| 1 | /* |
| 2 | ** $Id: lmathlib.c $ |
| 3 | ** Standard mathematical library |
| 4 | ** See Copyright Notice in lua.h |
| 5 | */ |
| 6 | |
| 7 | #define lmathlib_c |
| 8 | #define LUA_LIB |
| 9 | |
| 10 | #include "lprefix.h" |
| 11 | |
| 12 | |
| 13 | #include <float.h> |
| 14 | #include <limits.h> |
| 15 | #include <math.h> |
| 16 | #include <stdlib.h> |
| 17 | #include <time.h> |
| 18 | |
| 19 | #include "lua.h" |
| 20 | |
| 21 | #include "lauxlib.h" |
| 22 | #include "lualib.h" |
| 23 | |
| 24 | |
| 25 | #undef PI |
| 26 | #define PI (l_mathop(3.141592653589793238462643383279502884)) |
| 27 | |
| 28 | |
| 29 | static int math_abs (lua_State *L) { |
| 30 | if (lua_isinteger(L, 1)) { |
| 31 | lua_Integer n = lua_tointeger(L, 1); |
| 32 | if (n < 0) n = (lua_Integer)(0u - (lua_Unsigned)n); |
| 33 | lua_pushinteger(L, n); |
| 34 | } |
| 35 | else |
| 36 | lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1))); |
| 37 | return 1; |
| 38 | } |
| 39 | |
| 40 | static int math_sin (lua_State *L) { |
| 41 | lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1))); |
| 42 | return 1; |
| 43 | } |
| 44 | |
| 45 | static int math_cos (lua_State *L) { |
| 46 | lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1))); |
| 47 | return 1; |
| 48 | } |
| 49 | |
| 50 | static int math_tan (lua_State *L) { |
| 51 | lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1))); |
| 52 | return 1; |
| 53 | } |
| 54 | |
| 55 | static int math_asin (lua_State *L) { |
| 56 | lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1))); |
| 57 | return 1; |
| 58 | } |
| 59 | |
| 60 | static int math_acos (lua_State *L) { |
| 61 | lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1))); |
| 62 | return 1; |
| 63 | } |
| 64 | |
| 65 | static int math_atan (lua_State *L) { |
| 66 | lua_Number y = luaL_checknumber(L, 1); |
| 67 | lua_Number x = luaL_optnumber(L, 2, 1); |
| 68 | lua_pushnumber(L, l_mathop(atan2)(y, x)); |
| 69 | return 1; |
| 70 | } |
| 71 | |
| 72 | |
| 73 | static int math_toint (lua_State *L) { |
| 74 | int valid; |
| 75 | lua_Integer n = lua_tointegerx(L, 1, &valid); |
| 76 | if (l_likely(valid)) |
| 77 | lua_pushinteger(L, n); |
| 78 | else { |
| 79 | luaL_checkany(L, 1); |
| 80 | luaL_pushfail(L); /* value is not convertible to integer */ |
| 81 | } |
| 82 | return 1; |
| 83 | } |
| 84 | |
| 85 | |
| 86 | static void pushnumint (lua_State *L, lua_Number d) { |
| 87 | lua_Integer n; |
| 88 | if (lua_numbertointeger(d, &n)) /* does 'd' fit in an integer? */ |
| 89 | lua_pushinteger(L, n); /* result is integer */ |
| 90 | else |
| 91 | lua_pushnumber(L, d); /* result is float */ |
| 92 | } |
| 93 | |
| 94 | |
| 95 | static int math_floor (lua_State *L) { |
| 96 | if (lua_isinteger(L, 1)) |
| 97 | lua_settop(L, 1); /* integer is its own floor */ |
| 98 | else { |
| 99 | lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1)); |
| 100 | pushnumint(L, d); |
| 101 | } |
| 102 | return 1; |
| 103 | } |
| 104 | |
| 105 | |
| 106 | static int math_ceil (lua_State *L) { |
| 107 | if (lua_isinteger(L, 1)) |
| 108 | lua_settop(L, 1); /* integer is its own ceil */ |
| 109 | else { |
