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| For details on the license for this file, please see the 100| file, README, in this same directory. 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 111INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 112 113INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 114 115 .global slog10d 116slog10d: 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 128slog10: 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 142slog2d: 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 155slog2: 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 176continue: 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 184invalid: 185 bra t_operr 186 187 |end 188