linear_congruential_engine: Fixes for __lce_alg_picker (#81080)

This fixes two major mistakes in the implementation of
`linear_congruential_engine` that allowed it to produce incorrect
output. Specifically, these mistakes are in `__lce_alg_picker`, which is
used to determine whether Schrage's algorithm is valid and needed.

The first mistake is in the definition of `_OverflowOK`. The code
comment and the description of [D65041](https://reviews.llvm.org/D65041)
both indicate that it's supposed to be true iff `m` is a power of two.
However, the definition used does not work out to that, and instead is
true whenever `m` is even. This could result in
`linear_congruential_engine` using an invalid implementation, as it
would incorrectly assume that any integer overflow can't change the
result. I changed the implementation to one that accurately checks if
`m` is a power of two. Technically, this implementation has an edge case
where it considers `0` to be a power of two, but in this case this is
actually accurate behavior, as `m = 0` indicates a modulus of 2^w where
w is the size of `result_type` in bits, which *is* a power of two.

The second mistake is in the static assert. The original static assert
erroneously included an unnecessary `a != 0 || m != 0`. Combined with
the `|| !_MightOverflow`, this actually resulted in the static assert
being impossible to fail. Applying De Morgan's law and expanding
`_MightOverflow` gives that the only way this static assert can be
triggered is if `a == 0 && m == 0 && a != 0 && m != 0 && ...`, which
clearly cannot be true. I simply removed the explicit checks against `a`
and `m`, as the intended checks are already included in `_MightOverflow`
and `_SchrageOK`, and their inclusion doesn't provide any obvious
semantic benefit.

This should fix all the current instances where
`linear_congruential_engine` uses an invalid implementation. This
technically isn't a complete implementation, though, since the static
assert will cause some instantiations of `linear_congruential_engine`
not disallowed by the standard from compiling. However, this should
still be an improvement, as all compiling instantiations of
`linear_congruential_engine` should use a valid implementation. Fixing
the cases where the static assert triggers will require adding
additional implementations, some of which will be fairly non-trivial, so
I'd rather leave those for another PR so they don't hold up these more
important fixes.

Fixes #33554

libcxx/include/__random/linear_congruential_engine.h

@@ -31,10 +31,10 @@ template <unsigned long long __a,
           unsigned long long __m,
           unsigned long long _Mp,
           bool _MightOverflow = (__a != 0 && __m != 0 && __m - 1 > (_Mp - __c) / __a),
-          bool _OverflowOK    = ((__m | (__m - 1)) > __m),                    // m = 2^n
+          bool _OverflowOK    = ((__m & (__m - 1)) == 0ull),                  // m = 2^n
           bool _SchrageOK     = (__a != 0 && __m != 0 && __m % __a <= __m / __a)> // r <= q
 struct __lce_alg_picker {
-  static_assert(__a != 0 || __m != 0 || !_MightOverflow || _OverflowOK || _SchrageOK,
+  static_assert(!_MightOverflow || _OverflowOK || _SchrageOK,
                 "The current values of a, c, and m cannot generate a number "
                 "within bounds of linear_congruential_engine.");
 

libcxx/test/std/numerics/rand/rand.eng/rand.eng.lcong/alg.pass.cpp

@@ -22,48 +22,63 @@ int main(int, char**)
 {
     typedef unsigned long long T;
 
-    // m might overflow, but the overflow is OK so it shouldn't use schrage's algorithm
-    typedef std::linear_congruential_engine<T, 25214903917ull, 1, (1ull<<48)> E1;
+    // m might overflow, but the overflow is OK so it shouldn't use Schrage's algorithm
+    typedef std::linear_congruential_engine<T, 25214903917ull, 1, (1ull << 48)> E1;
     E1 e1;
     // make sure the right algorithm was used
-    assert(e1() == 25214903918);
-    assert(e1() == 205774354444503);
-    assert(e1() == 158051849450892);
+    assert(e1() == 25214903918ull);
+    assert(e1() == 205774354444503ull);
+    assert(e1() == 158051849450892ull);
     // make sure result is in bounds
-    assert(e1() < (1ull<<48));
-    assert(e1() < (1ull<<48));
-    assert(e1() < (1ull<<48));
-    assert(e1() < (1ull<<48));
-    assert(e1() < (1ull<<48));
+    assert(e1() < (1ull << 48));
+    assert(e1() < (1ull << 48));
+    assert(e1() < (1ull << 48));
+    assert(e1() < (1ull << 48));
+    assert(e1() < (1ull << 48));
 
