212 lines
6.3 KiB
Plaintext
212 lines
6.3 KiB
Plaintext
* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
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* M68000 Hi-Performance Microprocessor Division
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* M68040 Software Package
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*
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* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
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* All rights reserved.
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*
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* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
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* To the maximum extent permitted by applicable law,
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* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
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* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
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* PARTICULAR PURPOSE and any warranty against infringement with
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* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
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* and any accompanying written materials.
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*
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* To the maximum extent permitted by applicable law,
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* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
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* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
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* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
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* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
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* SOFTWARE. Motorola assumes no responsibility for the maintenance
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* and support of the SOFTWARE.
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*
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* You are hereby granted a copyright license to use, modify, and
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* distribute the SOFTWARE so long as this entire notice is retained
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* without alteration in any modified and/or redistributed versions,
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* and that such modified versions are clearly identified as such.
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* No licenses are granted by implication, estoppel or otherwise
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* under any patents or trademarks of Motorola, Inc.
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*
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* slog2.sa 3.1 12/10/90
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*
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* The entry point slog10 computes the base-10
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* logarithm of an input argument X.
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* slog10d does the same except the input value is a
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* denormalized number.
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* sLog2 and sLog2d are the base-2 analogues.
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*
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* INPUT: Double-extended value in memory location pointed to
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* by address register a0.
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*
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* OUTPUT: log_10(X) or log_2(X) returned in floating-point
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* register fp0.
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*
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* ACCURACY and MONOTONICITY: The returned result is within 1.7
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* ulps in 64 significant bit, i.e. within 0.5003 ulp
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* to 53 bits if the result is subsequently rounded
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* to double precision. The result is provably monotonic
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* in double precision.
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*
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* SPEED: Two timings are measured, both in the copy-back mode.
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* The first one is measured when the function is invoked
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* the first time (so the instructions and data are not
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* in cache), and the second one is measured when the
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* function is reinvoked at the same input argument.
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*
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* ALGORITHM and IMPLEMENTATION NOTES:
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*
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* slog10d:
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*
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* Step 0. If X < 0, create a NaN and raise the invalid operation
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* flag. Otherwise, save FPCR in D1; set FpCR to default.
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* Notes: Default means round-to-nearest mode, no floating-point
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* traps, and precision control = double extended.
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*
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* Step 1. Call slognd to obtain Y = log(X), the natural log of X.
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* Notes: Even if X is denormalized, log(X) is always normalized.
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*
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* Step 2. Compute log_10(X) = log(X) * (1/log(10)).
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* 2.1 Restore the user FPCR
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* 2.2 Return ans := Y * INV_L10.
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*
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*
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* slog10:
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*
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* Step 0. If X < 0, create a NaN and raise the invalid operation
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* flag. Otherwise, save FPCR in D1; set FpCR to default.
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* Notes: Default means round-to-nearest mode, no floating-point
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* traps, and precision control = double extended.
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*
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* Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
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*
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* Step 2. Compute log_10(X) = log(X) * (1/log(10)).
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* 2.1 Restore the user FPCR
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* 2.2 Return ans := Y * INV_L10.
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*
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*
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* sLog2d:
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*
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* Step 0. If X < 0, create a NaN and raise the invalid operation
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* flag. Otherwise, save FPCR in D1; set FpCR to default.
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* Notes: Default means round-to-nearest mode, no floating-point
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* traps, and precision control = double extended.
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*
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* Step 1. Call slognd to obtain Y = log(X), the natural log of X.
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* Notes: Even if X is denormalized, log(X) is always normalized.
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*
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* Step 2. Compute log_10(X) = log(X) * (1/log(2)).
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* 2.1 Restore the user FPCR
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* 2.2 Return ans := Y * INV_L2.
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*
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*
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* sLog2:
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*
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* Step 0. If X < 0, create a NaN and raise the invalid operation
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* flag. Otherwise, save FPCR in D1; set FpCR to default.
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* Notes: Default means round-to-nearest mode, no floating-point
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* traps, and precision control = double extended.
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*
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* Step 1. If X is not an integer power of two, i.e., X != 2^k,
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* go to Step 3.
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*
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* Step 2. Return k.
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* 2.1 Get integer k, X = 2^k.
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* 2.2 Restore the user FPCR.
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* 2.3 Return ans := convert-to-double-extended(k).
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*
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* Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
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*
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* Step 4. Compute log_2(X) = log(X) * (1/log(2)).
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* 4.1 Restore the user FPCR
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* 4.2 Return ans := Y * INV_L2.
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*
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SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package
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section 8
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xref t_frcinx
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xref t_operr
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xref slogn
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xref slognd
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INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000
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INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000
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xdef slog10d
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slog10d:
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*--entry point for Log10(X), X is denormalized
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move.l (a0),d0
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blt.w invalid
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move.l d1,-(sp)
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clr.l d1
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bsr slognd ...log(X), X denorm.
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fmove.l (sp)+,fpcr
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fmul.x INV_L10,fp0
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bra t_frcinx
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xdef slog10
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slog10:
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*--entry point for Log10(X), X is normalized
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move.l (a0),d0
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blt.w invalid
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move.l d1,-(sp)
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clr.l d1
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bsr slogn ...log(X), X normal.
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fmove.l (sp)+,fpcr
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fmul.x INV_L10,fp0
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bra t_frcinx
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xdef slog2d
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slog2d:
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*--entry point for Log2(X), X is denormalized
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move.l (a0),d0
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blt.w invalid
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move.l d1,-(sp)
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clr.l d1
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bsr slognd ...log(X), X denorm.
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fmove.l (sp)+,fpcr
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fmul.x INV_L2,fp0
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bra t_frcinx
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xdef slog2
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slog2:
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*--entry point for Log2(X), X is normalized
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move.l (a0),d0
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blt.w invalid
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move.l 8(a0),d0
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bne.b continue ...X is not 2^k
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move.l 4(a0),d0
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and.l #$7FFFFFFF,d0
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tst.l d0
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bne.b continue
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*--X = 2^k.
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move.w (a0),d0
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and.l #$00007FFF,d0
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sub.l #$3FFF,d0
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fmove.l d1,fpcr
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fmove.l d0,fp0
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bra t_frcinx
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continue:
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move.l d1,-(sp)
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clr.l d1
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bsr slogn ...log(X), X normal.
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fmove.l (sp)+,fpcr
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fmul.x INV_L2,fp0
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bra t_frcinx
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invalid:
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bra t_operr
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end
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