fpu_log.c revision 1.3
1 /* $NetBSD: fpu_log.c,v 1.3 1996/04/30 11:52:33 briggs Exp $ */ 2 3 /* 4 * Copyright (c) 1995 Ken Nakata 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 3. Neither the name of the author nor the names of its contributors 16 * may be used to endorse or promote products derived from this software 17 * without specific prior written permission. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 22 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 29 * SUCH DAMAGE. 30 * 31 * @(#)fpu_log.c 10/8/95 32 */ 33 34 #include <sys/types.h> 35 #include <sys/systm.h> 36 37 #include "fpu_emulate.h" 38 39 static u_int logA6[] = { 0x3FC2499A, 0xB5E4040B }; 40 static u_int logA5[] = { 0xBFC555B5, 0x848CB7DB }; 41 static u_int logA4[] = { 0x3FC99999, 0x987D8730 }; 42 static u_int logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 }; 43 static u_int logA2[] = { 0x3FD55555, 0x555555A4 }; 44 static u_int logA1[] = { 0xBFE00000, 0x00000008 }; 45 46 static u_int logB5[] = { 0x3F175496, 0xADD7DAD6 }; 47 static u_int logB4[] = { 0x3F3C71C2, 0xFE80C7E0 }; 48 static u_int logB3[] = { 0x3F624924, 0x928BCCFF }; 49 static u_int logB2[] = { 0x3F899999, 0x999995EC }; 50 static u_int logB1[] = { 0x3FB55555, 0x55555555 }; 51 52 /* sfpn = shortened fp number; can represent only positive numbers */ 53 static struct sfpn { 54 int sp_exp; 55 u_int sp_m0, sp_m1; 56 } logtbl[] = { 57 { 0x3FFE - 0x3fff, 0xFE03F80FU, 0xE03F80FEU }, 58 { 0x3FF7 - 0x3fff, 0xFF015358U, 0x833C47E2U }, 59 { 0x3FFE - 0x3fff, 0xFA232CF2U, 0x52138AC0U }, 60 { 0x3FF9 - 0x3fff, 0xBDC8D83EU, 0xAD88D549U }, 61 { 0x3FFE - 0x3fff, 0xF6603D98U, 0x0F6603DAU }, 62 { 0x3FFA - 0x3fff, 0x9CF43DCFU, 0xF5EAFD48U }, 63 { 0x3FFE - 0x3fff, 0xF2B9D648U, 0x0F2B9D65U }, 64 { 0x3FFA - 0x3fff, 0xDA16EB88U, 0xCB8DF614U }, 65 { 0x3FFE - 0x3fff, 0xEF2EB71FU, 0xC4345238U }, 66 { 0x3FFB - 0x3fff, 0x8B29B775U, 0x1BD70743U }, 67 { 0x3FFE - 0x3fff, 0xEBBDB2A5U, 0xC1619C8CU }, 68 { 0x3FFB - 0x3fff, 0xA8D839F8U, 0x30C1FB49U }, 69 { 0x3FFE - 0x3fff, 0xE865AC7BU, 0x7603A197U }, 70 { 0x3FFB - 0x3fff, 0xC61A2EB1U, 0x8CD907ADU }, 71 { 0x3FFE - 0x3fff, 0xE525982AU, 0xF70C880EU }, 72 { 0x3FFB - 0x3fff, 0xE2F2A47AU, 0xDE3A18AFU }, 73 { 0x3FFE - 0x3fff, 0xE1FC780EU, 0x1FC780E2U }, 74 { 0x3FFB - 0x3fff, 0xFF64898EU, 0xDF55D551U }, 75 { 0x3FFE - 0x3fff, 0xDEE95C4CU, 0xA037BA57U }, 76 { 0x3FFC - 0x3fff, 0x8DB956A9U, 0x7B3D0148U }, 77 { 0x3FFE - 0x3fff, 0xDBEB61EEU, 0xD19C5958U }, 78 { 0x3FFC - 0x3fff, 0x9B8FE100U, 0xF47BA1DEU }, 79 { 0x3FFE - 0x3fff, 0xD901B203U, 0x6406C80EU }, 80 { 0x3FFC - 0x3fff, 0xA9372F1DU, 0x0DA1BD17U }, 81 { 0x3FFE - 0x3fff, 0xD62B80D6U, 0x2B80D62CU }, 82 { 0x3FFC - 0x3fff, 0xB6B07F38U, 0xCE90E46BU }, 83 { 0x3FFE - 0x3fff, 0xD3680D36U, 0x80D3680DU }, 84 { 