     // m might overflow. The overflow is not OK and result will be in bounds
-    // so we should use shrage's algorithm
-    typedef std::linear_congruential_engine<T, (1ull<<2), 0, (1ull<<63) + 1> E2;
+    // so we should use Schrage's algorithm
+    typedef std::linear_congruential_engine<T, (1ull << 32), 0, (1ull << 63) + 1> E2;
     E2 e2;
-    // make sure shrage's algorithm is used (it would be 0s otherwise)
-    assert(e2() == 4);
-    assert(e2() == 16);
-    assert(e2() == 64);
+    // make sure Schrage's algorithm is used (it would be 0s after the first otherwise)
+    assert(e2() == (1ull << 32));
+    assert(e2() == (1ull << 63) - 1ull);
+    assert(e2() == (1ull << 63) - (1ull << 33) + 1ull);
     // make sure result is in bounds
-    assert(e2() < (1ull<<48) + 1);
-    assert(e2() < (1ull<<48) + 1);
-    assert(e2() < (1ull<<48) + 1);
-    assert(e2() < (1ull<<48) + 1);
-    assert(e2() < (1ull<<48) + 1);
+    assert(e2() < (1ull << 63) + 1);
+    assert(e2() < (1ull << 63) + 1);
+    assert(e2() < (1ull << 63) + 1);
+    assert(e2() < (1ull << 63) + 1);
+    assert(e2() < (1ull << 63) + 1);
 
-    // m will not overflow so we should not use shrage's algorithm
-    typedef std::linear_congruential_engine<T, 1ull, 1, (1ull<<48)> E3;
+    // m might overflow. The overflow is not OK and result will be in bounds
+    // so we should use Schrage's algorithm. m is even
+    typedef std::linear_congruential_engine<T, 0x18000001ull, 0x12347ull, (3ull << 56)> E3;
     E3 e3;
+    // make sure Schrage's algorithm is used
+    assert(e3() == 402727752ull);
+    assert(e3() == 162159612030764687ull);
+    assert(e3() == 108176466184989142ull);
+    // make sure result is in bounds
+    assert(e3() < (3ull << 56));
+    assert(e3() < (3ull << 56));
+    assert(e3() < (3ull << 56));
+    assert(e3() < (3ull << 56));
+    assert(e3() < (3ull << 56));
+
+    // m will not overflow so we should not use Schrage's algorithm
+    typedef std::linear_congruential_engine<T, 1ull, 1, (1ull << 48)> E4;
+    E4 e4;
     // make sure the correct algorithm was used
-    assert(e3() == 2);
-    assert(e3() == 3);
-    assert(e3() == 4);
+    assert(e4() == 2ull);
+    assert(e4() == 3ull);
+    assert(e4() == 4ull);
     // make sure result is in bounds
-    assert(e3() < (1ull<<48));
-    assert(e3() < (1ull<<48));
-    assert(e3() < (1ull<<48));
-    assert(e3() < (1ull<<48));
-    assert(e2() < (1ull<<48));
+    assert(e4() < (1ull << 48));
+    assert(e4() < (1ull << 48));
+    assert(e4() < (1ull << 48));
+    assert(e4() < (1ull << 48));
+    assert(e4() < (1ull << 48));
 
     return 0;
 }

libcxx/test/std/numerics/rand/rand.eng/rand.eng.lcong/assign.pass.cpp

@@ -15,6 +15,7 @@
 
 #include <random>
 #include <cassert>
+#include <climits>
 
 #include "test_macros.h"
 
