diff --git a/stl/inc/random b/stl/inc/random
index 4d684d36c1..b832a9bc19 100644
--- a/stl/inc/random
+++ b/stl/inc/random
@@ -238,19 +238,44 @@ private:
     vector<result_type> _Myvec;
 };
 
+_NODISCARD constexpr int _Generate_canonical_iterations(const int _Bits, const uint64_t _Gmin, const uint64_t _Gmax) {
+    // For a URBG type `G` with range == `(G::max() - G::min()) + 1`, returns the number of calls to generate at least
+    // _Bits bits of entropy. Specifically, max(1, ceil(_Bits / log2(range))).
+
+    _STL_INTERNAL_CHECK(0 <= _Bits && _Bits <= 64);
+
+    if (_Bits == 0 || (_Gmax == UINT64_MAX && _Gmin == 0)) {
+        return 1;
+    }
+
+    const auto _Range  = (_Gmax - _Gmin) + 1;
+    const auto _Target = ~uint64_t{0} >> (64 - _Bits);
+    uint64_t _Prod     = 1;
+    int _Ceil          = 0;
+    while (_Prod <= _Target) {
+        ++_Ceil;
+        if (_Prod > UINT64_MAX / _Range) {
+            break;
+        }
+
+        _Prod *= _Range;
+    }
+
+    return _Ceil;
+}
+
 template <class _Real, size_t _Bits, class _Gen>
 _NODISCARD _Real generate_canonical(_Gen& _Gx) { // build a floating-point value from random sequence
     _RNG_REQUIRE_REALTYPE(generate_canonical, _Real);
 
-    const size_t _Digits  = static_cast<size_t>(numeric_limits<_Real>::digits);
-    const size_t _Minbits = _Digits < _Bits ? _Digits : _Bits;
+    constexpr auto _Digits  = static_cast<size_t>(numeric_limits<_Real>::digits);
+    constexpr auto _Minbits = static_cast<int>(_Digits < _Bits ? _Digits : _Bits);
 
-    const _Real _Gxmin = static_cast<_Real>((_Gx.min)());
-    const _Real _Gxmax = static_cast<_Real>((_Gx.max)());
-    const _Real _Rx    = (_Gxmax - _Gxmin) + _Real{1};
+    constexpr auto _Gxmin = static_cast<_Real>((_Gen::min)());
+    constexpr auto _Gxmax = static_cast<_Real>((_Gen::max)());
+    constexpr auto _Rx    = (_Gxmax - _Gxmin) + _Real{1};
 
-    const int _Ceil = static_cast<int>(_STD ceil(static_cast<_Real>(_Minbits) / _STD log2(_Rx)));
-    const int _Kx   = _Ceil < 1 ? 1 : _Ceil;
+    constexpr int _Kx = _Generate_canonical_iterations(_Minbits, (_Gen::min)(), (_Gen::max)());
 
     _Real _Ans{0};
     _Real _Factor{1};
@@ -263,7 +288,45 @@ _NODISCARD _Real generate_canonical(_Gen& _Gx) { // build a floating-point value
     return _Ans / _Factor;
 }
 
-#define _NRAND(eng, resty) (_STD generate_canonical<resty, static_cast<size_t>(-1)>(eng))
+template <class _Gen, class = void>
+struct _Has_static_min_max : false_type {};
+
+// This checks a requirement of N4901 [rand.req.urng] `concept uniform_random_bit_generator` but doesn't attempt
+// to implement the whole concept - we just need to distinguish Standard machinery from tr1 machinery.
+template <class _Gen>
+struct _Has_static_min_max<_Gen, void_t<decltype(bool_constant<(_Gen::min)() < (_Gen::max)()>::value)>> : true_type {};
+
+template <class _Real, class _Gen>
+_NODISCARD _Real _Nrand_impl(_Gen& _Gx) { // build a floating-point value from random sequence
+    _RNG_REQUIRE_REALTYPE(_Nrand_impl, _Real);
+
+    constexpr auto _Digits  = static_cast<size_t>(numeric_limits<_Real>::digits);
+    constexpr auto _Bits    = ~size_t{0};
+    constexpr auto _Minbits = _Digits < _Bits ? _Digits : _Bits;
+
+    if constexpr (_Has_static_min_max<_Gen>::value && _Minbits <= 64) {
+        return _STD generate_canonical<_Real, _Minbits>(_Gx);
+    } else { // TRANSITION, for tr1 machinery only; Standard machinery can call generate_canonical directly
+        const _Real _Gxmin = static_cast<_Real>((_Gx.min)());
+        const _Real _Gxmax = static_cast<_Real>((_Gx.max)());
+        const _Real _Rx    = (_Gxmax - _Gxmin) + _Real{1};
+
+        const int _Ceil = static_cast<int>(_STD ceil(static_cast<_Real>(_Minbits) / _STD log2(_Rx)));
+        const int _Kx   = _Ceil < 1 ? 1 : _Ceil;
+
+        _Real _Ans{0};
+        _Real _Factor{1};
+
+        for (int _Idx = 0; _Idx < _Kx; ++_Idx) { // add in another set of bits
+            _Ans += (static_cast<_Real>(_Gx()) - _Gxmin) * _Factor;
+            _Factor *= _Rx;
+        }
+
+        return _Ans / _Factor;
+    }
+}
+
+#define _NRAND(eng, resty) (_Nrand_impl<resty>(eng))
 
