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using 'xoroshiro128+' for PRNG

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(plus a rotate at the final result to have better lower bits)
This commit is contained in:
Roberto Ierusalimschy
2018-04-04 13:12:53 -03:00
parent 03c6a05ec8
commit b44787652b
1 changed files with 88 additions and 87 deletions
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175
lmathlib.c
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@@ -1,5 +1,5 @@
/* /*
** $Id: lmathlib.c,v 1.127 2018/03/22 19:54:49 roberto Exp roberto $ ** $Id: lmathlib.c,v 1.128 2018/03/26 19:48:46 roberto Exp $
** Standard mathematical library ** Standard mathematical library
** See Copyright Notice in lua.h ** See Copyright Notice in lua.h
*/ */
@@ -247,7 +247,7 @@ static int math_type (lua_State *L) {
/* /*
** {================================================================== ** {==================================================================
** Pseudo-Random Number Generator based on 'xorshift128+'. ** Pseudo-Random Number Generator based on 'xoroshiro128+'.
** =================================================================== ** ===================================================================
*/ */
@@ -270,34 +270,45 @@ static int math_type (lua_State *L) {
/* a 64-bit value */ /* a 64-bit value */
typedef unsigned long long I; typedef unsigned long long I;
static I xorshift128plus (I *state) {
I x = state[0]; /* rotate left 'x' by 'n' bits */
I y = state[1]; static I rotl (I x, int n) {
state[0] = y; return (x << n) | (x >> (64 - n));
x ^= x << 23;
state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5));
return state[1] + y;
} }
static I nextrand (I *state) {
I s0 = state[0];
I s1 = state[1];
I res = s0 + s1;
res = rotl(res, 41); /* extra step to change place of lower bits */
s1 = s1 ^ s0;
state[0] = rotl(s0, 55) ^ (s1 ^ (s1 << 14));
state[1] = rotl(s1, 36);
return res;
}
/* must take care to not shift stuff by more than 63 slots */ /* must take care to not shift stuff by more than 63 slots */
#define shiftI (64 - FIGS) /* leave FIGS bits */
#define shiftF (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIG) */
/* /*
** Convert bits from a random integer into a float in the ** Convert bits from a random integer into a float in the
** interval [0,1). ** interval [0,1).
*/ */
#define maskFIG (~(~1LLU << (FIGS - 1))) /* use FIGS bits */
#define shiftFIG (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIGS) */
static lua_Number I2d (I x) { static lua_Number I2d (I x) {
return (lua_Number)(x >> shiftI) * shiftF; return (lua_Number)(x & maskFIG) * shiftFIG;
} }
/* convert an 'I' to a lua_Unsigned (using higher bits) */ /* convert an 'I' to a lua_Unsigned */
#define I2UInt(x) ((lua_Unsigned)((x) >> (64 - LUA_UNSIGNEDBITS))) #define I2UInt(x) ((lua_Unsigned)(x))
/* convert a lua_Integer to an 'I' */ /* convert a lua_Unsigned to an 'I' */
#define Int2I(x) ((I)(x)) #define Int2I(x) ((I)(x))
#else /* no long long }{ */ #else /* no long long }{ */
/* /*
@@ -330,14 +341,10 @@ static I packI (lu_int32 h, lu_int32 l) {
/* i ^ (i << n) */ /* i ^ (i << n) */
static I Ixorshl (I i, int n) { static I Ixorshl (I i, int n) {
lua_assert(n > 0 && n < 32);
return packI(i.h ^ ((i.h << n) | (i.l >> (32 - n))), i.l ^ (i.l << n)); return packI(i.h ^ ((i.h << n) | (i.l >> (32 - n))), i.l ^ (i.l << n));
} }
/* i ^ (i >> n) */
static I Ixorshr (I i, int n) {
return packI(i.h ^ (i.h >> n), i.l ^ ((i.l >> n) | (i.h << (32 - n))));
}
static I Ixor (I i1, I i2) { static I Ixor (I i1, I i2) {
return packI(i1.h ^ i2.h, i1.l ^ i2.l); return packI(i1.h ^ i2.h, i1.l ^ i2.l);
} }
@@ -349,18 +356,29 @@ static I Iadd (I i1, I i2) {
return result; return result;
