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|
* $OpenBSD: slogn.sa,v 1.3 2003/11/07 10:36:10 miod Exp $
* $NetBSD: slogn.sa,v 1.3 1994/10/26 07:49:54 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.
*
* slogn.sa 3.1 12/10/90
*
* slogn computes the natural logarithm of an
* input value. slognd does the same except the input value is a
* denormalized number. slognp1 computes log(1+X), and slognp1d
* computes log(1+X) for denormalized X.
*
* Input: Double-extended value in memory location pointed to by address
* register a0.
*
* Output: log(X) or log(1+X) returned in floating-point register 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 slogn takes approximately 190 cycles for input
* argument X such that |X-1| >= 1/16, which is the usual
* situation. For those arguments, slognp1 takes approximately
* 210 cycles. For the less common arguments, the program will
* run no worse than 10% slower.
*
* Algorithm:
* LOGN:
* Step 1. If |X-1| < 1/16, approximate log(X) by an odd polynomial in
* u, where u = 2(X-1)/(X+1). Otherwise, move on to Step 2.
*
* Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
* significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
* 2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
*
* Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
* log(1+u) = poly.
*
* Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
* by k*log(2) + (log(F) + poly). The values of log(F) are calculated
* beforehand and stored in the program.
*
* lognp1:
* Step 1: If |X| < 1/16, approximate log(1+X) by an odd polynomial in
* u where u = 2X/(2+X). Otherwise, move on to Step 2.
*
* Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
* of the algorithm for LOGN and compute log(1+X) as
* k*log(2) + log(F) + poly where poly approximates log(1+u),
* u = (Y-F)/F.
*
* Implementation Notes:
* Note 1. There are 64 different possible values for F, thus 64 log(F)'s
* need to be tabulated. Moreover, the values of 1/F are also
* tabulated so that the division in (Y-F)/F can be performed by a
* multiplication.
*
* Note 2. In Step 2 of lognp1, in order to preserved accuracy, the value
* Y-F has to be calculated carefully when 1/2 <= X < 3/2.
*
* Note 3. To fully exploit the pipeline, polynomials are usually separated
* into two parts evaluated independently before being added up.
*
slogn IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
include fpsp.h
BOUNDS1 DC.L $3FFEF07D,$3FFF8841
BOUNDS2 DC.L $3FFE8000,$3FFFC000
LOGOF2 DC.L $3FFE0000,$B17217F7,$D1CF79AC,$00000000
one DC.L $3F800000
zero DC.L $00000000
infty DC.L $7F800000
negone DC.L $BF800000
LOGA6 DC.L $3FC2499A,$B5E4040B
LOGA5 DC.L $BFC555B5,$848CB7DB
LOGA4 DC.L $3FC99999,$987D8730
LOGA3 DC.L $BFCFFFFF,$FF6F7E97
LOGA2 DC.L $3FD55555,$555555A4
LOGA1 DC.L $BFE00000,$00000008
LOGB5 DC.L $3F175496,$ADD7DAD6
LOGB4 DC.L $3F3C71C2,$FE80C7E0
LOGB3 DC.L $3F624924,$928BCCFF
LOGB2 DC.L $3F899999,$999995EC
LOGB1 DC.L $3FB55555,$55555555
TWO DC.L $40000000,$00000000
LTHOLD DC.L $3f990000,$80000000,$00000000,$00000000
LOGTBL:
DC.L $3FFE0000,$FE03F80F,$E03F80FE,$00000000