@@ -35,19 +36,41 @@ template <class T>
 void
 test()
 {
-    test1<T, 0, 0, 0>();
-    test1<T, 0, 1, 2>();
-    test1<T, 1, 1, 2>();
-    const T M(static_cast<T>(-1));
-    test1<T, 0, 0, M>();
-    test1<T, 0, M-2, M>();
-    test1<T, 0, M-1, M>();
-    test1<T, M-2, 0, M>();
-    test1<T, M-2, M-2, M>();
-    test1<T, M-2, M-1, M>();
-    test1<T, M-1, 0, M>();
-    test1<T, M-1, M-2, M>();
-    test1<T, M-1, M-1, M>();
+  const int W = sizeof(T) * CHAR_BIT;
+  const T M(static_cast<T>(-1));
+  const T A(static_cast<T>((static_cast<T>(1) << (W / 2)) - 1));
+
+  // Cases where m = 0
+  test1<T, 0, 0, 0>();
+  test1<T, A, 0, 0>();
+  test1<T, 0, 1, 0>();
+  test1<T, A, 1, 0>();
+
+  // Cases where m = 2^n for n < w
+  test1<T, 0, 0, 256>();
+  test1<T, 5, 0, 256>();
+  test1<T, 0, 1, 256>();
+  test1<T, 5, 1, 256>();
+
+  // Cases where m is odd and a = 0
+  test1<T, 0, 0, M>();
+  test1<T, 0, M - 2, M>();
+  test1<T, 0, M - 1, M>();
+
+  // Cases where m is odd and m % a <= m / a (Schrage)
+  test1<T, A, 0, M>();
+  test1<T, A, M - 2, M>();
+  test1<T, A, M - 1, M>();
+
+  /*
+  // Cases where m is odd and m % a > m / a (not implemented)
+  test1<T, M - 2, 0, M>();
+  test1<T, M - 2, M - 2, M>();
+  test1<T, M - 2, M - 1, M>();
+  test1<T, M - 1, 0, M>();
+  test1<T, M - 1, M - 2, M>();
+  test1<T, M - 1, M - 1, M>();
+  */
 }
 
 int main(int, char**)

libcxx/test/std/numerics/rand/rand.eng/rand.eng.lcong/copy.pass.cpp

@@ -35,19 +35,41 @@ template <class T>
 void
 test()
 {
-    test1<T, 0, 0, 0>();
-    test1<T, 0, 1, 2>();
-    test1<T, 1, 1, 2>();
-    const T M(static_cast<T>(-1));
-    test1<T, 0, 0, M>();
-    test1<T, 0, M-2, M>();
-    test1<T, 0, M-1, M>();
-    test1<T, M-2, 0, M>();
-    test1<T, M-2, M-2, M>();
-    test1<T, M-2, M-1, M>();
-    test1<T, M-1, 0, M>();
-    test1<T, M-1, M-2, M>();
-    test1<T, M-1, M-1, M>();
+  const int W = sizeof(T) * CHAR_BIT;
+  const T M(static_cast<T>(-1));
+  const T A(static_cast<T>((static_cast<T>(1) << (W / 2)) - 1));
+
+  // Cases where m = 0
+  test1<T, 0, 0, 0>();
+  test1<T, A, 0, 0>();
+  test1<T, 0, 1, 0>();
+  test1<T, A, 1, 0>();
+
+  // Cases where m = 2^n for n < w
+  test1<T, 0, 0, 256>();
+  test1<T, 5, 0, 256>();
+  test1<T, 0, 1, 256>();
+  test1<T, 5, 1, 256>();
+
+  // Cases where m is odd and a = 0
+  test1<T, 0, 0, M>();
+  test1<T, 0, M - 2, M>();
+  test1<T, 0, M - 1, M>();
+
+  // Cases where m is odd and m % a <= m / a (Schrage)
+  test1<T, A, 0, M>();
+  test1<T, A, M - 2, M>();
+  test1<T, A, M - 1, M>();
+
+  /*
+  // Cases where m is odd and m % a > m / a (not implemented)
+  test1<T, M - 2, 0, M>();
+  test1<T, M - 2, M - 2, M>();
+  test1<T, M - 2, M - 1, M>();
+  test1<T, M - 1, 0, M>();
+  test1<T, M - 1, M - 2, M>();
+  test1<T, M - 1, M - 1, M>();
+  */
 }
 
 int main(int, char**)