| 110 | lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1)); |
| 111 | pushnumint(L, d); |
| 112 | } |
| 113 | return 1; |
| 114 | } |
| 115 | |
| 116 | |
| 117 | static int math_fmod (lua_State *L) { |
| 118 | if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) { |
| 119 | lua_Integer d = lua_tointeger(L, 2); |
| 120 | if ((lua_Unsigned)d + 1u <= 1u) { /* special cases: -1 or 0 */ |
| 121 | luaL_argcheck(L, d != 0, 2, "zero" ); |
| 122 | lua_pushinteger(L, 0); /* avoid overflow with 0x80000... / -1 */ |
| 123 | } |
| 124 | else |
| 125 | lua_pushinteger(L, lua_tointeger(L, 1) % d); |
| 126 | } |
| 127 | else |
| 128 | lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1), |
| 129 | luaL_checknumber(L, 2))); |
| 130 | return 1; |
| 131 | } |
| 132 | |
| 133 | |
| 134 | /* |
| 135 | ** next function does not use 'modf', avoiding problems with 'double*' |
| 136 | ** (which is not compatible with 'float*') when lua_Number is not |
| 137 | ** 'double'. |
| 138 | */ |
| 139 | static int math_modf (lua_State *L) { |
| 140 | if (lua_isinteger(L ,1)) { |
| 141 | lua_settop(L, 1); /* number is its own integer part */ |
| 142 | lua_pushnumber(L, 0); /* no fractional part */ |
| 143 | } |
| 144 | else { |
| 145 | lua_Number n = luaL_checknumber(L, 1); |
| 146 | /* integer part (rounds toward zero) */ |
| 147 | lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n); |
| 148 | pushnumint(L, ip); |
| 149 | /* fractional part (test needed for inf/-inf) */ |
| 150 | lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip)); |
| 151 | } |
| 152 | return 2; |
| 153 | } |
| 154 | |
| 155 | |
| 156 | static int math_sqrt (lua_State *L) { |
| 157 | lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1))); |
| 158 | return 1; |
| 159 | } |
| 160 | |
| 161 | |
| 162 | static int math_ult (lua_State *L) { |
| 163 | lua_Integer a = luaL_checkinteger(L, 1); |
| 164 | lua_Integer b = luaL_checkinteger(L, 2); |
| 165 | lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b); |
| 166 | return 1; |
| 167 | } |
| 168 | |
| 169 | static int math_log (lua_State *L) { |
| 170 | lua_Number x = luaL_checknumber(L, 1); |
| 171 | lua_Number res; |
| 172 | if (lua_isnoneornil(L, 2)) |
| 173 | res = l_mathop(log)(x); |
| 174 | else { |
| 175 | lua_Number base = luaL_checknumber(L, 2); |
| 176 | #if !defined(LUA_USE_C89) |
| 177 | if (base == l_mathop(2.0)) |
| 178 | res = l_mathop(log2)(x); |
| 179 | else |
| 180 | #endif |
| 181 | if (base == l_mathop(10.0)) |
| 182 | res = l_mathop(log10)(x); |
| 183 | else |
| 184 | res = l_mathop(log)(x)/l_mathop(log)(base); |
| 185 | } |
| 186 | lua_pushnumber(L, res); |
| 187 | return 1; |
| 188 | } |
| 189 | |
| 190 | static int math_exp (lua_State *L) { |
| 191 | lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1))); |
| 192 | return 1; |
| 193 | } |
| 194 | |
| 195 | static int math_deg (lua_State *L) { |
| 196 | lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI)); |
| 197 | return 1; |
| 198 | } |
| 199 | |
| 200 | static int math_rad (lua_State *L) { |
| 201 | lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0))); |
| 202 | return 1; |
| 203 | } |
| 204 | |
| 205 | |
