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    1 /*
    2 ** $Id: lmathlib.c $
    3 ** Standard mathematical library
    4 ** See Copyright Notice in lua.h
    5 */
    6 
    7 #define lmathlib_c
    8 #define LUA_LIB
    9 
   10 #include "lprefix.h"
   11 
   12 
   13 #include <float.h>
   14 #include <limits.h>
   15 #include <math.h>
   16 #include <stdlib.h>
   17 #include <time.h>
   18 
   19 #include "lua.h"
   20 
   21 #include "lauxlib.h"
   22 #include "lualib.h"
   23 
   24 
   25 #undef PI
   26 #define PI  (l_mathop(3.141592653589793238462643383279502884))
   27 
   28 
   29 static int math_abs (lua_State *L) {
   30   if (lua_isinteger(L, 1)) {
   31     lua_Integer n = lua_tointeger(L, 1);
   32     if (n < 0) n = (lua_Integer)(0u - (lua_Unsigned)n);
   33     lua_pushinteger(L, n);
   34   }
   35   else
   36     lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1)));
   37   return 1;
   38 }
   39 
   40 static int math_sin (lua_State *L) {
   41   lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1)));
   42   return 1;
   43 }
   44 
   45 static int math_cos (lua_State *L) {
   46   lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1)));
   47   return 1;
   48 }
   49 
   50 static int math_tan (lua_State *L) {
   51   lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1)));
   52   return 1;
   53 }
   54 
   55 static int math_asin (lua_State *L) {
   56   lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1)));
   57   return 1;
   58 }
   59 
   60 static int math_acos (lua_State *L) {
   61   lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1)));
   62   return 1;
   63 }
   64 
   65 static int math_atan (lua_State *L) {
   66   lua_Number y = luaL_checknumber(L, 1);
   67   lua_Number x = luaL_optnumber(L, 2, 1);
   68   lua_pushnumber(L, l_mathop(atan2)(y, x));
   69   return 1;
   70 }
   71 
   72 
   73 static int math_toint (lua_State *L) {
   74   int valid;
   75   lua_Integer n = lua_tointegerx(L, 1, &valid);
   76   if (l_likely(valid))
   77     lua_pushinteger(L, n);
   78   else {
   79     luaL_checkany(L, 1);
   80     luaL_pushfail(L);  /* value is not convertible to integer */
   81   }
   82   return 1;
   83 }
   84 
   85 
   86 static void pushnumint (lua_State *L, lua_Number d) {
   87   lua_Integer n;
   88   if (lua_numbertointeger(d, &n))  /* does 'd' fit in an integer? */
   89     lua_pushinteger(L, n);  /* result is integer */
   90   else
   91     lua_pushnumber(L, d);  /* result is float */
   92 }
   93 
   94 
   95 static int math_floor (lua_State *L) {
   96   if (lua_isinteger(L, 1))
   97     lua_settop(L, 1);  /* integer is its own floor */
   98   else {
   99     lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1));
  100     pushnumint(L, d);
  101   }
  102   return 1;
  103 }
  104 
  105 
  106 static int math_ceil (lua_State *L) {
  107   if (lua_isinteger(L, 1))
  108     lua_settop(L, 1);  /* integer is its own ceil */
  109   else {
  110     lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1));
  111     pushnumint(L, d);
  112   }
  113   return 1;
  114 }
  115 
  116 
  117 static int math_fmod (lua_State *L) {
  118   if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) {
  119     lua_Integer d = lua_tointeger(L, 2);
  120     if ((lua_Unsigned)d + 1u <= 1u) {  /* special cases: -1 or 0 */
  121       luaL_argcheck(L, d != 0, 2, "zero");
  122       lua_pushinteger(L, 0);  /* avoid overflow with 0x80000... / -1 */
  123     }
  124     else
  125       lua_pushinteger(L, lua_tointeger(L, 1) % d);
  126   }
  127   else
  128     lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1),
  129                                      luaL_checknumber(L, 2)));
  130   return 1;
  131 }
  132 
  133 
  134 /*
  135 ** next function does not use 'modf', avoiding problems with 'double*'
  136 ** (which is not compatible with 'float*') when lua_Number is not
  137 ** 'double'.
