1 /* $NetBSD: fpu_log.c,v 1.18 2014/01/04 13:23:22 isaki 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/cdefs.h> 35 __KERNEL_RCSID(0, "$NetBSD: fpu_log.c,v 1.18 2014/01/04 13:23:22 isaki Exp $"); 36 37 #include <sys/types.h> 38 #include <sys/systm.h> 39 40 #include "fpu_emulate.h" 41 42 static uint32_t logA6[] = { 0x3FC2499A, 0xB5E4040B }; 43 static uint32_t logA5[] = { 0xBFC555B5, 0x848CB7DB }; 44 static uint32_t logA4[] = { 0x3FC99999, 0x987D8730 }; 45 static uint32_t logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 }; 46 static uint32_t logA2[] = { 0x3FD55555, 0x555555A4 }; 47 static uint32_t logA1[] = { 0xBFE00000, 0x00000008 }; 48 49 static uint32_t logB5[] = { 0x3F175496, 0xADD7DAD6 }; 50 static uint32_t logB4[] = { 0x3F3C71C2, 0xFE80C7E0 }; 51 static uint32_t logB3[] = { 0x3F624924, 0x928BCCFF }; 52 static uint32_t logB2[] = { 0x3F899999, 0x999995EC }; 53 static uint32_t logB1[] = { 0x3FB55555, 0x55555555 }; 54 55 /* sfpn = shortened fp number; can represent only positive numbers */ 56 static struct sfpn { 57 int sp_exp; 58 uint32_t sp_m0, sp_m1; 59 } logtbl[] = { 60 { 0x3FFE - 0x3fff, 0xFE03F80FU, 0xE03F80FEU }, 61 { 0x3FF7 - 0x3fff, 0xFF015358U, 0x833C47E2U }, 62 { 0x3FFE - 0x3fff, 0xFA232CF2U, 0x52138AC0U }, 63 { 0x3FF9 - 0x3fff, 0xBDC8D83EU, 0xAD88D549U }, 64 { 0x3FFE - 0x3fff, 0xF6603D98U, 0x0F6603DAU }, 65 { 0x3FFA - 0x3fff, 0x9CF43DCFU, 0xF5EAFD48U }, 66 { 0x3FFE - 0x3fff, 0xF2B9D648U, 0x0F2B9D65U }, 67 { 0x3FFA - 0x3fff, 0xDA16EB88U, 0xCB8DF614U }, 68 { 0x3FFE - 0x3fff, 0xEF2EB71FU, 0xC4345238U }, 69 { 0x3FFB - 0x3fff, 0x8B29B775U, 0x1BD70743U }, 70 { 0x3FFE - 0x3fff, 0xEBBDB2A5U, 0xC1619C8CU }, 71 { 0x3FFB - 0x3fff, 0xA8D839F8U, 0x30C1FB49U }, 72 { 0x3FFE - 0x3fff, 0xE865AC7BU, 0x7603A197U }, 73 { 0x3FFB - 0x3fff, 0xC61A2EB1U, 0x8CD907ADU }, 74 { 0x3FFE - 0x3fff, 0xE525982AU, 0xF70C880EU }, 75 { 0x3FFB - 0x3fff, 0xE2F2A47AU, 0xDE3A18AFU }, 76 { 0x3FFE - 0x3fff, 0xE1FC780EU, 0x1FC780E2U }, 77 { 0x3FFB - 0x3fff, 0xFF64898EU, 0xDF55D551U }, 78 { 0x3FFE - 0x3fff, 0xDEE95C4CU, 0xA037BA57U }, 79 { 0x3FFC - 0x3fff, 0x8DB956A9U, 0x7B3D0148U }, 80 { 0x3FFE - 0x3fff, 0xDBEB61EEU, 0xD19C5958U }, 81 { 0x3FFC - 0x3fff, 0x9B8FE100U, 0xF47BA1DEU }, 82 { 0x3FFE - 0x3fff, 0xD901B203U, 0x6406C80EU }, 83 { 0x3FFC - 0x3fff, 0xA9372F1DU, 0x0DA1BD17U }, 84 { 0x3FFE - 0x3fff, 0xD62B80D6U, 0x2B80D62CU }, 85 { 0x3FFC - 0x3fff, 0xB6B07F38U, 0xCE90E46BU }, 86 { 0x3FFE - 0x3fff, 0xD3680D36U, 0x80D3680DU }, 87 { 0x3FFC - 0x3fff, 0xC3FD0329U, 0x06488481U }, 88 { 0x3FFE - 0x3fff, 0xD0B69FCBU, 0xD2580D0BU }, 89 { 0x3FFC - 0x3fff, 0xD11DE0FFU, 0x15AB18CAU }, 90 { 0x3FFE - 0x3fff, 0xCE168A77U, 0x25080CE1U }, 91 { 0x3FFC - 0x3fff, 0xDE1433A1U, 0x6C66B150U }, 92 { 