fpu_log.c revision 1.8
1 /* $NetBSD: fpu_log.c,v 1.8 2003/07/15 02:43:10 lukem 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 1.8 2003/07/15 02:43:10 lukem Exp $"); 36 37 #include <sys/types.h> 38 #include <sys/systm.h> 39 40 #include "fpu_emulate.h" 41 42 static u_int logA6[] = { 0x3FC2499A, 0xB5E4040B }; 43 static u_int logA5[] = { 0xBFC555B5, 0x848CB7DB }; 44 static u_int logA4[] = { 0x3FC99999, 0x987D8730 }; 45 static u_int logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 }; 46 static u_int logA2[] = { 0x3FD55555, 0x555555A4 }; 47 static u_int logA1[] = { 0xBFE00000, 0x00000008 }; 48 49 static u_int logB5[] = { 0x3F175496, 0xADD7DAD6 }; 50 static u_int logB4[] = { 0x3F3C71C2, 0xFE80C7E0 }; 51 static u_int logB3[] = { 0x3F624924, 0x928BCCFF }; 52 static u_int logB2[] = { 0x3F899999, 0x999995EC }; 53 static u_int logB1[] = { 0x3FB55555, 0x55555555 }; 54 55 /* sfpn = shortened fp number; can represent only positive numbers */ 56 static struct sfpn { 57 int sp_exp; 58 u_int 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 __P((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(fe) 198 struct fpemu *fe; 199 { 200 static struct fpn X, F, U, V, W, KLOG2; 201 struct fpn *d; 202 int i, k; 203 204 CPYFPN(&X, &fe->fe_f2); 205 206 /* see if |X-1| < 1/16 approx. */ 207 if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) || 208 (0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) { 209 /* log near 1 */ 210 #if FPE_DEBUG 211 printf("__fpu_logn: log near 1\n"); 212 #endif 213 214 fpu_const(&fe->fe_f1, 0x32); 215 /* X+1 */ 216 d = fpu_add(fe); 217 CPYFPN(&V, d); 218 219 CPYFPN(&fe->fe_f1, &X); 220 fpu_const(&fe->fe_f2, 0x32); /* 1.0 */ 221 fe->fe_f2.fp_sign = 1; /* -1.0 */ 222 /* X-1 */ 223 d = fpu_add(fe); 224 CPYFPN(&fe->fe_f1, d); 225 /* 2(X-1) */ 226 fe->fe_f1.fp_exp++; /* *= 2 */ 227 CPYFPN(&fe->fe_f2, &V); 228 /* U=2(X-1)/(X+1) */ 229 d = fpu_div(fe); 230 CPYFPN(&U, d); 231 CPYFPN(&fe->fe_f1, d); 232 CPYFPN(&fe->fe_f2, d); 233 /* V=U*U */ 234 d = fpu_mul(fe); 235 CPYFPN(&V, d); 236 CPYFPN(&fe->fe_f1, d); 237 CPYFPN(&fe->fe_f2, d); 238 /* W=V*V */ 239 d = fpu_mul(fe); 240 CPYFPN(&W, d); 241 242 /* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */ 243 244 /* B1+W*(B3+W*B5) part */ 245 CPYFPN(&fe->fe_f1, d); 246 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5); 247 /* W*B5 */ 248 d = fpu_mul(fe); 249 CPYFPN(&fe->fe_f1, d); 250 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3); 251 /* B3+W*B5 */ 252 d = fpu_add(fe); 253 CPYFPN(&fe->fe_f1, d); 254 CPYFPN(&fe->fe_f2, &W); 255 /* W*(B3+W*B5) */ 256 d = fpu_mul(fe); 257 CPYFPN(&fe->fe_f1, d); 258 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1); 259 /* B1+W*(B3+W*B5) */ 260 d = fpu_add(fe); 261 CPYFPN(&X, d); 262 263 /* [V*(B2+W*B4)] part */ 264 CPYFPN(&fe->fe_f1, &W); 265 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4); 266 /* W*B4 */ 267 d = fpu_mul(fe); 268 CPYFPN(&fe->fe_f1, d); 269 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2); 