPTBL,%a1 	| ...LOAD ADDRESS OF TABLE OF 2^(J/64)
+	fmovel		N(%a6),%fp1		| ...N --> FLOATING FMT
+	movel		N(%a6),%d0
+	movel		%d0,%d2
+	andil		#0x3F,%d0		| ...D0 IS J
+	asll		#4,%d0		| ...DISPLACEMENT FOR 2^(J/64)
+	addal		%d0,%a1		| ...ADDRESS FOR 2^(J/64)
+	asrl		#6,%d2		| ...d2 IS L, N = 64L + J
+	movel		%d2,%d0
+	asrl		#1,%d0		| ...D0 IS M
+	subl		%d0,%d2		| ...d2 IS M', N = 64(M+M') + J
+	addil		#0x3FFF,%d2
+	movew		%d2,ADJFACT(%a6) 	| ...ADJFACT IS 2^(M')
+	movel		(%sp)+,%d2
+|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
+|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
+|--ADJFACT = 2^(M').
+|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
+
+	fmuls		#0x3C800000,%fp1  | ...(1/64)*N
+	movel		(%a1)+,FACT1(%a6)
+	movel		(%a1)+,FACT1HI(%a6)
+	movel		(%a1)+,FACT1LOW(%a6)
+	movew		(%a1)+,FACT2(%a6)
+	clrw		FACT2+2(%a6)
+
+	fsubx		%fp1,%fp0	 	| ...X - (1/64)*INT(64 X)
+
+	movew		(%a1)+,FACT2HI(%a6)
+	clrw		FACT2HI+2(%a6)
+	clrl		FACT2LOW(%a6)
+	addw		%d0,FACT1(%a6)
+	
+	fmulx		LOG2,%fp0	| ...FP0 IS R
+	addw		%d0,FACT2(%a6)
+
+	bra		expr
+
+EXPBORS:
+|--FPCR, D0 SAVED
+	cmpil		#0x3FFF8000,%d0
+	bgts		EXPBIG
+
+EXPSM:
+|--|X| IS SMALL, RETURN 1 + X
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fadds		#0x3F800000,%fp0  | ...RETURN 1 + X
+
+	bra		t_frcinx
+
+EXPBIG:
+|--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
+|--REGISTERS SAVE SO FAR ARE FPCR AND  D0
+	movel		X(%a6),%d0
+	cmpil		#0,%d0
+	blts		EXPNEG
+
+	bclrb		#7,(%a0)		|t_ovfl expects positive value
+	bra		t_ovfl
+
+EXPNEG:
+	bclrb		#7,(%a0)		|t_unfl expects positive value
+	bra		t_unfl
+
+	.global	stentoxd
+stentoxd:
+|--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
+
+	fmovel		%d1,%fpcr		| ...set user's rounding mode/precision
+	fmoves		#0x3F800000,%fp0  | ...RETURN 1 + X
+	movel		(%a0),%d0
+	orl		#0x00800001,%d0
+	fadds		%d0,%fp0
+	bra		t_frcinx
+
+	.global	stentox
+stentox:
+|--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
+	fmovemx	(%a0),%fp0-%fp0	| ...LOAD INPUT, do not set cc's
+
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	fmovex		%fp0,X(%a6)
+	andil		#0x7FFFFFFF,%d0
+
+	cmpil		#0x3FB98000,%d0		| ...|X| >= 2**(-70)?
+	bges		TENOK1
+	bra		EXPBORS
+
+TENOK1:
+	cmpil		#0x400B9B07,%d0		| ...|X| <= 16480*log2/log10 ?