| 206 | static int math_min (lua_State *L) { |
| 207 | int n = lua_gettop(L); /* number of arguments */ |
| 208 | int imin = 1; /* index of current minimum value */ |
| 209 | int i; |
| 210 | luaL_argcheck(L, n >= 1, 1, "value expected" ); |
| 211 | for (i = 2; i <= n; i++) { |
| 212 | if (lua_compare(L, i, imin, LUA_OPLT)) |
| 213 | imin = i; |
| 214 | } |
| 215 | lua_pushvalue(L, imin); |
| 216 | return 1; |
| 217 | } |
| 218 | |
| 219 | |
| 220 | static int math_max (lua_State *L) { |
| 221 | int n = lua_gettop(L); /* number of arguments */ |
| 222 | int imax = 1; /* index of current maximum value */ |
| 223 | int i; |
| 224 | luaL_argcheck(L, n >= 1, 1, "value expected" ); |
| 225 | for (i = 2; i <= n; i++) { |
| 226 | if (lua_compare(L, imax, i, LUA_OPLT)) |
| 227 | imax = i; |
| 228 | } |
| 229 | lua_pushvalue(L, imax); |
| 230 | return 1; |
| 231 | } |
| 232 | |
| 233 | |
| 234 | static int math_type (lua_State *L) { |
| 235 | if (lua_type(L, 1) == LUA_TNUMBER) |
| 236 | lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float" ); |
| 237 | else { |
| 238 | luaL_checkany(L, 1); |
| 239 | luaL_pushfail(L); |
| 240 | } |
| 241 | return 1; |
| 242 | } |
| 243 | |
| 244 | |
| 245 | |
| 246 | /* |
| 247 | ** {================================================================== |
| 248 | ** Pseudo-Random Number Generator based on 'xoshiro256**'. |
| 249 | ** =================================================================== |
| 250 | */ |
| 251 | |
| 252 | /* number of binary digits in the mantissa of a float */ |
| 253 | #define FIGS l_floatatt(MANT_DIG) |
| 254 | |
| 255 | #if FIGS > 64 |
| 256 | /* there are only 64 random bits; use them all */ |
| 257 | #undef FIGS |
| 258 | #define FIGS 64 |
| 259 | #endif |
| 260 | |
| 261 | |
| 262 | /* |
| 263 | ** LUA_RAND32 forces the use of 32-bit integers in the implementation |
| 264 | ** of the PRN generator (mainly for testing). |
| 265 | */ |
| 266 | #if !defined(LUA_RAND32) && !defined(Rand64) |
| 267 | |
| 268 | /* try to find an integer type with at least 64 bits */ |
| 269 | |
| 270 | #if (ULONG_MAX >> 31 >> 31) >= 3 |
| 271 | |
| 272 | /* 'long' has at least 64 bits */ |
| 273 | #define Rand64 unsigned long |
| 274 | |
| 275 | #elif !defined(LUA_USE_C89) && defined(LLONG_MAX) |
| 276 | |
| 277 | /* there is a 'long long' type (which must have at least 64 bits) */ |
| 278 | #define Rand64 unsigned long long |
| 279 | |
| 280 | #elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3 |
| 281 | |
| 282 | /* 'lua_Integer' has at least 64 bits */ |
| 283 | #define Rand64 lua_Unsigned |
| 284 | |
| 285 | #endif |
| 286 | |
| 287 | #endif |
| 288 | |
| 289 | |
| 290 | #if defined(Rand64) /* { */ |
| 291 | |
| 292 | /* |
| 293 | ** Standard implementation, using 64-bit integers. |
| 294 | ** If 'Rand64' has more than 64 bits, the extra bits do not interfere |
| 295 | ** with the 64 initial bits, except in a right shift. Moreover, the |
| 296 | ** final result has to discard the extra bits. |
| 297 | */ |
| 298 | |
| 299 | /* avoid using extra bits when needed */ |
| 300 | #define trim64(x) ((x) & 0xffffffffffffffffu) |
| 301 | |
| 302 | |
