* $NetBSD: stwotox.sa,v 1.3 1994/10/26 07:50:15 cgd Exp $
* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
* M68000 Hi-Performance Microprocessor Division
* M68040 Software Package
*
* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
* All rights reserved.
*
* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
* To the maximum extent permitted by applicable law,
* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
* PARTICULAR PURPOSE and any warranty against infringement with
* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
* and any accompanying written materials.
*
* To the maximum extent permitted by applicable law,
* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
* SOFTWARE. Motorola assumes no responsibility for the maintenance
* and support of the SOFTWARE.
*
* You are hereby granted a copyright license to use, modify, and
* distribute the SOFTWARE so long as this entire notice is retained
* without alteration in any modified and/or redistributed versions,
* and that such modified versions are clearly identified as such.
* No licenses are granted by implication, estoppel or otherwise
* under any patents or trademarks of Motorola, Inc.
*
* 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.
*
STWOTOX IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
include fpsp.h
BOUNDS1 DC.L $3FB98000,$400D80C0 ... 2^(-70),16480
BOUNDS2 DC.L $3FB98000,$400B9B07 ... 2^(-70),16480 LOG2/LOG10
L2TEN64 DC.L $406A934F,$0979A371 ... 64LOG10/LOG2
L10TWO1 DC.L $3F734413,$509F8000 ... LOG2/64LOG10
L10TWO2 DC.L $BFCD0000,$C0219DC1,$DA994FD2,$00000000
LOG10 DC.L $40000000,$935D8DDD,$AAA8AC17,$00000000
LOG2 DC.L $3FFE0000,$B17217F7,$D1CF79AC,$00000000
EXPA5 DC.L $3F56C16D,$6F7BD0B2
EXPA4 DC.L $3F811112,$302C712C
EXPA3 DC.L $3FA55555,$55554CC1
EXPA2 DC.L $3FC55555,$55554A54
EXPA1 DC.L $3FE00000,$00000000,$00000000,$00000000
HUGE DC.L $7FFE0000,$FFFFFFFF,$FFFFFFFF,$00000000
TINY DC.L $00010000,$FFFFFFFF,$FFFFFFFF,$00000000
EXPTBL
DC.L $3FFF0000,$80000000,$00000000,$3F738000
DC.L $3FFF0000,$8164D1F3,$BC030773,$3FBEF7CA
DC.L $3FFF0000,$82CD8698,$AC2BA1D7,$3FBDF8A9
DC.L $3FFF0000,$843A28C3,$ACDE4046,$3FBCD7C9
DC.L $3FFF0000,$85AAC367,$CC487B15,$BFBDE8DA
DC.L $3FFF0000,$871F6196,$9E8D1010,$3FBDE85C
DC.L $3FFF0000,$88980E80,$92DA8527,$3FBEBBF1
DC.L $3FFF0000,$8A14D575,$496EFD9A,$3FBB80CA
DC.L $3FFF0000,$8B95C1E3,$EA8BD6E7,$BFBA8373
DC.L $3FFF0000,$8D1ADF5B,$7E5BA9E6,$BFBE9670
DC.L $3FFF0000,$8EA4398B,$45CD53C0,$3FBDB700
DC.L $3FFF0000,$9031DC43,$1466B1DC,$3FBEEEB0
DC.L $3FFF0000,$91C3D373,$AB11C336,$3FBBFD6D
DC.L $3FFF0000,$935A2B2F,$13E6E92C,$BFBDB319
DC.L $3FFF0000,$94F4EFA8,$FEF70961,$3FBDBA2B
DC.L $3FFF0000,$96942D37,$20185A00,$3FBE91D5
DC.L $3FFF0000,$9837F051,$8DB8A96F,$3FBE8D5A
DC.L $3FFF0000,$99E04593,$20B7FA65,$BFBCDE7B