0x3FFC - 0x3fff, 0xC3FD0329U, 0x06488481U }, 85 { 0x3FFE - 0x3fff, 0xD0B69FCBU, 0xD2580D0BU }, 86 { 0x3FFC - 0x3fff, 0xD11DE0FFU, 0x15AB18CAU }, 87 { 0x3FFE - 0x3fff, 0xCE168A77U, 0x25080CE1U }, 88 { 0x3FFC - 0x3fff, 0xDE1433A1U, 0x6C66B150U }, 89 { 0x3FFE - 0x3fff, 0xCB8727C0U, 0x65C393E0U }, 90 { 0x3FFC - 0x3fff, 0xEAE10B5AU, 0x7DDC8ADDU }, 91 { 0x3FFE - 0x3fff, 0xC907DA4EU, 0x871146ADU }, 92 { 0x3FFC - 0x3fff, 0xF7856E5EU, 0xE2C9B291U }, 93 { 0x3FFE - 0x3fff, 0xC6980C69U, 0x80C6980CU }, 94 { 0x3FFD - 0x3fff, 0x82012CA5U, 0xA68206D7U }, 95 { 0x3FFE - 0x3fff, 0xC4372F85U, 0x5D824CA6U }, 96 { 0x3FFD - 0x3fff, 0x882C5FCDU, 0x7256A8C5U }, 97 { 0x3FFE - 0x3fff, 0xC1E4BBD5U, 0x95F6E947U }, 98 { 0x3FFD - 0x3fff, 0x8E44C60BU, 0x4CCFD7DEU }, 99 { 0x3FFE - 0x3fff, 0xBFA02FE8U, 0x0BFA02FFU }, 100 { 0x3FFD - 0x3fff, 0x944AD09EU, 0xF4351AF6U }, 101 { 0x3FFE - 0x3fff, 0xBD691047U, 0x07661AA3U }, 102 { 0x3FFD - 0x3fff, 0x9A3EECD4U, 0xC3EAA6B2U }, 103 { 0x3FFE - 0x3fff, 0xBB3EE721U, 0xA54D880CU }, 104 { 0x3FFD - 0x3fff, 0xA0218434U, 0x353F1DE8U }, 105 { 0x3FFE - 0x3fff, 0xB92143FAU, 0x36F5E02EU }, 106 { 0x3FFD - 0x3fff, 0xA5F2FCABU, 0xBBC506DAU }, 107 { 0x3FFE - 0x3fff, 0xB70FBB5AU, 0x19BE3659U }, 108 { 0x3FFD - 0x3fff, 0xABB3B8BAU, 0x2AD362A5U }, 109 { 0x3FFE - 0x3fff, 0xB509E68AU, 0x9B94821FU }, 110 { 0x3FFD - 0x3fff, 0xB1641795U, 0xCE3CA97BU }, 111 { 0x3FFE - 0x3fff, 0xB30F6352U, 0x8917C80BU }, 112 { 0x3FFD - 0x3fff, 0xB7047551U, 0x5D0F1C61U }, 113 { 0x3FFE - 0x3fff, 0xB11FD3B8U, 0x0B11FD3CU }, 114 { 0x3FFD - 0x3fff, 0xBC952AFEU, 0xEA3D13E1U }, 115 { 0x3FFE - 0x3fff, 0xAF3ADDC6U, 0x80AF3ADEU }, 116 { 0x3FFD - 0x3fff, 0xC2168ED0U, 0xF458BA4AU }, 117 { 0x3FFE - 0x3fff, 0xAD602B58U, 0x0AD602B6U }, 118 { 0x3FFD - 0x3fff, 0xC788F439U, 0xB3163BF1U }, 119 { 0x3FFE - 0x3fff, 0xAB8F69E2U, 0x8359CD11U }, 120 { 0x3FFD - 0x3fff, 0xCCECAC08U, 0xBF04565DU }, 121 { 0x3FFE - 0x3fff, 0xA9C84A47U, 0xA07F5638U }, 122 { 0x3FFD - 0x3fff, 0xD2420487U, 0x2DD85160U }, 123 { 0x3FFE - 0x3fff, 0xA80A80A8U, 0x0A80A80BU }, 124 { 0x3FFD - 0x3fff, 0xD7894992U, 0x3BC3588AU }, 125 { 0x3FFE - 0x3fff, 0xA655C439U, 0x2D7B73A8U }, 126 { 0x3FFD - 0x3fff, 0xDCC2C4B4U, 0x9887DACCU }, 127 { 0x3FFE - 0x3fff, 0xA4A9CF1DU, 0x96833751U }, 128 { 0x3FFD - 0x3fff, 0xE1EEBD3EU, 0x6D6A6B9EU }, 129 { 0x3FFE - 0x3fff, 0xA3065E3FU, 0xAE7CD0E0U }, 130 { 0x3FFD - 0x3fff, 0xE70D785CU, 0x2F9F5BDCU }, 131 { 0x3FFE - 0x3fff, 0xA16B312EU, 0xA8FC377DU }, 132 { 0x3FFD - 0x3fff, 0xEC1F392CU, 0x5179F283U }, 133 { 0x3FFE - 0x3fff, 0x9FD809FDU, 0x809FD80AU }, 134 { 0x3FFD - 0x3fff, 0xF12440D3U, 0xE36130E6U }, 135 { 0x3FFE - 0x3fff, 0x9E4CAD23U, 0xDD5F3A20U }, 136 { 0x3FFD - 0x3fff, 0xF61CCE92U, 0x346600BBU }, 137 { 0x3FFE - 0x3fff, 0x9CC8E160U, 0xC3FB19B9U }, 138 { 0x3FFD - 0x3fff, 0xFB091FD3U, 