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@ -1,5 +1,5 @@
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/*
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** $Id: lmathlib.c,v 1.119.1.1 2017/04/19 17:20:42 roberto Exp $
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** $Id: lmathlib.c $
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** Standard mathematical library
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** See Copyright Notice in lua.h
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*/
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@ -10,8 +10,11 @@
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#include "lprefix.h"
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#include <stdlib.h>
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#include <float.h>
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#include <limits.h>
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#include <math.h>
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#include <stdlib.h>
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#include <time.h>
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#include "lua.h"
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@ -23,19 +26,6 @@
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#define PI (l_mathop(3.141592653589793238462643383279502884))
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#if !defined(l_rand) /* { */
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#if defined(LUA_USE_POSIX)
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#define l_rand() random()
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#define l_srand(x) srandom(x)
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#define L_RANDMAX 2147483647 /* (2^31 - 1), following POSIX */
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#else
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#define l_rand() rand()
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#define l_srand(x) srand(x)
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#define L_RANDMAX RAND_MAX
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#endif
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#endif /* } */
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static int math_abs (lua_State *L) {
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if (lua_isinteger(L, 1)) {
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lua_Integer n = lua_tointeger(L, 1);
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@ -87,7 +77,7 @@ static int math_toint (lua_State *L) {
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lua_pushinteger(L, n);
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else {
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luaL_checkany(L, 1);
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lua_pushnil(L); /* value is not convertible to integer */
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luaL_pushfail(L); /* value is not convertible to integer */
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}
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return 1;
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}
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@ -239,22 +229,347 @@ static int math_max (lua_State *L) {
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return 1;
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}
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static int math_type (lua_State *L) {
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if (lua_type(L, 1) == LUA_TNUMBER)
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lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float");
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else {
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luaL_checkany(L, 1);
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luaL_pushfail(L);
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}
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return 1;
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}
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/*
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** {==================================================================
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** Pseudo-Random Number Generator based on 'xoshiro256**'.
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** ===================================================================
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*/
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/* number of binary digits in the mantissa of a float */
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#define FIGS l_floatatt(MANT_DIG)
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#if FIGS > 64
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/* there are only 64 random bits; use them all */
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#undef FIGS
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#define FIGS 64
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#endif
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/*
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** LUA_RAND32 forces the use of 32-bit integers in the implementation
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** of the PRN generator (mainly for testing).
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*/
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#if !defined(LUA_RAND32) && !defined(Rand64)
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/* try to find an integer type with at least 64 bits */
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#if (ULONG_MAX >> 31 >> 31) >= 3
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/* 'long' has at least 64 bits */
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#define Rand64 unsigned long
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#elif !defined(LUA_USE_C89) && defined(LLONG_MAX)
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/* there is a 'long long' type (which must have at least 64 bits) */
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#define Rand64 unsigned long long
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#elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3
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/* 'lua_Integer' has at least 64 bits */
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#define Rand64 lua_Unsigned
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#endif
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#endif
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#if defined(Rand64) /* { */
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/*
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** Standard implementation, using 64-bit integers.
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** If 'Rand64' has more than 64 bits, the extra bits do not interfere
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** with the 64 initial bits, except in a right shift. Moreover, the
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** final result has to discard the extra bits.
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*/
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/* avoid using extra bits when needed */
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#define trim64(x) ((x) & 0xffffffffffffffffu)
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/* rotate left 'x' by 'n' bits */
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static Rand64 rotl (Rand64 x, int n) {
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return (x << n) | (trim64(x) >> (64 - n));
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}
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static Rand64 nextrand (Rand64 *state) {
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Rand64 state0 = state[0];
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Rand64 state1 = state[1];
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Rand64 state2 = state[2] ^ state0;
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Rand64 state3 = state[3] ^ state1;
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Rand64 res = rotl(state1 * 5, 7) * 9;
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state[0] = state0 ^ state3;
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state[1] = state1 ^ state2;
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state[2] = state2 ^ (state1 << 17);
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state[3] = rotl(state3, 45);
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return res;
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}
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/* must take care to not shift stuff by more than 63 slots */
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/*
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** Convert bits from a random integer into a float in the
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** interval [0,1), getting the higher FIG bits from the
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** random unsigned integer and converting that to a float.