DC.L $3FFF0000,$9B8D39B9,$D54E5539,$BFBEBAAF
DC.L $3FFF0000,$9D3ED9A7,$2CFFB751,$BFBD86DA
DC.L $3FFF0000,$9EF53260,$91A111AE,$BFBEBEDD
DC.L $3FFF0000,$A0B0510F,$B9714FC2,$3FBCC96E
DC.L $3FFF0000,$A2704303,$0C496819,$BFBEC90B
DC.L $3FFF0000,$A43515AE,$09E6809E,$3FBBD1DB
DC.L $3FFF0000,$A5FED6A9,$B15138EA,$3FBCE5EB
DC.L $3FFF0000,$A7CD93B4,$E965356A,$BFBEC274
DC.L $3FFF0000,$A9A15AB4,$EA7C0EF8,$3FBEA83C
DC.L $3FFF0000,$AB7A39B5,$A93ED337,$3FBECB00
DC.L $3FFF0000,$AD583EEA,$42A14AC6,$3FBE9301
DC.L $3FFF0000,$AF3B78AD,$690A4375,$BFBD8367
DC.L $3FFF0000,$B123F581,$D2AC2590,$BFBEF05F
DC.L $3FFF0000,$B311C412,$A9112489,$3FBDFB3C
DC.L $3FFF0000,$B504F333,$F9DE6484,$3FBEB2FB
DC.L $3FFF0000,$B6FD91E3,$28D17791,$3FBAE2CB
DC.L $3FFF0000,$B8FBAF47,$62FB9EE9,$3FBCDC3C
DC.L $3FFF0000,$BAFF5AB2,$133E45FB,$3FBEE9AA
DC.L $3FFF0000,$BD08A39F,$580C36BF,$BFBEAEFD
DC.L $3FFF0000,$BF1799B6,$7A731083,$BFBCBF51
DC.L $3FFF0000,$C12C4CCA,$66709456,$3FBEF88A
DC.L $3FFF0000,$C346CCDA,$24976407,$3FBD83B2
DC.L $3FFF0000,$C5672A11,$5506DADD,$3FBDF8AB
DC.L $3FFF0000,$C78D74C8,$ABB9B15D,$BFBDFB17
DC.L $3FFF0000,$C9B9BD86,$6E2F27A3,$BFBEFE3C
DC.L $3FFF0000,$CBEC14FE,$F2727C5D,$BFBBB6F8
DC.L $3FFF0000,$CE248C15,$1F8480E4,$BFBCEE53
DC.L $3FFF0000,$D06333DA,$EF2B2595,$BFBDA4AE
DC.L $3FFF0000,$D2A81D91,$F12AE45A,$3FBC9124
DC.L $3FFF0000,$D4F35AAB,$CFEDFA1F,$3FBEB243
DC.L $3FFF0000,$D744FCCA,$D69D6AF4,$3FBDE69A
DC.L $3FFF0000,$D99D15C2,$78AFD7B6,$BFB8BC61
DC.L $3FFF0000,$DBFBB797,$DAF23755,$3FBDF610
DC.L $3FFF0000,$DE60F482,$5E0E9124,$BFBD8BE1
DC.L $3FFF0000,$E0CCDEEC,$2A94E111,$3FBACB12
DC.L $3FFF0000,$E33F8972,$BE8A5A51,$3FBB9BFE
DC.L $3FFF0000,$E5B906E7,$7C8348A8,$3FBCF2F4
DC.L $3FFF0000,$E8396A50,$3C4BDC68,$3FBEF22F
DC.L $3FFF0000,$EAC0C6E7,$DD24392F,$BFBDBF4A
DC.L $3FFF0000,$ED4F301E,$D9942B84,$3FBEC01A
DC.L $3FFF0000,$EFE4B99B,$DCDAF5CB,$3FBE8CAC
DC.L $3FFF0000,$F281773C,$59FFB13A,$BFBCBB3F
DC.L $3FFF0000,$F5257D15,$2486CC2C,$3FBEF73A
DC.L $3FFF0000,$F7D0DF73,$0AD13BB9,$BFB8B795
DC.L $3FFF0000,$FA83B2DB,$722A033A,$3FBEF84B
DC.L $3FFF0000,$FD3E0C0C,$F486C175,$BFBEF581
N equ L_SCR1
X equ FP_SCR1
XDCARE equ X+2
XFRAC equ X+4
ADJFACT equ FP_SCR2
FACT1 equ FP_SCR3
FACT1HI equ FACT1+4
FACT1LOW equ FACT1+8
FACT2 equ FP_SCR4
FACT2HI equ FACT2+4
FACT2LOW equ FACT2+8
xref t_unfl
xref t_ovfl
xref t_frcinx
xdef stwotoxd
stwotoxd:
*--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
fmove.l d1,fpcr ...set user's rounding mode/precision
Fmove.S #:3F800000,FP0 ...RETURN 1 + X
move.l (a0),d0
or.l #$00800001,d0
fadd.s d0,fp0
bra t_frcinx
xdef stwotox
stwotox:
*--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
FMOVEM.X (a0),FP0 ...LOAD INPUT, do not set cc's
MOVE.L (A0),D0
MOVE.W 4(A0),D0
FMOVE.X FP0,X(a6)
ANDI.L #$7FFFFFFF,D0
CMPI.L #$3FB98000,D0 ...|X| >= 2**(-70)?
