LCOV - code coverage report
Current view: top level - src/common - pg_prng.c (source / functions) Hit Total Coverage
Test: PostgreSQL 17devel Lines: 53 62 85.5 %
Date: 2023-11-29 04:11:06 Functions: 13 16 81.2 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /*-------------------------------------------------------------------------
       2             :  *
       3             :  * Pseudo-Random Number Generator
       4             :  *
       5             :  * We use Blackman and Vigna's xoroshiro128** 1.0 algorithm
       6             :  * to have a small, fast PRNG suitable for generating reasonably
       7             :  * good-quality 64-bit data.  This should not be considered
       8             :  * cryptographically strong, however.
       9             :  *
      10             :  * About these generators: https://prng.di.unimi.it/
      11             :  * See also https://en.wikipedia.org/wiki/List_of_random_number_generators
      12             :  *
      13             :  * Copyright (c) 2021-2023, PostgreSQL Global Development Group
      14             :  *
      15             :  * src/common/pg_prng.c
      16             :  *
      17             :  *-------------------------------------------------------------------------
      18             :  */
      19             : 
      20             : #include "c.h"
      21             : 
      22             : #include <math.h>
      23             : 
      24             : #include "common/pg_prng.h"
      25             : #include "port/pg_bitutils.h"
      26             : 
      27             : /* X/Open (XSI) requires <math.h> to provide M_PI, but core POSIX does not */
      28             : #ifndef M_PI
      29             : #define M_PI 3.14159265358979323846
      30             : #endif
      31             : 
      32             : 
      33             : /* process-wide state vector */
      34             : pg_prng_state pg_global_prng_state;
      35             : 
      36             : 
      37             : /*
      38             :  * 64-bit rotate left
      39             :  */
      40             : static inline uint64
      41    16656564 : rotl(uint64 x, int bits)
      42             : {
      43    16656564 :     return (x << bits) | (x >> (64 - bits));
      44             : }
      45             : 
      46             : /*
      47             :  * The basic xoroshiro128** algorithm.
      48             :  * Generates and returns a 64-bit uniformly distributed number,
      49             :  * updating the state vector for next time.
      50             :  *
      51             :  * Note: the state vector must not be all-zeroes, as that is a fixed point.
      52             :  */
      53             : static uint64
      54     5552188 : xoroshiro128ss(pg_prng_state *state)
      55             : {
      56     5552188 :     uint64      s0 = state->s0,
      57     5552188 :                 sx = state->s1 ^ s0,
      58     5552188 :                 val = rotl(s0 * 5, 7) * 9;
      59             : 
      60             :     /* update state */
      61     5552188 :     state->s0 = rotl(s0, 24) ^ sx ^ (sx << 16);
      62     5552188 :     state->s1 = rotl(sx, 37);
      63             : 
      64     5552188 :     return val;
      65             : }
      66             : 
      67             : /*
      68             :  * We use this generator just to fill the xoroshiro128** state vector
      69             :  * from a 64-bit seed.
      70             :  */
      71             : static uint64
      72       75308 : splitmix64(uint64 *state)
      73             : {
      74             :     /* state update */
      75       75308 :     uint64      val = (*state += UINT64CONST(0x9E3779B97f4A7C15));
      76             : 
      77             :     /* value extraction */
      78       75308 :     val = (val ^ (val >> 30)) * UINT64CONST(0xBF58476D1CE4E5B9);
      79       75308 :     val = (val ^ (val >> 27)) * UINT64CONST(0x94D049BB133111EB);
      80             : 
      81       75308 :     return val ^ (val >> 31);
      82             : }
      83             : 
      84             : /*
      85             :  * Initialize the PRNG state from a 64-bit integer,
      86             :  * taking care that we don't produce all-zeroes.