} }
/*
** Rotate left. As all offsets here are larger than 32, do a rotate right
** of 64 - offset.
*/
static I Irotli (I i, int n) {
n = 64 - n;
lua_assert(n > 0 && n < 32);
return packI((i.h >> n) | (i.l << (32 - n)),
(i.h << (32 - n)) | (i.l >> n));
}
/* /*
** implementation of 'xorshift128+' algorithm on 'I' values ** implementation of 'xoroshiro128+' algorithm on 'I' values
*/ */
static I xorshift128plus (I *state) { static I nextrand (I *state) {
I x = state[0]; I s0 = state[0];
I y = state[1]; I s1 = state[1];
state[0] = y; I res = Iadd(s0, s1);
x = Ixorshl(x, 23); /* x ^= x << 23; */ res = Irotli(res, 41);
/* state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5)); */ s1 = Ixor(s1, s0);
state[1] = Ixor(Ixorshr(x, 18), Ixorshr(y, 5)); state[0] = Ixor(Irotli(s0, 55), Ixorshl(s1, 14));
return Iadd(state[1], y); /* return state[1] + y; */ state[1] = Irotli(s1, 36);
return res;
} }
@@ -373,45 +391,39 @@ static I xorshift128plus (I *state) {
#if FIGS <= 32 #if FIGS <= 32
#define maskLOW 0 /* do not need bits from lower half */ #define maskHI 0 /* do not need bits from higher half */
#define maskHI (~(~(lu_int32)0 >> (FIGS - 1) >> 1)) /* use FIGS bits */ #define maskLOW (~(~UONE << (FIGS - 1))) /* use FIGS bits */
#define shiftHI 1 /* no shift */ #define shiftFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) /* 2^(-FIGS) */
#define shiftF (1 / l_mathop(4294967296.0)) /* 2^(-32) */
#else /* 32 < FIGS <= 64 */ #else /* 32 < FIGS <= 64 */
/* must take care to not shift stuff by more than 31 slots */ /* must take care to not shift stuff by more than 31 slots */
/* use FIGS - 32 bits from lower half */ /* use FIGS - 32 bits from higher half */
#define maskLOW (~(~(lu_int32)0 >> (FIGS - 33) >> 1)) #define maskHI (~(~UONE << (FIGS - 33)))
/* use all bits from higher half */ /* use all bits from lower half */
#define maskHI (~(lu_int32)0) #define maskLOW (~(lu_int32)0)
#define shiftHI l_mathop(4294967296.0) /* 2^32 */ /* 2^(-FIGS) == (1 / 2^33) / 2^(FIGS-33) */
#define shiftFIG ((lua_Number)(1.0 / 8589934592.0) / (UONE << (FIGS - 33)))
/* 2^(-64) */
#define shiftF ((lua_Number)(1 / (shiftHI * shiftHI)))
#endif #endif
#define twoto32 l_mathop(4294967296.0) /* 2^32 */
static lua_Number I2d (I x) { static lua_Number I2d (I x) {
lua_Number h = (lua_Number)(x.h & maskHI); lua_Number h = (lua_Number)(x.h & maskHI);
lua_Number l = (lua_Number)(x.l & maskLOW); lua_Number l = (lua_Number)(x.l & maskLOW);
return (h * shiftHI + l) * shiftF; return (h * twoto32 + l) * shiftFIG;
} }
static lua_Unsigned I2UInt (I x) { static lua_Unsigned I2UInt (I x) {
#if (LUA_MAXINTEGER >> 30) <= 1 return ((lua_Unsigned)x.h << 31 << 1) | (lua_Unsigned)x.l;
/* at most 32 bits; use only high bits */
return ((lua_Unsigned)x.h);
#else
/* at least 33 bits */
return ((lua_Unsigned)x.h << (LUA_UNSIGNEDBITS - 32)) |
(lua_Unsigned)x.l >> (64 - LUA_UNSIGNEDBITS);
#endif
} }
static I Int2I (lua_Unsigned n) { static I Int2I (lua_Unsigned n) {
return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0); return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0);
} }
@@ -427,47 +439,36 @@ typedef struct {
} RanState; } RanState;