DC.L $3FF70000,$FF015358,$833C47E2,$00000000
DC.L $3FFE0000,$FA232CF2,$52138AC0,$00000000
DC.L $3FF90000,$BDC8D83E,$AD88D549,$00000000
DC.L $3FFE0000,$F6603D98,$0F6603DA,$00000000
DC.L $3FFA0000,$9CF43DCF,$F5EAFD48,$00000000
DC.L $3FFE0000,$F2B9D648,$0F2B9D65,$00000000
DC.L $3FFA0000,$DA16EB88,$CB8DF614,$00000000
DC.L $3FFE0000,$EF2EB71F,$C4345238,$00000000
DC.L $3FFB0000,$8B29B775,$1BD70743,$00000000
DC.L $3FFE0000,$EBBDB2A5,$C1619C8C,$00000000
DC.L $3FFB0000,$A8D839F8,$30C1FB49,$00000000
DC.L $3FFE0000,$E865AC7B,$7603A197,$00000000
DC.L $3FFB0000,$C61A2EB1,$8CD907AD,$00000000
DC.L $3FFE0000,$E525982A,$F70C880E,$00000000
DC.L $3FFB0000,$E2F2A47A,$DE3A18AF,$00000000
DC.L $3FFE0000,$E1FC780E,$1FC780E2,$00000000
DC.L $3FFB0000,$FF64898E,$DF55D551,$00000000
DC.L $3FFE0000,$DEE95C4C,$A037BA57,$00000000
DC.L $3FFC0000,$8DB956A9,$7B3D0148,$00000000
DC.L $3FFE0000,$DBEB61EE,$D19C5958,$00000000
DC.L $3FFC0000,$9B8FE100,$F47BA1DE,$00000000
DC.L $3FFE0000,$D901B203,$6406C80E,$00000000
DC.L $3FFC0000,$A9372F1D,$0DA1BD17,$00000000
DC.L $3FFE0000,$D62B80D6,$2B80D62C,$00000000
DC.L $3FFC0000,$B6B07F38,$CE90E46B,$00000000
DC.L $3FFE0000,$D3680D36,$80D3680D,$00000000
DC.L $3FFC0000,$C3FD0329,$06488481,$00000000
DC.L $3FFE0000,$D0B69FCB,$D2580D0B,$00000000
DC.L $3FFC0000,$D11DE0FF,$15AB18CA,$00000000
DC.L $3FFE0000,$CE168A77,$25080CE1,$00000000
DC.L $3FFC0000,$DE1433A1,$6C66B150,$00000000
DC.L $3FFE0000,$CB8727C0,$65C393E0,$00000000
DC.L $3FFC0000,$EAE10B5A,$7DDC8ADD,$00000000
DC.L $3FFE0000,$C907DA4E,$871146AD,$00000000
DC.L $3FFC0000,$F7856E5E,$E2C9B291,$00000000
DC.L $3FFE0000,$C6980C69,$80C6980C,$00000000
DC.L $3FFD0000,$82012CA5,$A68206D7,$00000000
DC.L $3FFE0000,$C4372F85,$5D824CA6,$00000000
DC.L $3FFD0000,$882C5FCD,$7256A8C5,$00000000
DC.L $3FFE0000,$C1E4BBD5,$95F6E947,$00000000
DC.L $3FFD0000,$8E44C60B,$4CCFD7DE,$00000000
DC.L $3FFE0000,$BFA02FE8,$0BFA02FF,$00000000
DC.L $3FFD0000,$944AD09E,$F4351AF6,$00000000
DC.L $3FFE0000,$BD691047,$07661AA3,$00000000
DC.L $3FFD0000,$9A3EECD4,$C3EAA6B2,$00000000
DC.L $3FFE0000,$BB3EE721,$A54D880C,$00000000
DC.L $3FFD0000,$A0218434,$353F1DE8,$00000000
DC.L $3FFE0000,$B92143FA,$36F5E02E,$00000000
DC.L $3FFD0000,$A5F2FCAB,$BBC506DA,$00000000
DC.L $3FFE0000,$B70FBB5A,$19BE3659,$00000000
DC.L $3FFD0000,$ABB3B8BA,$2AD362A5,$00000000
DC.L $3FFE0000,$B509E68A,$9B94821F,$00000000
DC.L $3FFD0000,$B1641795,$CE3CA97B,$00000000
DC.L $3FFE0000,$B30F6352,$8917C80B,$00000000
DC.L $3FFD0000,$B7047551,$5D0F1C61,$00000000
DC.L $3FFE0000,$B11FD3B8,$0B11FD3C,$00000000
DC.L $3FFD0000,$BC952AFE,$EA3D13E1,$00000000
DC.L $3FFE0000,$AF3ADDC6,$80AF3ADE,$00000000
DC.L $3FFD0000,$C2168ED0,$F458BA4A,$00000000
DC.L $3FFE0000,$AD602B58,$0AD602B6,$00000000
DC.L $3FFD0000,$C788F439,$B3163BF1,$00000000
DC.L $3FFE0000,$AB8F69E2,$8359CD11,$00000000
DC.L $3FFD0000,$CCECAC08,$BF04565D,$00000000
DC.L $3FFE0000,$A9C84A47,$A07F5638,$00000000
DC.L $3FFD0000,$D2420487,$2DD85160,$00000000
DC.L $3FFE0000,$A80A80A8,$0A80A80B,$00000000
DC.L $3FFD0000,$D7894992,$3BC3588A,$00000000
DC.L $3FFE0000,$A655C439,$2D7B73A8,$00000000
DC.L $3FFD0000,$DCC2C4B4,$9887DACC,$00000000
