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//

//      $Id: slog2.S,v 1.2 2001-09-27 12:01:22 chris Exp $

//

//      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