Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | | |
Matt Waddel | e00d82d | 2006-02-11 17:55:48 -0800 | [diff] [blame] | 99 | | For details on the license for this file, please see the |
| 100 | | file, README, in this same directory. |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 101 | |
| 102 | |SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package |
| 103 | |
| 104 | |section 8 |
| 105 | |
| 106 | |xref t_frcinx |
| 107 | |xref t_operr |
| 108 | |xref slogn |
| 109 | |xref slognd |
| 110 | |
| 111 | INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 |
| 112 | |
| 113 | INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 |
| 114 | |
| 115 | .global slog10d |
| 116 | slog10d: |
| 117 | |--entry point for Log10(X), X is denormalized |
| 118 | movel (%a0),%d0 |
| 119 | blt invalid |
| 120 | movel %d1,-(%sp) |
| 121 | clrl %d1 |
| 122 | bsr slognd | ...log(X), X denorm. |
| 123 | fmovel (%sp)+,%fpcr |
| 124 | fmulx INV_L10,%fp0 |
| 125 | bra t_frcinx |
| 126 | |
| 127 | .global slog10 |
| 128 | slog10: |
| 129 | |--entry point for Log10(X), X is normalized |
| 130 | |
| 131 | movel (%a0),%d0 |
| 132 | blt invalid |
| 133 | movel %d1,-(%sp) |
| 134 | clrl %d1 |
| 135 | bsr slogn | ...log(X), X normal. |
| 136 | fmovel (%sp)+,%fpcr |
| 137 | fmulx INV_L10,%fp0 |
| 138 | bra t_frcinx |
| 139 | |
| 140 | |
| 141 | .global slog2d |
| 142 | slog2d: |
| 143 | |--entry point for Log2(X), X is denormalized |
| 144 | |
| 145 | movel (%a0),%d0 |
| 146 | blt invalid |
| 147 | movel %d1,-(%sp) |
| 148 | clrl %d1 |
| 149 | bsr slognd | ...log(X), X denorm. |
| 150 | fmovel (%sp)+,%fpcr |
| 151 | fmulx INV_L2,%fp0 |
| 152 | bra t_frcinx |
| 153 | |
| 154 | .global slog2 |
| 155 | slog2: |
| 156 | |--entry point for Log2(X), X is normalized |
| 157 | movel (%a0),%d0 |
| 158 | blt invalid |
| 159 | |
| 160 | movel 8(%a0),%d0 |
| 161 | bnes continue | ...X is not 2^k |
| 162 | |
| 163 | movel 4(%a0),%d0 |
| 164 | andl #0x7FFFFFFF,%d0 |
| 165 | tstl %d0 |
| 166 | bnes continue |
| 167 | |
| 168 | |--X = 2^k. |
| 169 | movew (%a0),%d0 |
| 170 | andl #0x00007FFF,%d0 |
| 171 | subl #0x3FFF,%d0 |
| 172 | fmovel %d1,%fpcr |
| 173 | fmovel %d0,%fp0 |
| 174 | bra t_frcinx |
| 175 | |
| 176 | continue: |
| 177 | movel %d1,-(%sp) |
| 178 | clrl %d1 |
| 179 | bsr slogn | ...log(X), X normal. |
| 180 | fmovel (%sp)+,%fpcr |
| 181 | fmulx INV_L2,%fp0 |
| 182 | bra t_frcinx |
| 183 | |
| 184 | invalid: |
| 185 | bra t_operr |
| 186 | |
| 187 | |end |