| 303 | /* rotate left 'x' by 'n' bits */ |
| 304 | static Rand64 rotl (Rand64 x, int n) { |
| 305 | return (x << n) | (trim64(x) >> (64 - n)); |
| 306 | } |
| 307 | |
| 308 | static Rand64 nextrand (Rand64 *state) { |
| 309 | Rand64 state0 = state[0]; |
| 310 | Rand64 state1 = state[1]; |
| 311 | Rand64 state2 = state[2] ^ state0; |
| 312 | Rand64 state3 = state[3] ^ state1; |
| 313 | Rand64 res = rotl(state1 * 5, 7) * 9; |
| 314 | state[0] = state0 ^ state3; |
| 315 | state[1] = state1 ^ state2; |
| 316 | state[2] = state2 ^ (state1 << 17); |
| 317 | state[3] = rotl(state3, 45); |
| 318 | return res; |
| 319 | } |
| 320 | |
| 321 | |
| 322 | /* must take care to not shift stuff by more than 63 slots */ |
| 323 | |
| 324 | |
| 325 | /* |
| 326 | ** Convert bits from a random integer into a float in the |
| 327 | ** interval [0,1), getting the higher FIG bits from the |
| 328 | ** random unsigned integer and converting that to a float. |
| 329 | */ |
| 330 | |
| 331 | /* must throw out the extra (64 - FIGS) bits */ |
| 332 | #define shift64_FIG (64 - FIGS) |
| 333 | |
| 334 | /* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */ |
| 335 | #define scaleFIG (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1))) |
| 336 | |
| 337 | static lua_Number I2d (Rand64 x) { |
| 338 | return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG; |
| 339 | } |
| 340 | |
| 341 | /* convert a 'Rand64' to a 'lua_Unsigned' */ |
| 342 | #define I2UInt(x) ((lua_Unsigned)trim64(x)) |
| 343 | |
| 344 | /* convert a 'lua_Unsigned' to a 'Rand64' */ |
| 345 | #define Int2I(x) ((Rand64)(x)) |
| 346 | |
| 347 | |
| 348 | #else /* no 'Rand64' }{ */ |
| 349 | |
| 350 | /* get an integer with at least 32 bits */ |
| 351 | #if LUAI_IS32INT |
| 352 | typedef unsigned int lu_int32; |
| 353 | #else |
| 354 | typedef unsigned long lu_int32; |
| 355 | #endif |
| 356 | |
| 357 | |
| 358 | /* |
| 359 | ** Use two 32-bit integers to represent a 64-bit quantity. |
| 360 | */ |
| 361 | typedef struct Rand64 { |
| 362 | lu_int32 h; /* higher half */ |
| 363 | lu_int32 l; /* lower half */ |
| 364 | } Rand64; |
| 365 | |
| 366 | |
| 367 | /* |
| 368 | ** If 'lu_int32' has more than 32 bits, the extra bits do not interfere |
| 369 | ** with the 32 initial bits, except in a right shift and comparisons. |
| 370 | ** Moreover, the final result has to discard the extra bits. |
| 371 | */ |
| 372 | |
| 373 | /* avoid using extra bits when needed */ |
| 374 | #define trim32(x) ((x) & 0xffffffffu) |
| 375 | |
| 376 | |
| 377 | /* |
| 378 | ** basic operations on 'Rand64' values |
| 379 | */ |
| 380 | |
| 381 | /* build a new Rand64 value */ |
| 382 | static Rand64 packI (lu_int32 h, lu_int32 l) { |
| 383 | Rand64 result; |
| 384 | result.h = h; |
| 385 | result.l = l; |
| 386 | return result; |
| 387 | } |
| 388 | |
| 389 | /* return i << n */ |
| 390 | static Rand64 Ishl (Rand64 i, int n) { |
| 391 | lua_assert(n > 0 && n < 32); |
| 392 | return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n); |
| 393 | } |
| 394 | |
| 395 | /* i1 ^= i2 */ |
| 396 | static void Ixor (Rand64 *i1, Rand64 i2) { |
| 397 | i1->h ^= i2.h; |
| 398 | i1->l ^= i2.l; |