      87             :  */
      88             : void
      89       37654 : pg_prng_seed(pg_prng_state *state, uint64 seed)
      90             : {
      91       37654 :     state->s0 = splitmix64(&seed);
      92       37654 :     state->s1 = splitmix64(&seed);
      93             :     /* Let's just make sure we didn't get all-zeroes */
      94       37654 :     (void) pg_prng_seed_check(state);
      95       37654 : }
      96             : 
      97             : /*
      98             :  * Initialize the PRNG state from a double in the range [-1.0, 1.0],
      99             :  * taking care that we don't produce all-zeroes.
     100             :  */
     101             : void
     102          14 : pg_prng_fseed(pg_prng_state *state, double fseed)
     103             : {
     104             :     /* Assume there's about 52 mantissa bits; the sign contributes too. */
     105          14 :     int64       seed = ((double) ((UINT64CONST(1) << 52) - 1)) * fseed;
     106             : 
     107          14 :     pg_prng_seed(state, (uint64) seed);
     108          14 : }
     109             : 
     110             : /*
     111             :  * Validate a PRNG seed value.
     112             :  */
     113             : bool
     114       67540 : pg_prng_seed_check(pg_prng_state *state)
     115             : {
     116             :     /*
     117             :      * If the seeding mechanism chanced to produce all-zeroes, insert
     118             :      * something nonzero.  Anything would do; use Knuth's LCG parameters.
     119             :      */
     120       67540 :     if (unlikely(state->s0 == 0 && state->s1 == 0))
     121             :     {
     122           0 :         state->s0 = UINT64CONST(0x5851F42D4C957F2D);
     123           0 :         state->s1 = UINT64CONST(0x14057B7EF767814F);
     124             :     }
     125             : 
     126             :     /* As a convenience for the pg_prng_strong_seed macro, return true */
     127       67540 :     return true;
     128             : }
     129             : 
     130             : /*
     131             :  * Select a random uint64 uniformly from the range [0, PG_UINT64_MAX].
     132             :  */
     133             : uint64
     134        3034 : pg_prng_uint64(pg_prng_state *state)
     135             : {
     136        3034 :     return xoroshiro128ss(state);
     137             : }
     138             : 
     139             : /*
     140             :  * Select a random uint64 uniformly from the range [rmin, rmax].
     141             :  * If the range is empty, rmin is always produced.
     142             :  */
     143             : uint64
     144     2093660 : pg_prng_uint64_range(pg_prng_state *state, uint64 rmin, uint64 rmax)
     145             : {
     146             :     uint64      val;
     147             : 
     148     2093660 :     if (likely(rmax > rmin))
     149             :     {
     150             :         /*
     151             :          * Use bitmask rejection method to generate an offset in 0..range.
     152             :          * Each generated val is less than twice "range", so on average we
     153             :          * should not have to iterate more than twice.
     154             :          */
     155     2093332 :         uint64      range = rmax - rmin;
     156     2093332 :         uint32      rshift = 63 - pg_leftmost_one_pos64(range);
     157             : 
     158             :         do
     159             :         {
     160     3281088 :             val = xoroshiro128ss(state) >> rshift;
     161     3281088 :         } while (val > range);
     162             :     }
     163             :     else
     164         328 :         val = 0;
     165             : 
     166     2093660 :     return rmin + val;
     167             : }
     168             : 
     169             : /*
     170             :  * Select a random int64 uniformly from the range [PG_INT64_MIN, PG_INT64_MAX].
     171             :  */
     172             : int64
     173           0 : pg_prng_int64(pg_prng_state *state)
     174             : {
     175           0 :     return (int64) xoroshiro128ss(state);
     176             : }
     177             : 
     178             : /*
     179             :  * Select a random int64 uniformly from the range [0, PG_INT64_MAX].
     180             :  */
     181             : int64
     182           0 : pg_prng_int64p(pg_prng_state *state)
     183             : {
     184           0 :     return (int64) (xoroshiro128ss(state) & UINT64CONST(0x7FFFFFFFFFFFFFFF));
     185             : }
     186             : 
     187             : /*
     188             :  * Select a random uint32 uniformly from the range [0, PG_UINT32_MAX].