DC.L $3FFE0000,$A4A9CF1D,$96833751,$00000000
DC.L $3FFD0000,$E1EEBD3E,$6D6A6B9E,$00000000
DC.L $3FFE0000,$A3065E3F,$AE7CD0E0,$00000000
DC.L $3FFD0000,$E70D785C,$2F9F5BDC,$00000000
DC.L $3FFE0000,$A16B312E,$A8FC377D,$00000000
DC.L $3FFD0000,$EC1F392C,$5179F283,$00000000
DC.L $3FFE0000,$9FD809FD,$809FD80A,$00000000
DC.L $3FFD0000,$F12440D3,$E36130E6,$00000000
DC.L $3FFE0000,$9E4CAD23,$DD5F3A20,$00000000
DC.L $3FFD0000,$F61CCE92,$346600BB,$00000000
DC.L $3FFE0000,$9CC8E160,$C3FB19B9,$00000000
DC.L $3FFD0000,$FB091FD3,$8145630A,$00000000
DC.L $3FFE0000,$9B4C6F9E,$F03A3CAA,$00000000
DC.L $3FFD0000,$FFE97042,$BFA4C2AD,$00000000
DC.L $3FFE0000,$99D722DA,$BDE58F06,$00000000
DC.L $3FFE0000,$825EFCED,$49369330,$00000000
DC.L $3FFE0000,$9868C809,$868C8098,$00000000
DC.L $3FFE0000,$84C37A7A,$B9A905C9,$00000000
DC.L $3FFE0000,$97012E02,$5C04B809,$00000000
DC.L $3FFE0000,$87224C2E,$8E645FB7,$00000000
DC.L $3FFE0000,$95A02568,$095A0257,$00000000
DC.L $3FFE0000,$897B8CAC,$9F7DE298,$00000000
DC.L $3FFE0000,$94458094,$45809446,$00000000
DC.L $3FFE0000,$8BCF55DE,$C4CD05FE,$00000000
DC.L $3FFE0000,$92F11384,$0497889C,$00000000
DC.L $3FFE0000,$8E1DC0FB,$89E125E5,$00000000
DC.L $3FFE0000,$91A2B3C4,$D5E6F809,$00000000
DC.L $3FFE0000,$9066E68C,$955B6C9B,$00000000
DC.L $3FFE0000,$905A3863,$3E06C43B,$00000000
DC.L $3FFE0000,$92AADE74,$C7BE59E0,$00000000
DC.L $3FFE0000,$8F1779D9,$FDC3A219,$00000000
DC.L $3FFE0000,$94E9BFF6,$15845643,$00000000
DC.L $3FFE0000,$8DDA5202,$37694809,$00000000
DC.L $3FFE0000,$9723A1B7,$20134203,$00000000
DC.L $3FFE0000,$8CA29C04,$6514E023,$00000000
DC.L $3FFE0000,$995899C8,$90EB8990,$00000000
DC.L $3FFE0000,$8B70344A,$139BC75A,$00000000
DC.L $3FFE0000,$9B88BDAA,$3A3DAE2F,$00000000
DC.L $3FFE0000,$8A42F870,$5669DB46,$00000000
DC.L $3FFE0000,$9DB4224F,$FFE1157C,$00000000
DC.L $3FFE0000,$891AC73A,$E9819B50,$00000000
DC.L $3FFE0000,$9FDADC26,$8B7A12DA,$00000000
DC.L $3FFE0000,$87F78087,$F78087F8,$00000000
DC.L $3FFE0000,$A1FCFF17,$CE733BD4,$00000000
DC.L $3FFE0000,$86D90544,$7A34ACC6,$00000000
DC.L $3FFE0000,$A41A9E8F,$5446FB9F,$00000000
DC.L $3FFE0000,$85BF3761,$2CEE3C9B,$00000000
DC.L $3FFE0000,$A633CD7E,$6771CD8B,$00000000
DC.L $3FFE0000,$84A9F9C8,$084A9F9D,$00000000
DC.L $3FFE0000,$A8489E60,$0B435A5E,$00000000
DC.L $3FFE0000,$83993052,$3FBE3368,$00000000
DC.L $3FFE0000,$AA59233C,$CCA4BD49,$00000000
DC.L $3FFE0000,$828CBFBE,$B9A020A3,$00000000
DC.L $3FFE0000,$AC656DAE,$6BCC4985,$00000000
DC.L $3FFE0000,$81848DA8,$FAF0D277,$00000000
DC.L $3FFE0000,$AE6D8EE3,$60BB2468,$00000000
DC.L $3FFE0000,$80808080,$80808081,$00000000
DC.L $3FFE0000,$B07197A2,$3C46C654,$00000000
ADJK equ L_SCR1
X equ FP_SCR1
XDCARE equ X+2
XFRAC equ X+4
F equ FP_SCR2
FFRAC equ F+4
KLOG2 equ FP_SCR3
SAVEU equ FP_SCR4
xref t_frcinx
xref t_extdnrm
xref t_operr
xref t_dz
xdef slognd
slognd:
*--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
MOVE.L #-100,ADJK(a6) ...INPUT = 2^(ADJK) * FP0
*----normalize the input value by left shifting k bits (k to be determined
*----below), adjusting exponent and storing -k to ADJK
*----the value TWOTO100 is no longer needed.
