stwotox.s

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|
|	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|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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