  138 */
  139 static int math_modf (lua_State *L) {
  140   if (lua_isinteger(L ,1)) {
  141     lua_settop(L, 1);  /* number is its own integer part */
  142     lua_pushnumber(L, 0);  /* no fractional part */
  143   }
  144   else {
  145     lua_Number n = luaL_checknumber(L, 1);
  146     /* integer part (rounds toward zero) */
  147     lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n);
  148     pushnumint(L, ip);
  149     /* fractional part (test needed for inf/-inf) */
  150     lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip));
  151   }
  152   return 2;
  153 }
  154 
  155 
  156 static int math_sqrt (lua_State *L) {
  157   lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1)));
  158   return 1;
  159 }
  160 
  161 
  162 static int math_ult (lua_State *L) {
  163   lua_Integer a = luaL_checkinteger(L, 1);
  164   lua_Integer b = luaL_checkinteger(L, 2);
  165   lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b);
  166   return 1;
  167 }
  168 
  169 static int math_log (lua_State *L) {
  170   lua_Number x = luaL_checknumber(L, 1);
  171   lua_Number res;
  172   if (lua_isnoneornil(L, 2))
  173     res = l_mathop(log)(x);
  174   else {
  175     lua_Number base = luaL_checknumber(L, 2);
  176 #if !defined(LUA_USE_C89)
  177     if (base == l_mathop(2.0))
  178       res = l_mathop(log2)(x);
  179     else
  180 #endif
  181     if (base == l_mathop(10.0))
  182       res = l_mathop(log10)(x);
  183     else
  184       res = l_mathop(log)(x)/l_mathop(log)(base);
  185   }
  186   lua_pushnumber(L, res);
  187   return 1;
  188 }
  189 
  190 static int math_exp (lua_State *L) {
  191   lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1)));
  192   return 1;
  193 }
  194 
  195 static int math_deg (lua_State *L) {
  196   lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI));
  197   return 1;
  198 }
  199 
  200 static int math_rad (lua_State *L) {
  201   lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0)));
  202   return 1;
  203 }
  204 
  205 
  206 static int math_min (lua_State *L) {
  207   int n = lua_gettop(L);  /* number of arguments */
  208   int imin = 1;  /* index of current minimum value */
  209   int i;
  210   luaL_argcheck(L, n >= 1, 1, "value expected");
  211   for (i = 2; i <= n; i++) {
  212     if (lua_compare(L, i, imin, LUA_OPLT))
  213       imin = i;
  214   }
  215   lua_pushvalue(L, imin);
  216   return 1;
  217 }
  218 
  219 
  220 static int math_max (lua_State *L) {
  221   int n = lua_gettop(L);  /* number of arguments */
  222   int imax = 1;  /* index of current maximum value */
  223   int i;
  224   luaL_argcheck(L, n >= 1, 1, "value expected");
  225   for (i = 2; i <= n; i++) {
  226     if (lua_compare(L, imax, i, LUA_OPLT))
  227       imax = i;
  228   }
  229   lua_pushvalue(L, imax);
  230   return 1;
  231 }
  232 
  233 
  234 static int math_type (lua_State *L) {
  235   if (lua_type(L, 1) == LUA_TNUMBER)
  236     lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float");
  237   else {
  238     luaL_checkany(L, 1);
  239     luaL_pushfail(L);
  240   }
  241   return 1;
  242 }
  243 
  244 
  245 
  246 /*
  247 ** {==================================================================
  248 ** Pseudo-Random Number Generator based on 'xoshiro256**'.
  249 ** ===================================================================
  250 */
  251 
  252 /* number of binary digits in the mantissa of a float */
  253 #define FIGS    l_floatatt(MANT_DIG)
  254 
  255 #if FIGS > 64
  256 /* there are only 64 random bits; use them all */
  257 #undef FIGS
  258 #define FIGS    64
  259 #endif
  260 
  261 
  262 /*
  263 ** LUA_RAND32 forces the use of 32-bit integers in the implementation
  264 ** of the PRN generator (mainly for testing).
  265 */
  266 #if !defined(LUA_RAND32) && !defined(Rand64)
  267 
  268 /* try to find an integer type with at least 64 bits */
  269 
  270 #if (ULONG_MAX >> 31 >> 31) >= 3
  271 
  272 /* 'long' has at least 64 bits */
  273 #define Rand64      unsigned long
  274 
  275 #elif !defined(LUA_USE_C89) && defined(LLONG_MAX)
  276 
  277 /* there is a 'long long' type (which must have at least 64 bits) */
  278 #define Rand64      unsigned long long
  279 
  280 #elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3
  281 
  282 /* 'lua_Integer' has at least 64 bits */
  283 #define Rand64      lua_Unsigned
  284 
  285 #endif
  286 
  287 #endif
  288 
  289 
  290 #if defined(Rand64)  /* { */
  291 
  292 /*
  293 ** Standard implementation, using 64-bit integers.