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*/
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/* must throw out the extra (64 - FIGS) bits */
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#define shift64_FIG (64 - FIGS)
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/* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */
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#define scaleFIG (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1)))
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static lua_Number I2d (Rand64 x) {
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return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG;
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}
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/* convert a 'Rand64' to a 'lua_Unsigned' */
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#define I2UInt(x) ((lua_Unsigned)trim64(x))
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/* convert a 'lua_Unsigned' to a 'Rand64' */
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#define Int2I(x) ((Rand64)(x))
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#else /* no 'Rand64' }{ */
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/* get an integer with at least 32 bits */
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#if LUAI_IS32INT
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typedef unsigned int lu_int32;
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#else
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typedef unsigned long lu_int32;
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#endif
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/*
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** This function uses 'double' (instead of 'lua_Number') to ensure that
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** all bits from 'l_rand' can be represented, and that 'RANDMAX + 1.0'
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** will keep full precision (ensuring that 'r' is always less than 1.0.)
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** Use two 32-bit integers to represent a 64-bit quantity.
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*/
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typedef struct Rand64 {
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lu_int32 h; /* higher half */
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lu_int32 l; /* lower half */
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} Rand64;
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/*
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** If 'lu_int32' has more than 32 bits, the extra bits do not interfere
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** with the 32 initial bits, except in a right shift and comparisons.
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** Moreover, the final result has to discard the extra bits.
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*/
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/* avoid using extra bits when needed */
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#define trim32(x) ((x) & 0xffffffffu)
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/*
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** basic operations on 'Rand64' values
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*/
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/* build a new Rand64 value */
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static Rand64 packI (lu_int32 h, lu_int32 l) {
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Rand64 result;
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result.h = h;
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result.l = l;
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return result;
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}
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/* return i << n */
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static Rand64 Ishl (Rand64 i, int n) {
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lua_assert(n > 0 && n < 32);
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return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n);
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}
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/* i1 ^= i2 */
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static void Ixor (Rand64 *i1, Rand64 i2) {
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i1->h ^= i2.h;
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i1->l ^= i2.l;
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}
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/* return i1 + i2 */
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static Rand64 Iadd (Rand64 i1, Rand64 i2) {
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Rand64 result = packI(i1.h + i2.h, i1.l + i2.l);
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if (trim32(result.l) < trim32(i1.l)) /* carry? */
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result.h++;
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return result;
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}
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/* return i * 5 */
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static Rand64 times5 (Rand64 i) {
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return Iadd(Ishl(i, 2), i); /* i * 5 == (i << 2) + i */
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}
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/* return i * 9 */
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static Rand64 times9 (Rand64 i) {
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return Iadd(Ishl(i, 3), i); /* i * 9 == (i << 3) + i */
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}
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/* return 'i' rotated left 'n' bits */
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static Rand64 rotl (Rand64 i, int n) {
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lua_assert(n > 0 && n < 32);
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return packI((i.h << n) | (trim32(i.l) >> (32 - n)),
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(trim32(i.h) >> (32 - n)) | (i.l << n));
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}
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/* for offsets larger than 32, rotate right by 64 - offset */
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static Rand64 rotl1 (Rand64 i, int n) {
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lua_assert(n > 32 && n < 64);
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n = 64 - n;
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return packI((trim32(i.h) >> n) | (i.l << (32 - n)),
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(i.h << (32 - n)) | (trim32(i.l) >> n));
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}
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/*
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** implementation of 'xoshiro256**' algorithm on 'Rand64' values
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*/
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static Rand64 nextrand (Rand64 *state) {
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Rand64 res = times9(rotl(times5(state[1]), 7));
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Rand64 t = Ishl(state[1], 17);
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Ixor(&state[2], state[0]);
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Ixor(&state[3], state[1]);
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Ixor(&state[1], state[2]);
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Ixor(&state[0], state[3]);
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Ixor(&state[2], t);
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state[3] = rotl1(state[3], 45);
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return res;
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}
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/*
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** Converts a 'Rand64' into a float.
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*/
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/* an unsigned 1 with proper type */
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#define UONE ((lu_int32)1)
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#if FIGS <= 32
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/* 2^(-FIGS) */
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#define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1)))
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/*
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** get up to 32 bits from higher half, shifting right to
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** throw out the extra bits.
