| 1 | /* IEEE floating point support routines, for GDB, the GNU Debugger. |
| 2 | Copyright (C) 1991, 1994, 1999, 2000 Free Software Foundation, Inc. |
| 3 | |
| 4 | This file is part of GDB. |
| 5 | |
| 6 | This program is free software; you can redistribute it and/or modify |
| 7 | it under the terms of the GNU General Public License as published by |
| 8 | the Free Software Foundation; either version 2 of the License, or |
| 9 | (at your option) any later version. |
| 10 | |
| 11 | This program is distributed in the hope that it will be useful, |
| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 14 | GNU General Public License for more details. |
| 15 | |
| 16 | You should have received a copy of the GNU General Public License |
| 17 | along with this program; if not, write to the Free Software |
| 18 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ |
| 19 | |
| 20 | #include "floatformat.h" |
| 21 | #include <math.h> /* ldexp */ |
| 22 | #ifdef __STDC__ |
| 23 | #include <stddef.h> |
| 24 | extern void *memcpy (void *s1, const void *s2, size_t n); |
| 25 | extern void *memset (void *s, int c, size_t n); |
| 26 | #else |
| 27 | extern char *memcpy (); |
| 28 | extern char *memset (); |
| 29 | #endif |
| 30 | |
| 31 | /* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not |
| 32 | going to bother with trying to muck around with whether it is defined in |
| 33 | a system header, what we do if not, etc. */ |
| 34 | #define FLOATFORMAT_CHAR_BIT 8 |
| 35 | |
| 36 | /* floatformats for IEEE single and double, big and little endian. */ |
| 37 | const struct floatformat floatformat_ieee_single_big = |
| 38 | { |
| 39 | floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23, |
| 40 | floatformat_intbit_no, |
| 41 | "floatformat_ieee_single_big" |
| 42 | }; |
| 43 | const struct floatformat floatformat_ieee_single_little = |
| 44 | { |
| 45 | floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23, |
| 46 | floatformat_intbit_no, |
| 47 | "floatformat_ieee_single_little" |
| 48 | }; |
| 49 | const struct floatformat floatformat_ieee_double_big = |
| 50 | { |
| 51 | floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52, |
| 52 | floatformat_intbit_no, |
| 53 | "floatformat_ieee_double_big" |
| 54 | }; |
| 55 | const struct floatformat floatformat_ieee_double_little = |
| 56 | { |
| 57 | floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52, |
| 58 | floatformat_intbit_no, |
| 59 | "floatformat_ieee_double_little" |
| 60 | }; |
| 61 | |
| 62 | /* floatformat for IEEE double, little endian byte order, with big endian word |
| 63 | ordering, as on the ARM. */ |
| 64 | |
| 65 | const struct floatformat floatformat_ieee_double_littlebyte_bigword = |
| 66 | { |
| 67 | floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52, |
| 68 | floatformat_intbit_no, |
| 69 | "floatformat_ieee_double_littlebyte_bigword" |
| 70 | }; |
| 71 | |
| 72 | const struct floatformat floatformat_i387_ext = |
| 73 | { |
| 74 | floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64, |
| 75 | floatformat_intbit_yes, |
| 76 | "floatformat_i387_ext" |
| 77 | }; |
| 78 | const struct floatformat floatformat_m68881_ext = |
| 79 | { |
| 80 | /* Note that the bits from 16 to 31 are unused. */ |
| 81 | floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64, |