| 399 | } |
| 400 | |
| 401 | /* return i1 + i2 */ |
| 402 | static Rand64 Iadd (Rand64 i1, Rand64 i2) { |
| 403 | Rand64 result = packI(i1.h + i2.h, i1.l + i2.l); |
| 404 | if (trim32(result.l) < trim32(i1.l)) /* carry? */ |
| 405 | result.h++; |
| 406 | return result; |
| 407 | } |
| 408 | |
| 409 | /* return i * 5 */ |
| 410 | static Rand64 times5 (Rand64 i) { |
| 411 | return Iadd(Ishl(i, 2), i); /* i * 5 == (i << 2) + i */ |
| 412 | } |
| 413 | |
| 414 | /* return i * 9 */ |
| 415 | static Rand64 times9 (Rand64 i) { |
| 416 | return Iadd(Ishl(i, 3), i); /* i * 9 == (i << 3) + i */ |
| 417 | } |
| 418 | |
| 419 | /* return 'i' rotated left 'n' bits */ |
| 420 | static Rand64 rotl (Rand64 i, int n) { |
| 421 | lua_assert(n > 0 && n < 32); |
| 422 | return packI((i.h << n) | (trim32(i.l) >> (32 - n)), |
| 423 | (trim32(i.h) >> (32 - n)) | (i.l << n)); |
| 424 | } |
| 425 | |
| 426 | /* for offsets larger than 32, rotate right by 64 - offset */ |
| 427 | static Rand64 rotl1 (Rand64 i, int n) { |
| 428 | lua_assert(n > 32 && n < 64); |
| 429 | n = 64 - n; |
| 430 | return packI((trim32(i.h) >> n) | (i.l << (32 - n)), |
| 431 | (i.h << (32 - n)) | (trim32(i.l) >> n)); |
| 432 | } |
| 433 | |
| 434 | /* |
| 435 | ** implementation of 'xoshiro256**' algorithm on 'Rand64' values |
| 436 | */ |
| 437 | static Rand64 nextrand (Rand64 *state) { |
| 438 | Rand64 res = times9(rotl(times5(state[1]), 7)); |
| 439 | Rand64 t = Ishl(state[1], 17); |
| 440 | Ixor(&state[2], state[0]); |
| 441 | Ixor(&state[3], state[1]); |
| 442 | Ixor(&state[1], state[2]); |
| 443 | Ixor(&state[0], state[3]); |
| 444 | Ixor(&state[2], t); |
| 445 | state[3] = rotl1(state[3], 45); |
| 446 | return res; |
| 447 | } |
| 448 | |
| 449 | |
| 450 | /* |
| 451 | ** Converts a 'Rand64' into a float. |
| 452 | */ |
| 453 | |
| 454 | /* an unsigned 1 with proper type */ |
| 455 | #define UONE ((lu_int32)1) |
| 456 | |
| 457 | |
| 458 | #if FIGS <= 32 |
| 459 | |
| 460 | /* 2^(-FIGS) */ |
| 461 | #define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) |
| 462 | |
| 463 | /* |
| 464 | ** get up to 32 bits from higher half, shifting right to |
| 465 | ** throw out the extra bits. |
| 466 | */ |
| 467 | static lua_Number I2d (Rand64 x) { |
| 468 | lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS)); |
| 469 | return h * scaleFIG; |
| 470 | } |
| 471 | |
| 472 | #else /* 32 < FIGS <= 64 */ |
| 473 | |
| 474 | /* must take care to not shift stuff by more than 31 slots */ |
| 475 | |
| 476 | /* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */ |
| 477 | #define scaleFIG \ |
| 478 | ((lua_Number)1.0 / (UONE << 30) / 8.0 / (UONE << (FIGS - 33))) |
| 479 | |
| 480 | /* |
| 481 | ** use FIGS - 32 bits from lower half, throwing out the other |
| 482 | ** (32 - (FIGS - 32)) = (64 - FIGS) bits |
| 483 | */ |
| 484 | #define shiftLOW (64 - FIGS) |
| 485 | |
| 486 | /* |
| 487 | ** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32) |
| 488 | */ |
| 489 | #define shiftHI ((lua_Number)(UONE << (FIGS - 33)) * 2.0) |
| 490 | |
| 491 | |
| 492 | static lua_Number I2d (Rand64 x) { |
| 493 | lua_Number h = (lua_Number)trim32(x.h) * shiftHI; |