0x3FFE - 0x3fff, 0xCB8727C0U, 0x65C393E0U }, 93 { 0x3FFC - 0x3fff, 0xEAE10B5AU, 0x7DDC8ADDU }, 94 { 0x3FFE - 0x3fff, 0xC907DA4EU, 0x871146ADU }, 95 { 0x3FFC - 0x3fff, 0xF7856E5EU, 0xE2C9B291U }, 96 { 0x3FFE - 0x3fff, 0xC6980C69U, 0x80C6980CU }, 97 { 0x3FFD - 0x3fff, 0x82012CA5U, 0xA68206D7U }, 98 { 0x3FFE - 0x3fff, 0xC4372F85U, 0x5D824CA6U }, 99 { 0x3FFD - 0x3fff, 0x882C5FCDU, 0x7256A8C5U }, 100 { 0x3FFE - 0x3fff, 0xC1E4BBD5U, 0x95F6E947U }, 101 { 0x3FFD - 0x3fff, 0x8E44C60BU, 0x4CCFD7DEU }, 102 { 0x3FFE - 0x3fff, 0xBFA02FE8U, 0x0BFA02FFU }, 103 { 0x3FFD - 0x3fff, 0x944AD09EU, 0xF4351AF6U }, 104 { 0x3FFE - 0x3fff, 0xBD691047U, 0x07661AA3U }, 105 { 0x3FFD - 0x3fff, 0x9A3EECD4U, 0xC3EAA6B2U }, 106 { 0x3FFE - 0x3fff, 0xBB3EE721U, 0xA54D880CU }, 107 { 0x3FFD - 0x3fff, 0xA0218434U, 0x353F1DE8U }, 108 { 0x3FFE - 0x3fff, 0xB92143FAU, 0x36F5E02EU }, 109 { 0x3FFD - 0x3fff, 0xA5F2FCABU, 0xBBC506DAU }, 110 { 0x3FFE - 0x3fff, 0xB70FBB5AU, 0x19BE3659U }, 111 { 0x3FFD - 0x3fff, 0xABB3B8BAU, 0x2AD362A5U }, 112 { 0x3FFE - 0x3fff, 0xB509E68AU, 0x9B94821FU }, 113 { 0x3FFD - 0x3fff, 0xB1641795U, 0xCE3CA97BU }, 114 { 0x3FFE - 0x3fff, 0xB30F6352U, 0x8917C80BU }, 115 { 0x3FFD - 0x3fff, 0xB7047551U, 0x5D0F1C61U }, 116 { 0x3FFE - 0x3fff, 0xB11FD3B8U, 0x0B11FD3CU }, 117 { 0x3FFD - 0x3fff, 0xBC952AFEU, 0xEA3D13E1U }, 118 { 0x3FFE - 0x3fff, 0xAF3ADDC6U, 0x80AF3ADEU }, 119 { 0x3FFD - 0x3fff, 0xC2168ED0U, 0xF458BA4AU }, 120 { 0x3FFE - 0x3fff, 0xAD602B58U, 0x0AD602B6U }, 121 { 0x3FFD - 0x3fff, 0xC788F439U, 0xB3163BF1U }, 122 { 0x3FFE - 0x3fff, 0xAB8F69E2U, 0x8359CD11U }, 123 { 0x3FFD - 0x3fff, 0xCCECAC08U, 0xBF04565DU }, 124 { 0x3FFE - 0x3fff, 0xA9C84A47U, 0xA07F5638U }, 125 { 0x3FFD - 0x3fff, 0xD2420487U, 0x2DD85160U }, 126 { 0x3FFE - 0x3fff, 0xA80A80A8U, 0x0A80A80BU }, 127 { 0x3FFD - 0x3fff, 0xD7894992U, 0x3BC3588AU }, 128 { 0x3FFE - 0x3fff, 0xA655C439U, 0x2D7B73A8U }, 129 { 0x3FFD - 0x3fff, 0xDCC2C4B4U, 0x9887DACCU }, 130 { 0x3FFE - 0x3fff, 0xA4A9CF1DU, 0x96833751U }, 131 { 0x3FFD - 0x3fff, 0xE1EEBD3EU, 0x6D6A6B9EU }, 132 { 0x3FFE - 0x3fff, 0xA3065E3FU, 0xAE7CD0E0U }, 133 { 0x3FFD - 0x3fff, 0xE70D785CU, 0x2F9F5BDCU }, 134 { 0x3FFE - 0x3fff, 0xA16B312EU, 0xA8FC377DU }, 135 { 0x3FFD - 0x3fff, 0xEC1F392CU, 0x5179F283U }, 136 { 0x3FFE - 0x3fff, 0x9FD809FDU, 0x809FD80AU }, 137 { 0x3FFD - 0x3fff, 0xF12440D3U, 0xE36130E6U }, 138 { 0x3FFE - 0x3fff, 0x9E4CAD23U, 0xDD5F3A20U }, 139 { 0x3FFD - 0x3fff, 0xF61CCE92U, 0x346600BBU }, 140 { 0x3FFE - 0x3fff, 0x9CC8E160U, 0xC3FB19B9U }, 141 { 0x3FFD - 0x3fff, 0xFB091FD3U, 0x8145630AU }, 142 { 0x3FFE - 0x3fff, 0x9B4C6F9EU, 0xF03A3CAAU }, 143 { 0x3FFD - 0x3fff, 0xFFE97042U, 0xBFA4C2ADU }, 144 { 0x3FFE - 0x3fff, 0x99D722DAU, 0xBDE58F06U }, 145 { 0x3FFE - 0x3fff, 