| 82 | floatformat_intbit_yes, |
| 83 | "floatformat_m68881_ext" |
| 84 | }; |
| 85 | const struct floatformat floatformat_i960_ext = |
| 86 | { |
| 87 | /* Note that the bits from 0 to 15 are unused. */ |
| 88 | floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64, |
| 89 | floatformat_intbit_yes, |
| 90 | "floatformat_i960_ext" |
| 91 | }; |
| 92 | const struct floatformat floatformat_m88110_ext = |
| 93 | { |
| 94 | floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64, |
| 95 | floatformat_intbit_yes, |
| 96 | "floatformat_m88110_ext" |
| 97 | }; |
| 98 | const struct floatformat floatformat_m88110_harris_ext = |
| 99 | { |
| 100 | /* Harris uses raw format 128 bytes long, but the number is just an ieee |
| 101 | double, and the last 64 bits are wasted. */ |
| 102 | floatformat_big,128, 0, 1, 11, 0x3ff, 0x7ff, 12, 52, |
| 103 | floatformat_intbit_no, |
| 104 | "floatformat_m88110_ext_harris" |
| 105 | }; |
| 106 | const struct floatformat floatformat_arm_ext_big = |
| 107 | { |
| 108 | /* Bits 1 to 16 are unused. */ |
| 109 | floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64, |
| 110 | floatformat_intbit_yes, |
| 111 | "floatformat_arm_ext_big" |
| 112 | }; |
| 113 | const struct floatformat floatformat_arm_ext_littlebyte_bigword = |
| 114 | { |
| 115 | /* Bits 1 to 16 are unused. */ |
| 116 | floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64, |
| 117 | floatformat_intbit_yes, |
| 118 | "floatformat_arm_ext_littlebyte_bigword" |
| 119 | }; |
| 120 | const struct floatformat floatformat_ia64_spill_big = |
| 121 | { |
| 122 | floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64, |
| 123 | floatformat_intbit_yes, |
| 124 | "floatformat_ia64_spill_big" |
| 125 | }; |
| 126 | const struct floatformat floatformat_ia64_spill_little = |
| 127 | { |
| 128 | floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64, |
| 129 | floatformat_intbit_yes, |
| 130 | "floatformat_ia64_spill_little" |
| 131 | }; |
| 132 | const struct floatformat floatformat_ia64_quad_big = |
| 133 | { |
| 134 | floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112, |
| 135 | floatformat_intbit_no, |
| 136 | "floatformat_ia64_quad_big" |
| 137 | }; |
| 138 | const struct floatformat floatformat_ia64_quad_little = |
| 139 | { |
| 140 | floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112, |
| 141 | floatformat_intbit_no, |
| 142 | "floatformat_ia64_quad_little" |
| 143 | }; |
| 144 | \f |
| 145 | static unsigned long get_field PARAMS ((unsigned char *, |
| 146 | enum floatformat_byteorders, |
| 147 | unsigned int, |
| 148 | unsigned int, |
| 149 | unsigned int)); |
| 150 | |
| 151 | /* Extract a field which starts at START and is LEN bytes long. DATA and |
| 152 | TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */ |
| 153 | static unsigned long |
| 154 | get_field (data, order, total_len, start, len) |
| 155 | unsigned char *data; |
| 156 | enum floatformat_byteorders order; |
| 157 | unsigned int total_len; |
| 158 | unsigned int start; |
| 159 | unsigned int len; |
| 160 | { |
| 161 | unsigned long result; |
| 162 | unsigned int cur_byte; |
| 163 | int cur_bitshift; |
| 164 | |
| 165 | /* Start at the least significant part of the field. */ |
| 166 | cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT; |
