src/lib_math.c

   1 /*
   2 ** Math library.
   3 ** Copyright (C) 2005-2011 Mike Pall. See Copyright Notice in luajit.h
   4 */
   5
   6 #include <math.h>
   7
   8 #define lib_math_c
   9 #define LUA_LIB
  10
  11 #include "lua.h"
  12 #include "lauxlib.h"
  13 #include "lualib.h"
  14
  15 #include "lj_obj.h"
  16 #include "lj_lib.h"
  17 #include "lj_vm.h"
  18
  19 /* ------------------------------------------------------------------------ */
  20
  21 #define LJLIB_MODULE_math
  22
  23 LJLIB_ASM(math_abs)             LJLIB_REC(.)
  24 {
  25   lj_lib_checknumber(L, 1);
  26   return FFH_RETRY;
  27 }
  28 LJLIB_ASM_(math_floor)          LJLIB_REC(math_round IRFPM_FLOOR)
  29 LJLIB_ASM_(math_ceil)           LJLIB_REC(math_round IRFPM_CEIL)
  30
  31 LJLIB_ASM(math_sqrt)            LJLIB_REC(math_unary IRFPM_SQRT)
  32 {
  33   lj_lib_checknum(L, 1);
  34   return FFH_RETRY;
  35 }
  36 LJLIB_ASM_(math_log)            LJLIB_REC(math_unary IRFPM_LOG)
  37 LJLIB_ASM_(math_log10)          LJLIB_REC(math_unary IRFPM_LOG10)
  38 LJLIB_ASM_(math_exp)            LJLIB_REC(math_unary IRFPM_EXP)
  39 LJLIB_ASM_(math_sin)            LJLIB_REC(math_unary IRFPM_SIN)
  40 LJLIB_ASM_(math_cos)            LJLIB_REC(math_unary IRFPM_COS)
  41 LJLIB_ASM_(math_tan)            LJLIB_REC(math_unary IRFPM_TAN)
  42 LJLIB_ASM_(math_asin)           LJLIB_REC(math_atrig FF_math_asin)
  43 LJLIB_ASM_(math_acos)           LJLIB_REC(math_atrig FF_math_acos)
  44 LJLIB_ASM_(math_atan)           LJLIB_REC(math_atrig FF_math_atan)
  45 LJLIB_ASM_(math_sinh)           LJLIB_REC(math_htrig IRCALL_sinh)
  46 LJLIB_ASM_(math_cosh)           LJLIB_REC(math_htrig IRCALL_cosh)
  47 LJLIB_ASM_(math_tanh)           LJLIB_REC(math_htrig IRCALL_tanh)
  48 LJLIB_ASM_(math_frexp)
  49 LJLIB_ASM_(math_modf)           LJLIB_REC(.)
  50
  51 LJLIB_PUSH(57.29577951308232)
  52 LJLIB_ASM_(math_deg)            LJLIB_REC(math_degrad)
  53
  54 LJLIB_PUSH(0.017453292519943295)
  55 LJLIB_ASM_(math_rad)            LJLIB_REC(math_degrad)
  56
  57 LJLIB_ASM(math_atan2)           LJLIB_REC(.)
  58 {
  59   lj_lib_checknum(L, 1);
  60   lj_lib_checknum(L, 2);
  61   return FFH_RETRY;
  62 }
  63 LJLIB_ASM_(math_pow)            LJLIB_REC(.)
  64 LJLIB_ASM_(math_fmod)
  65
  66 LJLIB_ASM(math_ldexp)           LJLIB_REC(.)
  67 {
  68   lj_lib_checknum(L, 1);
  69 #if LJ_DUALNUM && !LJ_TARGET_X86ORX64
  70   lj_lib_checkint(L, 2);
  71 #else
  72   lj_lib_checknum(L, 2);
  73 #endif
  74   return FFH_RETRY;
  75 }
  76
  77 LJLIB_ASM(math_min)             LJLIB_REC(math_minmax IR_MIN)
  78 {
  79   int i = 0;
  80   do { lj_lib_checknumber(L, ++i); } while (L->base+i < L->top);
  81   return FFH_RETRY;
  82 }
  83 LJLIB_ASM_(math_max)            LJLIB_REC(math_minmax IR_MAX)
  84
  85 LJLIB_PUSH(3.14159265358979323846) LJLIB_SET(pi)
  86 LJLIB_PUSH(1e310) LJLIB_SET(huge)
  87
  88 /* ------------------------------------------------------------------------ */
  89
  90 /* This implements a Tausworthe PRNG with period 2^223. Based on:
  91 **   Tables of maximally-equidistributed combined LFSR generators,
  92 **   Pierre L'Ecuyer, 1991, table 3, 1st entry.
  93 ** Full-period ME-CF generator with L=64, J=4, k=223, N1=49.