0x825EFCEDU, 0x49369330U }, 146 { 0x3FFE - 0x3fff, 0x9868C809U, 0x868C8098U }, 147 { 0x3FFE - 0x3fff, 0x84C37A7AU, 0xB9A905C9U }, 148 { 0x3FFE - 0x3fff, 0x97012E02U, 0x5C04B809U }, 149 { 0x3FFE - 0x3fff, 0x87224C2EU, 0x8E645FB7U }, 150 { 0x3FFE - 0x3fff, 0x95A02568U, 0x095A0257U }, 151 { 0x3FFE - 0x3fff, 0x897B8CACU, 0x9F7DE298U }, 152 { 0x3FFE - 0x3fff, 0x94458094U, 0x45809446U }, 153 { 0x3FFE - 0x3fff, 0x8BCF55DEU, 0xC4CD05FEU }, 154 { 0x3FFE - 0x3fff, 0x92F11384U, 0x0497889CU }, 155 { 0x3FFE - 0x3fff, 0x8E1DC0FBU, 0x89E125E5U }, 156 { 0x3FFE - 0x3fff, 0x91A2B3C4U, 0xD5E6F809U }, 157 { 0x3FFE - 0x3fff, 0x9066E68CU, 0x955B6C9BU }, 158 { 0x3FFE - 0x3fff, 0x905A3863U, 0x3E06C43BU }, 159 { 0x3FFE - 0x3fff, 0x92AADE74U, 0xC7BE59E0U }, 160 { 0x3FFE - 0x3fff, 0x8F1779D9U, 0xFDC3A219U }, 161 { 0x3FFE - 0x3fff, 0x94E9BFF6U, 0x15845643U }, 162 { 0x3FFE - 0x3fff, 0x8DDA5202U, 0x37694809U }, 163 { 0x3FFE - 0x3fff, 0x9723A1B7U, 0x20134203U }, 164 { 0x3FFE - 0x3fff, 0x8CA29C04U, 0x6514E023U }, 165 { 0x3FFE - 0x3fff, 0x995899C8U, 0x90EB8990U }, 166 { 0x3FFE - 0x3fff, 0x8B70344AU, 0x139BC75AU }, 167 { 0x3FFE - 0x3fff, 0x9B88BDAAU, 0x3A3DAE2FU }, 168 { 0x3FFE - 0x3fff, 0x8A42F870U, 0x5669DB46U }, 169 { 0x3FFE - 0x3fff, 0x9DB4224FU, 0xFFE1157CU }, 170 { 0x3FFE - 0x3fff, 0x891AC73AU, 0xE9819B50U }, 171 { 0x3FFE - 0x3fff, 0x9FDADC26U, 0x8B7A12DAU }, 172 { 0x3FFE - 0x3fff, 0x87F78087U, 0xF78087F8U }, 173 { 0x3FFE - 0x3fff, 0xA1FCFF17U, 0xCE733BD4U }, 174 { 0x3FFE - 0x3fff, 0x86D90544U, 0x7A34ACC6U }, 175 { 0x3FFE - 0x3fff, 0xA41A9E8FU, 0x5446FB9FU }, 176 { 0x3FFE - 0x3fff, 0x85BF3761U, 0x2CEE3C9BU }, 177 { 0x3FFE - 0x3fff, 0xA633CD7EU, 0x6771CD8BU }, 178 { 0x3FFE - 0x3fff, 0x84A9F9C8U, 0x084A9F9DU }, 179 { 0x3FFE - 0x3fff, 0xA8489E60U, 0x0B435A5EU }, 180 { 0x3FFE - 0x3fff, 0x83993052U, 0x3FBE3368U }, 181 { 0x3FFE - 0x3fff, 0xAA59233CU, 0xCCA4BD49U }, 182 { 0x3FFE - 0x3fff, 0x828CBFBEU, 0xB9A020A3U }, 183 { 0x3FFE - 0x3fff, 0xAC656DAEU, 0x6BCC4985U }, 184 { 0x3FFE - 0x3fff, 0x81848DA8U, 0xFAF0D277U }, 185 { 0x3FFE - 0x3fff, 0xAE6D8EE3U, 0x60BB2468U }, 186 { 0x3FFE - 0x3fff, 0x80808080U, 0x80808081U }, 187 { 0x3FFE - 0x3fff, 0xB07197A2U, 0x3C46C654U }, 188 }; 189 190 static struct fpn *__fpu_logn(struct fpemu *fe); 191 192 /* 193 * natural log - algorithm taken from Motorola FPSP, 194 * except this doesn't bother to check for invalid input. 