765 lines
18 KiB
C
765 lines
18 KiB
C
/*
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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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#define lmathlib_c
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#define LUA_LIB
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#include "lprefix.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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#include "lauxlib.h"
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#include "lualib.h"
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#undef PI
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#define PI (l_mathop(3.141592653589793238462643383279502884))
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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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if (n < 0) n = (lua_Integer)(0u - (lua_Unsigned)n);
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lua_pushinteger(L, n);
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}
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else
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lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_sin (lua_State *L) {
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lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_cos (lua_State *L) {
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lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_tan (lua_State *L) {
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lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_asin (lua_State *L) {
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lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_acos (lua_State *L) {
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lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_atan (lua_State *L) {
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lua_Number y = luaL_checknumber(L, 1);
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lua_Number x = luaL_optnumber(L, 2, 1);
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lua_pushnumber(L, l_mathop(atan2)(y, x));
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return 1;
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}
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static int math_toint (lua_State *L) {
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int valid;
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lua_Integer n = lua_tointegerx(L, 1, &valid);
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if (l_likely(valid))
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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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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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static void pushnumint (lua_State *L, lua_Number d) {
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lua_Integer n;
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if (lua_numbertointeger(d, &n)) /* does 'd' fit in an integer? */
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lua_pushinteger(L, n); /* result is integer */
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else
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lua_pushnumber(L, d); /* result is float */
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}
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static int math_floor (lua_State *L) {
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if (lua_isinteger(L, 1))
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lua_settop(L, 1); /* integer is its own floor */
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else {
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lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1));
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pushnumint(L, d);
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}
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return 1;
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}
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static int math_ceil (lua_State *L) {
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if (lua_isinteger(L, 1))
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lua_settop(L, 1); /* integer is its own ceil */
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else {
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lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1));
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pushnumint(L, d);
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}
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return 1;
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}
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static int math_fmod (lua_State *L) {
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if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) {
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lua_Integer d = lua_tointeger(L, 2);
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if ((lua_Unsigned)d + 1u <= 1u) { /* special cases: -1 or 0 */
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luaL_argcheck(L, d != 0, 2, "zero");
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lua_pushinteger(L, 0); /* avoid overflow with 0x80000... / -1 */
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}
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else
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lua_pushinteger(L, lua_tointeger(L, 1) % d);
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}
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else
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lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1),
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luaL_checknumber(L, 2)));
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return 1;
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}
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/*
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** next function does not use 'modf', avoiding problems with 'double*'
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** (which is not compatible with 'float*') when lua_Number is not
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** 'double'.
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*/
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static int math_modf (lua_State *L) {
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if (lua_isinteger(L ,1)) {
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lua_settop(L, 1); /* number is its own integer part */
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lua_pushnumber(L, 0); /* no fractional part */
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}
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else {
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lua_Number n = luaL_checknumber(L, 1);
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/* integer part (rounds toward zero) */
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lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n);
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pushnumint(L, ip);
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/* fractional part (test needed for inf/-inf) */
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lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip));
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}
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return 2;
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}
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static int math_sqrt (lua_State *L) {
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lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_ult (lua_State *L) {
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lua_Integer a = luaL_checkinteger(L, 1);
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lua_Integer b = luaL_checkinteger(L, 2);
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lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b);
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return 1;
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}
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static int math_log (lua_State *L) {
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lua_Number x = luaL_checknumber(L, 1);
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lua_Number res;
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if (lua_isnoneornil(L, 2))
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res = l_mathop(log)(x);
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else {
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lua_Number base = luaL_checknumber(L, 2);
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#if !defined(LUA_USE_C89)
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if (base == l_mathop(2.0))
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res = l_mathop(log2)(x);
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else
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#endif
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if (base == l_mathop(10.0))
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res = l_mathop(log10)(x);
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else
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res = l_mathop(log)(x)/l_mathop(log)(base);
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}
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lua_pushnumber(L, res);
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return 1;
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}
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static int math_exp (lua_State *L) {
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lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1)));
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return 1;
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}
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static int math_deg (lua_State *L) {
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lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI));
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return 1;
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}
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static int math_rad (lua_State *L) {
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lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0)));
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return 1;
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}
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static int math_min (lua_State *L) {
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int n = lua_gettop(L); /* number of arguments */
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int imin = 1; /* index of current minimum value */
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int i;
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luaL_argcheck(L, n >= 1, 1, "value expected");
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for (i = 2; i <= n; i++) {
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if (lua_compare(L, i, imin, LUA_OPLT))
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imin = i;
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}
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lua_pushvalue(L, imin);
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return 1;
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}
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static int math_max (lua_State *L) {
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int n = lua_gettop(L); /* number of arguments */
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int imax = 1; /* index of current maximum value */
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int i;
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luaL_argcheck(L, n >= 1, 1, "value expected");
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for (i = 2; i <= n; i++) {
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if (lua_compare(L, imax, i, LUA_OPLT))
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imax = i;
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}
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lua_pushvalue(L, imax);
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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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** 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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(l_mathop(1.0) / (UONE << 30) / l_mathop(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)) * l_mathop(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.
|
|
*/
|
|
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;
|
|
}
|
|
|