 _INLINE_VAR constexpr int _MP_len = 5;
 using _MP_arr                     = uint64_t[_MP_len];
diff --git a/tests/std/test.lst b/tests/std/test.lst
index 9296abdddd..152e1e4ff0 100644
--- a/tests/std/test.lst
+++ b/tests/std/test.lst
@@ -186,6 +186,7 @@ tests\GH_001638_dllexport_derived_classes
 tests\GH_001850_clog_tied_to_cout
 tests\GH_001858_iostream_exception
 tests\GH_001914_cached_position
+tests\GH_001964_constexpr_generate_canonical
 tests\GH_002030_asan_annotate_vector
 tests\GH_002039_byte_is_not_trivially_swappable
 tests\GH_002058_debug_iterator_race
diff --git a/tests/std/tests/GH_001964_constexpr_generate_canonical/env.lst b/tests/std/tests/GH_001964_constexpr_generate_canonical/env.lst
new file mode 100644
index 0000000000..19f025bd0e
--- /dev/null
+++ b/tests/std/tests/GH_001964_constexpr_generate_canonical/env.lst
@@ -0,0 +1,4 @@
+# Copyright (c) Microsoft Corporation.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+RUNALL_INCLUDE ..\usual_matrix.lst
diff --git a/tests/std/tests/GH_001964_constexpr_generate_canonical/test.cpp b/tests/std/tests/GH_001964_constexpr_generate_canonical/test.cpp
new file mode 100644
index 0000000000..b8d40cb9f1
--- /dev/null
+++ b/tests/std/tests/GH_001964_constexpr_generate_canonical/test.cpp
@@ -0,0 +1,64 @@
+// Copyright (c) Microsoft Corporation.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+#include <random>
+#include <utility>
+
+using namespace std;
+
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+
+int naive_iterations(const int bits, const uint64_t gmin, const uint64_t gmax) {
+    // Naive implementation of [rand.util.canonical]. Note that for large values of range, it's possible that
+    // log2(range) == bits when range < 2^bits. This can lead to incorrect results, so we can't use this function as
+    // a reference for all values.
+
+    const double range = static_cast<double>(gmax) - static_cast<double>(gmin) + 1.0;
+    return max(1, static_cast<int>(ceil(static_cast<double>(bits) / log2(range))));
+}
+
+void test(const int target_bits) {
+    // Increase the range until the number of iterations repeats.
+    uint64_t range = 2;
+    int k          = 0;
+    int prev_k     = -1;
+    while (k != prev_k) {
+        prev_k       = exchange(k, naive_iterations(target_bits, 1, range));
+        const int k1 = _Generate_canonical_iterations(target_bits, 1, range);
+        assert(k == k1);
+        ++range;
+    }
+
+    // Now only check the crossover points, where incrementing the range actually causes the number of iterations to
+    // increase.
+    while (--k != 0) {
+        // The largest range such that k iterations generating [1,range] produces less than target_bits bits.
+        if (k == 1) {
+            range = ~uint64_t{0} >> (64 - target_bits);
+        } else {
+            range = static_cast<uint64_t>(ceil(pow(2.0, static_cast<double>(target_bits) / k))) - 1;
+        }
+
+        int k0 = (k == 1) ? 2 : naive_iterations(target_bits, 1, range);
+        int k1 = _Generate_canonical_iterations(target_bits, 1, range);
+        assert(k0 == k1);
+        assert(k1 == k + 1);
+
+        k0 = (k == 1) ? 1 : naive_iterations(target_bits, 0, range);
+        k1 = _Generate_canonical_iterations(target_bits, 0, range);
+        assert(k0 == k1);
+        assert(k1 == k);
+    }
+}
+
+int main() {
+    STATIC_ASSERT(_Generate_canonical_iterations(53, 1, uint64_t{1} << 32) == 2);
+    STATIC_ASSERT(_Generate_canonical_iterations(64, 0, ~uint64_t{0}) == 1);
+
+    for (int bits = 0; bits <= 64; ++bits) {
+        test(bits);
+    }
+}