# lmathlib.c (5.4.6)

```/*
** \$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 (l_likely(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_Unsigned' 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  \
(l_mathop(1.0) / (UONE << 30) / l_mathop(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)) * l_mathop(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++)
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},
{"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;
}

```