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|
|       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.
|

|               Copyright (C) Motorola, Inc. 1990
|                       All Rights Reserved
|
|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 
|       The copyright notice above does not evidence any  
|       actual or intended publication of such source code.

|SLOG2    idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        |xref   t_frcinx        
        |xref   t_operr
        |xref   slogn
        |xref   slognd

INV_L10:  .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000

INV_L2:   .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000

        .global slog10d
slog10d:
|--entry point for Log10(X), X is denormalized
        movel           (%a0),%d0
        blt             invalid
        movel           %d1,-(%sp)
        clrl            %d1
        bsr             slognd                  | ...log(X), X denorm.
        fmovel          (%sp)+,%fpcr
        fmulx           INV_L10,%fp0
        bra             t_frcinx

        .global slog10
slog10:
|--entry point for Log10(X), X is normalized

        movel           (%a0),%d0
        blt             invalid
        movel           %d1,-(%sp)
        clrl            %d1
        bsr             slogn                   | ...log(X), X normal.
        fmovel          (%sp)+,%fpcr
        fmulx           INV_L10,%fp0
        bra             t_frcinx


        .global slog2d
slog2d:
|--entry point for Log2(X), X is denormalized

        movel           (%a0),%d0
        blt             invalid
        movel           %d1,-(%sp)
        clrl            %d1
        bsr             slognd                  | ...log(X), X denorm.
        fmovel          (%sp)+,%fpcr
        fmulx           INV_L2,%fp0
        bra             t_frcinx

        .global slog2
slog2:
|--entry point for Log2(X), X is normalized
        movel           (%a0),%d0
        blt             invalid

        movel           8(%a0),%d0
        bnes            continue                | ...X is not 2^k

        movel           4(%a0),%d0
        andl            #0x7FFFFFFF,%d0
        tstl            %d0
        bnes            continue

|--X = 2^k.
        movew           (%a0),%d0
        andl            #0x00007FFF,%d0
        subl            #0x3FFF,%d0
        fmovel          %d1,%fpcr
        fmovel          %d0,%fp0
        bra             t_frcinx

continue:
        movel           %d1,-(%sp)
        clrl            %d1
        bsr             slogn                   | ...log(X), X normal.
        fmovel          (%sp)+,%fpcr
        fmulx           INV_L2,%fp0
        bra             t_frcinx

invalid:
        bra             t_operr

        |end