text: /*
  ** $Id: lmathlib.c,v 1.119.1.1 2017/04/19 17:20:42 roberto Exp $
  ** Standard mathematical library
  ** See Copyright Notice in lua.h
  */
  
  #define lmathlib_c
  #define LUA_LIB
  
  #include "lprefix.h"
  
  
  #include <stdlib.h>
  #include <math.h>
  
  #include "lua.h"
  
  #include "lauxlib.h"
  #include "lualib.h"
  
  
  #undef PI
  #define PI	(l_mathop(3.141592653589793238462643383279502884))
  
  
  #if !defined(l_rand)		/* { */
  #if defined(LUA_USE_POSIX)
  #define l_rand()	random()
  #define l_srand(x)	srandom(x)
  #define L_RANDMAX	2147483647	/* (2^31 - 1), following POSIX */
  #else
  #define l_rand()	rand()
  #define l_srand(x)	srand(x)
  #define L_RANDMAX	RAND_MAX
  #endif
  #endif				/* } */
  
  
  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;
  }
  
  /*
  ** This function uses 'double' (instead of 'lua_Number') to ensure that
  ** all bits from 'l_rand' can be represented, and that 'RANDMAX + 1.0'
  ** will keep full precision (ensuring that 'r' is always less than 1.0.)
  */
  static int math_random (lua_State *L) {
    lua_Integer low, up;
    double r = (double)l_rand() * (1.0 / ((double)L_RANDMAX + 1.0));
    switch (lua_gettop(L)) {  /* check number of arguments */
      case 0: {  /* no arguments */
        lua_pushnumber(L, (lua_Number)r);  /* Number between 0 and 1 */
        return 1;
      }
      case 1: {  /* only upper limit */
        low = 1;
        up = luaL_checkinteger(L, 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");
    luaL_argcheck(L, low >= 0 || up <= LUA_MAXINTEGER + low, 1,
                     "interval too large");
    r *= (double)(up - low) + 1.0;
    lua_pushinteger(L, (lua_Integer)r + low);
    return 1;
  }
  
  
  static int math_randomseed (lua_State *L) {
    l_srand((unsigned int)(lua_Integer)luaL_checknumber(L, 1));
    (void)l_rand(); /* discard first value to avoid undesirable correlations */
    return 0;
  }
  
  
  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;
  }
  
  
  /*
  ** {==================================================================
  ** 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},
    {"random",     math_random},
    {"randomseed", math_randomseed},
    {"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 */
    {"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");
    return 1;
  }
  
  