libcxx/test/std/numerics/rand/rand.eng/rand.eng.lcong/default.pass.cpp

@@ -33,19 +33,41 @@ template <class T>
 void
 test()
 {
-    test1<T, 0, 0, 0>();
-    test1<T, 0, 1, 2>();
-    test1<T, 1, 1, 2>();
-    const T M(static_cast<T>(-1));
-    test1<T, 0, 0, M>();
-    test1<T, 0, M-2, M>();
-    test1<T, 0, M-1, M>();
-    test1<T, M-2, 0, M>();
-    test1<T, M-2, M-2, M>();
-    test1<T, M-2, M-1, M>();
-    test1<T, M-1, 0, M>();
-    test1<T, M-1, M-2, M>();
-    test1<T, M-1, M-1, M>();
+  const int W = sizeof(T) * CHAR_BIT;
+  const T M(static_cast<T>(-1));
+  const T A(static_cast<T>((static_cast<T>(1) << (W / 2)) - 1));
+
+  // Cases where m = 0
+  test1<T, 0, 0, 0>();
+  test1<T, A, 0, 0>();
+  test1<T, 0, 1, 0>();
+  test1<T, A, 1, 0>();
+
+  // Cases where m = 2^n for n < w
+  test1<T, 0, 0, 256>();
+  test1<T, 5, 0, 256>();
+  test1<T, 0, 1, 256>();
+  test1<T, 5, 1, 256>();
+
+  // Cases where m is odd and a = 0
+  test1<T, 0, 0, M>();
+  test1<T, 0, M - 2, M>();
+  test1<T, 0, M - 1, M>();
+
+  // Cases where m is odd and m % a <= m / a (Schrage)
+  test1<T, A, 0, M>();
+  test1<T, A, M - 2, M>();
+  test1<T, A, M - 1, M>();
+
+  /*
+  // Cases where m is odd and m % a > m / a (not implemented)
+  test1<T, M - 2, 0, M>();
+  test1<T, M - 2, M - 2, M>();
+  test1<T, M - 2, M - 1, M>();
+  test1<T, M - 1, 0, M>();
+  test1<T, M - 1, M - 2, M>();
+  test1<T, M - 1, M - 1, M>();
+  */
 }
 
 int main(int, char**)

libcxx/test/std/numerics/rand/rand.eng/rand.eng.lcong/values.pass.cpp

@@ -66,19 +66,41 @@ template <class T>
 void
 test()
 {
-    test1<T, 0, 0, 0>();
-    test1<T, 0, 1, 2>();
-    test1<T, 1, 1, 2>();
-    const T M(static_cast<T>(-1));
-    test1<T, 0, 0, M>();
-    test1<T, 0, M-2, M>();
-    test1<T, 0, M-1, M>();
-    test1<T, M-2, 0, M>();
-    test1<T, M-2, M-2, M>();
-    test1<T, M-2, M-1, M>();
-    test1<T, M-1, 0, M>();
-    test1<T, M-1, M-2, M>();
-    test1<T, M-1, M-1, M>();
+  const int W = sizeof(T) * CHAR_BIT;
+  const T M(static_cast<T>(-1));
+  const T A(static_cast<T>((static_cast<T>(1) << (W / 2)) - 1));
+
+  // Cases where m = 0
+  test1<T, 0, 0, 0>();
+  test1<T, A, 0, 0>();
+  test1<T, 0, 1, 0>();
+  test1<T, A, 1, 0>();
+
+  // Cases where m = 2^n for n < w
+  test1<T, 0, 0, 256>();
+  test1<T, 5, 0, 256>();
+  test1<T, 0, 1, 256>();
+  test1<T, 5, 1, 256>();
+
+  // Cases where m is odd and a = 0
+  test1<T, 0, 0, M>();
+  test1<T, 0, M - 2, M>();
+  test1<T, 0, M - 1, M>();
+
+  // Cases where m is odd and m % a <= m / a (Schrage)
+  test1<T, A, 0, M>();
+  test1<T, A, M - 2, M>();
+  test1<T, A, M - 1, M>();
+
+  /*
+  // Cases where m is odd and m % a > m / a (not implemented)
+  test1<T, M - 2, 0, M>();
+  test1<T, M - 2, M - 2, M>();
+  test1<T, M - 2, M - 1, M>();
+  test1<T, M - 1, 0, M>();
+  test1<T, M - 1, M - 2, M>();
+  test1<T, M - 1, M - 1, M>();
+  */
 }
 
 int main(int, char**)