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https://github.com/lua/lua
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in 'random', uses high-order bits instead of low-order
(better statistical properties)
This commit is contained in:
Roberto Ierusalimschy
parent
c5e3b2f814
commit
bdd10a08b1
117
lmathlib.c
117
lmathlib.c
@ -1,5 +1,5 @@
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/*
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** $Id: lmathlib.c,v 1.126 2018/03/16 14:18:18 roberto Exp roberto $
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** $Id: lmathlib.c,v 1.127 2018/03/22 19:54:49 roberto Exp roberto $
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** Standard mathematical library
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** See Copyright Notice in lua.h
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*/
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@ -281,19 +281,19 @@ static I xorshift128plus (I *state) {
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/* must take care to not shift stuff by more than 63 slots */
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#define maskFIG (~(~1LLU << (FIGS - 1))) /* use FIGS bits */
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#define shiftFIG (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIG) */
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#define shiftI (64 - FIGS) /* leave FIGS bits */
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#define shiftF (l_mathop(0.5) / (1LLU << (FIGS - 1))) /* 2^(-FIG) */
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/*
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** Convert bits from a random integer into a float in the
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** interval [0,1).
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*/
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static lua_Number I2d (I x) {
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return (lua_Number)(x & maskFIG) * shiftFIG;
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return (lua_Number)(x >> shiftI) * shiftF;
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}
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/* convert an 'I' to a lua_Unsigned */
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#define I2UInt(x) ((lua_Unsigned)(x))
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/* convert an 'I' to a lua_Unsigned (using higher bits) */
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#define I2UInt(x) ((lua_Unsigned)((x) >> (64 - LUA_UNSIGNEDBITS)))
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/* convert a lua_Integer to an 'I' */
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#define Int2I(x) ((I)(x))
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@ -373,40 +373,47 @@ static I xorshift128plus (I *state) {
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#if FIGS <= 32
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#define maskHF 0 /* do not need bits from higher half */
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#define maskLOW (~(~UONE << (FIGS - 1))) /* use FIG bits */
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#define shiftFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) /* 2^(-FIG) */
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#define maskLOW 0 /* do not need bits from lower half */
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#define maskHI (~(~(lu_int32)0 >> (FIGS - 1) >> 1)) /* use FIGS bits */
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#define shiftHI 1 /* no shift */
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#define shiftF (1 / l_mathop(4294967296.0)) /* 2^(-32) */
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#else /* 32 < FIGS <= 64 */
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/* must take care to not shift stuff by more than 31 slots */
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/* use FIG - 32 bits from higher half */
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#define maskHF (~(~UONE << (FIGS - 33)))
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/* use FIGS - 32 bits from lower half */
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#define maskLOW (~(~(lu_int32)0 >> (FIGS - 33) >> 1))
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/* use all bits from lower half */
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#define maskLOW (~(lu_int32)0)
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/* use all bits from higher half */
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#define maskHI (~(lu_int32)0)
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/* 2^(-FIG) == (1 / 2^33) / 2^(FIG-33) */
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#define shiftFIG ((lua_Number)(1.0 / 8589934592.0) / (UONE << (FIGS - 33)))
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#define shiftHI l_mathop(4294967296.0) /* 2^32 */
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/* 2^(-64) */
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#define shiftF ((lua_Number)(1 / (shiftHI * shiftHI)))
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#endif
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#define twoto32 l_mathop(4294967296.0) /* 2^32 */
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static lua_Number I2d (I x) {
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lua_Number h = (lua_Number)(x.h & maskHF);
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lua_Number h = (lua_Number)(x.h & maskHI);
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lua_Number l = (lua_Number)(x.l & maskLOW);
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return (h * twoto32 + l) * shiftFIG;
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return (h * shiftHI + l) * shiftF;
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}
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static lua_Unsigned I2UInt (I x) {
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return ((lua_Unsigned)x.h << 31 << 1) | x.l;
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#if (LUA_MAXINTEGER >> 30) <= 1
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/* at most 32 bits; use only high bits */
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return ((lua_Unsigned)x.h);
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#else
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/* at least 33 bits */
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return ((lua_Unsigned)x.h << (LUA_UNSIGNEDBITS - 32)) |
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(lua_Unsigned)x.l >> (64 - LUA_UNSIGNEDBITS);
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#endif
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}
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static I Int2I (lua_Integer n) {
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lua_Unsigned un = n;
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return packI((lu_int32)un, (lu_int32)(un >> 31 >> 1));
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static I Int2I (lua_Unsigned n) {
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return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n & ~(lu_int32)0);
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}
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#endif /* } */
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@ -420,35 +427,47 @@ typedef struct {
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} RanState;
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/*
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** Return the higher bit set in 'x' (first bit is 1).
