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* $OpenBSD: slog2.sa,v 1.2 1996/05/29 21:05:39 niklas Exp $
* $NetBSD: slog2.sa,v 1.2 1994/10/26 07:49:52 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.
*
* slog2.sa 3.1 12/10/90
*
* The entry point slog10 computes the base-10
* logarithm of an input argument X.
* slog10d does the same except the input value is a
* denormalized number.
* sLog2 and sLog2d are the base-2 analogues.
*
* INPUT: Double-extended value in memory location pointed to
* by address register a0.
*
* OUTPUT: log_10(X) or log_2(X) returned in floating-point
* register fp0.
*
* ACCURACY and MONOTONICITY: The returned result is within 1.7
* ulps in 64 significant bit, i.e. within 0.5003 ulp
* to 53 bits if the result is subsequently rounded
* to double precision. The result is provably monotonic
* in double precision.
*
* SPEED: Two timings are measured, both in the copy-back mode.
* The first one is measured when the function is invoked
* the first time (so the instructions and data are not
* in cache), and the second one is measured when the
* function is reinvoked at the same input argument.
*
* ALGORITHM and IMPLEMENTATION NOTES:
*
* slog10d:
*
* Step 0. If X < 0, create a NaN and raise the invalid operation
* flag. Otherwise, save FPCR in D1; set FpCR to default.
* Notes: Default means round-to-nearest mode, no floating-point
* traps, and precision control = double extended.
*
* Step 1. Call slognd to obtain Y = log(X), the natural log of X.
* Notes: Even if X is denormalized, log(X) is always normalized.
*
* Step 2. Compute log_10(X) = log(X) * (1/log(10)).
* 2.1 Restore the user FPCR
* 2.2 Return ans := Y * INV_L10.
*
*
* slog10:
*
* Step 0. If X < 0, create a NaN and raise the invalid operation
* flag. Otherwise, save FPCR in D1; set FpCR to default.
* Notes: Default means round-to-nearest mode, no floating-point
* traps, and precision control = double extended.
*
* Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
*
* Step 2. Compute log_10(X) = log(X) * (1/log(10)).
* 2.1 Restore the user FPCR
* 2.2 Return ans := Y * INV_L10.
*
*
* sLog2d:
*
* Step 0. If X < 0, create a NaN and raise the invalid operation
* flag. Otherwise, save FPCR in D1; set FpCR to default.
* Notes: Default means round-to-nearest mode, no floating-point
* traps, and precision control = double extended.
*
* Step 1. Call slognd to obtain Y = log(X), the natural log of X.
* Notes: Even if X is denormalized, log(X) is always normalized.
*
* Step 2. Compute log_10(X) = log(X) * (1/log(2)).
* 2.1 Restore the user FPCR
* 2.2 Return ans := Y * INV_L2.
*
*
* sLog2:
*
* Step 0. If X < 0, create a NaN and raise the invalid operation
* flag. Otherwise, save FPCR in D1; set FpCR to default.
* Notes: Default means round-to-nearest mode, no floating-point
* traps, and precision control = double extended.
*
* Step 1. If X is not an integer power of two, i.e., X != 2^k,
* go to Step 3.
*
* Step 2. Return k.
* 2.1 Get integer k, X = 2^k.
* 2.2 Restore the user FPCR.
* 2.3 Return ans := convert-to-double-extended(k).
*
* Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
*
* Step 4. Compute log_2(X) = log(X) * (1/log(2)).
* 4.1 Restore the user FPCR
* 4.2 Return ans := Y * INV_L2.
*
SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
xref t_frcinx
xref t_operr
xref slogn
xref slognd
INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000
INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000
xdef slog10d
slog10d:
*--entry point for Log10(X), X is denormalized
move.l (a0),d0
blt.w invalid
move.l d1,-(sp)
clr.l d1
bsr slognd ...log(X), X denorm.
fmove.l (sp)+,fpcr
fmul.x INV_L10,fp0
bra t_frcinx
xdef slog10
slog10:
*--entry point for Log10(X), X is normalized
move.l (a0),d0
blt.w invalid
move.l d1,-(sp)
clr.l d1
bsr slogn ...log(X), X normal.
fmove.l (sp)+,fpcr
fmul.x INV_L10,fp0
bra t_frcinx
xdef slog2d
slog2d:
*--entry point for Log2(X), X is denormalized
move.l (a0),d0
blt.w invalid
move.l d1,-(sp)
clr.l d1
bsr slognd ...log(X), X denorm.
fmove.l (sp)+,fpcr
fmul.x INV_L2,fp0
bra t_frcinx
xdef slog2
slog2:
*--entry point for Log2(X), X is normalized
move.l (a0),d0
blt.w invalid
move.l 8(a0),d0
bne.b continue ...X is not 2^k
move.l 4(a0),d0
and.l #$7FFFFFFF,d0
tst.l d0
bne.b continue
*--X = 2^k.
move.w (a0),d0
and.l #$00007FFF,d0
sub.l #$3FFF,d0
fmove.l d1,fpcr
fmove.l d0,fp0
bra t_frcinx
continue:
move.l d1,-(sp)
clr.l d1
bsr slogn ...log(X), X normal.
fmove.l (sp)+,fpcr
fmul.x INV_L2,fp0
bra t_frcinx
invalid:
bra t_operr
end
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