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| 1 | +#include<limits.h> |
| 2 | + |
| 3 | +/* We rely on the little endianness and EABI calling convention for this to |
| 4 | + work */ |
| 5 | + |
| 6 | +typedef struct double_unsigned_struct { |
| 7 | + unsigned low; |
| 8 | + unsigned high; |
| 9 | +} double_unsigned_struct; |
| 10 | + |
| 11 | +typedef struct unsigned_int_struct { |
| 12 | + unsigned low; |
| 13 | + int high; |
| 14 | +} unsigned_int_struct; |
| 15 | + |
| 16 | +#define REGS_RETURN(name, type) \ |
| 17 | + void name ## _return(type ret) {} |
| 18 | + |
| 19 | + |
| 20 | +/* Float helper functions */ |
| 21 | + |
| 22 | +#define FLOAT_EXP_BITS 8 |
| 23 | +#define FLOAT_FRAC_BITS 23 |
| 24 | + |
| 25 | +#define DOUBLE_EXP_BITS 11 |
| 26 | +#define DOUBLE_FRAC_BITS 52 |
| 27 | + |
| 28 | +#define ONE_EXP(type) ((1 << (type ## _EXP_BITS - 1)) - 1) |
| 29 | + |
| 30 | +REGS_RETURN(unsigned_int_struct, unsigned_int_struct) |
| 31 | +REGS_RETURN(double_unsigned_struct, double_unsigned_struct) |
| 32 | + |
| 33 | +/* float -> integer: (sign) 1.fraction x 2^(exponent - exp_for_one) */ |
| 34 | + |
| 35 | + |
| 36 | +/* float to [unsigned] long long conversion */ |
| 37 | +#define DEFINE__AEABIT_F2XLZ(name, with_sign) \ |
| 38 | +void __aeabi_ ## name(unsigned val) \ |
| 39 | +{ \ |
| 40 | + int exp, high_shift, sign; \ |
| 41 | + double_unsigned_struct ret; \ |
| 42 | + \ |
| 43 | + /* compute sign */ \ |
| 44 | + sign = val >> 31; \ |
| 45 | + \ |
| 46 | + /* compute real exponent */ \ |
| 47 | + exp = val >> FLOAT_FRAC_BITS; \ |
| 48 | + exp &= (1 << FLOAT_EXP_BITS) - 1; \ |
| 49 | + exp -= ONE_EXP(FLOAT); \ |
| 50 | + \ |
| 51 | + /* undefined behavior if truncated value cannot be represented */ \ |
| 52 | + if (with_sign) { \ |
| 53 | + if (exp > 62) /* |val| too big, double cannot represent LLONG_MAX */ \ |
| 54 | + return; \ |
| 55 | + } else { \ |
| 56 | + if ((sign && exp >= 0) || exp > 63) /* if val < 0 || val too big */ \ |
| 57 | + return; \ |
| 58 | + } \ |
| 59 | + \ |
| 60 | + val &= (1 << FLOAT_FRAC_BITS) - 1; \ |
| 61 | + if (exp >= 32) { \ |
| 62 | + ret.high = 1 << (exp - 32); \ |
| 63 | + if (exp - 32 >= FLOAT_FRAC_BITS) { \ |
| 64 | + ret.high |= val << (exp - 32 - FLOAT_FRAC_BITS); \ |
| 65 | + ret.low = 0; \ |
| 66 | + } else { \ |
| 67 | + high_shift = FLOAT_FRAC_BITS - (exp - 32); \ |
| 68 | + ret.high |= val >> high_shift; \ |
| 69 | + ret.low = val << (32 - high_shift); \ |
| 70 | + } \ |
| 71 | + } else { \ |
| 72 | + ret.high = 0; \ |
| 73 | + ret.low = 1 << exp; \ |
| 74 | + if (exp > FLOAT_FRAC_BITS) \ |