/*
** Return the higher bit set in 'x' (first bit is 1).
*/
static int higherbit (lua_Unsigned x) {
/* table of higher bits from 0 to 255 */
static const unsigned char hb[256] = {
0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
};
int l = 0;
while (x >= 256) { l += 8; x >>= 8; }
return l + hb[x];
}
/* /*
** Project the random integer 'ran' into the interval [0, n]. ** Project the random integer 'ran' into the interval [0, n].
** To get a uniform projection into [0,n], we first compute 'shf', the ** Because 'ran' has 2^B possible values, the projection can only be
** largest number that we can right-shift 'ran' and still get numbers ** uniform when the size of the interval is a power of 2 (exact
** as larger as 'n'. We then shift 'ran'; if the result is inside [0, n], ** division). To get a uniform projection into [0, n], we first compute
** we are done. Otherwise, we try with another 'ran' until we have a ** 'lim', the smallest Mersenne number not smaller than 'n'. We then
** result inside the interval. (We use right shifts to avoid the lowest ** project 'ran' into the interval [0, lim]. If the result is inside
** bits of 'ran', which has poorer distributions.) ** [0, n], we are done. Otherwise, we try with another 'ran' until we
** have a result inside the interval.
*/ */
static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n, static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
RanState *state) { RanState *state) {
if (n == 0) return 0; /* special case for the unit set */ lua_Unsigned lim = n;
else { if ((lim & (lim + 1)) > 0) { /* 'lim + 1' is not a power of 2? */
int shf = LUA_UNSIGNEDBITS - higherbit(n); /* compute the smallest (2^b - 1) not smaller than 'n' */
lua_assert(~(lua_Unsigned)0 >> shf >= n && /* not larger */ lim |= (lim >> 1);
~(lua_Unsigned)0 >> shf >> 1 < n); /* largest */ lim |= (lim >> 2);
while ((ran >>= shf) > n) lim |= (lim >> 4);
ran = I2UInt(xorshift128plus(state->s)); lim |= (lim >> 8);
return ran; lim |= (lim >> 16);
#if (LUA_MAXINTEGER >> 30 >> 2) > 0
lim |= (lim >> 32); /* integer type has more than 32 bits */
#endif
} }
lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2 */
&& lim >= n /* not smaller than 'n' */
&& (lim == 0 || (lim >> 1) < n)); /* it is the smallest one */
while ((ran &= lim) > n)
ran = I2UInt(nextrand(state->s));
return ran;
} }
@@ -475,7 +476,7 @@ static int math_random (lua_State *L) {
lua_Integer low, up; lua_Integer low, up;
lua_Unsigned p; lua_Unsigned p;
RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1)); RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
I rv = xorshift128plus(state->s); /* next pseudo-random value */ I rv = nextrand(state->s); /* next pseudo-random value */
switch (lua_gettop(L)) { /* check number of arguments */ switch (lua_gettop(L)) { /* check number of arguments */
case 0: { /* no arguments */ case 0: { /* no arguments */
lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */ lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */
@@ -511,7 +512,7 @@ static void setseed (I *state, lua_Unsigned n) {
state[0] = Int2I(n); state[0] = Int2I(n);
state[1] = Int2I(0xff); /* avoid a zero state */ state[1] = Int2I(0xff); /* avoid a zero state */
for (i = 0; i < 16; i++) for (i = 0; i < 16; i++)
xorshift128plus(state); /* discard initial values to "spread" seed */ nextrand(state); /* discard initial values to "spread" seed */
} }