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