| 75 | + ret.low |= val << (exp - FLOAT_FRAC_BITS); \ |
| 76 | + else \ |
| 77 | + ret.low = val >> (FLOAT_FRAC_BITS - exp); \ |
| 78 | + } \ |
| 79 | + \ |
| 80 | + /* encode negative integer using 2's complement */ \ |
| 81 | + if (with_sign && sign) { \ |
| 82 | + ret.low = ~ret.low; \ |
| 83 | + ret.high = ~ret.high; \ |
| 84 | + if (ret.low == UINT_MAX) { \ |
| 85 | + ret.low = 0; \ |
| 86 | + ret.high++; \ |
| 87 | + } else \ |
| 88 | + ret.low++; \ |
| 89 | + } \ |
| 90 | + \ |
| 91 | + double_unsigned_struct_return(ret); \ |
| 92 | +} |
| 93 | + |
| 94 | +/* float to unsigned long long conversion */ |
| 95 | +DEFINE__AEABIT_F2XLZ(f2ulz, 0) |
| 96 | + |
| 97 | +/* float to long long conversion */ |
| 98 | +DEFINE__AEABIT_F2XLZ(f2lz, 1) |
| 99 | + |
| 100 | +/* double to [unsigned] long long conversion */ |
| 101 | +#define DEFINE__AEABIT_D2XLZ(name, with_sign) \ |
| 102 | +void __aeabi_ ## name(double_unsigned_struct val) \ |
| 103 | +{ \ |
| 104 | + int exp, high_shift, sign; \ |
| 105 | + double_unsigned_struct ret; \ |
| 106 | + \ |
| 107 | + /* compute sign */ \ |
| 108 | + sign = val.high >> 31; \ |
| 109 | + \ |
| 110 | + /* compute real exponent */ \ |
| 111 | + exp = (val.high >> (DOUBLE_FRAC_BITS - 32)); \ |
| 112 | + exp &= (1 << DOUBLE_EXP_BITS) - 1; \ |
| 113 | + exp -= ONE_EXP(DOUBLE); \ |
| 114 | + \ |
| 115 | + /* undefined behavior if truncated value cannot be represented */ \ |
| 116 | + if (with_sign) { \ |
| 117 | + if (exp > 62) /* |val| too big, double cannot represent LLONG_MAX */ \ |
| 118 | + return; \ |
| 119 | + } else { \ |
| 120 | + if ((sign && exp >= 0) || exp > 63) /* if val < 0 || val too big */ \ |
| 121 | + return; \ |
| 122 | + } \ |
| 123 | + \ |
| 124 | + val.high &= (1 << (DOUBLE_FRAC_BITS - 32)) - 1; \ |
| 125 | + if (exp >= 32) { \ |
| 126 | + ret.high = 1 << (exp - 32); \ |
| 127 | + if (exp >= DOUBLE_FRAC_BITS) { \ |
| 128 | + high_shift = exp - DOUBLE_FRAC_BITS; \ |
| 129 | + ret.high |= val.high << high_shift; \ |
| 130 | + ret.high |= val.low >> (32 - high_shift); \ |
| 131 | + ret.low = val.low << high_shift; \ |
| 132 | + } else { \ |
| 133 | + high_shift = DOUBLE_FRAC_BITS - exp; \ |
| 134 | + ret.high |= val.high >> high_shift; \ |
| 135 | + ret.low = val.high << (32 - high_shift); \ |
| 136 | + ret.low |= val.low >> high_shift; \ |
| 137 | + } \ |
| 138 | + } else { \ |
| 139 | + ret.high = 0; \ |
| 140 | + ret.low = 1 << exp; \ |
| 141 | + if (exp > DOUBLE_FRAC_BITS - 32) { \ |
| 142 | + high_shift = exp - DOUBLE_FRAC_BITS - 32; \ |
| 143 | + ret.low |= val.high << high_shift; \ |
| 144 | + ret.low |= val.low >> (32 - high_shift); \ |
