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- /*
- ** $Id: lmathlib.c $
- ** Standard mathematical library
- ** See Copyright Notice in lua.h
- */
- #define lmathlib_c
- #define LUA_LIB
- #include "lprefix.h"
- #include <float.h>
- #include <limits.h>
- #include <math.h>
- #include <stdlib.h>
- #include <time.h>
- #include "lua.h"
- #include "lauxlib.h"
- #include "lualib.h"
- #undef PI
- #define PI (l_mathop(3.141592653589793238462643383279502884))
- static int math_abs (lua_State *L) {
- if (lua_isinteger(L, 1)) {
- lua_Integer n = lua_tointeger(L, 1);
- if (n < 0) n = (lua_Integer)(0u - (lua_Unsigned)n);
- lua_pushinteger(L, n);
- }
- else
- lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_sin (lua_State *L) {
- lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_cos (lua_State *L) {
- lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_tan (lua_State *L) {
- lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_asin (lua_State *L) {
- lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_acos (lua_State *L) {
- lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_atan (lua_State *L) {
- lua_Number y = luaL_checknumber(L, 1);
- lua_Number x = luaL_optnumber(L, 2, 1);
- lua_pushnumber(L, l_mathop(atan2)(y, x));
- return 1;
- }
- static int math_toint (lua_State *L) {
- int valid;
- lua_Integer n = lua_tointegerx(L, 1, &valid);
- if (valid)
- lua_pushinteger(L, n);
- else {
- luaL_checkany(L, 1);
- luaL_pushfail(L); /* value is not convertible to integer */
- }
- return 1;
- }
- static void pushnumint (lua_State *L, lua_Number d) {
- lua_Integer n;
- if (lua_numbertointeger(d, &n)) /* does 'd' fit in an integer? */
- lua_pushinteger(L, n); /* result is integer */
- else
- lua_pushnumber(L, d); /* result is float */
- }
- static int math_floor (lua_State *L) {
- if (lua_isinteger(L, 1))
- lua_settop(L, 1); /* integer is its own floor */
- else {
- lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1));
- pushnumint(L, d);
- }
- return 1;
- }
- static int math_ceil (lua_State *L) {
- if (lua_isinteger(L, 1))
- lua_settop(L, 1); /* integer is its own ceil */
- else {
- lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1));
- pushnumint(L, d);
- }
- return 1;
- }
- static int math_fmod (lua_State *L) {
- if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) {
- lua_Integer d = lua_tointeger(L, 2);
- if ((lua_Unsigned)d + 1u <= 1u) { /* special cases: -1 or 0 */
- luaL_argcheck(L, d != 0, 2, "zero");
- lua_pushinteger(L, 0); /* avoid overflow with 0x80000... / -1 */
- }
- else
- lua_pushinteger(L, lua_tointeger(L, 1) % d);
- }
- else
- lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1),
- luaL_checknumber(L, 2)));
- return 1;
- }
- /*
- ** next function does not use 'modf', avoiding problems with 'double*'
- ** (which is not compatible with 'float*') when lua_Number is not
- ** 'double'.
