using 'xoroshiro128+' for PRNG
(plus a rotate at the final result to have better lower bits)
diff --git a/lmathlib.c b/lmathlib.c
index 9432d40..3e5ceea 100644
--- a/lmathlib.c
+++ b/lmathlib.c
@@ -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
** See Copyright Notice in lua.h
*/
@@ -247,7 +247,7 @@
/*
** {==================================================================
-** Pseudo-Random Number Generator based on 'xorshift128+'.
+** Pseudo-Random Number Generator based on 'xoroshiro128+'.
** ===================================================================
*/
@@ -270,34 +270,45 @@
/* a 64-bit value */
typedef unsigned long long I;
-static I xorshift128plus (I *state) {
- I x = state[0];
- I y = state[1];
- state[0] = y;
- x ^= x << 23;
- state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5));
- return state[1] + y;
+
+/* rotate left 'x' by 'n' bits */
+static I rotl (I x, int n) {
+ return (x << n) | (x >> (64 - n));
}
+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 */
-#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
** 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) {
- return (lua_Number)(x >> shiftI) * shiftF;
+ return (lua_Number)(x & maskFIG) * shiftFIG;
}
-/* convert an 'I' to a lua_Unsigned (using higher bits) */
-#define I2UInt(x) ((lua_Unsigned)((x) >> (64 - LUA_UNSIGNEDBITS)))
+/* convert an 'I' to a lua_Unsigned */
+#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))
+
#else /* no long long }{ */
/*
@@ -330,14 +341,10 @@
/* i ^ (i << 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));
}
-/* 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) {
return packI(i1.h ^ i2.h, i1.l ^ i2.l);
}
@@ -349,18 +356,29 @@
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) {
- I x = state[0];
- I y = state[1];
- state[0] = y;
- x = Ixorshl(x, 23); /* x ^= x << 23; */
- /* state[1] = (x ^ (x >> 18)) ^ (y ^ (y >> 5)); */
- state[1] = Ixor(Ixorshr(x, 18), Ixorshr(y, 5));
- return Iadd(state[1], y); /* return state[1] + y; */
+static I nextrand (I *state) {
+ I s0 = state[0];
+ I s1 = state[1];
+ I res = Iadd(s0, s1);
+ res = Irotli(res, 41);
+ s1 = Ixor(s1, s0);
+ state[0] = Ixor(Irotli(s0, 55), Ixorshl(s1, 14));
+ state[1] = Irotli(s1, 36);
+ return res;
}
@@ -373,45 +391,39 @@
#if FIGS <= 32
-#define maskLOW 0 /* do not need bits from lower half */
-#define maskHI (~(~(lu_int32)0 >> (FIGS - 1) >> 1)) /* use FIGS bits */
-#define shiftHI 1 /* no shift */
-#define shiftF (1 / l_mathop(4294967296.0)) /* 2^(-32) */
+#define maskHI 0 /* do not need bits from higher half */
+#define maskLOW (~(~UONE << (FIGS - 1))) /* use FIGS bits */
+#define shiftFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) /* 2^(-FIGS) */
#else /* 32 < FIGS <= 64 */
/* must take care to not shift stuff by more than 31 slots */
-/* use FIGS - 32 bits from lower half */
-#define maskLOW (~(~(lu_int32)0 >> (FIGS - 33) >> 1))
+/* use FIGS - 32 bits from higher half */
+#define maskHI (~(~UONE << (FIGS - 33)))
-/* use all bits from higher half */
-#define maskHI (~(lu_int32)0)
+/* use all bits from lower half */
+#define maskLOW (~(lu_int32)0)
-#define shiftHI l_mathop(4294967296.0) /* 2^32 */
-
-/* 2^(-64) */
-#define shiftF ((lua_Number)(1 / (shiftHI * shiftHI)))
+/* 2^(-FIGS) == (1 / 2^33) / 2^(FIGS-33) */
+#define shiftFIG ((lua_Number)(1.0 / 8589934592.0) / (UONE << (FIGS - 33)))
#endif
+#define twoto32 l_mathop(4294967296.0) /* 2^32 */
+
static lua_Number I2d (I x) {
lua_Number h = (lua_Number)(x.h & maskHI);
lua_Number l = (lua_Number)(x.l & maskLOW);
- return (h * shiftHI + l) * shiftF;
+ return (h * twoto32 + l) * shiftFIG;
}
+
static lua_Unsigned I2UInt (I x) {
-#if (LUA_MAXINTEGER >> 30) <= 1
-/* 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
+ return ((lua_Unsigned)x.h << 31 << 1) | (lua_Unsigned)x.l;
}
+
static I Int2I (lua_Unsigned n) {
return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0);
}
@@ -428,46 +440,35 @@
/*
-** 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].
-** To get a uniform projection into [0,n], we first compute 'shf', the
-** largest number that we can right-shift 'ran' and still get numbers
-** as larger as 'n'. We then shift 'ran'; if the result is inside [0, n],
-** we are done. Otherwise, we try with another 'ran' until we have a
-** result inside the interval. (We use right shifts to avoid the lowest
-** bits of 'ran', which has poorer distributions.)
+** Because 'ran' has 2^B possible values, the projection can only be
+** uniform when the size of the interval is a power of 2 (exact
+** division). To get a uniform projection into [0, n], we first compute
+** 'lim', the smallest Mersenne number not smaller than 'n'. We then
+** project 'ran' into the interval [0, lim]. If the result is inside
+** [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,
RanState *state) {
- if (n == 0) return 0; /* special case for the unit set */
- else {
- int shf = LUA_UNSIGNEDBITS - higherbit(n);
- lua_assert(~(lua_Unsigned)0 >> shf >= n && /* not larger */
- ~(lua_Unsigned)0 >> shf >> 1 < n); /* largest */
- while ((ran >>= shf) > n)
- ran = I2UInt(xorshift128plus(state->s));
- return ran;
+ lua_Unsigned lim = n;
+ if ((lim & (lim + 1)) > 0) { /* 'lim + 1' is not a power of 2? */
+ /* compute the smallest (2^b - 1) not smaller than 'n' */
+ lim |= (lim >> 1);
+ lim |= (lim >> 2);
+ lim |= (lim >> 4);
+ lim |= (lim >> 8);
+ 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 @@
lua_Integer low, up;
lua_Unsigned p;
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 */
case 0: { /* no arguments */
lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */
@@ -511,7 +512,7 @@
state[0] = Int2I(n);
state[1] = Int2I(0xff); /* avoid a zero state */
for (i = 0; i < 16; i++)
- xorshift128plus(state); /* discard initial values to "spread" seed */
+ nextrand(state); /* discard initial values to "spread" seed */
}
