commit d5fcbe966bc501db8bf6a3809633f0b82e6ae547
Author: Pieter Wuille
Date: Tue Jun 18 12:39:56 2024 -0400
random: improve precision of MakeExponentiallyDistributed
diff --git a/src/random.cpp b/src/random.cpp
index 530dfff1ed..cb5c127e0d 100644
--- a/src/random.cpp
+++ b/src/random.cpp
@@ -775,5 +775,14 @@ void RandomInit()
double MakeExponentiallyDistributed(uint64_t uniform) noexcept
{
- return -std::log1p((uniform >> 16) * -0.0000000000000035527136788 /* -1/2^48 */);
+ // To convert uniform into an exponentially-distributed double, we use two steps:
+ // - Convert uniform into a uniformly-distributed double in range [0, 1), use the expression
+ // ((uniform >> 11) * 0x1.0p-53), as described in https://prng.di.unimi.it/ under
+ // "Generating uniform doubles in the unit interval". Call this value x.
+ // - Given an x in uniformly distributed in [0, 1), we find an exponentially distributed value
+ // by applying the quantile function to it. For the exponential distribution with mean 1 this
+ // is F(x) = -log(1 - x).
+ //
+ // Combining the two, and using log1p(x) = log(1 + x), we obtain the following:
+ return -std::log1p((uniform >> 11) * -0x1.0p-53);
}
@ b6b457db:c4570f8c
2024-07-16 00:13:01commit d5fcbe966bc501db8bf6a3809633f0b82e6ae547 Author: Pieter Wuille