BGE.B TWOOK1
BRA.W EXPBORS
TWOOK1:
CMPI.L #$400D80C0,D0 ...|X| > 16480?
BLE.B TWOMAIN
BRA.W EXPBORS
TWOMAIN:
*--USUAL CASE, 2^(-70) <= |X| <= 16480
FMOVE.X FP0,FP1
FMUL.S #:42800000,FP1 ...64 * X
FMOVE.L FP1,N(a6) ...N = ROUND-TO-INT(64 X)
MOVE.L d2,-(sp)
LEA EXPTBL,a1 ...LOAD ADDRESS OF TABLE OF 2^(J/64)
FMOVE.L N(a6),FP1 ...N --> FLOATING FMT
MOVE.L N(a6),D0
MOVE.L D0,d2
ANDI.L #$3F,D0 ...D0 IS J
ASL.L #4,D0 ...DISPLACEMENT FOR 2^(J/64)
ADDA.L D0,a1 ...ADDRESS FOR 2^(J/64)
ASR.L #6,d2 ...d2 IS L, N = 64L + J
MOVE.L d2,D0
ASR.L #1,D0 ...D0 IS M
SUB.L D0,d2 ...d2 IS M', N = 64(M+M') + J
ADDI.L #$3FFF,d2
MOVE.W d2,ADJFACT(a6) ...ADJFACT IS 2^(M')
MOVE.L (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.
FMUL.S #:3C800000,FP1 ...(1/64)*N
MOVE.L (a1)+,FACT1(a6)
MOVE.L (a1)+,FACT1HI(a6)
MOVE.L (a1)+,FACT1LOW(a6)
MOVE.W (a1)+,FACT2(a6)
clr.w FACT2+2(a6)
FSUB.X FP1,FP0 ...X - (1/64)*INT(64 X)
MOVE.W (a1)+,FACT2HI(a6)
clr.w FACT2HI+2(a6)
clr.l FACT2LOW(a6)
ADD.W D0,FACT1(a6)
FMUL.X LOG2,FP0 ...FP0 IS R
ADD.W D0,FACT2(a6)
BRA.W expr
EXPBORS:
*--FPCR, D0 SAVED
CMPI.L #$3FFF8000,D0
BGT.B EXPBIG
EXPSM:
*--|X| IS SMALL, RETURN 1 + X
FMOVE.L d1,FPCR ;restore users exceptions
FADD.S #:3F800000,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
MOVE.L X(a6),D0
TST.L D0
BLT.B EXPNEG
bclr.b #7,(a0) ;t_ovfl expects positive value
bra t_ovfl
EXPNEG:
bclr.b #7,(a0) ;t_unfl expects positive value
bra t_unfl
xdef stentoxd
stentoxd:
*--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
fmove.l d1,fpcr ...set user's rounding mode/precision
Fmove.S #:3F800000,FP0 ...RETURN 1 + X
move.l (a0),d0
or.l #$00800001,d0
fadd.s d0,fp0
bra t_frcinx
xdef stentox
stentox:
*--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
FMOVEM.X (a0),FP0 ...LOAD INPUT, do not set cc's
MOVE.L (A0),D0
MOVE.W 4(A0),D0
FMOVE.X FP0,X(a6)
ANDI.L #$7FFFFFFF,D0
CMPI.L #$3FB98000,D0 ...|X| >= 2**(-70)?