  294 ** If 'Rand64' has more than 64 bits, the extra bits do not interfere
  295 ** with the 64 initial bits, except in a right shift. Moreover, the
  296 ** final result has to discard the extra bits.
  297 */
  298 
  299 /* avoid using extra bits when needed */
  300 #define trim64(x)   ((x) & 0xffffffffffffffffu)
  301 
  302 
  303 /* rotate left 'x' by 'n' bits */
  304 static Rand64 rotl (Rand64 x, int n) {
  305   return (x << n) | (trim64(x) >> (64 - n));
  306 }
  307 
  308 static Rand64 nextrand (Rand64 *state) {
  309   Rand64 state0 = state[0];
  310   Rand64 state1 = state[1];
  311   Rand64 state2 = state[2] ^ state0;
  312   Rand64 state3 = state[3] ^ state1;
  313   Rand64 res = rotl(state1 * 5, 7) * 9;
  314   state[0] = state0 ^ state3;
  315   state[1] = state1 ^ state2;
  316   state[2] = state2 ^ (state1 << 17);
  317   state[3] = rotl(state3, 45);
  318   return res;
  319 }
  320 
  321 
  322 /* must take care to not shift stuff by more than 63 slots */
  323 
  324 
  325 /*
  326 ** Convert bits from a random integer into a float in the
  327 ** interval [0,1), getting the higher FIG bits from the
  328 ** random unsigned integer and converting that to a float.
  329 */
  330 
  331 /* must throw out the extra (64 - FIGS) bits */
  332 #define shift64_FIG (64 - FIGS)
  333 
  334 /* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */
  335 #define scaleFIG    (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1)))
  336 
  337 static lua_Number I2d (Rand64 x) {
  338   return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG;
  339 }
  340 
  341 /* convert a 'Rand64' to a 'lua_Unsigned' */
  342 #define I2UInt(x)   ((lua_Unsigned)trim64(x))
  343 
  344 /* convert a 'lua_Unsigned' to a 'Rand64' */
  345 #define Int2I(x)    ((Rand64)(x))
  346 
  347 
  348 #else   /* no 'Rand64'   }{ */
  349 
  350 /* get an integer with at least 32 bits */
  351 #if LUAI_IS32INT
  352 typedef unsigned int lu_int32;
  353 #else
  354 typedef unsigned long lu_int32;
  355 #endif
  356 
  357 
  358 /*
  359 ** Use two 32-bit integers to represent a 64-bit quantity.
  360 */
  361 typedef struct Rand64 {
  362   lu_int32 h;  /* higher half */
  363   lu_int32 l;  /* lower half */
  364 } Rand64;
  365 
  366 
  367 /*
  368 ** If 'lu_int32' has more than 32 bits, the extra bits do not interfere
  369 ** with the 32 initial bits, except in a right shift and comparisons.
  370 ** Moreover, the final result has to discard the extra bits.
  371 */
  372 
  373 /* avoid using extra bits when needed */
  374 #define trim32(x)   ((x) & 0xffffffffu)
  375 
  376 
  377 /*
  378 ** basic operations on 'Rand64' values
  379 */
  380 
  381 /* build a new Rand64 value */
  382 static Rand64 packI (lu_int32 h, lu_int32 l) {
  383   Rand64 result;
  384   result.h = h;
  385   result.l = l;
  386   return result;
  387 }
  388 
  389 /* return i << n */
  390 static Rand64 Ishl (Rand64 i, int n) {
  391   lua_assert(n > 0 && n < 32);
  392   return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n);
  393 }
  394 
  395 /* i1 ^= i2 */
  396 static void Ixor (Rand64 *i1, Rand64 i2) {
  397   i1->h ^= i2.h;
  398   i1->l ^= i2.l;
  399 }
  400 
  401 /* return i1 + i2 */
  402 static Rand64 Iadd (Rand64 i1, Rand64 i2) {
  403   Rand64 result = packI(i1.h + i2.h, i1.l + i2.l);
  404   if (trim32(result.l) < trim32(i1.l))  /* carry? */
  405     result.h++;
  406   return result;
  407 }
  408 
  409 /* return i * 5 */
  410 static Rand64 times5 (Rand64 i) {
  411   return Iadd(Ishl(i, 2), i);  /* i * 5 == (i << 2) + i */
  412 }
  413 
  414 /* return i * 9 */
  415 static Rand64 times9 (Rand64 i) {