| 145 | + } else \ |
| 146 | + ret.low = val.high >> (DOUBLE_FRAC_BITS - 32 - exp); \ |
| 147 | + } \ |
| 148 | + \ |
| 149 | + /* encode negative integer using 2's complement */ \ |
| 150 | + if (with_sign && sign) { \ |
| 151 | + ret.low = ~ret.low; \ |
| 152 | + ret.high = ~ret.high; \ |
| 153 | + if (ret.low == UINT_MAX) { \ |
| 154 | + ret.low = 0; \ |
| 155 | + ret.high++; \ |
| 156 | + } else \ |
| 157 | + ret.low++; \ |
| 158 | + } \ |
| 159 | + \ |
| 160 | + double_unsigned_struct_return(ret); \ |
| 161 | +} |
| 162 | + |
| 163 | +/* double to unsigned long long conversion */ |
| 164 | +DEFINE__AEABIT_D2XLZ(d2ulz, 0) |
| 165 | + |
| 166 | +/* double to long long conversion */ |
| 167 | +DEFINE__AEABIT_D2XLZ(d2lz, 1) |
| 168 | + |
| 169 | +/* long long to float conversion */ |
| 170 | +#define DEFINE__AEABI_XL2F(name, with_sign) \ |
| 171 | +unsigned __aeabi_ ## name(unsigned long long v) \ |
| 172 | +{ \ |
| 173 | + int s /* shift */, sign = 0; \ |
| 174 | + unsigned p = 0 /* power */, ret; \ |
| 175 | + double_unsigned_struct val; \ |
| 176 | + \ |
| 177 | + /* fraction in negative float is encoded in 1's complement */ \ |
| 178 | + if (with_sign && (v & (1 << 63))) { \ |
| 179 | + sign = 1; \ |
| 180 | + v = ~v + 1; \ |
| 181 | + } \ |
| 182 | + val.low = v; \ |
| 183 | + val.high = v >> 32; \ |
| 184 | + /* fill fraction bits */ \ |
| 185 | + for (s = 31, p = 1 << 31; p && !(val.high & p); s--, p >>= 1); \ |
| 186 | + if (p) { \ |
| 187 | + ret = val.high & (p - 1); \ |
| 188 | + if (s < FLOAT_FRAC_BITS) { \ |
| 189 | + ret <<= FLOAT_FRAC_BITS - s; \ |
| 190 | + ret |= val.low >> (32 - (FLOAT_FRAC_BITS - s)); \ |
| 191 | + } else \ |
| 192 | + ret >>= s - FLOAT_FRAC_BITS; \ |
| 193 | + s += 32; \ |
| 194 | + } else { \ |
| 195 | + for (s = 31, p = 1 << 31; p && !(val.low & p); s--, p >>= 1); \ |
| 196 | + if (p) { \ |
| 197 | + ret = val.low & (p - 1); \ |
| 198 | + if (s <= FLOAT_FRAC_BITS) \ |
| 199 | + ret <<= FLOAT_FRAC_BITS - s; \ |
| 200 | + else \ |
| 201 | + ret >>= s - FLOAT_FRAC_BITS; \ |
| 202 | + } else \ |
| 203 | + return 0; \ |
| 204 | + } \ |
| 205 | + \ |
| 206 | + /* fill exponent bits */ \ |
| 207 | + ret |= (s + ONE_EXP(FLOAT)) << FLOAT_FRAC_BITS; \ |
| 208 | + \ |
| 209 | + /* fill sign bit */ \ |
| 210 | + ret |= sign << 31; \ |
| 211 | + \ |
| 212 | + return ret; \ |
| 213 | +} |
| 214 | + |
| 215 | +/* unsigned long long to float conversion */ |
| 216 | +DEFINE__AEABI_XL2F(ul2f, 0) |
| 217 | + |
| 218 | +/* long long to float conversion */ |
| 219 | +DEFINE__AEABI_XL2F(l2f, 0) |
| 220 | + |
