'math.rand()' uses higher bits to produce float value
The call 'math.rand()' converts the higher bits of the internal unsigned
integer random to a float, instead of its lower bits. That ensures that
Lua compiled with different float precisions always generates equal (up
to the available precision) random numbers when given the same seed.
diff --git a/lmathlib.c b/lmathlib.c
index e8e88e7..f2bfff9 100644
--- a/lmathlib.c
+++ b/lmathlib.c
@@ -323,14 +323,18 @@
/*
** Convert bits from a random integer into a float in the
-** interval [0,1).
+** interval [0,1), getting the higher FIG bits from the
+** random unsigned integer and converting that to a float.
*/
-#define maskFIG (~(~(Rand64)1 << (FIGS - 1))) /* use FIGS bits */
-#define shiftFIG \
- (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1))) /* 2^(-FIGS) */
+
+/* must throw out the extra (64 - FIGS) bits */
+#define shift64_FIG (64 - FIGS)
+
+/* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */
+#define scaleFIG (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1)))
static lua_Number I2d (Rand64 x) {
- return (lua_Number)(x & maskFIG) * shiftFIG;
+ return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG;
}
/* convert a 'Rand64' to a 'lua_Unsigned' */
@@ -449,35 +453,49 @@
/* an unsigned 1 with proper type */
#define UONE ((lu_int32)1)
+
#if FIGS <= 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) */
+/* 2^(-FIGS) */
+#define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1)))
+
+/*
+** get up to 32 bits from higher half, shifting right to
+** throw out the extra bits.
+*/
+static lua_Number I2d (Rand64 x) {
+ lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS));
+ return h * scaleFIG;
+}
#else /* 32 < FIGS <= 64 */
/* must take care to not shift stuff by more than 31 slots */
-/* use FIGS - 32 bits from higher half */
-#define maskHI (~(~UONE << (FIGS - 33)))
+/* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */
+#define scaleFIG \
+ ((lua_Number)1.0 / (UONE << 30) / 8.0 / (UONE << (FIGS - 33)))
-/* use 32 bits from lower half */
-#define maskLOW (~(~UONE << 31))
+/*
+** use FIGS - 32 bits from lower half, throwing out the other
+** (32 - (FIGS - 32)) = (64 - FIGS) bits
+*/
+#define shiftLOW (64 - FIGS)
-/* 2^(-FIGS) == (1 / 2^33) / 2^(FIGS-33) */
-#define shiftFIG ((lua_Number)(1.0 / 8589934592.0) / (UONE << (FIGS - 33)))
+/*
+** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32)
+*/
+#define shiftHI ((lua_Number)(UONE << (FIGS - 33)) * 2.0)
-#endif
-
-#define twoto32 l_mathop(4294967296.0) /* 2^32 */
static lua_Number I2d (Rand64 x) {
- lua_Number h = (lua_Number)(x.h & maskHI);
- lua_Number l = (lua_Number)(x.l & maskLOW);
- return (h * twoto32 + l) * shiftFIG;
+ lua_Number h = (lua_Number)trim32(x.h) * shiftHI;
+ lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW);
+ return (h + l) * scaleFIG;
}
+#endif
+
/* convert a 'Rand64' to a 'lua_Unsigned' */
static lua_Unsigned I2UInt (Rand64 x) {
diff --git a/testes/math.lua b/testes/math.lua
index 7c780e5..dc5b84f 100644
--- a/testes/math.lua
+++ b/testes/math.lua
@@ -823,17 +823,19 @@
assert(random(0) == res)
math.randomseed(1007, 0)
- -- using lower bits to generate random floats; (the '% 2^32' converts
+ -- using higher bits to generate random floats; (the '% 2^32' converts
-- 32-bit integers to floats as unsigned)
local res
if floatbits <= 32 then
- -- get all bits from the lower half
- res = (l & ~(~0 << floatbits)) % 2^32
+ -- get all bits from the higher half
+ res = (h >> (32 - floatbits)) % 2^32
else
- -- get 32 bits from the lower half and the rest from the higher half
- res = ((h & ~(~0 << (floatbits - 32))) % 2^32) * 2^32 + (l % 2^32)
+ -- get 32 bits from the higher half and the rest from the lower half
+ res = (h % 2^32) * 2^(floatbits - 32) + ((l >> (64 - floatbits)) % 2^32)
end
- assert(random() * 2^floatbits == res)
+ local rand = random()
+ assert(eq(rand, 0x0.7a7040a5a323c9d6, 2^-floatbits))
+ assert(rand * 2^floatbits == res)
end
math.randomseed(0, os.time())