  416   return Iadd(Ishl(i, 3), i);  /* i * 9 == (i << 3) + i */
  417 }
  418 
  419 /* return 'i' rotated left 'n' bits */
  420 static Rand64 rotl (Rand64 i, int n) {
  421   lua_assert(n > 0 && n < 32);
  422   return packI((i.h << n) | (trim32(i.l) >> (32 - n)),
  423                (trim32(i.h) >> (32 - n)) | (i.l << n));
  424 }
  425 
  426 /* for offsets larger than 32, rotate right by 64 - offset */
  427 static Rand64 rotl1 (Rand64 i, int n) {
  428   lua_assert(n > 32 && n < 64);
  429   n = 64 - n;
  430   return packI((trim32(i.h) >> n) | (i.l << (32 - n)),
  431                (i.h << (32 - n)) | (trim32(i.l) >> n));
  432 }
  433 
  434 /*
  435 ** implementation of 'xoshiro256**' algorithm on 'Rand64' values
  436 */
  437 static Rand64 nextrand (Rand64 *state) {
  438   Rand64 res = times9(rotl(times5(state[1]), 7));
  439   Rand64 t = Ishl(state[1], 17);
  440   Ixor(&state[2], state[0]);
  441   Ixor(&state[3], state[1]);
  442   Ixor(&state[1], state[2]);
  443   Ixor(&state[0], state[3]);
  444   Ixor(&state[2], t);
  445   state[3] = rotl1(state[3], 45);
  446   return res;
  447 }
  448 
  449 
  450 /*
  451 ** Converts a 'Rand64' into a float.
  452 */
  453 
  454 /* an unsigned 1 with proper type */
  455 #define UONE        ((lu_int32)1)
  456 
  457 
  458 #if FIGS <= 32
  459 
  460 /* 2^(-FIGS) */
  461 #define scaleFIG       (l_mathop(0.5) / (UONE << (FIGS - 1)))
  462 
  463 /*
  464 ** get up to 32 bits from higher half, shifting right to
  465 ** throw out the extra bits.
  466 */
  467 static lua_Number I2d (Rand64 x) {
  468   lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS));
  469   return h * scaleFIG;
  470 }
  471 
  472 #else   /* 32 < FIGS <= 64 */
  473 
  474 /* must take care to not shift stuff by more than 31 slots */
  475 
  476 /* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */
  477 #define scaleFIG  \
  478     ((lua_Number)1.0 / (UONE << 30) / 8.0 / (UONE << (FIGS - 33)))
  479 
  480 /*
  481 ** use FIGS - 32 bits from lower half, throwing out the other
  482 ** (32 - (FIGS - 32)) = (64 - FIGS) bits
  483 */
  484 #define shiftLOW    (64 - FIGS)
  485 
  486 /*
  487 ** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32)
  488 */
  489 #define shiftHI     ((lua_Number)(UONE << (FIGS - 33)) * 2.0)
  490 
  491 
  492 static lua_Number I2d (Rand64 x) {
  493   lua_Number h = (lua_Number)trim32(x.h) * shiftHI;
  494   lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW);
  495   return (h + l) * scaleFIG;
  496 }
  497 
  498 #endif
  499 
  500 
  501 /* convert a 'Rand64' to a 'lua_Unsigned' */
  502 static lua_Unsigned I2UInt (Rand64 x) {
  503   return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l);
  504 }
  505 
  506 /* convert a 'lua_Unsigned' to a 'Rand64' */
  507 static Rand64 Int2I (lua_Unsigned n) {
  508   return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n);
  509 }
  510 
  511 #endif  /* } */
  512 
  513 
  514 /*
  515 ** A state uses four 'Rand64' values.
  516 */
  517 typedef struct {
  518   Rand64 s[4];
  519 } RanState;
  520 
  521 
  522 /*
  523 ** Project the random integer 'ran' into the interval [0, n].
  524 ** Because 'ran' has 2^B possible values, the projection can only be
  525 ** uniform when the size of the interval is a power of 2 (exact
  526 ** division). Otherwise, to get a uniform projection into [0, n], we
  527 ** first compute 'lim', the smallest Mersenne number not smaller than
  528 ** 'n'. We then project 'ran' into the interval [0, lim].  If the result
  529 ** is inside [0, n], we are done. Otherwise, we try with another 'ran',
  530 ** until we have a result inside the interval.