| 221 | +/* long long to double conversion */ |
| 222 | +#define __AEABI_XL2D(name, with_sign) \ |
| 223 | +void __aeabi_ ## name(unsigned long long v) \ |
| 224 | +{ \ |
| 225 | + int s, high_shift, sign = 0; \ |
| 226 | + unsigned tmp, p = 0; \ |
| 227 | + double_unsigned_struct val, ret; \ |
| 228 | + \ |
| 229 | + /* fraction in negative float is encoded in 1's complement */ \ |
| 230 | + if (with_sign && (v & (1ULL << 63))) { \ |
| 231 | + sign = 1; \ |
| 232 | + v = ~v + 1; \ |
| 233 | + } \ |
| 234 | + val.low = v; \ |
| 235 | + val.high = v >> 32; \ |
| 236 | + \ |
| 237 | + /* fill fraction bits */ \ |
| 238 | + for (s = 31, p = 1 << 31; p && !(val.high & p); s--, p >>= 1); \ |
| 239 | + if (p) { \ |
| 240 | + tmp = val.high & (p - 1); \ |
| 241 | + if (s < DOUBLE_FRAC_BITS - 32) { \ |
| 242 | + high_shift = DOUBLE_FRAC_BITS - 32 - s; \ |
| 243 | + ret.high = tmp << high_shift; \ |
| 244 | + ret.high |= val.low >> (32 - high_shift); \ |
| 245 | + ret.low = val.low << high_shift; \ |
| 246 | + } else { \ |
| 247 | + high_shift = s - (DOUBLE_FRAC_BITS - 32); \ |
| 248 | + ret.high = tmp >> high_shift; \ |
| 249 | + ret.low = tmp << (32 - high_shift); \ |
| 250 | + ret.low |= val.low >> high_shift; \ |
| 251 | + } \ |
| 252 | + s += 32; \ |
| 253 | + } else { \ |
| 254 | + for (s = 31, p = 1 << 31; p && !(val.low & p); s--, p >>= 1); \ |
| 255 | + if (p) { \ |
| 256 | + tmp = val.low & (p - 1); \ |
| 257 | + if (s <= DOUBLE_FRAC_BITS - 32) { \ |
| 258 | + high_shift = DOUBLE_FRAC_BITS - 32 - s; \ |
| 259 | + ret.high = tmp << high_shift; \ |
| 260 | + ret.low = 0; \ |
| 261 | + } else { \ |
| 262 | + high_shift = s - (DOUBLE_FRAC_BITS - 32); \ |
| 263 | + ret.high = tmp >> high_shift; \ |
| 264 | + ret.low = tmp << (32 - high_shift); \ |
| 265 | + } \ |
| 266 | + } else { \ |
| 267 | + ret.high = ret.low = 0; \ |
| 268 | + double_unsigned_struct_return(ret); \ |
| 269 | + } \ |
| 270 | + } \ |
| 271 | + \ |
| 272 | + /* fill exponent bits */ \ |
| 273 | + ret.high |= (s + ONE_EXP(DOUBLE)) << (DOUBLE_FRAC_BITS - 32); \ |
| 274 | + \ |
| 275 | + /* fill sign bit */ \ |
| 276 | + ret.high |= sign << 31; \ |
| 277 | + \ |
| 278 | + double_unsigned_struct_return(ret); \ |
| 279 | +} |
| 280 | + |
| 281 | +/* unsigned long long to double conversion */ |
| 282 | +__AEABI_XL2D(ul2d, 0) |
| 283 | + |
| 284 | +/* long long to double conversion */ |
| 285 | +__AEABI_XL2D(l2d, 1) |
| 286 | + |
| 287 | + |
| 288 | +/* Long long helper functions */ |
| 289 | + |
| 290 | +/* TODO: add error in case of den == 0 (see §4.3.1 and §4.3.2) */ |
| 291 | + |
| 292 | +#define define_aeabi_xdivmod_signed_type(basetype, type) \ |
