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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.     (l_mathop(1.0) / (UONE << 30) / l_mathop(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)) * l_mathop(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.  
  765.