| 167 | if (order == floatformat_little) |
| 168 | cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1; |
| 169 | cur_bitshift = |
| 170 | ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT; |
| 171 | result = *(data + cur_byte) >> (-cur_bitshift); |
| 172 | cur_bitshift += FLOATFORMAT_CHAR_BIT; |
| 173 | if (order == floatformat_little) |
| 174 | ++cur_byte; |
| 175 | else |
| 176 | --cur_byte; |
| 177 | |
| 178 | /* Move towards the most significant part of the field. */ |
| 179 | while ((unsigned int) cur_bitshift < len) |
| 180 | { |
| 181 | if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT) |
| 182 | /* This is the last byte; zero out the bits which are not part of |
| 183 | this field. */ |
| 184 | result |= |
| 185 | (*(data + cur_byte) & ((1 << (len - cur_bitshift)) - 1)) |
| 186 | << cur_bitshift; |
| 187 | else |
| 188 | result |= *(data + cur_byte) << cur_bitshift; |
| 189 | cur_bitshift += FLOATFORMAT_CHAR_BIT; |
| 190 | if (order == floatformat_little) |
| 191 | ++cur_byte; |
| 192 | else |
| 193 | --cur_byte; |
| 194 | } |
| 195 | return result; |
| 196 | } |
| 197 | |
| 198 | #ifndef min |
| 199 | #define min(a, b) ((a) < (b) ? (a) : (b)) |
| 200 | #endif |
| 201 | |
| 202 | /* Convert from FMT to a double. |
| 203 | FROM is the address of the extended float. |
| 204 | Store the double in *TO. */ |
| 205 | |
| 206 | void |
| 207 | floatformat_to_double (fmt, from, to) |
| 208 | const struct floatformat *fmt; |
| 209 | char *from; |
| 210 | double *to; |
| 211 | { |
| 212 | unsigned char *ufrom = (unsigned char *)from; |
| 213 | double dto; |
| 214 | long exponent; |
| 215 | unsigned long mant; |
| 216 | unsigned int mant_bits, mant_off; |
| 217 | int mant_bits_left; |
| 218 | int special_exponent; /* It's a NaN, denorm or zero */ |
| 219 | |
| 220 | exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize, |
| 221 | fmt->exp_start, fmt->exp_len); |
| 222 | /* Note that if exponent indicates a NaN, we can't really do anything useful |
| 223 | (not knowing if the host has NaN's, or how to build one). So it will |
| 224 | end up as an infinity or something close; that is OK. */ |
| 225 | |
| 226 | mant_bits_left = fmt->man_len; |
| 227 | mant_off = fmt->man_start; |
| 228 | dto = 0.0; |
| 229 | |
| 230 | special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan; |
| 231 | |
| 232 | /* Don't bias zero's, denorms or NaNs. */ |
| 233 | if (!special_exponent) |
| 234 | exponent -= fmt->exp_bias; |
| 235 | |
| 236 | /* Build the result algebraically. Might go infinite, underflow, etc; |
| 237 | who cares. */ |
| 238 | |
| 239 | /* If this format uses a hidden bit, explicitly add it in now. Otherwise, |
| 240 | increment the exponent by one to account for the integer bit. */ |
| 241 | |
| 242 | if (!special_exponent) |
| 243 | { |
| 244 | if (fmt->intbit == floatformat_intbit_no) |
| 245 | dto = ldexp (1.0, exponent); |
| 246 | else |
| 247 | exponent++; |
| 248 | } |
| 249 | |
| 250 | while (mant_bits_left > 0) |
| 251 | { |
| 252 | mant_bits = min (mant_bits_left, 32); |
| 253 | |
| 254 | mant = get_field (ufrom, fmt->byteorder, fmt->totalsize, |
| 255 | mant_off, mant_bits); |
| 256 | |
| 257 | dto += ldexp ((double)mant, exponent - mant_bits); |
| 258 | exponent -= mant_bits; |
| 259 | mant_off += mant_bits; |
| 260 | mant_bits_left -= mant_bits; |
