3 ** Copyright (C) 2005-2014 Mike Pall. See Copyright Notice in luajit.h
19 /* ------------------------------------------------------------------------ */
21 #define LJLIB_MODULE_math
23 LJLIB_ASM(math_abs
) LJLIB_REC(.)
25 lj_lib_checknumber(L
, 1);
28 LJLIB_ASM_(math_floor
) LJLIB_REC(math_round IRFPM_FLOOR
)
29 LJLIB_ASM_(math_ceil
) LJLIB_REC(math_round IRFPM_CEIL
)
31 LJLIB_ASM(math_sqrt
) LJLIB_REC(math_unary IRFPM_SQRT
)
33 lj_lib_checknum(L
, 1);
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(.)
50 LJLIB_ASM(math_log
) LJLIB_REC(math_log
)
52 double x
= lj_lib_checknum(L
, 1);
53 if (L
->base
+1 < L
->top
) {
54 double y
= lj_lib_checknum(L
, 2);
56 x
= log(x
); y
= 1.0 / log(y
);
58 x
= lj_vm_log2(x
); y
= 1.0 / lj_vm_log2(y
);
60 setnumV(L
->base
-1, x
*y
); /* Do NOT join the expression to x / y. */
66 LJLIB_LUA(math_deg
) /* function(x) return x * 57.29577951308232 end */
67 LJLIB_LUA(math_rad
) /* function(x) return x * 0.017453292519943295 end */
69 LJLIB_ASM(math_atan2
) LJLIB_REC(.)
71 lj_lib_checknum(L
, 1);
72 lj_lib_checknum(L
, 2);
75 LJLIB_ASM_(math_pow
) LJLIB_REC(.)
78 LJLIB_ASM(math_ldexp
) LJLIB_REC(.)
80 lj_lib_checknum(L
, 1);
81 #if LJ_DUALNUM && !LJ_TARGET_X86ORX64
82 lj_lib_checkint(L
, 2);
84 lj_lib_checknum(L
, 2);
89 LJLIB_ASM(math_min
) LJLIB_REC(math_minmax IR_MIN
)
92 do { lj_lib_checknumber(L
, ++i
); } while (L
->base
+i
< L
->top
);
95 LJLIB_ASM_(math_max
) LJLIB_REC(math_minmax IR_MAX
)
97 LJLIB_PUSH(3.14159265358979323846) LJLIB_SET(pi
)
98 LJLIB_PUSH(1e310
) LJLIB_SET(huge
)
100 /* ------------------------------------------------------------------------ */
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.
110 uint64_t gen
[4]; /* State of the 4 LFSR generators. */
111 int valid
; /* State is valid. */
114 /* Union needed for bit-pattern conversion between uint64_t and double. */
115 typedef union { uint64_t u64
; double d
; } U64double
;
117 /* Update generator i and compute a running xor of all states. */
118 #define TW223_GEN(i, k, q, s) \
120 z = (((z<<q)^z) >> (k-s)) ^ ((z&((uint64_t)(int64_t)-1 << (64-k)))<<s); \
121 r ^= z; rs->gen[i] = z;
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
)
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);
134 /* PRNG initialization function. */
135 static void random_init(RandomState
*rs
, double d
)
137 uint32_t r
= 0x11090601; /* 64-k[i] as four 8 bit constants. */
139 for (i
= 0; i
< 4; i
++) {
141 uint32_t m
= 1u << (r
&255);
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. */
148 for (i
= 0; i
< 10; i
++)
149 lj_math_random_step(rs
);
152 /* PRNG extract function. */
153 LJLIB_PUSH(top
-2) /* Upvalue holds userdata with RandomState. */
154 LJLIB_CF(math_random
) LJLIB_REC(.)
156 int n
= (int)(L
->top
- L
->base
);
157 RandomState
*rs
= (RandomState
*)(uddata(udataV(lj_lib_upvalue(L
, 1))));
160 if (LJ_UNLIKELY(!rs
->valid
)) random_init(rs
, 0.0);
161 u
.u64
= lj_math_random_step(rs
);
167 lj_lib_checknumber(L
, 1);
168 if (tvisint(L
->base
)) {
169 r1
= (lua_Number
)intV(L
->base
);
175 double r1
= lj_lib_checknum(L
, 1);
178 d
= lj_vm_floor(d
*r1
) + 1.0; /* d is an int in range [1, r1] */
182 lj_lib_checknumber(L
, 2);
183 if (tvisint(L
->base
+1)) {
184 r2
= (lua_Number
)intV(L
->base
+1);
187 r2
= numV(L
->base
+1);
190 double r2
= lj_lib_checknum(L
, 2);
192 d
= lj_vm_floor(d
*(r2
-r1
+1.0)) + r1
; /* d is an int in range [r1, r2] */
196 setintV(L
->top
-1, lj_num2int(d
));
200 } /* else: d is a double in range [0, 1] */
201 setnumV(L
->top
++, d
);
205 /* PRNG seed function. */
206 LJLIB_PUSH(top
-2) /* Upvalue holds userdata with RandomState. */
207 LJLIB_CF(math_randomseed
)
209 RandomState
*rs
= (RandomState
*)(uddata(udataV(lj_lib_upvalue(L
, 1))));
210 random_init(rs
, lj_lib_checknum(L
, 1));
214 /* ------------------------------------------------------------------------ */
216 #include "lj_libdef.h"
218 LUALIB_API
int luaopen_math(lua_State
*L
)
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) && !LJ_52
225 lua_getfield(L
, -1, "fmod");
226 lua_setfield(L
, -2, "mod");