  531 */
  532 static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
  533                              RanState *state) {
  534   if ((n & (n + 1)) == 0)  /* is 'n + 1' a power of 2? */
  535     return ran & n;  /* no bias */
  536   else {
  537     lua_Unsigned lim = n;
  538     /* compute the smallest (2^b - 1) not smaller than 'n' */
  539     lim |= (lim >> 1);
  540     lim |= (lim >> 2);
  541     lim |= (lim >> 4);
  542     lim |= (lim >> 8);
  543     lim |= (lim >> 16);
  544 #if (LUA_MAXUNSIGNED >> 31) >= 3
  545     lim |= (lim >> 32);  /* integer type has more than 32 bits */
  546 #endif
  547     lua_assert((lim & (lim + 1)) == 0  /* 'lim + 1' is a power of 2, */
  548       && lim >= n  /* not smaller than 'n', */
  549       && (lim >> 1) < n);  /* and it is the smallest one */
  550     while ((ran &= lim) > n)  /* project 'ran' into [0..lim] */
  551       ran = I2UInt(nextrand(state->s));  /* not inside [0..n]? try again */
  552     return ran;
  553   }
  554 }
  555 
  556 
  557 static int math_random (lua_State *L) {
  558   lua_Integer low, up;
  559   lua_Unsigned p;
  560   RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
  561   Rand64 rv = nextrand(state->s);  /* next pseudo-random value */
  562   switch (lua_gettop(L)) {  /* check number of arguments */
  563     case 0: {  /* no arguments */
  564       lua_pushnumber(L, I2d(rv));  /* float between 0 and 1 */
  565       return 1;
  566     }
  567     case 1: {  /* only upper limit */
  568       low = 1;
  569       up = luaL_checkinteger(L, 1);
  570       if (up == 0) {  /* single 0 as argument? */
  571         lua_pushinteger(L, I2UInt(rv));  /* full random integer */
  572         return 1;
  573       }
  574       break;
  575     }
  576     case 2: {  /* lower and upper limits */
  577       low = luaL_checkinteger(L, 1);
  578       up = luaL_checkinteger(L, 2);
  579       break;
  580     }
  581     default: return luaL_error(L, "wrong number of arguments");
  582   }
  583   /* random integer in the interval [low, up] */
  584   luaL_argcheck(L, low <= up, 1, "interval is empty");
  585   /* project random integer into the interval [0, up - low] */
  586   p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state);
  587   lua_pushinteger(L, p + (lua_Unsigned)low);
  588   return 1;
  589 }
  590 
  591 
  592 static void setseed (lua_State *L, Rand64 *state,
  593                      lua_Unsigned n1, lua_Unsigned n2) {
  594   int i;
  595   state[0] = Int2I(n1);
  596   state[1] = Int2I(0xff);  /* avoid a zero state */
  597   state[2] = Int2I(n2);
  598   state[3] = Int2I(0);
  599   for (i = 0; i < 16; i++)
  600     nextrand(state);  /* discard initial values to "spread" seed */
  601   lua_pushinteger(L, n1);
  602   lua_pushinteger(L, n2);
  603 }
  604 
  605 
  606 /*
  607 ** Set a "random" seed. To get some randomness, use the current time
  608 ** and the address of 'L' (in case the machine does address space layout
  609 ** randomization).
  610 */
  611 static void randseed (lua_State *L, RanState *state) {
  612   lua_Unsigned seed1 = (lua_Unsigned)time(NULL);
  613   lua_Unsigned seed2 = (lua_Unsigned)(size_t)L;
  614   setseed(L, state->s, seed1, seed2);
  615 }
  616 
  617 
  618 static int math_randomseed (lua_State *L) {
  619   RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
  620   if (lua_isnone(L, 1)) {
  621     randseed(L, state);
  622   }
  623   else {
  624     lua_Integer n1 = luaL_checkinteger(L, 1);
  625     lua_Integer n2 = luaL_optinteger(L, 2, 0);
  626     setseed(L, state->s, n1, n2);
  627   }
  628   return 2;  /* return seeds */
  629 }
  630 
  631 
  632 static const luaL_Reg randfuncs[] = {
  633   {"random", math_random},
  634   {"randomseed", math_randomseed},
  635   {NULL, NULL}
  636 };
  637 
  638 
  639 /*
  640 ** Register the random functions and initialize their state.
