1994-10-26 10:48:18 +03:00
|
|
|
* $NetBSD: slog2.sa,v 1.2 1994/10/26 07:49:52 cgd Exp $
|
|
|
|
|
|
1994-07-05 21:50:24 +04:00
|
|
|
* 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
|
