/*
** $Id: lmathlib.c,v 1.127 2018/03/22 19:54:49 roberto Exp roberto $
** 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 "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);
lua_pushnil(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) {
if (lua_isinteger(L, 1))
lua_pushliteral(L, "integer");
else
lua_pushliteral(L, "float");
}
else {
luaL_checkany(L, 1);
lua_pushnil(L);
}
return 1;
}
/*
** {==================================================================
** Pseudo-Random Number Generator based on 'xorshift128+'.
** ===================================================================
*/
/* number of binary digits in the mantissa of a float */
#define FIGS l_mathlim(MANT_DIG)
#if FIGS > 64
/* there are only 64 random bits; use them all */
#undef FIGS
#define FIGS 64
#endif
#if !defined(LUA_USE_C89) && defined(LLONG_MAX) && !defined(LUA_DEBUG) /* { */
/*
** Assume long long.
*/
/* a 64-bit value */
typedef unsigned long long I;
static I xorshift128plus (I *state) {
I x = state[0];
I y = state[1];
state[0] = y;
x ^= x << 23;
state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5));
return state[1] + y;
}
/* must take care to not shift stuff by more than 63 slots */
#define shiftI (64 - FIGS) /* leave FIGS bits */
#define shiftF (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIG) */
/*
** Convert bits from a random integer into a float in the
** interval [0,1).
*/
static lua_Number I2d (I x) {
return (lua_Number)(x >> shiftI) * shiftF;
}
/* convert an 'I' to a lua_Unsigned (using higher bits) */
#define I2UInt(x) ((lua_Unsigned)((x) >> (64 - LUA_UNSIGNEDBITS)))
/* convert a lua_Integer to an 'I' */
#define Int2I(x) ((I)(x))
#else /* no long long }{ */
/*
** Use two 32-bit integers to represent a 64-bit quantity.
*/
#if LUAI_BITSINT >= 32
typedef unsigned int lu_int32;
#else
typedef unsigned long lu_int32;
#endif
/* a 64-bit value */
typedef struct I {
lu_int32 h; /* higher half */
lu_int32 l; /* lower half */
} I;
/*
** basic operations on 'I' values
*/
static I packI (lu_int32 h, lu_int32 l) {
I result;
result.h = h;
result.l = l;
return result;
}
/* i ^ (i << n) */
static I Ixorshl (I i, int n) {
return packI(i.h ^ ((i.h << n) | (i.l >> (32 - n))), i.l ^ (i.l << n));
}
/* i ^ (i >> n) */
static I Ixorshr (I i, int n) {
return packI(i.h ^ (i.h >> n), i.l ^ ((i.l >> n) | (i.h << (32 - n))));
}
static I Ixor (I i1, I i2) {
return packI(i1.h ^ i2.h, i1.l ^ i2.l);
}
static I Iadd (I i1, I i2) {
I result = packI(i1.h + i2.h, i1.l + i2.l);
if (result.l < i1.l) /* carry? */
result.h++;
return result;
}
/*
** implementation of 'xorshift128+' algorithm on 'I' values
*/
static I xorshift128plus (I *state) {
I x = state[0];
I y = state[1];
state[0] = y;
x = Ixorshl(x, 23); /* x ^= x << 23; */
/* state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5)); */
state[1] = Ixor(Ixorshr(x, 18), Ixorshr(y, 5));
return Iadd(state[1], y); /* return state[1] + y; */
}
/*
** Converts an 'I' into a float.
*/
/* an unsigned 1 with proper type */
#define UONE ((lu_int32)1)
#if FIGS <= 32
#define maskLOW 0 /* do not need bits from lower half */
#define maskHI (~(~(lu_int32)0 >> (FIGS - 1) >> 1)) /* use FIGS bits */
#define shiftHI 1 /* no shift */
#define shiftF (1 / l_mathop(4294967296.0)) /* 2^(-32) */
#else /* 32 < FIGS <= 64 */
/* must take care to not shift stuff by more than 31 slots */
/* use FIGS - 32 bits from lower half */
#define maskLOW (~(~(lu_int32)0 >> (FIGS - 33) >> 1))
/* use all bits from higher half */
#define maskHI (~(lu_int32)0)
#define shiftHI l_mathop(4294967296.0) /* 2^32 */
/* 2^(-64) */
#define shiftF ((lua_Number)(1 / (shiftHI * shiftHI)))
#endif
static lua_Number I2d (I x) {
lua_Number h = (lua_Number)(x.h & maskHI);
lua_Number l = (lua_Number)(x.l & maskLOW);
return (h * shiftHI + l) * shiftF;
}
static lua_Unsigned I2UInt (I x) {
#if (LUA_MAXINTEGER >> 30) <= 1
/* at most 32 bits; use only high bits */
return ((lua_Unsigned)x.h);
#else
/* at least 33 bits */
return ((lua_Unsigned)x.h << (LUA_UNSIGNEDBITS - 32)) |
(lua_Unsigned)x.l >> (64 - LUA_UNSIGNEDBITS);
#endif
}
static I Int2I (lua_Unsigned n) {
return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0);
}
#endif /* } */
/*
** A state uses two 'I' values.
*/
typedef struct {
I s[2];
} RanState;
/*
** Return the higher bit set in 'x' (first bit is 1).
*/
static int higherbit (lua_Unsigned x) {
/* table of higher bits from 0 to 255 */
static const unsigned char hb[256] = {
0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
};
int l = 0;
while (x >= 256) { l += 8; x >>= 8; }
return l + hb[x];
}
/*
** Project the random integer 'ran' into the interval [0, n].
** To get a uniform projection into [0,n], we first compute 'shf', the
** largest number that we can right-shift 'ran' and still get numbers
** as larger as 'n'. We then shift 'ran'; if the result is inside [0, n],
** we are done. Otherwise, we try with another 'ran' until we have a
** result inside the interval. (We use right shifts to avoid the lowest
** bits of 'ran', which has poorer distributions.)
*/
static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
RanState *state) {
if (n == 0) return 0; /* special case for the unit set */
else {
int shf = LUA_UNSIGNEDBITS - higherbit(n);
lua_assert(~(lua_Unsigned)0 >> shf >= n && /* not larger */
~(lua_Unsigned)0 >> shf >> 1 < n); /* largest */
while ((ran >>= shf) > n)
ran = I2UInt(xorshift128plus(state->s));
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));
I rv = xorshift128plus(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 (I *state, lua_Unsigned n) {
int i;
state[0] = Int2I(n);
state[1] = Int2I(0xff); /* avoid a zero state */
for (i = 0; i < 16; i++)
xorshift128plus(state); /* discard initial values to "spread" seed */
}
static int math_randomseed (lua_State *L) {
RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
lua_Integer n = luaL_checkinteger(L, 1);
setseed(state->s, n);
return 0;
}
static const luaL_Reg randfuncs[] = {
{"random", math_random},
{"randomseed", math_randomseed},
{NULL, NULL}
};
static void setrandfunc (lua_State *L) {
RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0);
setseed(state->s, 0);
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;
}