0x8145630AU }, 139 { 0x3FFE - 0x3fff, 0x9B4C6F9EU, 0xF03A3CAAU }, 140 { 0x3FFD - 0x3fff, 0xFFE97042U, 0xBFA4C2ADU }, 141 { 0x3FFE - 0x3fff, 0x99D722DAU, 0xBDE58F06U }, 142 { 0x3FFE - 0x3fff, 0x825EFCEDU, 0x49369330U }, 143 { 0x3FFE - 0x3fff, 0x9868C809U, 0x868C8098U }, 144 { 0x3FFE - 0x3fff, 0x84C37A7AU, 0xB9A905C9U }, 145 { 0x3FFE - 0x3fff, 0x97012E02U, 0x5C04B809U }, 146 { 0x3FFE - 0x3fff, 0x87224C2EU, 0x8E645FB7U }, 147 { 0x3FFE - 0x3fff, 0x95A02568U, 0x095A0257U }, 148 { 0x3FFE - 0x3fff, 0x897B8CACU, 0x9F7DE298U }, 149 { 0x3FFE - 0x3fff, 0x94458094U, 0x45809446U }, 150 { 0x3FFE - 0x3fff, 0x8BCF55DEU, 0xC4CD05FEU }, 151 { 0x3FFE - 0x3fff, 0x92F11384U, 0x0497889CU }, 152 { 0x3FFE - 0x3fff, 0x8E1DC0FBU, 0x89E125E5U }, 153 { 0x3FFE - 0x3fff, 0x91A2B3C4U, 0xD5E6F809U }, 154 { 0x3FFE - 0x3fff, 0x9066E68CU, 0x955B6C9BU }, 155 { 0x3FFE - 0x3fff, 0x905A3863U, 0x3E06C43BU }, 156 { 0x3FFE - 0x3fff, 0x92AADE74U, 0xC7BE59E0U }, 157 { 0x3FFE - 0x3fff, 0x8F1779D9U, 0xFDC3A219U }, 158 { 0x3FFE - 0x3fff, 0x94E9BFF6U, 0x15845643U }, 159 { 0x3FFE - 0x3fff, 0x8DDA5202U, 0x37694809U }, 160 { 0x3FFE - 0x3fff, 0x9723A1B7U, 0x20134203U }, 161 { 0x3FFE - 0x3fff, 0x8CA29C04U, 0x6514E023U }, 162 { 0x3FFE - 0x3fff, 0x995899C8U, 0x90EB8990U }, 163 { 0x3FFE - 0x3fff, 0x8B70344AU, 0x139BC75AU }, 164 { 0x3FFE - 0x3fff, 0x9B88BDAAU, 0x3A3DAE2FU }, 165 { 0x3FFE - 0x3fff, 0x8A42F870U, 0x5669DB46U }, 166 { 0x3FFE - 0x3fff, 0x9DB4224FU, 0xFFE1157CU }, 167 { 0x3FFE - 0x3fff, 0x891AC73AU, 0xE9819B50U }, 168 { 0x3FFE - 0x3fff, 0x9FDADC26U, 0x8B7A12DAU }, 169 { 0x3FFE - 0x3fff, 0x87F78087U, 0xF78087F8U }, 170 { 0x3FFE - 0x3fff, 0xA1FCFF17U, 0xCE733BD4U }, 171 { 0x3FFE - 0x3fff, 0x86D90544U, 0x7A34ACC6U }, 172 { 0x3FFE - 0x3fff, 0xA41A9E8FU, 0x5446FB9FU }, 173 { 0x3FFE - 0x3fff, 0x85BF3761U, 0x2CEE3C9BU }, 174 { 0x3FFE - 0x3fff, 0xA633CD7EU, 0x6771CD8BU }, 175 { 0x3FFE - 0x3fff, 0x84A9F9C8U, 0x084A9F9DU }, 176 { 0x3FFE - 0x3fff, 0xA8489E60U, 0x0B435A5EU }, 177 { 0x3FFE - 0x3fff, 0x83993052U, 0x3FBE3368U }, 178 { 0x3FFE - 0x3fff, 0xAA59233CU, 0xCCA4BD49U }, 179 { 0x3FFE - 0x3fff, 0x828CBFBEU, 0xB9A020A3U }, 180 { 0x3FFE - 0x3fff, 0xAC656DAEU, 0x6BCC4985U }, 181 { 0x3FFE - 0x3fff, 0x81848DA8U, 0xFAF0D277U }, 182 { 0x3FFE - 0x3fff, 0xAE6D8EE3U, 0x60BB2468U }, 183 { 0x3FFE - 0x3fff, 0x80808080U, 0x80808081U }, 184 { 0x3FFE - 0x3fff, 0xB07197A2U, 0x3C46C654U }, 185 }; 186 187 static struct fpn *__fpu_logn __P((struct fpemu *fe)); 188 189 /* 190 * natural log - algorithm taken from Motorola FPSP, 191 * except this doesn't bother to check for invalid input. 