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 128SLOG2 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 137INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000 138 139INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000 140 141 xdef slog10d 142slog10d: 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 154slog10: 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 168slog2d: 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 181slog2: 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 202continue: 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 210invalid: 211 bra t_operr 212 213 end 214