- */
- static int math_modf (lua_State *L) {
- if (lua_isinteger(L ,1)) {
- lua_settop(L, 1); /* number is its own integer part */
- lua_pushnumber(L, 0); /* no fractional part */
- }
- else {
- lua_Number n = luaL_checknumber(L, 1);
- /* integer part (rounds toward zero) */
- lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n);
- pushnumint(L, ip);
- /* fractional part (test needed for inf/-inf) */
- lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip));
- }
- return 2;
- }
- static int math_sqrt (lua_State *L) {
- lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_ult (lua_State *L) {
- lua_Integer a = luaL_checkinteger(L, 1);
- lua_Integer b = luaL_checkinteger(L, 2);
- lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b);
- return 1;
- }
- static int math_log (lua_State *L) {
- lua_Number x = luaL_checknumber(L, 1);
- lua_Number res;
- if (lua_isnoneornil(L, 2))
- res = l_mathop(log)(x);
- else {
- lua_Number base = luaL_checknumber(L, 2);
- #if !defined(LUA_USE_C89)
- if (base == l_mathop(2.0))
- res = l_mathop(log2)(x); else
- #endif
- if (base == l_mathop(10.0))
- res = l_mathop(log10)(x);
- else
- res = l_mathop(log)(x)/l_mathop(log)(base);
- }
- lua_pushnumber(L, res);
- return 1;
- }
- static int math_exp (lua_State *L) {
- lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_deg (lua_State *L) {
- lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI));
- return 1;
- }
- static int math_rad (lua_State *L) {
- lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0)));
- return 1;
- }
- static int math_min (lua_State *L) {
- int n = lua_gettop(L); /* number of arguments */
- int imin = 1; /* index of current minimum value */
- int i;
- luaL_argcheck(L, n >= 1, 1, "value expected");
- for (i = 2; i <= n; i++) {
- if (lua_compare(L, i, imin, LUA_OPLT))
- imin = i;
- }
- lua_pushvalue(L, imin);
- return 1;
- }
- static int math_max (lua_State *L) {
- int n = lua_gettop(L); /* number of arguments */
- int imax = 1; /* index of current maximum value */
- int i;
- luaL_argcheck(L, n >= 1, 1, "value expected");
- for (i = 2; i <= n; i++) {
- if (lua_compare(L, imax, i, LUA_OPLT))
- imax = i;
- }
- lua_pushvalue(L, imax);
- return 1;
- }
- static int math_type (lua_State *L) {
- if (lua_type(L, 1) == LUA_TNUMBER)
- lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float");
- else {
- luaL_checkany(L, 1);
- luaL_pushfail(L);
- }
- return 1;
- }
- /*
- ** {==================================================================
- ** Pseudo-Random Number Generator based on 'xoshiro256**'.
- ** ===================================================================
- */
- /* number of binary digits in the mantissa of a float */
- #define FIGS l_floatatt(MANT_DIG)
- #if FIGS > 64
- /* there are only 64 random bits; use them all */
- #undef FIGS
- #define FIGS 64
- #endif
- /*
- ** LUA_RAND32 forces the use of 32-bit integers in the implementation
- ** of the PRN generator (mainly for testing).
- */
- #if !defined(LUA_RAND32) && !defined(Rand64)
- /* try to find an integer type with at least 64 bits */
- #if (ULONG_MAX >> 31 >> 31) >= 3
- /* 'long' has at least 64 bits */
- #define Rand64 unsigned long
- #elif !defined(LUA_USE_C89) && defined(LLONG_MAX)
- /* there is a 'long long' type (which must have at least 64 bits) */
- #define Rand64 unsigned long long
- #elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3
- /* 'lua_Integer' has at least 64 bits */
- #define Rand64 lua_Unsigned
- #endif
- #endif
- #if defined(Rand64) /* { */
- /*
- ** Standard implementation, using 64-bit integers.
- ** If 'Rand64' has more than 64 bits, the extra bits do not interfere
- ** with the 64 initial bits, except in a right shift. Moreover, the
- ** final result has to discard the extra bits.
- */
- /* avoid using extra bits when needed */
- #define trim64(x) ((x) & 0xffffffffffffffffu)
- /* rotate left 'x' by 'n' bits */
- static Rand64 rotl (Rand64 x, int n) {
- return (x << n) | (trim64(x) >> (64 - n));
- }
- static Rand64 nextrand (Rand64 *state) {
- Rand64 state0 = state[0];
- Rand64 state1 = state[1];
- Rand64 state2 = state[2] ^ state0;
- Rand64 state3 = state[3] ^ state1;
- Rand64 res = rotl(state1 * 5, 7) * 9;
- state[0] = state0 ^ state3;
- state[1] = state1 ^ state2;
- state[2] = state2 ^ (state1 << 17);
- state[3] = rotl(state3, 45);
- return res;
- }
- /* must take care to not shift stuff by more than 63 slots */
- /*
- ** Convert bits from a random integer into a float in the
- ** interval [0,1), getting the higher FIG bits from the
- ** random unsigned integer and converting that to a float.