| 494 | lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW); |
| 495 | return (h + l) * scaleFIG; |
| 496 | } |
| 497 | |
| 498 | #endif |
| 499 | |
| 500 | |
| 501 | /* convert a 'Rand64' to a 'lua_Unsigned' */ |
| 502 | static lua_Unsigned I2UInt (Rand64 x) { |
| 503 | return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l); |
| 504 | } |
| 505 | |
| 506 | /* convert a 'lua_Unsigned' to a 'Rand64' */ |
| 507 | static Rand64 Int2I (lua_Unsigned n) { |
| 508 | return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n); |
| 509 | } |
| 510 | |
| 511 | #endif /* } */ |
| 512 | |
| 513 | |
| 514 | /* |
| 515 | ** A state uses four 'Rand64' values. |
| 516 | */ |
| 517 | typedef struct { |
| 518 | Rand64 s[4]; |
| 519 | } RanState; |
| 520 | |
| 521 | |
| 522 | /* |
| 523 | ** Project the random integer 'ran' into the interval [0, n]. |
| 524 | ** Because 'ran' has 2^B possible values, the projection can only be |
| 525 | ** uniform when the size of the interval is a power of 2 (exact |
| 526 | ** division). Otherwise, to get a uniform projection into [0, n], we |
| 527 | ** first compute 'lim', the smallest Mersenne number not smaller than |
| 528 | ** 'n'. We then project 'ran' into the interval [0, lim]. If the result |
| 529 | ** is inside [0, n], we are done. Otherwise, we try with another 'ran', |
| 530 | ** until we have a result inside the interval. |
| 531 | */ |
| 532 | static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n, |
| 533 | RanState *state) { |
| 534 | if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */ |
| 535 | return ran & n; /* no bias */ |
| 536 | else { |
| 537 | lua_Unsigned lim = n; |
| 538 | /* compute the smallest (2^b - 1) not smaller than 'n' */ |
| 539 | lim |= (lim >> 1); |
| 540 | lim |= (lim >> 2); |
| 541 | lim |= (lim >> 4); |
| 542 | lim |= (lim >> 8); |
| 543 | lim |= (lim >> 16); |
| 544 | #if (LUA_MAXUNSIGNED >> 31) >= 3 |
| 545 | lim |= (lim >> 32); /* integer type has more than 32 bits */ |
| 546 | #endif |
| 547 | lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2, */ |
| 548 | && lim >= n /* not smaller than 'n', */ |
| 549 | && (lim >> 1) < n); /* and it is the smallest one */ |
| 550 | while ((ran &= lim) > n) /* project 'ran' into [0..lim] */ |
| 551 | ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */ |
| 552 | return ran; |
| 553 | } |
| 554 | } |
| 555 | |
| 556 | |
| 557 | static int math_random (lua_State *L) { |
| 558 | lua_Integer low, up; |
| 559 | lua_Unsigned p; |
| 560 | RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1)); |
| 561 | Rand64 rv = nextrand(state->s); /* next pseudo-random value */ |
| 562 | switch (lua_gettop(L)) { /* check number of arguments */ |
| 563 | case 0: { /* no arguments */ |
| 564 | lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */ |
| 565 | return 1; |
| 566 | } |
| 567 | case 1: { /* only upper limit */ |
| 568 | low = 1; |
| 569 | up = luaL_checkinteger(L, 1); |
| 570 | if (up == 0) { /* single 0 as argument? */ |
| 571 | lua_pushinteger(L, I2UInt(rv)); /* full random integer */ |
| 572 | return 1; |
| 573 | } |
| 574 | break; |
| 575 | } |