195 */ 196 static struct fpn * 197 __fpu_logn(struct fpemu *fe) 198 { 199 static struct fpn X, F, U, V, W, KLOG2; 200 struct fpn *d; 201 int i, k; 202 203 CPYFPN(&X, &fe->fe_f2); 204 205 /* see if |X-1| < 1/16 approx. */ 206 if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) || 207 (0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) { 208 /* log near 1 */ 209 #if FPE_DEBUG 210 printf("__fpu_logn: log near 1\n"); 211 #endif 212 213 fpu_const(&fe->fe_f1, FPU_CONST_1); 214 /* X+1 */ 215 d = fpu_add(fe); 216 CPYFPN(&V, d); 217 218 CPYFPN(&fe->fe_f1, &X); 219 fpu_const(&fe->fe_f2, FPU_CONST_1); 220 fe->fe_f2.fp_sign = 1; /* -1.0 */ 221 /* X-1 */ 222 d = fpu_add(fe); 223 CPYFPN(&fe->fe_f1, d); 224 /* 2(X-1) */ 225 fe->fe_f1.fp_exp++; /* *= 2 */ 226 CPYFPN(&fe->fe_f2, &V); 227 /* U=2(X-1)/(X+1) */ 228 d = fpu_div(fe); 229 CPYFPN(&U, d); 230 CPYFPN(&fe->fe_f1, d); 231 CPYFPN(&fe->fe_f2, d); 232 /* V=U*U */ 233 d = fpu_mul(fe); 234 CPYFPN(&V, d); 235 CPYFPN(&fe->fe_f1, d); 236 CPYFPN(&fe->fe_f2, d); 237 /* W=V*V */ 238 d = fpu_mul(fe); 239 CPYFPN(&W, d); 240 241 /* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */ 242 243 /* B1+W*(B3+W*B5) part */ 244 CPYFPN(&fe->fe_f1, d); 245 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5); 246 /* W*B5 */ 247 d = fpu_mul(fe); 248 CPYFPN(&fe->fe_f1, d); 249 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3); 250 /* B3+W*B5 */ 251 d = fpu_add(fe); 252 CPYFPN(&fe->fe_f1, d); 253 CPYFPN(&fe->fe_f2, &W); 254 /* W*(B3+W*B5) */ 255 d = fpu_mul(fe); 256 CPYFPN(&fe->fe_f1, d); 257 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1); 258 /* B1+W*(B3+W*B5) */ 259 d = fpu_add(fe); 260 CPYFPN(&X, d); 261 262 /* [V*(B2+W*B4)] part */ 263 CPYFPN(&fe->fe_f1, &W); 264 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4); 265 /* W*B4 */ 266 d = fpu_mul(fe); 267 CPYFPN(&fe->fe_f1, d); 268 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2); 269 /* B2+W*B4 */ 270 d = fpu_add(fe); 271 CPYFPN(&fe->fe_f1, d); 272 CPYFPN(&fe->fe_f2, &V); 273 /* V*(B2+W*B4) */ 274 d = fpu_mul(fe); 275 CPYFPN(&fe->fe_f1, d); 276 CPYFPN(&fe->fe_f2, &X); 277 /* B1+W*(B3+W*B5)+V*(B2+W*B4) */ 278 d = fpu_add(fe); 279 CPYFPN(&fe->fe_f1, d); 280 CPYFPN(&fe->fe_f2, &V); 281 /* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 282 d = fpu_mul(fe); 283 CPYFPN(&fe->fe_f1, d); 284 CPYFPN(&fe->fe_f2, &U); 285 /* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 286 d = fpu_mul(fe); 287 CPYFPN(&fe->fe_f1, d); 288 CPYFPN(&fe->fe_f2, &U); 289 /* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 290 d = fpu_add(fe); 291 } else /* the usual case */ { 292 #if FPE_DEBUG 293 printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n", 294 X.fp_exp, X.fp_mant[0], X.fp_mant[1]); 295 #endif 296 297 k = X.fp_exp; 298 /* X <- Y */ 299 X.fp_exp = fe->fe_f2.fp_exp = 0; 300 301 /* get the most significant 7 bits of X */ 302 F.fp_class = FPC_NUM; 303 F.fp_sign = 0; 304 F.fp_exp = X.fp_exp; 305 F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG)); 306 F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG)); 307 F.fp_mant[1] = F.fp_mant[2] = 0; 308 F.fp_sticky = 0; 309 310 #if FPE_DEBUG 311 printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n", 312 fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0], 313 fe->fe_f2.fp_mant[1], k); 314 printf("__fpu_logn: F=(%d,%08x,%08x...)