- */
- /* must throw out the extra (64 - FIGS) bits */
- #define shift64_FIG (64 - FIGS)
- /* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */
- #define scaleFIG (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1)))
- static lua_Number I2d (Rand64 x) {
- return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG;
- }
- /* convert a 'Rand64' to a 'lua_Unsigned' */
- #define I2UInt(x) ((lua_Unsigned)trim64(x))
- /* convert a 'lua_Unsigned' to a 'Rand64' */
- #define Int2I(x) ((Rand64)(x))
- #else /* no 'Rand64' }{ */
- /* get an integer with at least 32 bits */
- #if LUAI_IS32INT
- typedef unsigned int lu_int32;
- #else
- typedef unsigned long lu_int32;
- #endif
- /*
- ** Use two 32-bit integers to represent a 64-bit quantity.
- */
- typedef struct Rand64 {
- lu_int32 h; /* higher half */
- lu_int32 l; /* lower half */
- } Rand64;
- /*
- ** If 'lu_int32' has more than 32 bits, the extra bits do not interfere
- ** with the 32 initial bits, except in a right shift and comparisons.
- ** Moreover, the final result has to discard the extra bits.
- */
- /* avoid using extra bits when needed */
- #define trim32(x) ((x) & 0xffffffffu)
- /*
- ** basic operations on 'Rand64' values
- */
- /* build a new Rand64 value */
- static Rand64 packI (lu_int32 h, lu_int32 l) {
- Rand64 result;
- result.h = h;
- result.l = l;
- return result;
- }
- /* return i << n */
- static Rand64 Ishl (Rand64 i, int n) {
- lua_assert(n > 0 && n < 32);
- return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n);
- }
- /* i1 ^= i2 */
- static void Ixor (Rand64 *i1, Rand64 i2) {
- i1->h ^= i2.h;
- i1->l ^= i2.l;
- }
- /* return i1 + i2 */
- static Rand64 Iadd (Rand64 i1, Rand64 i2) {
- Rand64 result = packI(i1.h + i2.h, i1.l + i2.l);
- if (trim32(result.l) < trim32(i1.l)) /* carry? */
- result.h++;
- return result;
- }
- /* return i * 5 */
- static Rand64 times5 (Rand64 i) {
- return Iadd(Ishl(i, 2), i); /* i * 5 == (i << 2) + i */
- }
- /* return i * 9 */
- static Rand64 times9 (Rand64 i) {
- return Iadd(Ishl(i, 3), i); /* i * 9 == (i << 3) + i */
- }
- /* return 'i' rotated left 'n' bits */
- static Rand64 rotl (Rand64 i, int n) {
- lua_assert(n > 0 && n < 32);
- return packI((i.h << n) | (trim32(i.l) >> (32 - n)),
- (trim32(i.h) >> (32 - n)) | (i.l << n));
- }
- /* for offsets larger than 32, rotate right by 64 - offset */
- static Rand64 rotl1 (Rand64 i, int n) {
- lua_assert(n > 32 && n < 64);
- n = 64 - n;
- return packI((trim32(i.h) >> n) | (i.l << (32 - n)),
- (i.h << (32 - n)) | (trim32(i.l) >> n));
- }
- /*
- ** implementation of 'xoshiro256**' algorithm on 'Rand64' values
- */
- static Rand64 nextrand (Rand64 *state) {
- Rand64 res = times9(rotl(times5(state[1]), 7));
- Rand64 t = Ishl(state[1], 17);
- Ixor(&state[2], state[0]);
- Ixor(&state[3], state[1]);
- Ixor(&state[1], state[2]);
- Ixor(&state[0], state[3]);
- Ixor(&state[2], t);
- state[3] = rotl1(state[3], 45);
- return res;
- }
- /*
- ** Converts a 'Rand64' into a float.
- */
- /* an unsigned 1 with proper type */
- #define UONE ((lu_int32)1)
- #if FIGS <= 32
- /* 2^(-FIGS) */
- #define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1)))
- /*
- ** get up to 32 bits from higher half, shifting right to
- ** throw out the extra bits.