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*/
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static int higherbit (lua_Unsigned x) {
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/* table of higher bits from 0 to 255 */
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static const unsigned char hb[256] = {
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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,
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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,
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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,
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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,
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8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
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8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
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8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
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8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
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};
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int l = 0;
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while (x >= 256) { l += 8; x >>= 8; }
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return l + hb[x];
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}
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/*
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** Project the random integer 'ran' into the interval [0, n].
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** Because 'ran' has 2^B possible values, the projection can only be
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** uniform when the size of the interval [0, n] is a power of 2 (exact
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** division). To get a uniform projection into [0,lim], we first
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** compute 'lim', the smallest (2^b - 1) not smaller than 'n'. If the
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** random number is inside [0, n], we are done. Otherwise, we try with
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** another 'ran' until we have a result inside the interval.
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** To get a uniform projection into [0,n], we first compute 'shf', the
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** largest number that we can right-shift 'ran' and still get numbers
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** as larger as 'n'. We then shift 'ran'; if the result is inside [0, n],
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** we are done. Otherwise, we try with another 'ran' until we have a
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** result inside the interval. (We use right shifts to avoid the lowest
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** bits of 'ran', which has poorer distributions.)
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*/
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static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
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RanState *state) {
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lua_Unsigned lim = n;
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if ((lim & (lim + 1)) > 0) { /* 'lim + 1' is not a power of 2? */
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/* compute the smallest (2^b - 1) not smaller than 'n' */
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lim |= (lim >> 1);
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lim |= (lim >> 2);
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lim |= (lim >> 4);
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lim |= (lim >> 8);
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lim |= (lim >> 16);
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#if (LUA_MAXINTEGER >> 30 >> 2) > 0
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lim |= (lim >> 32); /* integer type has more than 32 bits */
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#endif
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if (n == 0) return 0; /* special case for the unit set */
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else {
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int shf = LUA_UNSIGNEDBITS - higherbit(n);
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lua_assert(~(lua_Unsigned)0 >> shf >= n && /* not larger */
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~(lua_Unsigned)0 >> shf >> 1 < n); /* largest */
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while ((ran >>= shf) > n)
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ran = I2UInt(xorshift128plus(state->s));
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return ran;
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}
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lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2 */
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&& lim >= n /* not smaller than 'n' */
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&& (lim == 0 || (lim >> 1) < n)); /* it is the smallest one */
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while ((ran & lim) > n)
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ran = I2UInt(xorshift128plus(state->s));
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return ran & lim;
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}
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@ -487,12 +506,12 @@ static int math_random (lua_State *L) {
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}
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static void setseed (I *state, lua_Integer n) {
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static void setseed (I *state, lua_Unsigned n) {
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int i;
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state[0] = Int2I(n);
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state[1] = Int2I(~n);
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state[1] = Int2I(0xff); /* avoid a zero state */
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for (i = 0; i < 16; i++)
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xorshift128plus(state); /* discard initial values */
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xorshift128plus(state); /* discard initial values to "spread" seed */
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}
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