     189             :  */
     190             : uint32
     191       60254 : pg_prng_uint32(pg_prng_state *state)
     192             : {
     193             :     /*
     194             :      * Although xoroshiro128** is not known to have any weaknesses in
     195             :      * randomness of low-order bits, we prefer to use the upper bits of its
     196             :      * result here and below.
     197             :      */
     198       60254 :     uint64      v = xoroshiro128ss(state);
     199             : 
     200       60254 :     return (uint32) (v >> 32);
     201             : }
     202             : 
     203             : /*
     204             :  * Select a random int32 uniformly from the range [PG_INT32_MIN, PG_INT32_MAX].
     205             :  */
     206             : int32
     207           0 : pg_prng_int32(pg_prng_state *state)
     208             : {
     209           0 :     uint64      v = xoroshiro128ss(state);
     210             : 
     211           0 :     return (int32) (v >> 32);
     212             : }
     213             : 
     214             : /*
     215             :  * Select a random int32 uniformly from the range [0, PG_INT32_MAX].
     216             :  */
     217             : int32
     218           2 : pg_prng_int32p(pg_prng_state *state)
     219             : {
     220           2 :     uint64      v = xoroshiro128ss(state);
     221             : 
     222           2 :     return (int32) (v >> 33);
     223             : }
     224             : 
     225             : /*
     226             :  * Select a random double uniformly from the range [0.0, 1.0).
     227             :  *
     228             :  * Note: if you want a result in the range (0.0, 1.0], the standard way
     229             :  * to get that is "1.0 - pg_prng_double(state)".
     230             :  */
     231             : double
     232     1378068 : pg_prng_double(pg_prng_state *state)
     233             : {
     234     1378068 :     uint64      v = xoroshiro128ss(state);
     235             : 
     236             :     /*
     237             :      * As above, assume there's 52 mantissa bits in a double.  This result
     238             :      * could round to 1.0 if double's precision is less than that; but we
     239             :      * assume IEEE float arithmetic elsewhere in Postgres, so this seems OK.
     240             :      */
     241     1378068 :     return ldexp((double) (v >> (64 - 52)), -52);
     242             : }
     243             : 
     244             : /*
     245             :  * Select a random double from the normal distribution with
     246             :  * mean = 0.0 and stddev = 1.0.
     247             :  *
     248             :  * To get a result from a different normal distribution use
     249             :  *   STDDEV * pg_prng_double_normal() + MEAN
     250             :  *
     251             :  * Uses https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
     252             :  */
     253             : double
     254       13326 : pg_prng_double_normal(pg_prng_state *state)
     255             : {
     256             :     double      u1,
     257             :                 u2,
     258             :                 z0;
     259             : 
     260             :     /*
     261             :      * pg_prng_double generates [0, 1), but for the basic version of the
     262             :      * Box-Muller transform the two uniformly distributed random numbers are
     263             :      * expected to be in (0, 1]; in particular we'd better not compute log(0).
     264             :      */
     265       13326 :     u1 = 1.0 - pg_prng_double(state);
     266       13326 :     u2 = 1.0 - pg_prng_double(state);
     267             : 
     268             :     /* Apply Box-Muller transform to get one normal-valued output */
     269       13326 :     z0 = sqrt(-2.0 * log(u1)) * sin(2.0 * M_PI * u2);
     270       13326 :     return z0;
     271             : }
     272             : 
     273             : /*
     274             :  * Select a random boolean value.
     275             :  */
     276             : bool
     277      829742 : pg_prng_bool(pg_prng_state *state)
     278             : {
     279      829742 :     uint64      v = xoroshiro128ss(state);
     280             : 
     281      829742 :     return (bool) (v >> 63);
     282             : }

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