in 'random', uses high-order bits instead of low-order
(better statistical properties)
diff --git a/lmathlib.c b/lmathlib.c
index 55b44f8..9432d40 100644
--- a/lmathlib.c
+++ b/lmathlib.c
@@ -1,5 +1,5 @@
/*
-** $Id: lmathlib.c,v 1.126 2018/03/16 14:18:18 roberto Exp roberto $
+** $Id: lmathlib.c,v 1.127 2018/03/22 19:54:49 roberto Exp roberto $
** Standard mathematical library
** See Copyright Notice in lua.h
*/
@@ -281,19 +281,19 @@
/* must take care to not shift stuff by more than 63 slots */
-#define maskFIG (~(~1LLU << (FIGS - 1))) /* use FIGS bits */
-#define shiftFIG (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIG) */
+#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).
*/
static lua_Number I2d (I x) {
- return (lua_Number)(x & maskFIG) * shiftFIG;
+ return (lua_Number)(x >> shiftI) * shiftF;
}
-/* convert an 'I' to a lua_Unsigned */
-#define I2UInt(x) ((lua_Unsigned)(x))
+/* convert an 'I' to a lua_Unsigned (using higher bits) */
+#define I2UInt(x) ((lua_Unsigned)((x) >> (64 - LUA_UNSIGNEDBITS)))
/* convert a lua_Integer to an 'I' */
#define Int2I(x) ((I)(x))
@@ -373,40 +373,47 @@
#if FIGS <= 32
-#define maskHF 0 /* do not need bits from higher half */
-#define maskLOW (~(~UONE << (FIGS - 1))) /* use FIG bits */
-#define shiftFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) /* 2^(-FIG) */
+#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) */
#else /* 32 < FIGS <= 64 */
/* must take care to not shift stuff by more than 31 slots */
-/* use FIG - 32 bits from higher half */
-#define maskHF (~(~UONE << (FIGS - 33)))
+/* use FIGS - 32 bits from lower half */
+#define maskLOW (~(~(lu_int32)0 >> (FIGS - 33) >> 1))
-/* use all bits from lower half */
-#define maskLOW (~(lu_int32)0)
+/* use all bits from higher half */
+#define maskHI (~(lu_int32)0)
-/* 2^(-FIG) == (1 / 2^33) / 2^(FIG-33) */
-#define shiftFIG ((lua_Number)(1.0 / 8589934592.0) / (UONE << (FIGS - 33)))
+#define shiftHI l_mathop(4294967296.0) /* 2^32 */
+
+/* 2^(-64) */
+#define shiftF ((lua_Number)(1 / (shiftHI * shiftHI)))
#endif
-#define twoto32 l_mathop(4294967296.0) /* 2^32 */
-
static lua_Number I2d (I x) {
- lua_Number h = (lua_Number)(x.h & maskHF);
+ lua_Number h = (lua_Number)(x.h & maskHI);
lua_Number l = (lua_Number)(x.l & maskLOW);
- return (h * twoto32 + l) * shiftFIG;
+ return (h * shiftHI + l) * shiftF;
}
static lua_Unsigned I2UInt (I x) {
- return ((lua_Unsigned)x.h << 31 << 1) | x.l;
+#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
}
-static I Int2I (lua_Integer n) {
- lua_Unsigned un = n;
- return packI((lu_int32)un, (lu_int32)(un >> 31 >> 1));
+static I Int2I (lua_Unsigned n) {
+ return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0);
}
#endif /* } */
@@ -421,34 +428,46 @@
/*
+** 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].
-** Because 'ran' has 2^B possible values, the projection can only be
-** uniform when the size of the interval [0, n] is a power of 2 (exact
-** division). To get a uniform projection into [0,lim], we first
-** compute 'lim', the smallest (2^b - 1) not smaller than 'n'. If the
-** random number is inside [0, n], we are done. Otherwise, we try with
-** another 'ran' until we have a result inside the interval.
+** 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.)
*/
static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
RanState *state) {
- 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
+ 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_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(xorshift128plus(state->s));
- return ran & lim;
}
@@ -487,12 +506,12 @@
}
-static void setseed (I *state, lua_Integer n) {
+static void setseed (I *state, lua_Unsigned n) {
int i;
state[0] = Int2I(n);
- state[1] = Int2I(~n);
+ state[1] = Int2I(0xff); /* avoid a zero state */
for (i = 0; i < 16; i++)
- xorshift128plus(state); /* discard initial values */
+ xorshift128plus(state); /* discard initial values to "spread" seed */
}