| 261 | } |
| 262 | |
| 263 | /* Negate it if negative. */ |
| 264 | if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1)) |
| 265 | dto = -dto; |
| 266 | *to = dto; |
| 267 | } |
| 268 | \f |
| 269 | static void put_field PARAMS ((unsigned char *, enum floatformat_byteorders, |
| 270 | unsigned int, |
| 271 | unsigned int, |
| 272 | unsigned int, |
| 273 | unsigned long)); |
| 274 | |
| 275 | /* Set a field which starts at START and is LEN bytes long. DATA and |
| 276 | TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER. */ |
| 277 | static void |
| 278 | put_field (data, order, total_len, start, len, stuff_to_put) |
| 279 | unsigned char *data; |
| 280 | enum floatformat_byteorders order; |
| 281 | unsigned int total_len; |
| 282 | unsigned int start; |
| 283 | unsigned int len; |
| 284 | unsigned long stuff_to_put; |
| 285 | { |
| 286 | unsigned int cur_byte; |
| 287 | int cur_bitshift; |
| 288 | |
| 289 | /* Start at the least significant part of the field. */ |
| 290 | cur_byte = (start + len) / FLOATFORMAT_CHAR_BIT; |
| 291 | if (order == floatformat_little) |
| 292 | cur_byte = (total_len / FLOATFORMAT_CHAR_BIT) - cur_byte - 1; |
| 293 | cur_bitshift = |
| 294 | ((start + len) % FLOATFORMAT_CHAR_BIT) - FLOATFORMAT_CHAR_BIT; |
| 295 | *(data + cur_byte) &= |
| 296 | ~(((1 << ((start + len) % FLOATFORMAT_CHAR_BIT)) - 1) << (-cur_bitshift)); |
| 297 | *(data + cur_byte) |= |
| 298 | (stuff_to_put & ((1 << FLOATFORMAT_CHAR_BIT) - 1)) << (-cur_bitshift); |
| 299 | cur_bitshift += FLOATFORMAT_CHAR_BIT; |
| 300 | if (order == floatformat_little) |
| 301 | ++cur_byte; |
| 302 | else |
| 303 | --cur_byte; |
| 304 | |
| 305 | /* Move towards the most significant part of the field. */ |
| 306 | while ((unsigned int) cur_bitshift < len) |
| 307 | { |
| 308 | if (len - cur_bitshift < FLOATFORMAT_CHAR_BIT) |
| 309 | { |
| 310 | /* This is the last byte. */ |
| 311 | *(data + cur_byte) &= |
| 312 | ~((1 << (len - cur_bitshift)) - 1); |
| 313 | *(data + cur_byte) |= (stuff_to_put >> cur_bitshift); |
| 314 | } |
| 315 | else |
| 316 | *(data + cur_byte) = ((stuff_to_put >> cur_bitshift) |
| 317 | & ((1 << FLOATFORMAT_CHAR_BIT) - 1)); |
| 318 | cur_bitshift += FLOATFORMAT_CHAR_BIT; |
| 319 | if (order == floatformat_little) |
| 320 | ++cur_byte; |
| 321 | else |
| 322 | --cur_byte; |
| 323 | } |
| 324 | } |
| 325 | |
| 326 | /* The converse: convert the double *FROM to an extended float |
| 327 | and store where TO points. Neither FROM nor TO have any alignment |
| 328 | restrictions. */ |
| 329 | |
| 330 | void |
| 331 | floatformat_from_double (fmt, from, to) |
| 332 | const struct floatformat *fmt; |
| 333 | double *from; |
| 334 | char *to; |
| 335 | { |
| 336 | double dfrom; |
| 337 | int exponent; |
| 338 | double mant; |
| 339 | unsigned int mant_bits, mant_off; |
| 340 | int mant_bits_left; |
| 341 | unsigned char *uto = (unsigned char *)to; |
| 342 | |
| 343 | memcpy (&dfrom, from, sizeof (dfrom)); |
| 344 | memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT); |
| 345 | if (dfrom == 0) |
| 346 | return; /* Result is zero */ |
| 347 | if (dfrom != dfrom) |
| 348 | { |
| 349 | /* From is NaN */ |
| 350 | put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, |
| 351 | fmt->exp_len, fmt->exp_nan); |
