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/*-------------------------------------------------------------------------
*
* Pseudo-Random Number Generator
*
* We use Blackman and Vigna's xoroshiro128** 1.0 algorithm
* to have a small, fast PRNG suitable for generating reasonably
* good-quality 64-bit data. This should not be considered
* cryptographically strong, however.
*
* About these generators: https://prng.di.unimi.it/
* See also https://en.wikipedia.org/wiki/List_of_random_number_generators
*
* Copyright (c) 2021-2023, PostgreSQL Global Development Group
*
* src/common/pg_prng.c
*
*-------------------------------------------------------------------------
*/
#include "c.h"
#include <math.h>
#include "common/pg_prng.h"
#include "port/pg_bitutils.h"
/* X/Open (XSI) requires <math.h> to provide M_PI, but core POSIX does not */
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
/* process-wide state vector */
__thread pg_prng_state pg_global_prng_state;
/*
* 64-bit rotate left
*/
static inline uint64
rotl(uint64 x, int bits)
{
return (x << bits) | (x >> (64 - bits));
}
/*
* The basic xoroshiro128** algorithm.
* Generates and returns a 64-bit uniformly distributed number,
* updating the state vector for next time.
*
* Note: the state vector must not be all-zeroes, as that is a fixed point.
*/
static uint64
xoroshiro128ss(pg_prng_state *state)
{
uint64 s0 = state->s0,
sx = state->s1 ^ s0,
val = rotl(s0 * 5, 7) * 9;
/* update state */
state->s0 = rotl(s0, 24) ^ sx ^ (sx << 16);
state->s1 = rotl(sx, 37);
return val;
}
/*
* We use this generator just to fill the xoroshiro128** state vector
* from a 64-bit seed.
*/
static uint64
splitmix64(uint64 *state)
{
/* state update */
uint64 val = (*state += UINT64CONST(0x9E3779B97f4A7C15));
/* value extraction */
val = (val ^ (val >> 30)) * UINT64CONST(0xBF58476D1CE4E5B9);
val = (val ^ (val >> 27)) * UINT64CONST(0x94D049BB133111EB);
return val ^ (val >> 31);
}
/*
* Initialize the PRNG state from a 64-bit integer,
* taking care that we don't produce all-zeroes.
*/
void
pg_prng_seed(pg_prng_state *state, uint64 seed)
{
state->s0 = splitmix64(&seed);
state->s1 = splitmix64(&seed);
/* Let's just make sure we didn't get all-zeroes */
(void) pg_prng_seed_check(state);
}
/*
* Initialize the PRNG state from a double in the range [-1.0, 1.0],
* taking care that we don't produce all-zeroes.
*/
void
pg_prng_fseed(pg_prng_state *state, double fseed)
{
/* Assume there's about 52 mantissa bits; the sign contributes too. */
int64 seed = ((double) ((UINT64CONST(1) << 52) - 1)) * fseed;
pg_prng_seed(state, (uint64) seed);
}
/*
* Validate a PRNG seed value.
*/
bool
pg_prng_seed_check(pg_prng_state *state)
{
/*
* If the seeding mechanism chanced to produce all-zeroes, insert
* something nonzero. Anything would do; use Knuth's LCG parameters.
*/
if (unlikely(state->s0 == 0 && state->s1 == 0))
{
state->s0 = UINT64CONST(0x5851F42D4C957F2D);
state->s1 = UINT64CONST(0x14057B7EF767814F);
}
/* As a convenience for the pg_prng_strong_seed macro, return true */
return true;
}
/*
* Select a random uint64 uniformly from the range [0, PG_UINT64_MAX].
*/
uint64
pg_prng_uint64(pg_prng_state *state)
{
return xoroshiro128ss(state);
}
/*
* Select a random uint64 uniformly from the range [rmin, rmax].
* If the range is empty, rmin is always produced.
*/
uint64
pg_prng_uint64_range(pg_prng_state *state, uint64 rmin, uint64 rmax)
{
uint64 val;
if (likely(rmax > rmin))
{
/*
* Use bitmask rejection method to generate an offset in 0..range.
* Each generated val is less than twice "range", so on average we
* should not have to iterate more than twice.
*/
uint64 range = rmax - rmin;
uint32 rshift = 63 - pg_leftmost_one_pos64(range);
do
{
val = xoroshiro128ss(state) >> rshift;
} while (val > range);
}
else
val = 0;
return rmin + val;
}
/*
* Select a random int64 uniformly from the range [PG_INT64_MIN, PG_INT64_MAX].
*/
int64
pg_prng_int64(pg_prng_state *state)
{
return (int64) xoroshiro128ss(state);
}
/*
* Select a random int64 uniformly from the range [0, PG_INT64_MAX].
*/
int64
pg_prng_int64p(pg_prng_state *state)
{
return (int64) (xoroshiro128ss(state) & UINT64CONST(0x7FFFFFFFFFFFFFFF));
}
/*
* Select a random uint32 uniformly from the range [0, PG_UINT32_MAX].
*/
uint32
pg_prng_uint32(pg_prng_state *state)
{
/*
* Although xoroshiro128** is not known to have any weaknesses in
* randomness of low-order bits, we prefer to use the upper bits of its
* result here and below.
*/
uint64 v = xoroshiro128ss(state);
return (uint32) (v >> 32);
}
/*
* Select a random int32 uniformly from the range [PG_INT32_MIN, PG_INT32_MAX].
*/
int32
pg_prng_int32(pg_prng_state *state)
{
uint64 v = xoroshiro128ss(state);
return (int32) (v >> 32);
}
/*
* Select a random int32 uniformly from the range [0, PG_INT32_MAX].
*/
int32
pg_prng_int32p(pg_prng_state *state)
{
uint64 v = xoroshiro128ss(state);
return (int32) (v >> 33);
}
/*
* Select a random double uniformly from the range [0.0, 1.0).
*
* Note: if you want a result in the range (0.0, 1.0], the standard way
* to get that is "1.0 - pg_prng_double(state)".
*/
double
pg_prng_double(pg_prng_state *state)
{
uint64 v = xoroshiro128ss(state);
/*
* As above, assume there's 52 mantissa bits in a double. This result
* could round to 1.0 if double's precision is less than that; but we
* assume IEEE float arithmetic elsewhere in Postgres, so this seems OK.
*/
return ldexp((double) (v >> (64 - 52)), -52);
}
/*
* Select a random double from the normal distribution with
* mean = 0.0 and stddev = 1.0.
*
* To get a result from a different normal distribution use
* STDDEV * pg_prng_double_normal() + MEAN
*
* Uses https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
*/
double
pg_prng_double_normal(pg_prng_state *state)
{
double u1,
u2,
z0;
/*
* pg_prng_double generates [0, 1), but for the basic version of the
* Box-Muller transform the two uniformly distributed random numbers are
* expected to be in (0, 1]; in particular we'd better not compute log(0).
*/
u1 = 1.0 - pg_prng_double(state);
u2 = 1.0 - pg_prng_double(state);
/* Apply Box-Muller transform to get one normal-valued output */
z0 = sqrt(-2.0 * log(u1)) * sin(2.0 * M_PI * u2);
return z0;
}
/*
* Select a random boolean value.
*/
bool
pg_prng_bool(pg_prng_state *state)
{
uint64 v = xoroshiro128ss(state);
return (bool) (v >> 63);
}
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