xref: /freebsd/contrib/lua/src/lmathlib.c (revision e6bfd18d21b225af6a0ed67ceeaf1293b7b9eba5)
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