*----Note that this code assumes the denormalized input is NON-ZERO.
MoveM.L D2-D7,-(A7) ...save some registers
Clr.L D3 ...D3 is exponent of smallest norm. #
Move.L 4(A0),D4
Move.L 8(A0),D5 ...(D4,D5) is (Hi_X,Lo_X)
Clr.L D2 ...D2 used for holding K
Tst.L D4
BNE.B HiX_not0
HiX_0:
Move.L D5,D4
Clr.L D5
Move.L #32,D2
Clr.L D6
BFFFO D4{0:32},D6
LSL.L D6,D4
Add.L D6,D2 ...(D3,D4,D5) is normalized
Move.L D3,X(a6)
Move.L D4,XFRAC(a6)
Move.L D5,XFRAC+4(a6)
Neg.L D2
Move.L D2,ADJK(a6)
FMove.X X(a6),FP0
MoveM.L (A7)+,D2-D7 ...restore registers
LEA X(a6),A0
Bra.B LOGBGN ...begin regular log(X)
HiX_not0:
Clr.L D6
BFFFO D4{0:32},D6 ...find first 1
Move.L D6,D2 ...get k
LSL.L D6,D4
Move.L D5,D7 ...a copy of D5
LSL.L D6,D5
Neg.L D6
AddI.L #32,D6
LSR.L D6,D7
Or.L D7,D4 ...(D3,D4,D5) normalized
Move.L D3,X(a6)
Move.L D4,XFRAC(a6)
Move.L D5,XFRAC+4(a6)
Neg.L D2
Move.L D2,ADJK(a6)
FMove.X X(a6),FP0
MoveM.L (A7)+,D2-D7 ...restore registers
LEA X(a6),A0
Bra.B LOGBGN ...begin regular log(X)
xdef slogn
slogn:
*--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
FMOVE.X (A0),FP0 ...LOAD INPUT
CLR.L ADJK(a6)
LOGBGN:
*--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
*--A FINITE, NON-ZERO, NORMALIZED NUMBER.
move.l (a0),d0
move.w 4(a0),d0
move.l (a0),X(a6)
move.l 4(a0),X+4(a6)
move.l 8(a0),X+8(a6)
TST.L D0 ...CHECK IF X IS NEGATIVE
BLT.W LOGNEG ...LOG OF NEGATIVE ARGUMENT IS INVALID
CMP2.L BOUNDS1,D0 ...X IS POSITIVE, CHECK IF X IS NEAR 1
BCC.W LOGNEAR1 ...BOUNDS IS ROUGHLY [15/16, 17/16]
LOGMAIN:
*--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
*--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
*--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
*--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
*-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
*--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
*--LOG(1+U) CAN BE VERY EFFICIENT.
*--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
*--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
*--GET K, Y, F, AND ADDRESS OF 1/F.
ASR.L #8,D0
ASR.L #8,D0 ...SHIFTED 16 BITS, BIASED EXPO. OF X
SUBI.L #$3FFF,D0 ...THIS IS K
ADD.L ADJK(a6),D0 ...ADJUST K, ORIGINAL INPUT MAY BE DENORM.
