Linear Congruential Generator - Parameters in Common Use

Parameters in Common Use

The most efficient LCGs have an m equal to a power of 2, most often m = 232 or m = 264, because this allows the modulus operation to be computed by merely truncating all but the rightmost 32 or 64 bits. The following table lists the parameters of LCGs in common use, including built-in rand functions in runtime libraries of various compilers.

Source m a c output bits of seed in rand / Random(L)
Numerical Recipes 232 1664525 1013904223
Borland C/C++ 232 22695477 1 bits 30..16 in rand, 30..0 in lrand
glibc (used by GCC) 231 1103515245 12345 bits 30..0
ANSI C: Watcom, Digital Mars, CodeWarrior, IBM VisualAge C/C++ 231 1103515245 12345 bits 30..16
Borland Delphi, Virtual Pascal 232 134775813 1 bits 63..32 of (seed * L)
Microsoft Visual/Quick C/C++ 232 214013 (343FD16) 2531011 (269EC316) bits 30..16
Microsoft Visual Basic (6 and earlier) 224 1140671485 (43FD43FD16) 12820163 (C39EC316)
RtlUniform from Native API 231 − 1 2147483629 (7FFFFFED16) 2147483587 (7FFFFFC316)
Apple CarbonLib 231 − 1 16807 0 see MINSTD
MMIX by Donald Knuth 264 6364136223846793005 1442695040888963407
Newlib 264 6364136223846793005 1 bits 63...32
VAX's MTH$RANDOM, old versions of glibc 232 69069 1
Java's java.util.Random 248 25214903917 11 bits 47...16
LC53 in Forth 232 − 5 232 − 333333333 0

As shown above, LCGs do not always use all of the bits in the values they produce. For example, the Java implementation operates with 48-bit values at each iteration but returns only their 32 most significant bits. This is because the higher-order bits have longer periods than the lower order bits (see below). LCGs that use this truncation technique produce statistically better values than those that do not.

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