| 293 | +typedef struct type { \ |
| 294 | + basetype quot; \ |
| 295 | + unsigned basetype rem; \ |
| 296 | +} type |
| 297 | + |
| 298 | +#define define_aeabi_xdivmod_unsigned_type(basetype, type) \ |
| 299 | +typedef struct type { \ |
| 300 | + basetype quot; \ |
| 301 | + basetype rem; \ |
| 302 | +} type |
| 303 | + |
| 304 | +#define AEABI_UXDIVMOD(name,type, rettype, typemacro) \ |
| 305 | +static inline rettype aeabi_ ## name (type num, type den) \ |
| 306 | +{ \ |
| 307 | + rettype ret; \ |
| 308 | + type quot = 0; \ |
| 309 | + \ |
| 310 | + /* Increase quotient while it is less than numerator */ \ |
| 311 | + while (num >= den) { \ |
| 312 | + type q = 1; \ |
| 313 | + \ |
| 314 | + /* Find closest power of two */ \ |
| 315 | + while ((q << 1) * den <= num && q * den <= typemacro ## _MAX / 2) \ |
| 316 | + q <<= 1; \ |
| 317 | + \ |
| 318 | + /* Compute difference between current quotient and numerator */ \ |
| 319 | + num -= q * den; \ |
| 320 | + quot += q; \ |
| 321 | + } \ |
| 322 | + ret.quot = quot; \ |
| 323 | + ret.rem = num; \ |
| 324 | + return ret; \ |
| 325 | +} |
| 326 | + |
| 327 | +#define __AEABI_XDIVMOD(name, type, uiname, rettype, urettype, typemacro) \ |
| 328 | +void __aeabi_ ## name(type numerator, type denominator) \ |
| 329 | +{ \ |
| 330 | + unsigned type num, den; \ |
| 331 | + urettype uxdiv_ret; \ |
| 332 | + rettype ret; \ |
| 333 | + \ |
| 334 | + num = numerator & typemacro ## _MAX; \ |
| 335 | + den = denominator & typemacro ## _MAX; \ |
| 336 | + uxdiv_ret = aeabi_ ## uiname(num, den); \ |
| 337 | + /* signs differ */ \ |
| 338 | + if ((numerator & typemacro ## _MIN) != (denominator & typemacro ## _MIN)) \ |
| 339 | + ret.quot = uxdiv_ret.quot * -1; \ |
| 340 | + else \ |
| 341 | + ret.quot = uxdiv_ret.quot; \ |
| 342 | + if (numerator & typemacro ## _MIN) \ |
| 343 | + ret.rem = uxdiv_ret.rem * -1; \ |
| 344 | + else \ |
| 345 | + ret.rem = uxdiv_ret.rem; \ |
| 346 | + \ |
| 347 | + rettype ## _return(ret); \ |
| 348 | +} |
| 349 | + |
| 350 | +define_aeabi_xdivmod_signed_type(long long, lldiv_t); |
| 351 | +define_aeabi_xdivmod_unsigned_type(unsigned long long, ulldiv_t); |
| 352 | +define_aeabi_xdivmod_signed_type(int, idiv_t); |
| 353 | +define_aeabi_xdivmod_unsigned_type(unsigned, uidiv_t); |
| 354 | + |
| 355 | +REGS_RETURN(lldiv_t, lldiv_t) |
| 356 | +REGS_RETURN(ulldiv_t, ulldiv_t) |
| 357 | +REGS_RETURN(idiv_t, idiv_t) |
| 358 | +REGS_RETURN(uidiv_t, uidiv_t) |
| 359 | + |
| 360 | +AEABI_UXDIVMOD(uldivmod, unsigned long long, ulldiv_t, ULONG) |
| 361 | + |