- */
- static lua_Number I2d (Rand64 x) {
- lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS));
- return h * scaleFIG;
- }
- #else /* 32 < FIGS <= 64 */
- /* must take care to not shift stuff by more than 31 slots */
- /* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */
- #define scaleFIG \
- ((lua_Number)1.0 / (UONE << 30) / 8.0 / (UONE << (FIGS - 33)))
- /*
- ** use FIGS - 32 bits from lower half, throwing out the other
- ** (32 - (FIGS - 32)) = (64 - FIGS) bits
- */
- #define shiftLOW (64 - FIGS)
- /*
- ** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32)
- */
- #define shiftHI ((lua_Number)(UONE << (FIGS - 33)) * 2.0)
- static lua_Number I2d (Rand64 x) {
- lua_Number h = (lua_Number)trim32(x.h) * shiftHI;
- lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW);
- return (h + l) * scaleFIG;
- }
- #endif
- /* convert a 'Rand64' to a 'lua_Unsigned' */
- static lua_Unsigned I2UInt (Rand64 x) {
- return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l);
- }
- /* convert a 'lua_Unsigned' to a 'Rand64' */
- static Rand64 Int2I (lua_Unsigned n) {
- return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n);
- }
- #endif /* } */
- /*
- ** A state uses four 'Rand64' values.
- */
- typedef struct {
- Rand64 s[4];
- } RanState;
- /*
- ** Project the random integer 'ran' into the interval [0, n].
- ** Because 'ran' has 2^B possible values, the projection can only be
- ** uniform when the size of the interval is a power of 2 (exact
- ** division). Otherwise, to get a uniform projection into [0, n], we
- ** first compute 'lim', the smallest Mersenne number not smaller than
- ** 'n'. We then project 'ran' into the interval [0, lim]. If the result
- ** is inside [0, n], we are done. Otherwise, we try with another 'ran',
- ** until we have a result inside the interval.
- */
- static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
- RanState *state) {
- if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */
- return ran & n; /* no bias */
- else {
- lua_Unsigned lim = n;
- /* compute the smallest (2^b - 1) not smaller than 'n' */
- lim |= (lim >> 1);
- lim |= (lim >> 2);
- lim |= (lim >> 4);
- lim |= (lim >> 8);
- lim |= (lim >> 16);
- #if (LUA_MAXUNSIGNED >> 31) >= 3
- lim |= (lim >> 32); /* integer type has more than 32 bits */
- #endif
- lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2, */
- && lim >= n /* not smaller than 'n', */
- && (lim >> 1) < n); /* and it is the smallest one */
- while ((ran &= lim) > n) /* project 'ran' into [0..lim] */
- ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */
- return ran;
- }
- }
- static int math_random (lua_State *L) {
- lua_Integer low, up;
- lua_Unsigned p;
- RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
- Rand64 rv = nextrand(state->s); /* next pseudo-random value */
- switch (lua_gettop(L)) { /* check number of arguments */
- case 0: { /* no arguments */
- lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */
- return 1;
- }
- case 1: { /* only upper limit */
- low = 1;
- up = luaL_checkinteger(L, 1);
- if (up == 0) { /* single 0 as argument? */
- lua_pushinteger(L, I2UInt(rv)); /* full random integer */
- return 1;
- }
- break;
- }
- case 2: { /* lower and upper limits */
- low = luaL_checkinteger(L, 1);
- up = luaL_checkinteger(L, 2);
- break;
- }
- default: return luaL_error(L, "wrong number of arguments");
- }
- /* random integer in the interval [low, up] */
- luaL_argcheck(L, low <= up, 1, "interval is empty");
- /* project random integer into the interval [0, up - low] */
- p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state);
- lua_pushinteger(L, p + (lua_Unsigned)low);
- return 1;
- }
- static void setseed (lua_State *L, Rand64 *state,
- lua_Unsigned n1, lua_Unsigned n2) {
- int i;
- state[0] = Int2I(n1);
- state[1] = Int2I(0xff); /* avoid a zero state */
- state[2] = Int2I(n2);
- state[3] = Int2I(0);
- for (i = 0; i < 16; i++)
- nextrand(state); /* discard initial values to "spread" seed */
- lua_pushinteger(L, n1);
- lua_pushinteger(L, n2);
- }
- /*
- ** Set a "random" seed. To get some randomness, use the current time
- ** and the address of 'L' (in case the machine does address space layout
- ** randomization).