  641 */
  642 static void setrandfunc (lua_State *L) {
  643   RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0);
  644   randseed(L, state);  /* initialize with a "random" seed */
  645   lua_pop(L, 2);  /* remove pushed seeds */
  646   luaL_setfuncs(L, randfuncs, 1);
  647 }
  648 
  649 /* }================================================================== */
  650 
  651 
  652 /*
  653 ** {==================================================================
  654 ** Deprecated functions (for compatibility only)
  655 ** ===================================================================
  656 */
  657 #if defined(LUA_COMPAT_MATHLIB)
  658 
  659 static int math_cosh (lua_State *L) {
  660   lua_pushnumber(L, l_mathop(cosh)(luaL_checknumber(L, 1)));
  661   return 1;
  662 }
  663 
  664 static int math_sinh (lua_State *L) {
  665   lua_pushnumber(L, l_mathop(sinh)(luaL_checknumber(L, 1)));
  666   return 1;
  667 }
  668 
  669 static int math_tanh (lua_State *L) {
  670   lua_pushnumber(L, l_mathop(tanh)(luaL_checknumber(L, 1)));
  671   return 1;
  672 }
  673 
  674 static int math_pow (lua_State *L) {
  675   lua_Number x = luaL_checknumber(L, 1);
  676   lua_Number y = luaL_checknumber(L, 2);
  677   lua_pushnumber(L, l_mathop(pow)(x, y));
  678   return 1;
  679 }
  680 
  681 static int math_frexp (lua_State *L) {
  682   int e;
  683   lua_pushnumber(L, l_mathop(frexp)(luaL_checknumber(L, 1), &e));
  684   lua_pushinteger(L, e);
  685   return 2;
  686 }
  687 
  688 static int math_ldexp (lua_State *L) {
  689   lua_Number x = luaL_checknumber(L, 1);
  690   int ep = (int)luaL_checkinteger(L, 2);
  691   lua_pushnumber(L, l_mathop(ldexp)(x, ep));
  692   return 1;
  693 }
  694 
  695 static int math_log10 (lua_State *L) {
  696   lua_pushnumber(L, l_mathop(log10)(luaL_checknumber(L, 1)));
  697   return 1;
  698 }
  699 
  700 #endif
  701 /* }================================================================== */
  702 
  703 
  704 
  705 static const luaL_Reg mathlib[] = {
  706   {"abs",   math_abs},
  707   {"acos",  math_acos},
  708   {"asin",  math_asin},
  709   {"atan",  math_atan},
  710   {"ceil",  math_ceil},
  711   {"cos",   math_cos},
  712   {"deg",   math_deg},
  713   {"exp",   math_exp},
  714   {"tointeger", math_toint},
  715   {"floor", math_floor},
  716   {"fmod",   math_fmod},
  717   {"ult",   math_ult},
  718   {"log",   math_log},
  719   {"max",   math_max},
  720   {"min",   math_min},
  721   {"modf",   math_modf},
  722   {"rad",   math_rad},
  723   {"sin",   math_sin},
  724   {"sqrt",  math_sqrt},
  725   {"tan",   math_tan},
  726   {"type", math_type},
  727 #if defined(LUA_COMPAT_MATHLIB)
  728   {"atan2", math_atan},
  729   {"cosh",   math_cosh},
  730   {"sinh",   math_sinh},
  731   {"tanh",   math_tanh},
  732   {"pow",   math_pow},
  733   {"frexp", math_frexp},
  734   {"ldexp", math_ldexp},
  735   {"log10", math_log10},
  736 #endif
  737   /* placeholders */
  738   {"random", NULL},
  739   {"randomseed", NULL},
  740   {"pi", NULL},
  741   {"huge", NULL},
  742   {"maxinteger", NULL},
  743   {"mininteger", NULL},
  744   {NULL, NULL}
  745 };
  746 
  747 
  748 /*
  749 ** Open math library
  750 */
  751 LUAMOD_API int luaopen_math (lua_State *L) {
  752   luaL_newlib(L, mathlib);
  753   lua_pushnumber(L, PI);
  754   lua_setfield(L, -2, "pi");
  755   lua_pushnumber(L, (lua_Number)HUGE_VAL);
  756   lua_setfield(L, -2, "huge");
  757   lua_pushinteger(L, LUA_MAXINTEGER);
  758   lua_setfield(L, -2, "maxinteger");
  759   lua_pushinteger(L, LUA_MININTEGER);
  760   lua_setfield(L, -2, "mininteger");
  761   setrandfunc(L);
  762   return 1;
  763 }
  764