| 576 | case 2: { /* lower and upper limits */ |
| 577 | low = luaL_checkinteger(L, 1); |
| 578 | up = luaL_checkinteger(L, 2); |
| 579 | break; |
| 580 | } |
| 581 | default: return luaL_error(L, "wrong number of arguments" ); |
| 582 | } |
| 583 | /* random integer in the interval [low, up] */ |
| 584 | luaL_argcheck(L, low <= up, 1, "interval is empty" ); |
| 585 | /* project random integer into the interval [0, up - low] */ |
| 586 | p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state); |
| 587 | lua_pushinteger(L, p + (lua_Unsigned)low); |
| 588 | return 1; |
| 589 | } |
| 590 | |
| 591 | |
| 592 | static void setseed (lua_State *L, Rand64 *state, |
| 593 | lua_Unsigned n1, lua_Unsigned n2) { |
| 594 | int i; |
| 595 | state[0] = Int2I(n1); |
| 596 | state[1] = Int2I(0xff); /* avoid a zero state */ |
| 597 | state[2] = Int2I(n2); |
| 598 | state[3] = Int2I(0); |
| 599 | for (i = 0; i < 16; i++) |
| 600 | nextrand(state); /* discard initial values to "spread" seed */ |
| 601 | lua_pushinteger(L, n1); |
| 602 | lua_pushinteger(L, n2); |
| 603 | } |
| 604 | |
| 605 | |
| 606 | /* |
| 607 | ** Set a "random" seed. To get some randomness, use the current time |
| 608 | ** and the address of 'L' (in case the machine does address space layout |
| 609 | ** randomization). |
| 610 | */ |
| 611 | static void randseed (lua_State *L, RanState *state) { |
| 612 | lua_Unsigned seed1 = (lua_Unsigned)time(NULL); |
| 613 | lua_Unsigned seed2 = (lua_Unsigned)(size_t)L; |
| 614 | setseed(L, state->s, seed1, seed2); |
| 615 | } |
| 616 | |
| 617 | |
| 618 | static int math_randomseed (lua_State *L) { |
| 619 | RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1)); |
| 620 | if (lua_isnone(L, 1)) { |
| 621 | randseed(L, state); |
| 622 | } |
| 623 | else { |
| 624 | lua_Integer n1 = luaL_checkinteger(L, 1); |
| 625 | lua_Integer n2 = luaL_optinteger(L, 2, 0); |
| 626 | setseed(L, state->s, n1, n2); |
| 627 | } |
| 628 | return 2; /* return seeds */ |
| 629 | } |
| 630 | |
| 631 | |
| 632 | static const luaL_Reg randfuncs[] = { |
| 633 | {"random" , math_random}, |
| 634 | {"randomseed" , math_randomseed}, |
| 635 | {NULL, NULL} |
| 636 | }; |
| 637 | |
| 638 | |
| 639 | /* |
| 640 | ** Register the random functions and initialize their state. |
| 641 | */ |
| 642 | static void setrandfunc (lua_State *L) { |
| 643 | RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0); |
| 644 | randseed(L, state); /* initialize with a "random" seed */ |
| 645 | lua_pop(L, 2); /* remove pushed seeds */ |
| 646 | luaL_setfuncs(L, randfuncs, 1); |
| 647 | } |
| 648 | |
| 649 | /* }================================================================== */ |
| 650 | |
| 651 | |
| 652 | /* |
| 653 | ** {================================================================== |
| 654 | ** Deprecated functions (for compatibility only) |
| 655 | ** =================================================================== |
| 656 | */ |
| 657 | #if defined(LUA_COMPAT_MATHLIB) |
| 658 | |
| 659 | static int math_cosh (lua_State *L) { |
| 660 | lua_pushnumber(L, l_mathop(cosh)(luaL_checknumber(L, 1))); |
| 661 | return 1; |
| 662 | } |
| 663 | |
