lib_math.c (6178B)
1 /* 2 ** Math library. 3 ** Copyright (C) 2005-2016 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_log10) LJLIB_REC(math_unary IRFPM_LOG10) 37 LJLIB_ASM_(math_exp) LJLIB_REC(math_unary IRFPM_EXP) 38 LJLIB_ASM_(math_sin) LJLIB_REC(math_unary IRFPM_SIN) 39 LJLIB_ASM_(math_cos) LJLIB_REC(math_unary IRFPM_COS) 40 LJLIB_ASM_(math_tan) LJLIB_REC(math_unary IRFPM_TAN) 41 LJLIB_ASM_(math_asin) LJLIB_REC(math_atrig FF_math_asin) 42 LJLIB_ASM_(math_acos) LJLIB_REC(math_atrig FF_math_acos) 43 LJLIB_ASM_(math_atan) LJLIB_REC(math_atrig FF_math_atan) 44 LJLIB_ASM_(math_sinh) LJLIB_REC(math_htrig IRCALL_sinh) 45 LJLIB_ASM_(math_cosh) LJLIB_REC(math_htrig IRCALL_cosh) 46 LJLIB_ASM_(math_tanh) LJLIB_REC(math_htrig IRCALL_tanh) 47 LJLIB_ASM_(math_frexp) 48 LJLIB_ASM_(math_modf) LJLIB_REC(.) 49 50 LJLIB_ASM(math_log) LJLIB_REC(math_log) 51 { 52 double x = lj_lib_checknum(L, 1); 53 if (L->base+1 < L->top) { 54 double y = lj_lib_checknum(L, 2); 55 #ifdef LUAJIT_NO_LOG2 56 x = log(x); y = 1.0 / log(y); 57 #else 58 x = lj_vm_log2(x); y = 1.0 / lj_vm_log2(y); 59 #endif 60 setnumV(L->base-1-LJ_FR2, x*y); /* Do NOT join the expression to x / y. */ 61 return FFH_RES(1); 62 } 63 return FFH_RETRY; 64 } 65 66 LJLIB_LUA(math_deg) /* function(x) return x * 57.29577951308232 end */ 67 LJLIB_LUA(math_rad) /* function(x) return x * 0.017453292519943295 end */ 68 69 LJLIB_ASM(math_atan2) LJLIB_REC(.) 70 { 71 lj_lib_checknum(L, 1); 72 lj_lib_checknum(L, 2); 73 return FFH_RETRY; 74 } 75 LJLIB_ASM_(math_pow) LJLIB_REC(.) 76 LJLIB_ASM_(math_fmod) 77 78 LJLIB_ASM(math_ldexp) LJLIB_REC(.) 79 { 80 lj_lib_checknum(L, 1); 81 #if LJ_DUALNUM && !LJ_TARGET_X86ORX64 82 lj_lib_checkint(L, 2); 83 #else 84 lj_lib_checknum(L, 2); 85 #endif 86 return FFH_RETRY; 87 } 88 89 LJLIB_ASM(math_min) LJLIB_REC(math_minmax IR_MIN) 90 { 91 int i = 0; 92 do { lj_lib_checknumber(L, ++i); } while (L->base+i < L->top); 93 return FFH_RETRY; 94 } 95 LJLIB_ASM_(math_max) LJLIB_REC(math_minmax IR_MAX) 96 97 LJLIB_PUSH(3.14159265358979323846) LJLIB_SET(pi) 98 LJLIB_PUSH(1e310) LJLIB_SET(huge) 99 100 /* ------------------------------------------------------------------------ */ 101 102 /* This implements a Tausworthe PRNG with period 2^223. Based on: 103 ** Tables of maximally-equidistributed combined LFSR generators, 104 ** Pierre L'Ecuyer, 1991, table 3, 1st entry. 105 ** Full-period ME-CF generator with L=64, J=4, k=223, N1=49. 106 */ 107 108 /* PRNG state. */ 109 struct RandomState { 110 uint64_t gen[4]; /* State of the 4 LFSR generators. */ 111 int valid; /* State is valid. */ 112 }; 113 114 /* Union needed for bit-pattern conversion between uint64_t and double. */ 115 typedef union { uint64_t u64; double d; } U64double; 116 117 /* Update generator i and compute a running xor of all states. */ 118 #define TW223_GEN(i, k, q, s) \ 119 z = rs->gen[i]; \ 120 z = (((z<<q)^z) >> (k-s)) ^ ((z&((uint64_t)(int64_t)-1 << (64-k)))<<s); \ 121 r ^= z; rs->gen[i] = z; 122 123 /* PRNG