192 */ 193 static struct fpn * 194 __fpu_logn(fe) 195 struct fpemu *fe; 196 { 197 static struct fpn X, F, U, V, W, KLOG2; 198 struct fpn *d; 199 int i, k; 200 201 CPYFPN(&X, &fe->fe_f2); 202 203 /* see if |X-1| < 1/16 approx. */ 204 if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) || 205 (0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) { 206 /* log near 1 */ 207 if (fpu_debug_level & DL_ARITH) 208 printf("__fpu_logn: log near 1\n"); 209 210 fpu_const(&fe->fe_f1, 0x32); 211 /* X+1 */ 212 d = fpu_add(fe); 213 CPYFPN(&V, d); 214 215 CPYFPN(&fe->fe_f1, &X); 216 fpu_const(&fe->fe_f2, 0x32); /* 1.0 */ 217 fe->fe_f2.fp_sign = 1; /* -1.0 */ 218 /* X-1 */ 219 d = fpu_add(fe); 220 CPYFPN(&fe->fe_f1, d); 221 /* 2(X-1) */ 222 fe->fe_f1.fp_exp++; /* *= 2 */ 223 CPYFPN(&fe->fe_f2, &V); 224 /* U=2(X-1)/(X+1) */ 225 d = fpu_div(fe); 226 CPYFPN(&U, d); 227 CPYFPN(&fe->fe_f1, d); 228 CPYFPN(&fe->fe_f2, d); 229 /* V=U*U */ 230 d = fpu_mul(fe); 231 CPYFPN(&V, d); 232 CPYFPN(&fe->fe_f1, d); 233 CPYFPN(&fe->fe_f2, d); 234 /* W=V*V */ 235 d = fpu_mul(fe); 236 CPYFPN(&W, d); 237 238 /* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */ 239 240 /* B1+W*(B3+W*B5) part */ 241 CPYFPN(&fe->fe_f1, d); 242 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5); 243 /* W*B5 */ 244 d = fpu_mul(fe); 245 CPYFPN(&fe->fe_f1, d); 246 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3); 247 /* B3+W*B5 */ 248 d = fpu_add(fe); 249 CPYFPN(&fe->fe_f1, d); 250 CPYFPN(&fe->fe_f2, &W); 251 /* W*(B3+W*B5) */ 252 d = fpu_mul(fe); 253 CPYFPN(&fe->fe_f1, d); 254 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1); 255 /* B1+W*(B3+W*B5) */ 256 d = fpu_add(fe); 257 CPYFPN(&X, d); 258 259 /* [V*(B2+W*B4)] part */ 260 CPYFPN(&fe->fe_f1, &W); 261 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4); 262 /* W*B4 */ 263 d = fpu_mul(fe); 264 CPYFPN(&fe->fe_f1, d); 265 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2); 266 /* B2+W*B4 */ 267 d = fpu_add(fe); 268 CPYFPN(&fe->fe_f1, d); 269 CPYFPN(&fe->fe_f2, &V); 270 /* V*(B2+W*B4) */ 271 d = fpu_mul(fe); 272 CPYFPN(&fe->fe_f1, d); 273 CPYFPN(&fe->fe_f2, &X); 274 /* B1+W*(B3+W*B5)+V*(B2+W*B4) */ 275 d = fpu_add(fe); 276 CPYFPN(&fe->fe_f1, d); 277 CPYFPN(&fe->fe_f2, &V); 278 /* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 279 d = fpu_mul(fe); 280 CPYFPN(&fe->fe_f1, d); 281 CPYFPN(&fe->fe_f2, &U); 282 /* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 283 d = fpu_mul(fe); 284 CPYFPN(&fe->fe_f1, d); 285 CPYFPN(&fe->fe_f2, &U); 286 /* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 287 d = fpu_add(fe); 288 } else /* the usual case */ { 289 if (fpu_debug_level & DL_ARITH) 290 printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n", 291 X.fp_exp, X.fp_mant[0], X.fp_mant[1]); 292 293 k = X.fp_exp; 294 /* X <- Y */ 295 X.fp_exp = fe->fe_f2.fp_exp = 0; 296 297 /* get the most significant 7 bits of X */ 298 F.fp_class = FPC_NUM; 299 F.fp_sign = 0; 300 F.fp_exp = X.fp_exp; 