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Warning about discard() by powers of two with power-of-two moduli #173

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Merged
mborland merged 1 commit into from
Nov 3, 2026
Merged

Warning about discard() by powers of two with power-of-two moduli #173

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18 changes: 18 additions & 0 deletions doc/generators.qbk
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Expand Up @@ -115,3 +115,21 @@ If you need either double or float as the return type prefer __xoshiro256d or __
[note These random number generators are not intended for use in applications
where non-deterministic random numbers are required. See __random_device
for a choice of (hopefully) non-deterministic random number generators.]

[warning For linear congruential generators with a power-of-two modulus, such
as __rand48, `discard()` by a power of two yields strongly correlated streams.
These are the first outputs of a default-constructed __rand48 (left) and of a
copy after `discard(UINT64_C(1) << 47)` (right):
``
0x055424a4 0x455424a4
0x3a2ccef5 0x7a2ccef5
0x6adb4a65 0x2adb4a65
0x2b019719 0x6b019719
0x4861f4ef 0x0861f4ef
0x0039e5ef 0x4039e5ef
0x1802eeec 0x5802eeec
0x7ec68b3f 0x3ec68b3f
``
The two streams differ only in the top bit, at every step. In general, for
__rand48, `discard()` by 2[sup 17+t] leaves the lowest t bits of the outputs of
the two streams identical.]
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