slog2.sa revision 1.1
1 * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP 2 * M68000 Hi-Performance Microprocessor Division 3 * M68040 Software Package 4 * 5 * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. 6 * All rights reserved. 7 * 8 * THE SOFTWARE is provided on an "AS IS" basis and without warranty. 9 * To the maximum extent permitted by applicable law, 10 * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, 11 * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A 12 * PARTICULAR PURPOSE and any warranty against infringement with 13 * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) 14 * and any accompanying written materials. 15 * 16 * To the maximum extent permitted by applicable law, 17 * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER 18 * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS 19 * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR 20 * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE 21 * SOFTWARE. Motorola assumes no responsibility for the maintenance 22 * and support of the SOFTWARE. 23 * 24 * You are hereby granted a copyright license to use, modify, and 25 * distribute the SOFTWARE so long as this entire notice is retained 26 * without alteration in any modified and/or redistributed versions, 27 * and that such modified versions are clearly identified as such. 28 * No licenses are granted by implication, estoppel or otherwise 29 * under any patents or trademarks of Motorola, Inc. 30 31 * 32 * slog2.sa 3.1 12/10/90 33 * 34 * The entry point slog10 computes the base-10 35 * logarithm of an input argument X. 36 * slog10d does the same except the input value is a 37 * denormalized number. 38 * sLog2 and sLog2d are the base-2 analogues. 39 * 40 * INPUT: Double-extended value in memory location pointed to 41 * by address register a0. 42 * 43 * OUTPUT: log_10(X) or log_2(X) returned in floating-point 44 * register fp0. 45 * 46 * ACCURACY and MONOTONICITY: The returned result is within 1.7 47 * ulps in 64 significant bit, i.e. within 0.5003 ulp 48 * to 53 bits if the result is subsequently rounded 49 * to double precision. The result is provably monotonic 50 * in double precision. 51 * 52 * SPEED: Two timings are measured, both in the copy-back mode. 53 * The first one is measured when the function is invoked 54 * the first time (so the instructions and data are not 55 * in cache), and the second one is measured when the 56 * function is reinvoked at the same input argument. 57 * 58 * ALGORITHM and IMPLEMENTATION NOTES: 59 * 60 * slog10d: 61 * 62 * Step 0. If X < 0, create a NaN and raise the invalid operation 63 * flag. Otherwise, save FPCR in D1; set FpCR to default. 64 * Notes: Default means round-to-nearest mode, no floating-point 65 * traps, and precision control = double extended. 66 * 67 * Step 1. Call slognd to obtain Y = log(X), the natural log of X. 68 * Notes: Even if X is denormalized, log(X) is always normalized. 69 * 70 * Step 2. Compute log_10(X) = log(X) * (1/log(10)). 71 * 2.1 Restore the user FPCR 72 * 2.2 Return ans := Y * INV_L10. 73 * 74 * 75 * slog10: 76 * 77 * Step 0. If X < 0, create a NaN and raise the invalid operation 78 * flag. Otherwise, save FPCR in D1; set FpCR to default. 79 * Notes: Default means round-to-nearest mode, no floating-point 80 * traps, and precision control = double extended. 81 * 82 * Step 1. Call sLogN to obtain Y = log(X), the natural log of X. 83 * 84 * Step 2. Compute log_10(X) = log(X) * (1/log(10)). 85 * 2.1 Restore the user FPCR 86 * 2.2 Return ans := Y * INV_L10. 87 * 88 * 89 * sLog2d: 90 * 91 * Step 0. If X < 0, create a NaN and raise the invalid operation 92 * flag. Otherwise, save FPCR in D1; set FpCR to default. 93 * Notes: Default means round-to-nearest mode, no floating-point 94 * traps, and precision control = double extended. 95 * 96 * Step 1. Call slognd to obtain Y = log(X), the natural log of X. 97 * Notes: Even if X is denormalized, log(X) is always normalized. 98 * 99 * Step 2. Compute log_10(X) = log(X) * (1/log(2)). 100 * 2.1 Restore the user FPCR 101 * 2.2 Return ans := Y * INV_L2. 102 * 103 * 104 * sLog2: 105 * 106 * Step 0. If X < 0, create a NaN and raise the invalid operation 107 * flag. Otherwise, save FPCR in D1; set FpCR to default. 108 * Notes: Default means round-to-nearest mode, no floating-point 109 * traps, and precision control = double extended. 110 * 111 * Step 1. If X is not an integer power of two, i.e., X != 2^k, 112 * go to Step 3. 113 * 114 * Step 2. Return k. 115 * 2.1 Get integer k, X = 2^k. 116 * 2.2 Restore the user FPCR. 117 * 2.3 Return ans := convert-to-double-extended(k). 118 * 119 * Step 3. Call sLogN to obtain Y = log(X), the natural log of X. 120 * 121 * Step 4. Compute log_2(X) = log(X) * (1/log(2)). 122 * 4.1 Restore the user FPCR 123 * 4.2 Return ans := Y * INV_L2. 124 * 125 126 SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package 127 128 section 8 129 130 xref t_frcinx 131 xref t_operr 132 xref slogn 133 xref slognd 134 135 INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000 136 137 INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000 138 139 xdef slog10d 140 slog10d: 141 *--entry point for Log10(X), X is denormalized 142 move.l (a0),d0 143 blt.w invalid 144 move.l d1,-(sp) 145 clr.l d1 146 bsr slognd ...log(X), X denorm. 147 fmove.l (sp)+,fpcr 148 fmul.x INV_L10,fp0 149 bra t_frcinx 150 151 xdef slog10 152 slog10: 153 *--entry point for Log10(X), X is normalized 154 155 move.l (a0),d0 156 blt.w invalid 157 move.l d1,-(sp) 158 clr.l d1 159 bsr slogn ...log(X), X normal. 160 fmove.l (sp)+,fpcr 161 fmul.x INV_L10,fp0 162 bra t_frcinx 163 164 165 xdef slog2d 166 slog2d: 167 *--entry point for Log2(X), X is denormalized 168 169 move.l (a0),d0 170 blt.w invalid 171 move.l d1,-(sp) 172 clr.l d1 173 bsr slognd ...log(X), X denorm. 174 fmove.l (sp)+,fpcr 175 fmul.x INV_L2,fp0 176 bra t_frcinx 177 178 xdef slog2 179 slog2: 180 *--entry point for Log2(X), X is normalized 181 move.l (a0),d0 182 blt.w invalid 183 184 move.l 8(a0),d0 185 bne.b continue ...X is not 2^k 186 187 move.l 4(a0),d0 188 and.l #$7FFFFFFF,d0 189 tst.l d0 190 bne.b continue 191 192 *--X = 2^k. 193 move.w (a0),d0 194 and.l #$00007FFF,d0 195 sub.l #$3FFF,d0 196 fmove.l d1,fpcr 197 fmove.l d0,fp0 198 bra t_frcinx 199 200 continue: 201 move.l d1,-(sp) 202 clr.l d1 203 bsr slogn ...log(X), X normal. 204 fmove.l (sp)+,fpcr 205 fmul.x INV_L2,fp0 206 bra t_frcinx 207 208 invalid: 209 bra t_operr 210 211 end 212
Indexes created Sat Nov 01 20:09:51 GMT 2025