270 /* B2+W*B4 */ 271 d = fpu_add(fe); 272 CPYFPN(&fe->fe_f1, d); 273 CPYFPN(&fe->fe_f2, &V); 274 /* V*(B2+W*B4) */ 275 d = fpu_mul(fe); 276 CPYFPN(&fe->fe_f1, d); 277 CPYFPN(&fe->fe_f2, &X); 278 /* B1+W*(B3+W*B5)+V*(B2+W*B4) */ 279 d = fpu_add(fe); 280 CPYFPN(&fe->fe_f1, d); 281 CPYFPN(&fe->fe_f2, &V); 282 /* 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*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 287 d = fpu_mul(fe); 288 CPYFPN(&fe->fe_f1, d); 289 CPYFPN(&fe->fe_f2, &U); 290 /* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */ 291 d = fpu_add(fe); 292 } else /* the usual case */ { 293 #if FPE_DEBUG 294 printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n", 295 X.fp_exp, X.fp_mant[0], X.fp_mant[1]); 296 #endif 297 298 k = X.fp_exp; 299 /* X <- Y */ 300 X.fp_exp = fe->fe_f2.fp_exp = 0; 301 302 /* get the most significant 7 bits of X */ 303 F.fp_class = FPC_NUM; 304 F.fp_sign = 0; 305 F.fp_exp = X.fp_exp; 306 F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG)); 307 F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG)); 308 F.fp_mant[1] = F.fp_mant[2] = 0; 309 F.fp_sticky = 0; 310 311 #if FPE_DEBUG 312 printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n", 313 fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0], 314 fe->fe_f2.fp_mant[1], k); 315 printf("__fpu_logn: F=(%d,%08x,%08x...)\n", 316 F.fp_exp, F.fp_mant[0], F.fp_mant[1]); 317 #endif 318 319 /* index to the table */ 320 i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e; 321 322 #if FPE_DEBUG 323 printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i); 324 #endif 325 326 CPYFPN(&fe->fe_f1, &F); 327 /* -F */ 328 fe->fe_f1.fp_sign = 1; 329 /* Y-F */ 330 d = fpu_add(fe); 331 CPYFPN(&fe->fe_f1, d); 332 333 /* fe_f2 = 1/F */ 334 fe->fe_f2.fp_class = FPC_NUM; 335 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 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] = (u_int)(logtbl[i].sp_m1 << (FP_LG + 1)); 341 342 #if FPE_DEBUG 343 printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp, 344 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 345 #endif 346 347 /* U = (Y-F) * (1/F) */ 348 d = fpu_mul(fe); 349 CPYFPN(&U, d); 350 351 /* KLOG2 = K * ln(2) */ 352 /* fe_f1 == (fpn)k */ 353 fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k); 354 (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */); 355 #if FPE_DEBUG 356 printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", fe->fe_f1.fp_exp, 357 fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]); 358 printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp, 359 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 360 #endif 361 /* K * LOGOF2 */ 362 d = fpu_mul(fe); 363 CPYFPN(&KLOG2, d); 364 365 /* V=U*U */ 366 CPYFPN(&fe->fe_f1, &U); 367 CPYFPN(&fe->fe_f2, &U); 368 d = fpu_mul(fe); 369 CPYFPN(&V, d); 370 371 /* 372 * approximation of LOG(1+U) by 373 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6))) 374 */ 375 376 /* (U+V*(A1+V*(A3+V*A5))) part */ 377 CPYFPN(&fe->fe_f1, d); 378 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5); 379 /* V*A5 */ 380 d = fpu_mul(fe); 381 382 CPYFPN(&fe->fe_f1, d); 383 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3); 384 /* A3+V*A5 */ 385 d = fpu_add(fe); 386 387 CPYFPN(&fe->fe_f1, d); 388 CPYFPN(&fe->fe_f2, &V); 389 /* V*(A3+V*A5) */ 390 d = fpu_mul(fe); 391 392 CPYFPN(&fe->fe_f1, d); 393 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1); 394 /* A1+V*(A3+V*A5) */ 395 d = fpu_add(fe); 396 397 CPYFPN(&fe->fe_f1, d); 398 CPYFPN(&fe->fe_f2, &V); 399 /* V*(A1+V*(A3+V*A5)) */ 400 d = fpu_mul(fe); 401 402 CPYFPN(&fe->fe_f1, d); 403 CPYFPN(&fe->fe_f2, &U); 404 /* U+V*(A1+V*(A3+V*A5)) */ 405 d = fpu_add(fe); 406 407 CPYFPN(&X, d); 408 409 /* (U*V*(A2+V*(A4+V*A6))) part */ 410 CPYFPN(&fe->fe_f1, &V); 411 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6); 412 /* V*A6 */ 413 d = fpu_mul(fe); 414 CPYFPN(&fe->fe_f1, d); 415 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4); 416 /* A4+V*A6 */ 417 d = fpu_add(fe); 418 CPYFPN(&fe->fe_f1, d); 419 CPYFPN(&fe->fe_f2, &V); 420 /* V*(A4+V*A6) */ 421 d = fpu_mul(fe); 422 CPYFPN(&fe->fe_f1, d); 423 fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2); 424 /* A2+V*(A4+V*A6) */ 425 d = fpu_add(fe); 426 CPYFPN(&fe->fe_f1, d); 427 CPYFPN(&fe->fe_f2, &V); 428 /* V*(A2+V*(A4+V*A6)) */ 429 d = fpu_mul(fe); 430 CPYFPN(&fe->fe_f1, d); 431 CPYFPN(&fe->fe_f2, &U); 432 /* U*V*(A2+V*(A4+V*A6)) */ 433 d = fpu_mul(fe); 434 CPYFPN(&fe->fe_f1, d); 435 i++; 436 /* fe_f2 = logtbl[i+1] (== LOG(F)) */ 437 fe->fe_f2.fp_class = FPC_NUM; 438 fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0; 439 fe->fe_f2.fp_exp = logtbl[i].sp_exp; 440 fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG)); 441 fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) | 442 (logtbl[i].sp_m1 >> (31 - FP_LG)); 443 fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1)); 444 445 #if FPE_DEBUG 446 printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", fe->fe_f2.fp_exp, 447 fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]); 448 #endif 449 450 /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ 451 d = fpu_add(fe); 452 CPYFPN(&fe->fe_f1, d); 453 CPYFPN(&fe->fe_f2, &X); 454 /* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 455 d = fpu_add(fe); 456 457 #if FPE_DEBUG 458 printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n", 459 d->fp_sign ? '-' : '+', d->fp_exp, 460 d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]); 461 #endif 462 463 CPYFPN(&fe->fe_f1, d); 464 CPYFPN(&fe->fe_f2, &KLOG2); 465 /* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */ 466 d = fpu_add(fe); 467 } 468 469 return d; 470 } 471 472 struct fpn * 473 fpu_log10(fe) 474 struct fpemu *fe; 475 { 476 struct fpn *fp = &fe->fe_f2; 477 u_int fpsr; 478 479 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 480 481 if (fp->fp_class >= FPC_NUM) { 482 if (fp->fp_sign) { /* negative number or Inf */ 483 fp = fpu_newnan(fe); 484 fpsr |= FPSR_OPERR; 485 } else if (fp->fp_class == FPC_NUM) { 486 /* the real work here */ 487 fp = __fpu_logn(fe); 488 if (fp != &fe->fe_f1) 489 CPYFPN(&fe->fe_f1, fp); 490 (void)fpu_const(&fe->fe_f2, 0x31 /* ln(10) */); 491 fp = fpu_div(fe); 492 } /* else if fp == +Inf, return +Inf */ 493 } else if (fp->fp_class == FPC_ZERO) { 494 /* return -Inf */ 495 fp->fp_class = FPC_INF; 496 fp->fp_sign = 1; 497 fpsr |= FPSR_DZ; 498 } else if (fp->fp_class == FPC_SNAN) { 499 fpsr |= FPSR_SNAN; 500 fp = fpu_newnan(fe); 501 } else { 502 fp = fpu_newnan(fe); 503 } 504 505 fe->fe_fpsr = fpsr; 506 507 return fp; 508 } 509 510 struct fpn * 511 fpu_log2(fe) 512 struct fpemu *fe; 513 { 514 struct fpn *fp = &fe->fe_f2; 515 u_int fpsr; 516 517 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 518 519 if (fp->fp_class >= FPC_NUM) { 520 if (fp->fp_sign) { /* negative number or Inf */ 521 fp = fpu_newnan(fe); 522 fpsr |= FPSR_OPERR; 523 } else if (fp->fp_class == FPC_NUM) { 524 /* the real work here */ 525 if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 && 526 fp->fp_mant[2] == 0) { 527 /* fp == 2.0 ^ exp <--> log2(fp) == exp */ 528 fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, &fp->fp_exp); 529 fp = &fe->fe_f3; 530 } else { 531 fp = __fpu_logn(fe); 532 if (fp != &fe->fe_f1) 533 CPYFPN(&fe->fe_f1, fp); 534 (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */); 535 fp = fpu_div(fe); 536 } 537 } /* else if fp == +Inf, return +Inf */ 538 } else if (fp->fp_class == FPC_ZERO) { 539 /* return -Inf */ 540 fp->fp_class = FPC_INF; 541 fp->fp_sign = 1; 542 fpsr |= FPSR_DZ; 543 } else if (fp->fp_class == FPC_SNAN) { 544 fpsr |= FPSR_SNAN; 545 fp = fpu_newnan(fe); 546 } else { 547 fp = fpu_newnan(fe); 548 } 549 550 fe->fe_fpsr = fpsr; 551 return fp; 552 } 553 554 struct fpn * 555 fpu_logn(fe) 556 struct fpemu *fe; 557 { 558 struct fpn *fp = &fe->fe_f2; 559 u_int fpsr; 560 561 fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */ 562 563 if (fp->fp_class >= FPC_NUM) { 564 if (fp->fp_sign) { /* negative number or Inf */ 565 fp = fpu_newnan(fe); 566 fpsr |= FPSR_OPERR; 567 } else if (fp->fp_class == FPC_NUM) { 568 /* the real work here */ 569 fp = __fpu_logn(fe); 570 } /* else if fp == +Inf, return +Inf */ 571 } else if (fp->fp_class == FPC_ZERO) { 572 /* return -Inf */ 573 fp->fp_class = FPC_INF; 574 fp->fp_sign = 1; 575 fpsr |= FPSR_DZ; 576 } else if (fp->fp_class == FPC_SNAN) { 577 fpsr |= FPSR_SNAN; 578 fp = fpu_newnan(fe); 579 } else { 580 fp = fpu_newnan(fe); 581 } 582 583 fe->fe_fpsr = fpsr; 584 585 return fp; 586 } 587 588 struct fpn * 589 fpu_lognp1(fe) 590 struct fpemu *fe; 591 { 592 struct fpn *fp; 593 594 /* build a 1.0 */ 595 fp = fpu_const(&fe->fe_f1, 0x32); /* get 1.0 */ 596 /* fp = 1.0 + f2 */ 597 fp = fpu_add(fe); 598 599 /* copy the result to the src opr */ 600 if (&fe->fe_f2 != fp) 601 CPYFPN(&fe->fe_f2, fp); 602 603 return fpu_logn(fe); 604 } 605
Indexes created Sun Sep 28 16:09:52 GMT 2025