\n", 315 F.fp_exp, F.fp_mant[0], F.fp_mant[1]); 316 #endif 317 318 /* index to the table */ 319 i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e; 320 321 #if FPE_DEBUG 322 printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i); 323 #endif 324 325 CPYFPN(&fe->fe_f1, &F); 326 /* -F */ 327 fe->fe_f1.fp_sign = 1; 328 /* Y-F */ 329 d = fpu_add(fe); 330 CPYFPN(&fe->fe_f1, d); 331 332 /* fe_f2 = 1/F */ 333 fe->fe_f2.fp_class = FPC_NUM; 334 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] 335 = 0; 336 fe->fe_f2.fp_exp = logtbl[i].sp_exp; 337 fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG)); 338 fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) | 339 (logtbl[i].sp_m1 >> (31 - FP_LG)); 340 fe->fe_f2.fp_mant[2] = 341 (uint32_t)(logtbl[i].sp_m1 << (FP_LG + 1)); 342 343 #if FPE_DEBUG 344 printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp, 345 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 346 #endif 347 348 /* U = (Y-F) * (1/F) */ 349 d = fpu_mul(fe); 350 CPYFPN(&U, d); 351 352 /* KLOG2 = K * ln(2) */ 353 /* fe_f1 == (fpn)k */ 354 fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k); 355 (void)fpu_const(&fe->fe_f2, FPU_CONST_LN_2); 356 #if FPE_DEBUG 357 printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", 358 fe->fe_f1.fp_exp, 359 fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]); 360 printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", 361 fe->fe_f2.fp_exp, 362 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 363 #endif 364 /* K * LOGOF2 */ 365 d = fpu_mul(fe); 366 CPYFPN(&KLOG2, d); 367 368 /* V=U*U */ 369 CPYFPN(&fe->fe_f1, &U); 370 CPYFPN(&fe->fe_f2, &U); 371 d = fpu_mul(fe); 372 CPYFPN(&V, d); 373 374 /* 375 * approximation of LOG(1+U) by 376 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6))) 377 */ 378 379 /* (U+V*(A1+V*(A3+V*A5))) part */ 380 CPYFPN(&fe->fe_f1, d); 381 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5); 382 /* V*A5 */ 383 d = fpu_mul(fe); 384 385 CPYFPN(&fe->fe_f1, d); 386 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3); 387 /* A3+V*A5 */ 388 d = fpu_add(fe); 389 390 CPYFPN(&fe->fe_f1, d); 391 CPYFPN(&fe->fe_f2, &V); 392 /* V*(A3+V*A5) */ 393 d = fpu_mul(fe); 394 395 CPYFPN(&fe->fe_f1, d); 396 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1); 397 /* A1+V*(A3+V*A5) */ 398 d = fpu_add(fe); 399 400 CPYFPN(&fe->fe_f1, d); 401 CPYFPN(&fe->fe_f2, &V); 