step function. Returns a double in the range 1.0 <= d < 2.0. */ 124 LJ_NOINLINE uint64_t LJ_FASTCALL lj_math_random_step(RandomState *rs) 125 { 126 uint64_t z, r = 0; 127 TW223_GEN(0, 63, 31, 18) 128 TW223_GEN(1, 58, 19, 28) 129 TW223_GEN(2, 55, 24, 7) 130 TW223_GEN(3, 47, 21, 8) 131 return (r & U64x(000fffff,ffffffff)) | U64x(3ff00000,00000000); 132 } 133 134 /* PRNG initialization function. */ 135 static void random_init(RandomState *rs, double d) 136 { 137 uint32_t r = 0x11090601; /* 64-k[i] as four 8 bit constants. */ 138 int i; 139 for (i = 0; i < 4; i++) { 140 U64double u; 141 uint32_t m = 1u << (r&255); 142 r >>= 8; 143 u.d = d = d * 3.14159265358979323846 + 2.7182818284590452354; 144 if (u.u64 < m) u.u64 += m; /* Ensure k[i] MSB of gen[i] are non-zero. */ 145 rs->gen[i] = u.u64; 146 } 147 rs->valid = 1; 148 for (i = 0; i < 10; i++) 149 lj_math_random_step(rs); 150 } 151 152 /* PRNG extract function. */ 153 LJLIB_PUSH(top-2) /* Upvalue holds userdata with RandomState. */ 154 LJLIB_CF(math_random) LJLIB_REC(.) 155 { 156 int n = (int)(L->top - L->base); 157 RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1)))); 158 U64double u; 159 double d; 160 if (LJ_UNLIKELY(!rs->valid)) random_init(rs, 0.0); 161 u.u64 = lj_math_random_step(rs); 162 d = u.d - 1.0; 163 if (n > 0) { 164 #if LJ_DUALNUM 165 int isint = 1; 166 double r1; 167 lj_lib_checknumber(L, 1); 168 if (tvisint(L->base)) { 169 r1 = (lua_Number)intV(L->base); 170 } else { 171 isint = 0; 172 r1 = numV(L->base); 173 } 174 #else 175 double r1 = lj_lib_checknum(L, 1); 176 #endif 177 if (n == 1) { 178 d = lj_vm_floor(d*r1) + 1.0; /* d is an int in range [1, r1] */ 179 } else { 180 #if LJ_DUALNUM 181 double r2; 182 lj_lib_checknumber(L, 2); 183 if (tvisint(L->base+1)) { 184 r2 = (lua_Number)intV(L->base+1); 185 } else { 186 isint = 0; 187 r2 = numV(L->base+1); 188 } 189 #else 190 double r2 = lj_lib_checknum(L, 2); 191 #endif 192 d = lj_vm_floor(d*(r2-r1+1.0)) + r1; /* d is an int in range [r1, r2] */ 193 } 194 #if LJ_DUALNUM 195 if (isint) { 196 setintV(L->top-1, lj_num2int(d)); 197 return 1; 198 } 199 #endif 200 } /* else: d is a double in range [0, 1] */ 201 setnumV(L->top++, d); 202 return 1; 203 } 204 205 /* PRNG seed function. */ 206 LJLIB_PUSH(top-2) /* Upvalue holds userdata with RandomState. */ 207 LJLIB_CF(math_randomseed) 208 { 209 RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1)))); 210 random_init(rs, lj_lib_checknum(L, 1)); 211 return 0; 212 } 213 214 /* ------------------------------------------------------------------------ */ 215 216 #include "lj_libdef.h" 217 218 LUALIB_API int luaopen_math(lua_State *L) 219 { 220 RandomState *rs; 221 rs = (RandomState *)lua_newuserdata(L, sizeof(RandomState)); 222 rs->valid = 0; /* Use lazy initialization to save some time on startup. */ 223 LJ_LIB_REG(L, LUA_MATHLIBNAME, math); 224 #if defined(LUA_COMPAT_MOD) 225 lua_getfield(L, -1, "fmod"); 226 lua_setfield(L, -2, "mod"); 227 #endif 228 return 1; 229 } 230