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*/
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static lua_Number I2d (Rand64 x) {
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lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS));
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return h * scaleFIG;
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}
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#else /* 32 < FIGS <= 64 */
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/* must take care to not shift stuff by more than 31 slots */
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/* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */
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#define scaleFIG \
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((lua_Number)1.0 / (UONE << 30) / 8.0 / (UONE << (FIGS - 33)))
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/*
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** use FIGS - 32 bits from lower half, throwing out the other
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** (32 - (FIGS - 32)) = (64 - FIGS) bits
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*/
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#define shiftLOW (64 - FIGS)
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/*
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** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32)
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*/
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#define shiftHI ((lua_Number)(UONE << (FIGS - 33)) * 2.0)
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static lua_Number I2d (Rand64 x) {
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lua_Number h = (lua_Number)trim32(x.h) * shiftHI;
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lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW);
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return (h + l) * scaleFIG;
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}
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#endif
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/* convert a 'Rand64' to a 'lua_Unsigned' */
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static lua_Unsigned I2UInt (Rand64 x) {
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return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l);
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}
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/* convert a 'lua_Unsigned' to a 'Rand64' */
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static Rand64 Int2I (lua_Unsigned n) {
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return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n);
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}
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#endif /* } */
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/*
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** A state uses four 'Rand64' values.
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*/
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typedef struct {
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Rand64 s[4];
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} RanState;
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/*
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** Project the random integer 'ran' into the interval [0, n].
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** Because 'ran' has 2^B possible values, the projection can only be
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** uniform when the size of the interval is a power of 2 (exact
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** division). Otherwise, to get a uniform projection into [0, n], we
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** first compute 'lim', the smallest Mersenne number not smaller than
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** 'n'. We then project 'ran' into the interval [0, lim]. If the result
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** is inside [0, n], we are done. Otherwise, we try with another 'ran',
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** until we have a result inside the interval.
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*/
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static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
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RanState *state) {
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if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */
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return ran & n; /* no bias */
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else {
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lua_Unsigned lim = n;
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/* compute the smallest (2^b - 1) not smaller than 'n' */
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lim |= (lim >> 1);
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lim |= (lim >> 2);
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lim |= (lim >> 4);
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lim |= (lim >> 8);
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lim |= (lim >> 16);
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#if (LUA_MAXUNSIGNED >> 31) >= 3
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lim |= (lim >> 32); /* integer type has more than 32 bits */
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#endif
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lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2, */
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&& lim >= n /* not smaller than 'n', */
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&& (lim >> 1) < n); /* and it is the smallest one */
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while ((ran &= lim) > n) /* project 'ran' into [0..lim] */
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ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */
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return ran;
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}
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}
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static int math_random (lua_State *L) {
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lua_Integer low, up;
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double r = (double)l_rand() * (1.0 / ((double)L_RANDMAX + 1.0));
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lua_Unsigned p;
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RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
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Rand64 rv = nextrand(state->s); /* next pseudo-random value */
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switch (lua_gettop(L)) { /* check number of arguments */
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case 0: { /* no arguments */
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lua_pushnumber(L, (lua_Number)r); /* Number between 0 and 1 */
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lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */
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return 1;
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}
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case 1: { /* only upper limit */
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low = 1;
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up = luaL_checkinteger(L, 1);
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if (up == 0) { /* single 0 as argument? */
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lua_pushinteger(L, I2UInt(rv)); /* full random integer */
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return 1;
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}
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break;
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}
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case 2: { /* lower and upper limits */
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@ -266,35 +581,72 @@ static int math_random (lua_State *L) {
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}
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/* random integer in the interval [low, up] */
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luaL_argcheck(L, low <= up, 1, "interval is empty");
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luaL_argcheck(L, low >= 0 || up <= LUA_MAXINTEGER + low, 1,
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"interval too large");
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r *= (double)(up - low) + 1.0;
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lua_pushinteger(L, (lua_Integer)r + low);
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/* project random integer into the interval [0, up - low] */
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p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state);
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lua_pushinteger(L, p + (lua_Unsigned)low);
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return 1;
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}
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static int math_randomseed (lua_State *L) {
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l_srand((unsigned int)(lua_Integer)luaL_checknumber(L, 1));
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(void)l_rand(); /* discard first value to avoid undesirable correlations */
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return 0;
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static void setseed (lua_State *L, Rand64 *state,
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lua_Unsigned n1, lua_Unsigned n2) {
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int i;
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state[0] = Int2I(n1);
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state[1] = Int2I(0xff); /* avoid a zero state */
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state[2] = Int2I(n2);
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state[3] = Int2I(0);
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for (i = 0; i < 16; i++)
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nextrand(state); /* discard initial values to "spread" seed */
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lua_pushinteger(L, n1);
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lua_pushinteger(L, n2);
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}
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static int math_type (lua_State *L) {
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if (lua_type(L, 1) == LUA_TNUMBER) {
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if (lua_isinteger(L, 1))
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lua_pushliteral(L, "integer");
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else
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lua_pushliteral(L, "float");
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/*
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** Set a "random" seed. To get some randomness, use the current time
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** and the address of 'L' (in case the machine does address space layout
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** randomization).