+	bles		TENMAIN
+	bra		EXPBORS
+
+TENMAIN:
+|--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
+
+	fmovex		%fp0,%fp1
+	fmuld		L2TEN64,%fp1	| ...X*64*LOG10/LOG2
+	
+	fmovel		%fp1,N(%a6)		| ...N=INT(X*64*LOG10/LOG2)
+	movel		%d2,-(%sp)
+	lea		EXPTBL,%a1 	| ...LOAD ADDRESS OF TABLE OF 2^(J/64)
+	fmovel		N(%a6),%fp1		| ...N --> FLOATING FMT
+	movel		N(%a6),%d0
+	movel		%d0,%d2
+	andil		#0x3F,%d0		| ...D0 IS J
+	asll		#4,%d0		| ...DISPLACEMENT FOR 2^(J/64)
+	addal		%d0,%a1		| ...ADDRESS FOR 2^(J/64)
+	asrl		#6,%d2		| ...d2 IS L, N = 64L + J
+	movel		%d2,%d0
+	asrl		#1,%d0		| ...D0 IS M
+	subl		%d0,%d2		| ...d2 IS M', N = 64(M+M') + J
+	addil		#0x3FFF,%d2
+	movew		%d2,ADJFACT(%a6) 	| ...ADJFACT IS 2^(M')
+	movel		(%sp)+,%d2
+
+|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
+|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
+|--ADJFACT = 2^(M').
+|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
+
+	fmovex		%fp1,%fp2
+
+	fmuld		L10TWO1,%fp1	| ...N*(LOG2/64LOG10)_LEAD
+	movel		(%a1)+,FACT1(%a6)
+
+	fmulx		L10TWO2,%fp2	| ...N*(LOG2/64LOG10)_TRAIL
+
+	movel		(%a1)+,FACT1HI(%a6)
+	movel		(%a1)+,FACT1LOW(%a6)
+	fsubx		%fp1,%fp0		| ...X - N L_LEAD
+	movew		(%a1)+,FACT2(%a6)
+
+	fsubx		%fp2,%fp0		| ...X - N L_TRAIL
+
+	clrw		FACT2+2(%a6)
+	movew		(%a1)+,FACT2HI(%a6)
+	clrw		FACT2HI+2(%a6)
+	clrl		FACT2LOW(%a6)
+
+	fmulx		LOG10,%fp0	| ...FP0 IS R
+	
+	addw		%d0,FACT1(%a6)
+	addw		%d0,FACT2(%a6)
+
+expr:
+|--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
+|--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
+|--FP0 IS R. THE FOLLOWING CODE COMPUTES
+|--	2**(M'+M) * 2**(J/64) * EXP(R)
+
+	fmovex		%fp0,%fp1
+	fmulx		%fp1,%fp1		| ...FP1 IS S = R*R
+
+	fmoved		EXPA5,%fp2	| ...FP2 IS A5
+	fmoved		EXPA4,%fp3	| ...FP3 IS A4
+
+	fmulx		%fp1,%fp2		| ...FP2 IS S*A5
+	fmulx		%fp1,%fp3		| ...FP3 IS S*A4
+
+	faddd		EXPA3,%fp2	| ...FP2 IS A3+S*A5
+	faddd		EXPA2,%fp3	| ...FP3 IS A2+S*A4
+
+	fmulx		%fp1,%fp2		| ...FP2 IS S*(A3+S*A5)
+	fmulx		%fp1,%fp3		| ...FP3 IS S*(A2+S*A4)
+
+	faddd		EXPA1,%fp2	| ...FP2 IS A1+S*(A3+S*A5)
+	fmulx		%fp0,%fp3		| ...FP3 IS R*S*(A2+S*A4)
+
+	fmulx		%fp1,%fp2		| ...FP2 IS S*(A1+S*(A3+S*A5))
+	faddx		%fp3,%fp0		| ...FP0 IS R+R*S*(A2+S*A4)
+	
+	faddx		%fp2,%fp0		| ...FP0 IS EXP(R) - 1
+	
+
+|--FINAL RECONSTRUCTION PROCESS
+|--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1)  -  (1 OR 0)
+
+	fmulx		FACT1(%a6),%fp0
+	faddx		FACT2(%a6),%fp0
+	faddx		FACT1(%a6),%fp0
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	clrw		ADJFACT+2(%a6)
+	movel		#0x80000000,ADJFACT+4(%a6)
+	clrl		ADJFACT+8(%a6)
+	fmulx		ADJFACT(%a6),%fp0	| ...FINAL ADJUSTMENT
+
+	bra		t_frcinx
+
+	|end