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@@ -522,16 +522,18 @@ typedef struct {
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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 is a power of 2 (exact
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-** division). To get a uniform projection into [0, n], we first compute
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-** 'lim', the smallest Mersenne number not smaller than 'n'. We then
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-** project 'ran' into the interval [0, lim]. If the result is inside
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-** [0, n], we are done. Otherwise, we try with another 'ran', until we
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-** have a result inside the interval.
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+** division). Otherwise, to get a uniform projection into [0, n], we
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+** first compute 'lim', the smallest Mersenne number not smaller than
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+** 'n'. We then project 'ran' into the interval [0, lim]. If the result
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+** is inside [0, n], we are done. Otherwise, we try with another 'ran',
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+** until we have a result inside the interval.
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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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+ if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */
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+ return ran & n; /* no bias */
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+ else {
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+ lua_Unsigned lim = n;
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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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@@ -541,13 +543,13 @@ static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
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#if (LUA_MAXUNSIGNED >> 31) >= 3
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lim |= (lim >> 32); /* integer type has more than 32 bits */
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#endif
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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 >> 1) < n); /* and it is the smallest one */
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+ while ((ran &= lim) > n) /* project 'ran' into [0..lim] */
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+ ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */
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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)); /* and it is the smallest one */
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- while ((ran &= lim) > n) /* project 'ran' into [0..lim] */
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- ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */
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- return ran;
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}
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