| 362 | +__AEABI_XDIVMOD(ldivmod, long long, uldivmod, lldiv_t, ulldiv_t, LLONG) |
| 363 | + |
| 364 | +void __aeabi_uldivmod(unsigned long long num, unsigned long long den) |
| 365 | +{ |
| 366 | + ulldiv_t_return(aeabi_uldivmod(num, den)); |
| 367 | +} |
| 368 | + |
| 369 | +void __aeabi_llsl(double_unsigned_struct val, int shift) |
| 370 | +{ |
| 371 | + double_unsigned_struct ret; |
| 372 | + |
| 373 | + if (shift >= 32) { |
| 374 | + val.high = val.low; |
| 375 | + val.low = 0; |
| 376 | + shift -= 32; |
| 377 | + } |
| 378 | + if (shift > 0) { |
| 379 | + ret.low = val.low << shift; |
| 380 | + ret.high = (val.high << shift) | (val.low >> (32 - shift)); |
| 381 | + double_unsigned_struct_return(ret); |
| 382 | + return; |
| 383 | + } |
| 384 | + double_unsigned_struct_return(val); |
| 385 | +} |
| 386 | + |
| 387 | +#define aeabi_lsr(val, shift, fill, type) \ |
| 388 | + type ## _struct ret; \ |
| 389 | + \ |
| 390 | + if (shift >= 32) { \ |
| 391 | + val.low = val.high; \ |
| 392 | + val.high = fill; \ |
| 393 | + shift -= 32; \ |
| 394 | + } \ |
| 395 | + if (shift > 0) { \ |
| 396 | + ret.high = val.high >> shift; \ |
| 397 | + ret.low = (val.high << (32 - shift)) | (val.low >> shift); \ |
| 398 | + type ## _struct_return(ret); \ |
| 399 | + return; \ |
| 400 | + } \ |
| 401 | + type ## _struct_return(val); |
| 402 | + |
| 403 | +void __aeabi_llsr(double_unsigned_struct val, int shift) |
| 404 | +{ |
| 405 | + aeabi_lsr(val, shift, 0, double_unsigned); |
| 406 | +} |
| 407 | + |
| 408 | +void __aeabi_lasr(unsigned_int_struct val, int shift) |
| 409 | +{ |
| 410 | + aeabi_lsr(val, shift, val.high >> 31, unsigned_int); |
| 411 | +} |
| 412 | + |
| 413 | + |
| 414 | +/* Integer division functions */ |
| 415 | + |
| 416 | +AEABI_UXDIVMOD(uidivmod, unsigned, uidiv_t, UINT) |
| 417 | + |
| 418 | +int __aeabi_idiv(int numerator, int denominator) |
| 419 | +{ |
| 420 | + unsigned num, den; |
| 421 | + uidiv_t ret; |
| 422 | + |
| 423 | + num = numerator & INT_MAX; |
| 424 | + den = denominator & INT_MAX; |
| 425 | + ret = aeabi_uidivmod(num, den); |
| 426 | + if ((numerator & INT_MIN) != (denominator & INT_MIN)) /* signs differ */ |
| 427 | + ret.quot *= -1; |
| 428 | + return ret.quot; |
| 429 | +} |
| 430 | + |
| 431 | +unsigned __aeabi_uidiv(unsigned num, unsigned den) |
| 432 | +{ |
| 433 | + return aeabi_uidivmod(num, den).quot; |
| 434 | +} |
| 435 | + |
| 436 | +__AEABI_XDIVMOD(idivmod, int, uidivmod, idiv_t, uidiv_t, INT) |
| 437 | + |
| 438 | +void __aeabi_uidivmod(unsigned num, unsigned den) |
| 439 | +{ |
| 440 | + uidiv_t_return(aeabi_uidivmod(num, den)); |
| 441 | +} |