| 664 | static int math_sinh (lua_State *L) { |
| 665 | lua_pushnumber(L, l_mathop(sinh)(luaL_checknumber(L, 1))); |
| 666 | return 1; |
| 667 | } |
| 668 | |
| 669 | static int math_tanh (lua_State *L) { |
| 670 | lua_pushnumber(L, l_mathop(tanh)(luaL_checknumber(L, 1))); |
| 671 | return 1; |
| 672 | } |
| 673 | |
| 674 | static int math_pow (lua_State *L) { |
| 675 | lua_Number x = luaL_checknumber(L, 1); |
| 676 | lua_Number y = luaL_checknumber(L, 2); |
| 677 | lua_pushnumber(L, l_mathop(pow)(x, y)); |
| 678 | return 1; |
| 679 | } |
| 680 | |
| 681 | static int math_frexp (lua_State *L) { |
| 682 | int e; |
| 683 | lua_pushnumber(L, l_mathop(frexp)(luaL_checknumber(L, 1), &e)); |
| 684 | lua_pushinteger(L, e); |
| 685 | return 2; |
| 686 | } |
| 687 | |
| 688 | static int math_ldexp (lua_State *L) { |
| 689 | lua_Number x = luaL_checknumber(L, 1); |
| 690 | int ep = (int)luaL_checkinteger(L, 2); |
| 691 | lua_pushnumber(L, l_mathop(ldexp)(x, ep)); |
| 692 | return 1; |
| 693 | } |
| 694 | |
| 695 | static int math_log10 (lua_State *L) { |
| 696 | lua_pushnumber(L, l_mathop(log10)(luaL_checknumber(L, 1))); |
| 697 | return 1; |
| 698 | } |
| 699 | |
| 700 | #endif |
| 701 | /* }================================================================== */ |
| 702 | |
| 703 | |
| 704 | |
| 705 | static const luaL_Reg mathlib[] = { |
| 706 | {"abs" , math_abs}, |
| 707 | {"acos" , math_acos}, |
| 708 | {"asin" , math_asin}, |
| 709 | {"atan" , math_atan}, |
| 710 | {"ceil" , math_ceil}, |
| 711 | {"cos" , math_cos}, |
| 712 | {"deg" , math_deg}, |
| 713 | {"exp" , math_exp}, |
| 714 | {"tointeger" , math_toint}, |
| 715 | {"floor" , math_floor}, |
| 716 | {"fmod" , math_fmod}, |
| 717 | {"ult" , math_ult}, |
| 718 | {"log" , math_log}, |
| 719 | {"max" , math_max}, |
| 720 | {"min" , math_min}, |
| 721 | {"modf" , math_modf}, |
| 722 | {"rad" , math_rad}, |
| 723 | {"sin" , math_sin}, |
| 724 | {"sqrt" , math_sqrt}, |
| 725 | {"tan" , math_tan}, |
| 726 | {"type" , math_type}, |
| 727 | #if defined(LUA_COMPAT_MATHLIB) |
| 728 | {"atan2" , math_atan}, |
| 729 | {"cosh" , math_cosh}, |
| 730 | {"sinh" , math_sinh}, |
| 731 | {"tanh" , math_tanh}, |
| 732 | {"pow" , math_pow}, |
| 733 | {"frexp" , math_frexp}, |
| 734 | {"ldexp" , math_ldexp}, |
| 735 | {"log10" , math_log10}, |
| 736 | #endif |
| 737 | /* placeholders */ |
| 738 | {"random" , NULL}, |
| 739 | {"randomseed" , NULL}, |
| 740 | {"pi" , NULL}, |
| 741 | {"huge" , NULL}, |
| 742 | {"maxinteger" , NULL}, |
| 743 | {"mininteger" , NULL}, |
| 744 | {NULL, NULL} |
| 745 | }; |
| 746 | |
| 747 | |
| 748 | /* |
| 749 | ** Open math library |
| 750 | */ |
| 751 | LUAMOD_API int luaopen_math (lua_State *L) { |
| 752 | luaL_newlib(L, mathlib); |
| 753 | lua_pushnumber(L, PI); |
| 754 | lua_setfield(L, -2, "pi" ); |
| 755 | lua_pushnumber(L, (lua_Number)HUGE_VAL); |
| 756 | lua_setfield(L, -2, "huge" ); |
| 757 | lua_pushinteger(L, LUA_MAXINTEGER); |
| 758 | lua_setfield(L, -2, "maxinteger" ); |
| 759 | lua_pushinteger(L, LUA_MININTEGER); |
| 760 | lua_setfield(L, -2, "mininteger" ); |
| 761 | setrandfunc(L); |
| 762 | return 1; |
| 763 | } |
| 764 | |
| 765 | |