301 F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG)); 302 F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG)); 303 F.fp_mant[1] = F.fp_mant[2] = F.fp_mant[3] = 0; 304 F.fp_sticky = 0; 305 306 if (fpu_debug_level & DL_ARITH) { 307 printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n", 308 fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0], 309 fe->fe_f2.fp_mant[1], k); 310 printf("__fpu_logn: F=(%d,%08x,%08x...)\n", 311 F.fp_exp, F.fp_mant[0], F.fp_mant[1]); 312 } 313 314 /* index to the table */ 315 i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e; 316 317 if (fpu_debug_level & DL_ARITH) 318 printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i); 319 320 CPYFPN(&fe->fe_f1, &F); 321 /* -F */ 322 fe->fe_f1.fp_sign = 1; 323 /* Y-F */ 324 d = fpu_add(fe); 325 CPYFPN(&fe->fe_f1, d); 326 327 /* fe_f2 = 1/F */ 328 fe->fe_f2.fp_class = FPC_NUM; 329 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[3] = 0; 330 fe->fe_f2.fp_exp = logtbl[i].sp_exp; 331 fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG)); 332 fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) | 333 (logtbl[i].sp_m1 >> (31 - FP_LG)); 334 fe->fe_f2.fp_mant[2] = (u_int)(logtbl[i].sp_m1 << (FP_LG + 1)); 335 336 if (fpu_debug_level & DL_ARITH) 337 printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp, 338 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 339 340 /* U = (Y-F) * (1/F) */ 341 d = fpu_mul(fe); 342 CPYFPN(&U, d); 343 344 /* KLOG2 = K * ln(2) */ 345 /* fe_f1 == (fpn)k */ 346 fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k); 347 (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */); 348 if (fpu_debug_level & DL_ARITH) { 349 printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", fe->fe_f1.fp_exp, 350 fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]); 351 printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp, 352 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 353 } 354 /* K * LOGOF2 */ 355 d = fpu_mul(fe); 356 CPYFPN(&KLOG2, d); 357 358 /* V=U*U */ 359 CPYFPN(&fe->fe_f1, &U); 360 CPYFPN(&fe->fe_f2, &U); 361 d = fpu_mul(fe); 362 CPYFPN(&V, d); 363 364 /* 365 * approximation of LOG(1+U) by 366 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6))) 367 */ 368 369 /* (U+V*(A1+V*(A3+V*A5))) part */ 370 CPYFPN(&fe->fe_f1, d); 371 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5); 372 /* V*A5 */ 373 d = fpu_mul(fe); 374 375 CPYFPN(&fe->fe_f1, d); 376 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3); 377 /* A3+V*A5 */ 378 d = fpu_add(fe); 379 380 CPYFPN(&fe->fe_f1, d); 381 CPYFPN(&fe->fe_f2, &V); 382 /* V*(A3+V*A5) */ 383 d = fpu_mul(fe); 384 385 CPYFPN(&fe->fe_f1, d); 386 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1); 387 /* A1+V*(A3+V*A5) */ 388 d = fpu_add(fe); 389 390 CPYFPN(&fe->fe_f1, d); 391 CPYFPN(&fe->fe_f2, &V); 392 /* V*(A1+V*(A3+V*A5)) */ 393 d = fpu_mul(fe); 394 395 CPYFPN(&fe->fe_f1, d); 396 CPYFPN(&fe->fe_f2, &U); 397 /* U+V*(A1+V*(A3+V*A5)) */ 398 d = fpu_add(fe); 399 400 CPYFPN(&X, d); 401 402 /* (U*V*(A2+V*(A4+V*A6))) part */ 403 CPYFPN(&fe->fe_f1, &V); 404 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6); 405 /* V*A6 */ 406 d = fpu_mul(fe); 407 CPYFPN(&fe->fe_f1, d); 408 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4); 409 /* A4+V*A6 */ 410 d = fpu_add(fe); 411 CPYFPN(&fe->fe_f1, d); 412 CPYFPN(&fe->fe_f2, &V); 413 /* V*(A4+V*A6) */ 414 d = fpu_mul(fe); 415 CPYFPN(&fe->fe_f1, d); 416 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2); 417 /* A2+V*(A4+V*A6) */ 418 d = fpu_add(fe); 419 CPYFPN(&fe->fe_f1, d); 420 CPYFPN(&fe->fe_f2, &V); 421 /* V*(A2+V*(A4+V*A6)) */ 422 d = fpu_mul(fe); 423 CPYFPN(&fe->fe_f1, d); 424 CPYFPN(&fe->fe_f2, &U); 425 /* U*V*(A2+V*(A4+V*A6)) */ 426 d = fpu_mul(fe); 427 CPYFPN(&fe->fe_f1, d); 428 i++; 429 /* fe_f2 = logtbl[i+1] (== LOG(F)) */ 430 fe->fe_f2.fp_class = FPC_NUM; 431 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[3] = 0; 432 fe->fe_f2.fp_exp = logtbl[i].sp_exp; 433 fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG)); 434 fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) | 435 (logtbl[i].sp_m1 >> (31 - FP_LG)); 436 fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1)); 437 438 if (fpu_debug_level & DL_ARITH) 439 printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", fe->fe_f2.fp_exp, 440 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 441 442 /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ 443 d = fpu_add(fe); 444 CPYFPN(&fe->fe_f1, d); 445 CPYFPN(&fe->fe_f2, &X); 446 /* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 447 d = fpu_add(fe); 448 449 if (fpu_debug_level & DL_ARITH) 450 printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x,%08x)\n", 451 d->fp_sign ? '-' : '+', d->fp_exp, 452 d->fp_mant[0], d->fp_mant[1], d->fp_mant[2], d->fp_mant[3]); 453 454 CPYFPN(&fe->fe_f1, d); 455 CPYFPN(&fe->fe_f2, &KLOG2); 456 /* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 457 d = fpu_add(fe); 458 } 459 460 return d; 461 } 462 463 struct fpn * 464 fpu_log10(fe) 465 struct fpemu *fe; 466 { 467 struct fpn *fp = &fe->fe_f2; 468 u_int fpsr; 469 470 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 471 472 if (fp->fp_class >= FPC_NUM) { 473 if (fp->fp_sign) { /* negative number or Inf */ 474 fp = fpu_newnan(fe); 475 fpsr |= FPSR_OPERR; 476 } else if (fp->fp_class == FPC_NUM) { 477 /* the real work here */ 478 fp = __fpu_logn(fe); 479 if (fp != &fe->fe_f1) 480 CPYFPN(&fe->fe_f1, fp); 481 (void)fpu_const(&fe->fe_f2, 0x31 /* ln(10) */); 482 fp = fpu_div(fe); 483 } /* else if fp == +Inf, return +Inf */ 484 } else if (fp->fp_class == FPC_ZERO) { 485 /* return -Inf */ 486 fp->fp_class = FPC_INF; 487 fp->fp_sign = 1; 488 fpsr |= FPSR_DZ; 489 } else if (fp->fp_class == FPC_SNAN) { 490 fpsr |= FPSR_SNAN; 491 fp = fpu_newnan(fe); 492 } else { 493 fp = fpu_newnan(fe); 494 } 495 496 fe->fe_fpsr = fpsr; 497 498 return fp; 499 } 500 501 struct fpn * 502 fpu_log2(fe) 503 struct fpemu *fe; 504 { 505 struct fpn *fp = &fe->fe_f2; 506 u_int fpsr; 507 508 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 509 510 if (fp->fp_class >= FPC_NUM) { 511 if (fp->fp_sign) { /* negative number or Inf */ 512 fp = fpu_newnan(fe); 513 fpsr |= FPSR_OPERR; 514 } else if (fp->fp_class == FPC_NUM) { 515 /* the real work here */ 516 if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 && 517 fp->fp_mant[2] == 0 && fp->fp_mant[3] == 0) { 518 /* fp == 2.0 ^ exp <--> log2(fp) == exp */ 519 fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, &fp->fp_exp); 520 fp = &fe->fe_f3; 521 } else { 522 fp = __fpu_logn(fe); 523 if (fp != &fe->fe_f1) 524 CPYFPN(&fe->fe_f1, fp); 525 (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */); 526 fp = fpu_div(fe); 527 } 528 } /* else if fp == +Inf, return +Inf */ 529 } else if (fp->fp_class == FPC_ZERO) { 530 /* return -Inf */ 531 fp->fp_class = FPC_INF; 532 fp->fp_sign = 1; 533 fpsr |= FPSR_DZ; 534 } else if (fp->fp_class == FPC_SNAN) { 535 fpsr |= FPSR_SNAN; 536 fp = fpu_newnan(fe); 537 } else { 538 fp = fpu_newnan(fe); 539 } 540 541 fe->fe_fpsr = fpsr; 542 return fp; 543 } 544 545 struct fpn * 546 fpu_logn(fe) 547 struct fpemu *fe; 548 { 549 struct fpn *fp = &fe->fe_f2; 550 u_int fpsr; 551 552 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 553 554 if (fp->fp_class >= FPC_NUM) { 555 if (fp->fp_sign) { /* negative number or Inf */ 556 fp = fpu_newnan(fe); 557 fpsr |= FPSR_OPERR; 558 } else if (fp->fp_class == FPC_NUM) { 559 /* the real work here */ 560 fp = __fpu_logn(fe); 561 } /* else if fp == +Inf, return +Inf */ 562 } else if (fp->fp_class == FPC_ZERO) { 563 /* return -Inf */ 564 fp->fp_class = FPC_INF; 565 fp->fp_sign = 1; 566 fpsr |= FPSR_DZ; 567 } else if (fp->fp_class == FPC_SNAN) { 568 fpsr |= FPSR_SNAN; 569 fp = fpu_newnan(fe); 570 } else { 571 fp = fpu_newnan(fe); 572 } 573 574 fe->fe_fpsr = fpsr; 575 576 return fp; 577 } 578 579 struct fpn * 580 fpu_lognp1(fe) 581 struct fpemu *fe; 582 { 583 struct fpn *fp; 584 585 /* build a 1.0 */ 586 fp = fpu_const(&fe->fe_f1, 0x32); /* get 1.0 */ 587 /* fp = 1.0 + f2 */ 588 fp = fpu_add(fe); 589 590 /* copy the result to the src opr */ 591 if (&fe->fe_f2 != fp) 592 CPYFPN(&fe->fe_f2, fp); 593 594 return fpu_logn(fe); 595 } 596
Indexes created Sat Sep 27 22:09:54 GMT 2025