- */
- static void randseed (lua_State *L, RanState *state) {
- lua_Unsigned seed1 = (lua_Unsigned)time(NULL);
- lua_Unsigned seed2 = (lua_Unsigned)(size_t)L;
- setseed(L, state->s, seed1, seed2);
- }
- static int math_randomseed (lua_State *L) {
- RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
- if (lua_isnone(L, 1)) {
- randseed(L, state);
- }
- else {
- lua_Integer n1 = luaL_checkinteger(L, 1);
- lua_Integer n2 = luaL_optinteger(L, 2, 0);
- setseed(L, state->s, n1, n2);
- }
- return 2; /* return seeds */
- }
- static const luaL_Reg randfuncs[] = {
- {"random", math_random},
- {"randomseed", math_randomseed},
- {NULL, NULL}
- };
- /*
- ** Register the random functions and initialize their state.
- */
- static void setrandfunc (lua_State *L) {
- RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0);
- randseed(L, state); /* initialize with a "random" seed */
- lua_pop(L, 2); /* remove pushed seeds */
- luaL_setfuncs(L, randfuncs, 1);
- }
- /* }================================================================== */
- /*
- ** {==================================================================
- ** Deprecated functions (for compatibility only)
- ** ===================================================================
- */
- #if defined(LUA_COMPAT_MATHLIB)
- static int math_cosh (lua_State *L) {
- lua_pushnumber(L, l_mathop(cosh)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_sinh (lua_State *L) {
- lua_pushnumber(L, l_mathop(sinh)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_tanh (lua_State *L) {
- lua_pushnumber(L, l_mathop(tanh)(luaL_checknumber(L, 1)));
- return 1;
- }
- static int math_pow (lua_State *L) {
- lua_Number x = luaL_checknumber(L, 1);
- lua_Number y = luaL_checknumber(L, 2);
- lua_pushnumber(L, l_mathop(pow)(x, y));
- return 1;
- }
- static int math_frexp (lua_State *L) {
- int e;
- lua_pushnumber(L, l_mathop(frexp)(luaL_checknumber(L, 1), &e));
- lua_pushinteger(L, e);
- return 2;
- }
- static int math_ldexp (lua_State *L) {
- lua_Number x = luaL_checknumber(L, 1);
- int ep = (int)luaL_checkinteger(L, 2);
- lua_pushnumber(L, l_mathop(ldexp)(x, ep));
- return 1;
- }
- static int math_log10 (lua_State *L) {
- lua_pushnumber(L, l_mathop(log10)(luaL_checknumber(L, 1)));
- return 1;
- }
- #endif
- /* }================================================================== */
- static const luaL_Reg mathlib[] = {
- {"abs", math_abs},
- {"acos", math_acos},
- {"asin", math_asin},
- {"atan", math_atan},
- {"ceil", math_ceil},
- {"cos", math_cos},
- {"deg", math_deg},
- {"exp", math_exp},
- {"tointeger", math_toint},
- {"floor", math_floor},
- {"fmod", math_fmod},
- {"ult", math_ult},
- {"log", math_log},
- {"max", math_max},
- {"min", math_min},
- {"modf", math_modf},
- {"rad", math_rad},
- {"sin", math_sin},
- {"sqrt", math_sqrt},
- {"tan", math_tan},
- {"type", math_type},
- #if defined(LUA_COMPAT_MATHLIB)
- {"atan2", math_atan},
- {"cosh", math_cosh},
- {"sinh", math_sinh},
- {"tanh", math_tanh},
- {"pow", math_pow},
- {"frexp", math_frexp},
- {"ldexp", math_ldexp},
- {"log10", math_log10},
- #endif
- /* placeholders */
- {"random", NULL},
- {"randomseed", NULL},
- {"pi", NULL},
- {"huge", NULL},
- {"maxinteger", NULL},
- {"mininteger", NULL},
- {NULL, NULL}
- };
- /*
- ** Open math library
- */
- LUAMOD_API int luaopen_math (lua_State *L) {
- luaL_newlib(L, mathlib);
- lua_pushnumber(L, PI);
- lua_setfield(L, -2, "pi");
- lua_pushnumber(L, (lua_Number)HUGE_VAL);
- lua_setfield(L, -2, "huge");
- lua_pushinteger(L, LUA_MAXINTEGER);
- lua_setfield(L, -2, "maxinteger");
- lua_pushinteger(L, LUA_MININTEGER);
- lua_setfield(L, -2, "mininteger");
- setrandfunc(L);
- return 1;
- }
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