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### 512. Seeding `subtract_with_carry_01` from a single unsigned long

Section: 26.6.4 [rand.eng], 99 [tr.rand.eng.sub1] Status: NAD Editorial Submitter: Walter Brown Opened: 2005-07-03 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

Paragraph 8 specifies the algorithm by which a `subtract_with_carry_01` engine is to be seeded given a single unsigned long. This algorithm is seriously flawed in the case where the engine parameter w (also known as word_size) exceeds 31 [bits]. The key part of the paragraph reads:

> sets x(-r) ... x(-1) to (lcg(1)*2**(-w)) mod 1

and so forth.

Since the specified linear congruential engine, lcg, delivers numbers with a maximum of 2147483563 (just a shade under 31 bits), then when w is, for example, 48, each of the x(i) will be less than 2**-17. The consequence is that roughly the first 400 numbers delivered will be conspicuously close to either zero or one.

Unfortunately, this is not an innocuous flaw: One of the predefined engines in [tr.rand.predef], namely `ranlux64_base_01`, has w = 48 and would exhibit this poor behavior, while the original N1378 proposal states that these pre-defined engines are intended to be of "known good properties."

Proposed resolution:

In 5.1.4.4 [tr.rand.eng.sub1], replace the "effects" clause for void seed(unsigned long value = 19780503) by

> Effects: If `value == 0`, sets value to `19780503`. In any case, with a linear congruential generator `lcg`(i) having parameters `mlcg = 2147483563`, `alcg = 40014`, `clcg = 0`, and `lcg(0) = value`, sets carry`(-1)` and `x(-r) … x(-1)` as if executing

> >     linear_congruential<unsigned long, 40014, 0, 2147483563> lcg(value);
> >     seed(lcg);

> to `(lcg(1) · 2-w) mod 1 … (lcg(r) · 2-w) mod 1`, respectively. If `x(-1) == 0`, sets carry`(-1) = 2-w`, else sets carry`(-1) = 0`.

[ Jens provided revised wording post Mont Tremblant. ]

[ Berlin: N1932 adopts the originally-proposed resolution of the issue. Jens's supplied wording is a clearer description of what is intended. Moved to Ready. ]

Rationale:

Jens: I'm using an explicit type here, because fixing the prose would probably not qualify for the (with issue 504 even stricter) requirements we have for seed(Gen&).

[ Portland: Subsumed by N2111. ]