BGE.B TENOK1
BRA.W EXPBORS
TENOK1:
CMPI.L #$400B9B07,D0 ...|X| <= 16480*log2/log10 ?
BLE.B TENMAIN
BRA.W EXPBORS
TENMAIN:
*--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
FMOVE.X FP0,FP1
FMUL.D L2TEN64,FP1 ...X*64*LOG10/LOG2
FMOVE.L FP1,N(a6) ...N=INT(X*64*LOG10/LOG2)
MOVE.L d2,-(sp)
LEA EXPTBL,a1 ...LOAD ADDRESS OF TABLE OF 2^(J/64)
FMOVE.L N(a6),FP1 ...N --> FLOATING FMT
MOVE.L N(a6),D0
MOVE.L D0,d2
ANDI.L #$3F,D0 ...D0 IS J
ASL.L #4,D0 ...DISPLACEMENT FOR 2^(J/64)
ADDA.L D0,a1 ...ADDRESS FOR 2^(J/64)
ASR.L #6,d2 ...d2 IS L, N = 64L + J
MOVE.L d2,D0
ASR.L #1,D0 ...D0 IS M
SUB.L D0,d2 ...d2 IS M', N = 64(M+M') + J
ADDI.L #$3FFF,d2
MOVE.W d2,ADJFACT(a6) ...ADJFACT IS 2^(M')
MOVE.L (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.
FMOVE.X FP1,FP2
FMUL.D L10TWO1,FP1 ...N*(LOG2/64LOG10)_LEAD
MOVE.L (a1)+,FACT1(a6)
FMUL.X L10TWO2,FP2 ...N*(LOG2/64LOG10)_TRAIL
MOVE.L (a1)+,FACT1HI(a6)
MOVE.L (a1)+,FACT1LOW(a6)
FSUB.X FP1,FP0 ...X - N L_LEAD
MOVE.W (a1)+,FACT2(a6)
FSUB.X FP2,FP0 ...X - N L_TRAIL
clr.w FACT2+2(a6)
MOVE.W (a1)+,FACT2HI(a6)
clr.w FACT2HI+2(a6)
clr.l FACT2LOW(a6)
FMUL.X LOG10,FP0 ...FP0 IS R
ADD.W D0,FACT1(a6)
ADD.W 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)
FMOVE.X FP0,FP1
FMUL.X FP1,FP1 ...FP1 IS S = R*R
FMOVE.D EXPA5,FP2 ...FP2 IS A5
FMOVE.D EXPA4,FP3 ...FP3 IS A4
FMUL.X FP1,FP2 ...FP2 IS S*A5
FMUL.X FP1,FP3 ...FP3 IS S*A4
FADD.D EXPA3,FP2 ...FP2 IS A3+S*A5
FADD.D EXPA2,FP3 ...FP3 IS A2+S*A4
FMUL.X FP1,FP2 ...FP2 IS S*(A3+S*A5)
FMUL.X FP1,FP3 ...FP3 IS S*(A2+S*A4)
FADD.D EXPA1,FP2 ...FP2 IS A1+S*(A3+S*A5)
FMUL.X FP0,FP3 ...FP3 IS R*S*(A2+S*A4)
FMUL.X FP1,FP2 ...FP2 IS S*(A1+S*(A3+S*A5))
FADD.X FP3,FP0 ...FP0 IS R+R*S*(A2+S*A4)
FADD.X 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)
FMUL.X FACT1(a6),FP0
FADD.X FACT2(a6),FP0
FADD.X FACT1(a6),FP0
FMOVE.L d1,FPCR ;restore users exceptions
clr.w ADJFACT+2(a6)
move.l #$80000000,ADJFACT+4(a6)
clr.l ADJFACT+8(a6)
FMUL.X ADJFACT(a6),FP0 ...FINAL ADJUSTMENT
bra t_frcinx
end