arch/m68k/fpsp040/slog2.S

   1 |
   2 |       slog2.sa 3.1 12/10/90
   3 |
   4 |       The entry point slog10 computes the base-10
   5 |       logarithm of an input argument X.
   6 |       slog10d does the same except the input value is a
   7 |       denormalized number.
   8 |       sLog2 and sLog2d are the base-2 analogues.
   9 |
  10 |       INPUT:  Double-extended value in memory location pointed to
  11 |               by address register a0.
  12 |
  13 |       OUTPUT: log_10(X) or log_2(X) returned in floating-point
  14 |               register fp0.
  15 |
  16 |       ACCURACY and MONOTONICITY: The returned result is within 1.7
  17 |               ulps in 64 significant bit, i.e. within 0.5003 ulp
  18 |               to 53 bits if the result is subsequently rounded
  19 |               to double precision. The result is provably monotonic
  20 |               in double precision.
  21 |
  22 |       SPEED:  Two timings are measured, both in the copy-back mode.
  23 |               The first one is measured when the function is invoked
  24 |               the first time (so the instructions and data are not
  25 |               in cache), and the second one is measured when the
  26 |               function is reinvoked at the same input argument.
  27 |
  28 |       ALGORITHM and IMPLEMENTATION NOTES:
  29 |
  30 |       slog10d:
  31 |
  32 |       Step 0.   If X < 0, create a NaN and raise the invalid operation
  33 |                 flag. Otherwise, save FPCR in D1; set FpCR to default.
  34 |       Notes:    Default means round-to-nearest mode, no floating-point
  35 |                 traps, and precision control = double extended.
  36 |
  37 |       Step 1.   Call slognd to obtain Y = log(X), the natural log of X.
  38 |       Notes:    Even if X is denormalized, log(X) is always normalized.
  39 |
  40 |       Step 2.   Compute log_10(X) = log(X) * (1/log(10)).
  41 |            2.1  Restore the user FPCR
  42 |            2.2  Return ans := Y * INV_L10.
  43 |
  44 |
  45 |       slog10:
  46 |
  47 |       Step 0.   If X < 0, create a NaN and raise the invalid operation
  48 |                 flag. Otherwise, save FPCR in D1; set FpCR to default.
  49 |       Notes:    Default means round-to-nearest mode, no floating-point
  50 |                 traps, and precision control = double extended.
  51 |
  52 |       Step 1.   Call sLogN to obtain Y = log(X), the natural log of X.
  53 |
  54 |       Step 2.   Compute log_10(X) = log(X) * (1/log(10)).
  55 |            2.1  Restore the user FPCR
  56 |            2.2  Return ans := Y * INV_L10.
  57 |
  58 |
  59 |       sLog2d:
  60 |
  61 |       Step 0.   If X < 0, create a NaN and raise the invalid operation
  62 |                 flag. Otherwise, save FPCR in D1; set FpCR to default.
  63 |       Notes:    Default means round-to-nearest mode, no floating-point
  64 |                 traps, and precision control = double extended.
  65 |
  66 |       Step 1.   Call slognd to obtain Y = log(X), the natural log of X.
  67 |       Notes:    Even if X is denormalized, log(X) is always normalized.
  68 |
  69 |       Step 2.   Compute log_10(X) = log(X) * (1/log(2)).
  70 |            2.1  Restore the user FPCR
  71 |            2.2  Return ans := Y * INV_L2.
  72 |
  73 |
  74 |       sLog2:
  75 |
  76 |       Step 0.   If X < 0, create a NaN and raise the invalid operation
  77 |                 flag. Otherwise, save FPCR in D1; set FpCR to default.
  78 |       Notes:    Default means round-to-nearest mode, no floating-point
  79 |                 traps, and precision control = double extended.
  80 |
  81 |       Step 1.   If X is not an integer power of two, i.e., X != 2^k,
  82 |                 go to Step 3.
  83 |
  84 |       Step 2.   Return k.
  85 |            2.1  Get integer k, X = 2^k.
  86 |            2.2  Restore the user FPCR.
  87 |            2.3  Return ans := convert-to-double-extended(k).
  88 |
  89 |       Step 3.   Call sLogN to obtain Y = log(X), the natural log of X.
  90 |
  91 |       Step 4.   Compute log_2(X) = log(X) * (1/log(2)).
  92 |            4.1  Restore the user FPCR
  93 |            4.2  Return ans := Y * INV_L2.
  94 |
  95
  96 |               Copyright (C) Motorola, Inc. 1990
  97 |                       All Rights Reserved
  98 |
  99 |       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
 100 |       The copyright notice above does not evidence any
 101 |       actual or intended publication of such source code.
 102
 103 |SLOG2    idnt    2,1 | Motorola 040 Floating Point Software Package
 104
 105         |section        8
 106
 107         |xref   t_frcinx
 108         |xref   t_operr
 109         |xref   slogn
 110         |xref   slognd
 111
 112 INV_L10:  .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
 113
 114 INV_L2:   .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
 115
 116         .global slog10d
 117 slog10d:
 118 |--entry point for Log10(X), X is denormalized
 119         movel           (%a0),%d0
 120         blt             invalid
 121         movel           %d1,-(%sp)
 122         clrl            %d1
 123         bsr             slognd                  | ...log(X), X denorm.
 124         fmovel          (%sp)+,%fpcr
 125         fmulx           INV_L10,%fp0
 126         bra             t_frcinx
 127
 128         .global slog10
 129 slog10:
 130 |--entry point for Log10(X), X is normalized
 131
 132         movel           (%a0),%d0
 133         blt             invalid
 134         movel           %d1,-(%sp)
 135         clrl            %d1
 136         bsr             slogn                   | ...log(X), X normal.
 137         fmovel          (%sp)+,%fpcr
 138         fmulx           INV_L10,%fp0
 139         bra             t_frcinx
 140
 141
 142         .global slog2d
 143 slog2d:
 144 |--entry point for Log2(X), X is denormalized
 145
 146         movel           (%a0),%d0
 147         blt             invalid
 148         movel           %d1,-(%sp)
 149         clrl            %d1
 150         bsr             slognd                  | ...log(X), X denorm.
 151         fmovel          (%sp)+,%fpcr
 152         fmulx           INV_L2,%fp0
 153         bra             t_frcinx
 154
 155         .global slog2
 156 slog2:
 157 |--entry point for Log2(X), X is normalized
 158         movel           (%a0),%d0
 159         blt             invalid
 160
 161         movel           8(%a0),%d0
 162         bnes            continue                | ...X is not 2^k
 163
 164         movel           4(%a0),%d0
 165         andl            #0x7FFFFFFF,%d0
 166         tstl            %d0
 167         bnes            continue
 168
 169 |--X = 2^k.
 170         movew           (%a0),%d0
 171         andl            #0x00007FFF,%d0
 172         subl            #0x3FFF,%d0
 173         fmovel          %d1,%fpcr
 174         fmovel          %d0,%fp0
 175         bra             t_frcinx
 176
 177 continue:
 178         movel           %d1,-(%sp)
 179         clrl            %d1
 180         bsr             slogn                   | ...log(X), X normal.
 181         fmovel          (%sp)+,%fpcr
 182         fmulx           INV_L2,%fp0
 183         bra             t_frcinx
 184
 185 invalid:
 186         bra             t_operr
 187
 188         |end