402 /* V*(A1+V*(A3+V*A5)) */ 403 d = fpu_mul(fe); 404 405 CPYFPN(&fe->fe_f1, d); 406 CPYFPN(&fe->fe_f2, &U); 407 /* U+V*(A1+V*(A3+V*A5)) */ 408 d = fpu_add(fe); 409 410 CPYFPN(&X, d); 411 412 /* (U*V*(A2+V*(A4+V*A6))) part */ 413 CPYFPN(&fe->fe_f1, &V); 414 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6); 415 /* V*A6 */ 416 d = fpu_mul(fe); 417 CPYFPN(&fe->fe_f1, d); 418 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4); 419 /* A4+V*A6 */ 420 d = fpu_add(fe); 421 CPYFPN(&fe->fe_f1, d); 422 CPYFPN(&fe->fe_f2, &V); 423 /* V*(A4+V*A6) */ 424 d = fpu_mul(fe); 425 CPYFPN(&fe->fe_f1, d); 426 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2); 427 /* A2+V*(A4+V*A6) */ 428 d = fpu_add(fe); 429 CPYFPN(&fe->fe_f1, d); 430 CPYFPN(&fe->fe_f2, &V); 431 /* V*(A2+V*(A4+V*A6)) */ 432 d = fpu_mul(fe); 433 CPYFPN(&fe->fe_f1, d); 434 CPYFPN(&fe->fe_f2, &U); 435 /* U*V*(A2+V*(A4+V*A6)) */ 436 d = fpu_mul(fe); 437 CPYFPN(&fe->fe_f1, d); 438 i++; 439 /* fe_f2 = logtbl[i+1] (== LOG(F)) */ 440 fe->fe_f2.fp_class = FPC_NUM; 441 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] 442 = 0; 443 fe->fe_f2.fp_exp = logtbl[i].sp_exp; 444 fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG)); 445 fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) | 446 (logtbl[i].sp_m1 >> (31 - FP_LG)); 447 fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1)); 448 449 #if FPE_DEBUG 450 printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", 451 fe->fe_f2.fp_exp, 452 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 453 #endif 454 455 /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ 456 d = fpu_add(fe); 457 CPYFPN(&fe->fe_f1, d); 458 CPYFPN(&fe->fe_f2, &X); 459 /* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 460 d = fpu_add(fe); 461 462 #if FPE_DEBUG 463 printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n", 464 d->fp_sign ? '-' : '+', d->fp_exp, 465 d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]); 466 #endif 467 468 CPYFPN(&fe->fe_f1, d); 469 CPYFPN(&fe->fe_f2, &KLOG2); 470 /* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 471 d = fpu_add(fe); 472 } 473 474 return d; 475 } 476 477 struct fpn * 478 fpu_log10(struct fpemu *fe) 479 { 480 struct fpn *fp = &fe->fe_f2; 481 uint32_t fpsr; 482 483 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 484 485 if (fp->fp_class >= FPC_NUM) { 486 if (fp->fp_sign) { /* negative number or Inf */ 487 fp = fpu_newnan(fe); 488 fpsr |= FPSR_OPERR; 489 } else if (fp->fp_class == FPC_NUM) { 490 /* the real work here */ 491 fp = __fpu_logn(fe); 492 if (fp != &fe->fe_f1) 493 CPYFPN(&fe->fe_f1, fp); 494 (void)fpu_const(&fe->fe_f2, FPU_CONST_LN_10); 495 fp = fpu_div(fe); 496 } /* else if fp == +Inf, return +Inf */ 497 } else if (fp->fp_class == FPC_ZERO) { 498 /* return -Inf */ 499 fp->fp_class = FPC_INF; 500 fp->fp_sign = 1; 501 fpsr |= FPSR_DZ; 502 } else if (fp->fp_class == FPC_SNAN) { 503 fpsr |= FPSR_SNAN; 504 fp = fpu_newnan(fe); 505 } else { 506 fp = fpu_newnan(fe); 507 } 508 509 fe->fe_fpsr = fpsr; 510 511 return fp; 512 } 513 514 struct fpn * 515 fpu_log2(struct fpemu *fe) 516 { 517 struct fpn *fp = &fe->fe_f2; 518 uint32_t fpsr; 519 520 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 521 522 if (fp->fp_class >= FPC_NUM) { 523 if (fp->fp_sign) { /* negative number or Inf */ 524 fp = fpu_newnan(fe); 525 fpsr |= FPSR_OPERR; 526 } else if (fp->fp_class == FPC_NUM) { 527 /* the real work here */ 528 if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 && 529 fp->fp_mant[2] == 0) { 530 /* fp == 2.0 ^ exp <--> log2(fp) == exp */ 531 fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, 532 &fp->fp_exp); 533 fp = &fe->fe_f3; 534 } else { 535 fp = __fpu_logn(fe); 536 if (fp != &fe->fe_f1) 537 CPYFPN(&fe->fe_f1, fp); 538 (void)fpu_const(&fe->fe_f2, FPU_CONST_LN_2); 539 fp = fpu_div(fe); 540 } 541 } /* else if fp == +Inf, return +Inf */ 542 } else if (fp->fp_class == FPC_ZERO) { 543 /* return -Inf */ 544 fp->fp_class = FPC_INF; 545 fp->fp_sign = 1; 546 fpsr |= FPSR_DZ; 547 } else if (fp->fp_class == FPC_SNAN) { 548 fpsr |= FPSR_SNAN; 549 fp = fpu_newnan(fe); 550 } else { 551 fp = fpu_newnan(fe); 552 } 553 554 fe->fe_fpsr = fpsr; 555 return fp; 556 } 557 558 struct fpn * 559 fpu_logn(struct fpemu *fe) 560 { 561 struct fpn *fp = &fe->fe_f2; 562 uint32_t fpsr; 563 564 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 565 566 if (fp->fp_class >= FPC_NUM) { 567 if (fp->fp_sign) { /* negative number or Inf */ 568 fp = fpu_newnan(fe); 569 fpsr |= FPSR_OPERR; 570 } else if (fp->fp_class == FPC_NUM) { 571 /* the real work here */ 572 fp = __fpu_logn(fe); 573 } /* else if fp == +Inf, return +Inf */ 574 } else if (fp->fp_class == FPC_ZERO) { 575 /* return -Inf */ 576 fp->fp_class = FPC_INF; 577 fp->fp_sign = 1; 578 fpsr |= FPSR_DZ; 579 } else if (fp->fp_class == FPC_SNAN) { 580 fpsr |= FPSR_SNAN; 581 fp = fpu_newnan(fe); 582 } else { 583 fp = fpu_newnan(fe); 584 } 585 586 fe->fe_fpsr = fpsr; 587 588 return fp; 589 } 590 591 struct fpn * 592 fpu_lognp1(struct fpemu *fe) 593 { 594 struct fpn *fp; 595 596 /* if src is +0/-0, return +0/-0 */ 597 if (ISZERO(&fe->fe_f2)) 598 return &fe->fe_f2; 599 600 /* build a 1.0 */ 601 fp = fpu_const(&fe->fe_f1, FPU_CONST_1); 602 /* fp = 1.0 + f2 */ 603 fp = fpu_add(fe); 604 605 /* copy the result to the src opr */ 606 CPYFPN(&fe->fe_f2, fp); 607 608 return fpu_logn(fe); 609 } 610
Indexes created Mon Sep 22 13:09:51 GMT 2025