LEA LOGTBL,A0 ...BASE ADDRESS OF 1/F AND LOG(F)
FMOVE.L D0,FP1 ...CONVERT K TO FLOATING-POINT FORMAT
*--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
MOVE.L #$3FFF0000,X(a6) ...X IS NOW Y, I.E. 2^(-K)*X
MOVE.L XFRAC(a6),FFRAC(a6)
ANDI.L #$FE000000,FFRAC(a6) ...FIRST 7 BITS OF Y
ORI.L #$01000000,FFRAC(a6) ...GET F: ATTACH A 1 AT THE EIGHTH BIT
MOVE.L FFRAC(a6),D0 ...READY TO GET ADDRESS OF 1/F
ANDI.L #$7E000000,D0
ASR.L #8,D0
ASR.L #8,D0
ASR.L #4,D0 ...SHIFTED 20, D0 IS THE DISPLACEMENT
ADDA.L D0,A0 ...A0 IS THE ADDRESS FOR 1/F
FMOVE.X X(a6),FP0
move.l #$3fff0000,F(a6)
clr.l F+8(a6)
FSUB.X F(a6),FP0 ...Y-F
FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2 WHILE FP0 IS NOT READY
*--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
*--REGISTERS SAVED: FPCR, FP1, FP2
LP1CONT1:
*--AN RE-ENTRY POINT FOR LOGNP1
FMUL.X (A0),FP0 ...FP0 IS U = (Y-F)/F
FMUL.X LOGOF2,FP1 ...GET K*LOG2 WHILE FP0 IS NOT READY
FMOVE.X FP0,FP2
FMUL.X FP2,FP2 ...FP2 IS V=U*U
FMOVE.X FP1,KLOG2(a6) ...PUT K*LOG2 IN MEMEORY, FREE FP1
*--LOG(1+U) IS APPROXIMATED BY
*--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
*--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))]
FMOVE.X FP2,FP3
FMOVE.X FP2,FP1
FMUL.D LOGA6,FP1 ...V*A6
FMUL.D LOGA5,FP2 ...V*A5
FADD.D LOGA4,FP1 ...A4+V*A6
FADD.D LOGA3,FP2 ...A3+V*A5
FMUL.X FP3,FP1 ...V*(A4+V*A6)
FMUL.X FP3,FP2 ...V*(A3+V*A5)
FADD.D LOGA2,FP1 ...A2+V*(A4+V*A6)
FADD.D LOGA1,FP2 ...A1+V*(A3+V*A5)
FMUL.X FP3,FP1 ...V*(A2+V*(A4+V*A6))
ADDA.L #16,A0 ...ADDRESS OF LOG(F)
FMUL.X FP3,FP2 ...V*(A1+V*(A3+V*A5)), FP3 RELEASED
FMUL.X FP0,FP1 ...U*V*(A2+V*(A4+V*A6))
FADD.X FP2,FP0 ...U+V*(A1+V*(A3+V*A5)), FP2 RELEASED
FADD.X (A0),FP1 ...LOG(F)+U*V*(A2+V*(A4+V*A6))
FMOVEm.X (sp)+,FP2/fp3 ...RESTORE FP2
FADD.X FP1,FP0 ...FP0 IS LOG(F) + LOG(1+U)
fmove.l d1,fpcr
FADD.X KLOG2(a6),FP0 ...FINAL ADD
bra t_frcinx
LOGNEAR1:
*--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
FMOVE.X FP0,FP1
FSUB.S one,FP1 ...FP1 IS X-1
FADD.S one,FP0 ...FP0 IS X+1
FADD.X FP1,FP1 ...FP1 IS 2(X-1)
*--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
*--IN U, U = 2(X-1)/(X+1) = FP1/FP0
LP1CONT2:
*--THIS IS AN RE-ENTRY POINT FOR LOGNP1
FDIV.X FP0,FP1 ...FP1 IS U
FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2
*--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
*--LET V=U*U, W=V*V, CALCULATE
*--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
*--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] )
FMOVE.X FP1,FP0
FMUL.X FP0,FP0 ...FP0 IS V
FMOVE.X FP1,SAVEU(a6) ...STORE U IN MEMORY, FREE FP1
FMOVE.X FP0,FP1
FMUL.X FP1,FP1 ...FP1 IS W
FMOVE.D LOGB5,FP3
FMOVE.D LOGB4,FP2
FMUL.X FP1,FP3 ...W*B5
FMUL.X FP1,FP2 ...W*B4
FADD.D LOGB3,FP3 ...B3+W*B5
FADD.D LOGB2,FP2 ...B2+W*B4
FMUL.X FP3,FP1 ...W*(B3+W*B5), FP3 RELEASED
FMUL.X FP0,FP2 ...V*(B2+W*B4)
FADD.D LOGB1,FP1 ...B1+W*(B3+W*B5)
FMUL.X SAVEU(a6),FP0 ...FP0 IS U*V
FADD.X FP2,FP1 ...B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
FMOVEm.X (sp)+,FP2/fp3 ...FP2 RESTORED
