1 * $NetBSD: slog2.sa,v 1.2 1994/10/26 07:49:52 cgd Exp $ 2 3 * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP 4 * M68000 Hi-Performance Microprocessor Division 5 * M68040 Software Package 6 * 7 * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. 8 * All rights reserved. 9 * 10 * THE SOFTWARE is provided on an "AS IS" basis and without warranty. 11 * To the maximum extent permitted by applicable law, 12 * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, 13 * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A 14 * PARTICULAR PURPOSE and any warranty against infringement with 15 * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) 16 * and any accompanying written materials. 17 * 18 * To the maximum extent permitted by applicable law, 19 * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER 20 * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS 21 * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR 22 * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE 23 * SOFTWARE. Motorola assumes no responsibility for the maintenance 24 * and support of the SOFTWARE. 25 * 26 * You are hereby granted a copyright license to use, modify, and 27 * distribute the SOFTWARE so long as this entire notice is retained 28 * without alteration in any modified and/or redistributed versions, 29 * and that such modified versions are clearly identified as such. 30 * No licenses are granted by implication, estoppel or otherwise 31 * under any patents or trademarks of Motorola, Inc. 32 33 * 34 * slog2.sa 3.1 12/10/90 35 * 36 * The entry point slog10 computes the base-10 37 * logarithm of an input argument X. 38 * slog10d does the same except the input value is a 39 * denormalized number. 40 * sLog2 and sLog2d are the base-2 analogues. 41 * 42 * INPUT: Double-extended value in memory location pointed to 43 * by address register a0. 44 * 45 * OUTPUT: log_10(X) or log_2(X) returned in floating-point 46 * register fp0. 47 * 48 * ACCURACY and MONOTONICITY: The returned result is within 1.7 49 * ulps in 64 significant bit, i.e. within 0.5003 ulp 50 * to 53 bits if the result is subsequently rounded 51 * to double precision. The result is provably monotonic 52 * in double precision. 53 * 54 * SPEED: Two timings are measured, both in the copy-back mode. 55 * The first one is measured when the function is invoked 56 * the first time (so the instructions and data are not 57 * in cache), and the second one is measured when the 58 * function is reinvoked at the same input argument. 59 * 60 * ALGORITHM and IMPLEMENTATION NOTES: 61 * 62 * slog10d: 63 * 64 * Step 0. If X < 0, create a NaN and raise the invalid operation 65 * flag. Otherwise, save FPCR in D1; set FpCR to default. 66 * Notes: Default means round-to-nearest mode, no floating-point 67 * traps, and precision control = double extended. 68 * 69 * Step 1. Call slognd to obtain Y = log(X), the natural log of X. 70 * Notes: Even if X is denormalized, log(X) is always normalized. 71 * 72 * Step 2. Compute log_10(X) = log(X) * (1/log(10)). 73 * 2.1 Restore the user FPCR 74 * 2.2 Return ans := Y * INV_L10. 75 * 76 * 77 * slog10: 78 * 79 * Step 0. If X < 0, create a NaN and raise the invalid operation 80 * flag. Otherwise, save FPCR in D1; set FpCR to default. 81 * Notes: Default means round-to-nearest mode, no floating-point 82 * traps, and precision control = double extended. 83 * 84 * Step 1. Call sLogN to obtain Y = log(X), the natural log of X. 85 * 86 * Step 2. Compute log_10(X) = log(X) * (1/log(10)). 87 * 2.1 Restore the user FPCR 88 * 2.2 Return ans := Y * INV_L10. 89 * 90 * 91 * sLog2d: 92 * 93 * Step 0. If X < 0, create a NaN and raise the invalid operation 94 * flag. Otherwise, save FPCR in D1; set FpCR to default. 95 * Notes: Default means round-to-nearest mode, no floating-point 96 * traps, and precision control = double extended. 97 * 98 * Step 1. Call slognd to obtain Y = log(X), the natural log of X. 99 * Notes: Even if X is denormalized, log(X) is always normalized. 100 * 101 * Step 2. Compute log_10(X) = log(X) * (1/log(2)). 102 * 2.1 Restore the user FPCR 103 * 2.2 Return ans := Y * INV_L2. 104 * 105 * 106 * sLog2: 107 * 108 * Step 0. If X < 0, create a NaN and raise the invalid operation 109 * flag. Otherwise, save FPCR in D1; set FpCR to default. 110 * Notes: Default means round-to-nearest mode, no floating-point 111 * traps, and precision control = double extended. 112 * 113 * Step 1. If X is not an integer power of two, i.e., X != 2^k, 114 * go to Step 3. 115 * 116 * Step 2. Return k. 117 * 2.1 Get integer k, X = 2^k. 118 * 2.2 Restore the user FPCR. 119 * 2.3 Return ans := convert-to-double-extended(k). 120 * 121 * Step 3. Call sLogN to obtain Y = log(X), the natural log of X. 122 * 123 * Step 4. Compute log_2(X) = log(X) * (1/log(2)). 124 * 4.1 Restore the user FPCR 125 * 4.2 Return ans := Y * INV_L2. 126 * 127 128 SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package 129 130 section 8 131 132 xref t_frcinx 133 xref t_operr 134 xref slogn 135 xref slognd 136 137 INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000 138 139 INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000 140 141 xdef slog10d 142 slog10d: 143 *--entry point for Log10(X), X is denormalized 144 move.l (a0),d0 145 blt.w invalid 146 move.l d1,-(sp) 147 clr.l d1 148 bsr slognd ...log(X), X denorm. 149 fmove.l (sp)+,fpcr 150 fmul.x INV_L10,fp0 151 bra t_frcinx 152 153 xdef slog10 154 slog10: 155 *--entry point for Log10(X), X is normalized 156 157 move.l (a0),d0 158 blt.w invalid 159 move.l d1,-(sp) 160 clr.l d1 161 bsr slogn ...log(X), X normal. 162 fmove.l (sp)+,fpcr 163 fmul.x INV_L10,fp0 164 bra t_frcinx 165 166 167 xdef slog2d 168 slog2d: 169 *--entry point for Log2(X), X is denormalized 170 171 move.l (a0),d0 172 blt.w invalid 173 move.l d1,-(sp) 174 clr.l d1 175 bsr slognd ...log(X), X denorm. 176 fmove.l (sp)+,fpcr 177 fmul.x INV_L2,fp0 178 bra t_frcinx 179 180 xdef slog2 181 slog2: 182 *--entry point for Log2(X), X is normalized 183 move.l (a0),d0 184 blt.w invalid 185 186 move.l 8(a0),d0 187 bne.b continue ...X is not 2^k 188 189 move.l 4(a0),d0 190 and.l #$7FFFFFFF,d0 191 tst.l d0 192 bne.b continue 193 194 *--X = 2^k. 195 move.w (a0),d0 196 and.l #$00007FFF,d0 197 sub.l #$3FFF,d0 198 fmove.l d1,fpcr 199 fmove.l d0,fp0 200 bra t_frcinx 201 202 continue: 203 move.l d1,-(sp) 204 clr.l d1 205 bsr slogn ...log(X), X normal. 206 fmove.l (sp)+,fpcr 207 fmul.x INV_L2,fp0 208 bra t_frcinx 209 210 invalid: 211 bra t_operr 212 213 end 214
Indexes created Fri Oct 31 11:10:07 GMT 2025