  94 */
  95
  96 /* PRNG state. */
  97 struct RandomState {
  98   uint64_t gen[4];      /* State of the 4 LFSR generators. */
  99   int valid;            /* State is valid. */
 100 };
 101
 102 /* Union needed for bit-pattern conversion between uint64_t and double. */
 103 typedef union { uint64_t u64; double d; } U64double;
 104
 105 /* Update generator i and compute a running xor of all states. */
 106 #define TW223_GEN(i, k, q, s) \
 107   z = rs->gen[i]; \
 108   z = (((z<<q)^z) >> (k-s)) ^ ((z&((uint64_t)(int64_t)-1 << (64-k)))<<s); \
 109   r ^= z; rs->gen[i] = z;
 110
 111 /* PRNG step function. Returns a double in the range 1.0 <= d < 2.0. */
 112 LJ_NOINLINE uint64_t LJ_FASTCALL lj_math_random_step(RandomState *rs)
 113 {
 114   uint64_t z, r = 0;
 115   TW223_GEN(0, 63, 31, 18)
 116   TW223_GEN(1, 58, 19, 28)
 117   TW223_GEN(2, 55, 24,  7)
 118   TW223_GEN(3, 47, 21,  8)
 119   return (r & U64x(000fffff,ffffffff)) | U64x(3ff00000,00000000);
 120 }
 121
 122 /* PRNG initialization function. */
 123 static void random_init(RandomState *rs, double d)
 124 {
 125   uint32_t r = 0x11090601;  /* 64-k[i] as four 8 bit constants. */
 126   int i;
 127   for (i = 0; i < 4; i++) {
 128     U64double u;
 129     uint32_t m = 1u << (r&255);
 130     r >>= 8;
 131     u.d = d = d * 3.14159265358979323846 + 2.7182818284590452354;
 132     if (u.u64 < m) u.u64 += m;  /* Ensure k[i] MSB of gen[i] are non-zero. */
 133     rs->gen[i] = u.u64;
 134   }
 135   rs->valid = 1;
 136   for (i = 0; i < 10; i++)
 137     lj_math_random_step(rs);
 138 }
 139
 140 /* PRNG extract function. */
 141 LJLIB_PUSH(top-2)  /* Upvalue holds userdata with RandomState. */
 142 LJLIB_CF(math_random)           LJLIB_REC(.)
 143 {
 144   int n = (int)(L->top - L->base);
 145   RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1))));
 146   U64double u;
 147   double d;
 148   if (LJ_UNLIKELY(!rs->valid)) random_init(rs, 0.0);
 149   u.u64 = lj_math_random_step(rs);
 150   d = u.d - 1.0;
 151   if (n > 0) {
 152 #if LJ_DUALNUM
 153     int isint = 1;
 154     double r1;
 155     lj_lib_checknumber(L, 1);
 156     if (tvisint(L->base)) {
 157       r1 = (lua_Number)intV(L->base);
 158     } else {
 159       isint = 0;
 160       r1 = numV(L->base);
 161     }
 162 #else
 163     double r1 = lj_lib_checknum(L, 1);
 164 #endif
 165     if (n == 1) {
 166       d = lj_vm_floor(d*r1) + 1.0;  /* d is an int in range [1, r1] */
 167     } else {
 168 #if LJ_DUALNUM
 169       double r2;
 170       lj_lib_checknumber(L, 2);
 171       if (tvisint(L->base+1)) {
 172         r2 = (lua_Number)intV(L->base+1);
 173       } else {
 174         isint = 0;
 175         r2 = numV(L->base+1);
 176       }
 177 #else
 178       double r2 = lj_lib_checknum(L, 2);
 179 #endif
 180       d = lj_vm_floor(d*(r2-r1+1.0)) + r1;  /* d is an int in range [r1, r2] */
 181     }
 182 #if LJ_DUALNUM
 183     if (isint) {
 184       setintV(L->top-1, lj_num2int(d));
 185       return 1;
 186     }
 187 #endif
 188   }  /* else: d is a double in range [0, 1] */
 189   setnumV(L->top++, d);
 190   return 1;
 191 }
 192
 193 /* PRNG seed function. */
 194 LJLIB_PUSH(top-2)  /* Upvalue holds userdata with RandomState. */
 195 LJLIB_CF(math_randomseed)
 196 {
 197   RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1))));
 198   random_init(rs, lj_lib_checknum(L, 1));
 199   return 0;
 200 }
 201
 202 /* ------------------------------------------------------------------------ */
 203
 204 #include "lj_libdef.h"
 205
 206 LUALIB_API int luaopen_math(lua_State *L)
 207 {
 208   RandomState *rs;
 209   rs = (RandomState *)lua_newuserdata(L, sizeof(RandomState));
 210   rs->valid = 0;  /* Use lazy initialization to save some time on startup. */
 211   LJ_LIB_REG(L, LUA_MATHLIBNAME, math);
 212 #if defined(LUA_COMPAT_MOD)
 213   lua_getfield(L, -1, "fmod");
 214   lua_setfield(L, -2, "mod");
 215 #endif
 216   return 1;
 217 }
 218