FMUL.X FP1,FP0 ...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
fmove.l d1,fpcr
FADD.X SAVEU(a6),FP0
bra t_frcinx
rts
LOGNEG:
*--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
bra t_operr
xdef slognp1d
slognp1d:
*--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
* Simply return the denorm
bra t_extdnrm
xdef slognp1
slognp1:
*--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
FMOVE.X (A0),FP0 ...LOAD INPUT
fabs.x fp0 ;test magnitude
fcmp.x LTHOLD,fp0 ;compare with min threshold
fbgt.w LP1REAL ;if greater, continue
fmove.l #0,fpsr ;clr N flag from compare
fmove.l d1,fpcr
fmove.x (a0),fp0 ;return signed argument
bra t_frcinx
LP1REAL:
FMOVE.X (A0),FP0 ...LOAD INPUT
CLR.L ADJK(a6)
FMOVE.X FP0,FP1 ...FP1 IS INPUT Z
FADD.S one,FP0 ...X := ROUND(1+Z)
FMOVE.X FP0,X(a6)
MOVE.W XFRAC(a6),XDCARE(a6)
MOVE.L X(a6),D0
TST.L D0
BLE.W LP1NEG0 ...LOG OF ZERO OR -VE
CMP2.L BOUNDS2,D0
BCS.W LOGMAIN ...BOUNDS2 IS [1/2,3/2]
*--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
*--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
*--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
LP1NEAR1:
*--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
CMP2.L BOUNDS1,D0
BCS.B LP1CARE
LP1ONE16:
*--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
*--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
FADD.X FP1,FP1 ...FP1 IS 2Z
FADD.S one,FP0 ...FP0 IS 1+X
*--U = FP1/FP0
BRA.W LP1CONT2
LP1CARE:
*--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
*--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
*--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
*--THERE ARE ONLY TWO CASES.
*--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
*--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z
*--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
*--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
MOVE.L XFRAC(a6),FFRAC(a6)
ANDI.L #$FE000000,FFRAC(a6)
ORI.L #$01000000,FFRAC(a6) ...F OBTAINED
CMPI.L #$3FFF8000,D0 ...SEE IF 1+Z > 1
BGE.B KISZERO
KISNEG1:
FMOVE.S TWO,FP0
move.l #$3fff0000,F(a6)
clr.l F+8(a6)
FSUB.X F(a6),FP0 ...2-F
MOVE.L FFRAC(a6),D0
ANDI.L #$7E000000,D0
ASR.L #8,D0
ASR.L #8,D0
ASR.L #4,D0 ...D0 CONTAINS DISPLACEMENT FOR 1/F
FADD.X FP1,FP1 ...GET 2Z
FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2
FADD.X FP1,FP0 ...FP0 IS Y-F = (2-F)+2Z
LEA LOGTBL,A0 ...A0 IS ADDRESS OF 1/F
ADDA.L D0,A0
FMOVE.S negone,FP1 ...FP1 IS K = -1
BRA.W LP1CONT1
KISZERO:
FMOVE.S one,FP0
move.l #$3fff0000,F(a6)
clr.l F+8(a6)
FSUB.X F(a6),FP0 ...1-F
MOVE.L FFRAC(a6),D0
ANDI.L #$7E000000,D0
ASR.L #8,D0
ASR.L #8,D0
ASR.L #4,D0
FADD.X FP1,FP0 ...FP0 IS Y-F
FMOVEm.X FP2/fp3,-(sp) ...FP2 SAVED
LEA LOGTBL,A0
ADDA.L D0,A0 ...A0 IS ADDRESS OF 1/F
FMOVE.S zero,FP1 ...FP1 IS K = 0
BRA.W LP1CONT1
LP1NEG0:
*--FPCR SAVED. D0 IS X IN COMPACT FORM.
TST.L D0
BLT.B LP1NEG
LP1ZERO:
FMOVE.S negone,FP0
fmove.l d1,fpcr
bra t_dz
LP1NEG:
FMOVE.S zero,FP0
fmove.l d1,fpcr
bra t_operr
end
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