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*/
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static void randseed (lua_State *L, RanState *state) {
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lua_Unsigned seed1 = (lua_Unsigned)time(NULL);
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lua_Unsigned seed2 = (lua_Unsigned)(size_t)L;
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setseed(L, state->s, seed1, seed2);
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}
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static int math_randomseed (lua_State *L) {
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RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
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if (lua_isnone(L, 1)) {
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randseed(L, state);
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}
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else {
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luaL_checkany(L, 1);
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lua_pushnil(L);
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lua_Integer n1 = luaL_checkinteger(L, 1);
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lua_Integer n2 = luaL_optinteger(L, 2, 0);
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|
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setseed(L, state->s, n1, n2);
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|
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}
|
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|
|
return 1;
|
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|
|
return 2; /* return seeds */
|
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|
|
}
|
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|
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static const luaL_Reg randfuncs[] = {
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|
|
{"random", math_random},
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|
|
{"randomseed", math_randomseed},
|
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|
|
{NULL, NULL}
|
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|
|
};
|
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|
|
/*
|
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|
|
|
** Register the random functions and initialize their state.
|
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|
|
*/
|
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|
|
static void setrandfunc (lua_State *L) {
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RanState *state = (RanState *)lua_newuserdata(L, sizeof(RanState));
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randseed(L, state); /* initialize with a "random" seed */
|
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lua_pop(L, 2); /* remove pushed seeds */
|
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|
|
luaL_setfuncs(L, randfuncs, 1);
|
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|
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}
|
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|
|
/* }================================================================== */
|
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|
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|
|
/*
|
|
|
|
|
** {==================================================================
|
|
|
|
|
@ -367,8 +719,6 @@ static const luaL_Reg mathlib[] = {
|
|
|
|
|
{"min", math_min},
|
|
|
|
|
{"modf", math_modf},
|
|
|
|
|
{"rad", math_rad},
|
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|
|
{"random", math_random},
|
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|
|
{"randomseed", math_randomseed},
|
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|
|
{"sin", math_sin},
|
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|
|
{"sqrt", math_sqrt},
|
|
|
|
|
{"tan", math_tan},
|
|
|
|
|
@ -384,6 +734,8 @@ static const luaL_Reg mathlib[] = {
|
|
|
|
|
{"log10", math_log10},
|
|
|
|
|
#endif
|
|
|
|
|
/* placeholders */
|
|
|
|
|
{"random", NULL},
|
|
|
|
|
{"randomseed", NULL},
|
|
|
|
|
{"pi", NULL},
|
|
|
|
|
{"huge", NULL},
|
|
|
|
|
{"maxinteger", NULL},
|
|
|
|
|
@ -405,6 +757,7 @@ LUAMOD_API int luaopen_math (lua_State *L) {
|
|
|
|
|
lua_setfield(L, -2, "maxinteger");
|
|
|
|
|
lua_pushinteger(L, LUA_MININTEGER);
|
|
|
|
|
lua_setfield(L, -2, "mininteger");
|
|
|
|
|
setrandfunc(L);
|
|
|
|
|
return 1;
|
|
|
|
|
}
|
|
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Dibyendu Majumdar
4 years ago