| 352 | /* Be sure it's not infinity, but NaN value is irrel */ |
| 353 | put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start, |
| 354 | 32, 1); |
| 355 | return; |
| 356 | } |
| 357 | |
| 358 | /* If negative, set the sign bit. */ |
| 359 | if (dfrom < 0) |
| 360 | { |
| 361 | put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1); |
| 362 | dfrom = -dfrom; |
| 363 | } |
| 364 | |
| 365 | /* How to tell an infinity from an ordinary number? FIXME-someday */ |
| 366 | |
| 367 | mant = frexp (dfrom, &exponent); |
| 368 | put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start, fmt->exp_len, |
| 369 | exponent + fmt->exp_bias - 1); |
| 370 | |
| 371 | mant_bits_left = fmt->man_len; |
| 372 | mant_off = fmt->man_start; |
| 373 | while (mant_bits_left > 0) |
| 374 | { |
| 375 | unsigned long mant_long; |
| 376 | mant_bits = mant_bits_left < 32 ? mant_bits_left : 32; |
| 377 | |
| 378 | mant *= 4294967296.0; |
| 379 | mant_long = (unsigned long)mant; |
| 380 | mant -= mant_long; |
| 381 | |
| 382 | /* If the integer bit is implicit, then we need to discard it. |
| 383 | If we are discarding a zero, we should be (but are not) creating |
| 384 | a denormalized number which means adjusting the exponent |
| 385 | (I think). */ |
| 386 | if ((unsigned int) mant_bits_left == fmt->man_len |
| 387 | && fmt->intbit == floatformat_intbit_no) |
| 388 | { |
| 389 | mant_long &= 0x7fffffff; |
| 390 | mant_bits -= 1; |
| 391 | } |
| 392 | else if (mant_bits < 32) |
| 393 | { |
| 394 | /* The bits we want are in the most significant MANT_BITS bits of |
| 395 | mant_long. Move them to the least significant. */ |
| 396 | mant_long >>= 32 - mant_bits; |
| 397 | } |
| 398 | |
| 399 | put_field (uto, fmt->byteorder, fmt->totalsize, |
| 400 | mant_off, mant_bits, mant_long); |
| 401 | mant_off += mant_bits; |
| 402 | mant_bits_left -= mant_bits; |
| 403 | } |
| 404 | } |
| 405 | |
| 406 | |
| 407 | #ifdef IEEE_DEBUG |
| 408 | |
| 409 | /* This is to be run on a host which uses IEEE floating point. */ |
| 410 | |
| 411 | void |
| 412 | ieee_test (n) |
| 413 | double n; |
| 414 | { |
| 415 | double result; |
| 416 | char exten[16]; |
| 417 | |
| 418 | floatformat_to_double (&floatformat_ieee_double_big, &n, &result); |
| 419 | if (n != result) |
| 420 | printf ("Differ(to): %.20g -> %.20g\n", n, result); |
| 421 | floatformat_from_double (&floatformat_ieee_double_big, &n, &result); |
| 422 | if (n != result) |
| 423 | printf ("Differ(from): %.20g -> %.20g\n", n, result); |
| 424 | |
| 425 | floatformat_from_double (&floatformat_m68881_ext, &n, exten); |
| 426 | floatformat_to_double (&floatformat_m68881_ext, exten, &result); |
| 427 | if (n != result) |
| 428 | printf ("Differ(to+from): %.20g -> %.20g\n", n, result); |
| 429 | |
| 430 | #if IEEE_DEBUG > 1 |
| 431 | /* This is to be run on a host which uses 68881 format. */ |
| 432 | { |
| 433 | long double ex = *(long double *)exten; |
| 434 | if (ex != n) |
| 435 | printf ("Differ(from vs. extended): %.20g\n", n); |
| 436 | } |
| 437 | #endif |
| 438 | } |
| 439 | |
| 440 | int |
| 441 | main () |
| 442 | { |
| 443 | ieee_test (0.5); |
| 444 | ieee_test (256.0); |
| 445 | ieee_test (0.12345); |
| 446 | ieee_test (234235.78907234); |
| 447 | ieee_test (-512.0); |
| 448 | ieee_test (-0.004321); |
| 449 | return 0; |
| 450 | } |
| 451 | #endif |