1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
|
/*
** Math library.
** Copyright (C) 2005-2010 Mike Pall. See Copyright Notice in luajit.h
*/
#include <math.h>
#define lib_math_c
#define LUA_LIB
#include "lua.h"
#include "lauxlib.h"
#include "lualib.h"
#include "lj_obj.h"
#include "lj_lib.h"
/* ------------------------------------------------------------------------ */
#define LJLIB_MODULE_math
LJLIB_ASM(math_abs) LJLIB_REC(.)
{
lj_lib_checknum(L, 1);
return FFH_RETRY;
}
LJLIB_ASM_(math_floor) LJLIB_REC(math_round IRFPM_FLOOR)
LJLIB_ASM_(math_ceil) LJLIB_REC(math_round IRFPM_CEIL)
LJLIB_ASM_(math_sqrt) LJLIB_REC(math_unary IRFPM_SQRT)
LJLIB_ASM_(math_log) LJLIB_REC(math_unary IRFPM_LOG)
LJLIB_ASM_(math_log10) LJLIB_REC(math_unary IRFPM_LOG10)
LJLIB_ASM_(math_exp) LJLIB_REC(math_unary IRFPM_EXP)
LJLIB_ASM_(math_sin) LJLIB_REC(math_unary IRFPM_SIN)
LJLIB_ASM_(math_cos) LJLIB_REC(math_unary IRFPM_COS)
LJLIB_ASM_(math_tan) LJLIB_REC(math_unary IRFPM_TAN)
LJLIB_ASM_(math_asin) LJLIB_REC(math_atrig FF_math_asin)
LJLIB_ASM_(math_acos) LJLIB_REC(math_atrig FF_math_acos)
LJLIB_ASM_(math_atan) LJLIB_REC(math_atrig FF_math_atan)
LJLIB_ASM_(math_sinh) LJLIB_REC(math_htrig IRCALL_sinh)
LJLIB_ASM_(math_cosh) LJLIB_REC(math_htrig IRCALL_cosh)
LJLIB_ASM_(math_tanh) LJLIB_REC(math_htrig IRCALL_tanh)
LJLIB_ASM_(math_frexp)
LJLIB_ASM_(math_modf) LJLIB_REC(.)
LJLIB_PUSH(57.29577951308232)
LJLIB_ASM_(math_deg) LJLIB_REC(math_degrad)
LJLIB_PUSH(0.017453292519943295)
LJLIB_ASM_(math_rad) LJLIB_REC(math_degrad)
LJLIB_ASM(math_atan2) LJLIB_REC(math_binary IR_ATAN2)
{
lj_lib_checknum(L, 1);
lj_lib_checknum(L, 2);
return FFH_RETRY;
}
LJLIB_ASM_(math_ldexp) LJLIB_REC(math_binary IR_LDEXP)
LJLIB_ASM_(math_pow) LJLIB_REC(.)
LJLIB_ASM_(math_fmod)
LJLIB_ASM(math_min) LJLIB_REC(math_minmax IR_MIN)
{
int i = 0;
do { lj_lib_checknum(L, ++i); } while (L->base+i < L->top);
return FFH_RETRY;
}
LJLIB_ASM_(math_max) LJLIB_REC(math_minmax IR_MAX)
LJLIB_PUSH(3.14159265358979323846) LJLIB_SET(pi)
LJLIB_PUSH(1e310) LJLIB_SET(huge)
LJ_FUNCA double lj_wrapper_sinh(double x) { return sinh(x); }
LJ_FUNCA double lj_wrapper_cosh(double x) { return cosh(x); }
LJ_FUNCA double lj_wrapper_tanh(double x) { return tanh(x); }
/* ------------------------------------------------------------------------ */
/* This implements a Tausworthe PRNG with period 2^223. Based on:
** Tables of maximally-equidistributed combined LFSR generators,
** Pierre L'Ecuyer, 1991, table 3, 1st entry.
** Full-period ME-CF generator with L=64, J=4, k=223, N1=49.
*/
/* PRNG state. */
struct RandomState {
uint64_t gen[4]; /* State of the 4 LFSR generators. */
int valid; /* State is valid. */
};
/* Union needed for bit-pattern conversion between uint64_t and double. */
typedef union { uint64_t u64; double d; } U64double;
/* Update generator i and compute a running xor of all states. */
#define TW223_GEN(i, k, q, s) \
z = rs->gen[i]; \
z = (((z<<q)^z) >> (k-s)) ^ ((z&((uint64_t)(int64_t)-1 << (64-k)))<<s); \
r ^= z; rs->gen[i] = z;
/* PRNG step function. Returns a double in the range 1.0 <= d < 2.0. */
LJ_NOINLINE uint64_t LJ_FASTCALL lj_math_random_step(RandomState *rs)
{
uint64_t z, r = 0;
TW223_GEN(0, 63, 31, 18)
TW223_GEN(1, 58, 19, 28)
TW223_GEN(2, 55, 24, 7)
TW223_GEN(3, 47, 21, 8)
return (r & U64x(000fffff,ffffffff)) | U64x(3ff00000,00000000);
}
/* PRNG initialization function. */
static void random_init(RandomState *rs, double d)
{
uint32_t r = 0x11090601; /* 64-k[i] as four 8 bit constants. */
int i;
for (i = 0; i < 4; i++) {
U64double u;
uint32_t m = 1u << (r&255);
r >>= 8;
u.d = d = d * 3.14159265358979323846 + 2.7182818284590452354;
if (u.u64 < m) u.u64 += m; /* Ensure k[i] MSB of gen[i] are non-zero. */
rs->gen[i] = u.u64;
}
rs->valid = 1;
for (i = 0; i < 10; i++)
lj_math_random_step(rs);
}
/* PRNG extract function. */
LJLIB_PUSH(top-2) /* Upvalue holds userdata with RandomState. */
LJLIB_CF(math_random) LJLIB_REC(.)
{
int n = cast_int(L->top - L->base);
RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1))));
U64double u;
double d;
if (LJ_UNLIKELY(!rs->valid)) random_init(rs, 0.0);
u.u64 = lj_math_random_step(rs);
d = u.d - 1.0;
if (n > 0) {
double r1 = lj_lib_checknum(L, 1);
if (n == 1) {
d = floor(d*r1) + 1.0; /* d is an int in range [1, r1] */
} else {
double r2 = lj_lib_checknum(L, 2);
d = floor(d*(r2-r1+1.0)) + r1; /* d is an int in range [r1, r2] */
}
} /* else: d is a double in range [0, 1] */
setnumV(L->top++, d);
return 1;
}
/* PRNG seed function. */
LJLIB_PUSH(top-2) /* Upvalue holds userdata with RandomState. */
LJLIB_CF(math_randomseed)
{
RandomState *rs = (RandomState *)(uddata(udataV(lj_lib_upvalue(L, 1))));
random_init(rs, lj_lib_checknum(L, 1));
return 0;
}
/* ------------------------------------------------------------------------ */
#include "lj_libdef.h"
LUALIB_API int luaopen_math(lua_State *L)
{
RandomState *rs;
rs = (RandomState *)lua_newuserdata(L, sizeof(RandomState));
rs->valid = 0; /* Use lazy initialization to save some time on startup. */
LJ_LIB_REG(L, math);
#if defined(LUA_COMPAT_MOD)
lua_getfield(L, -1, "fmod");
lua_setfield(L, -2, "mod");
#endif
return 1;
}
|
