[libc-commits] [libc] [libc][math] Improve the error analysis and accuracy for pow function. (PR #102098)

[via libc-commits]

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@@ -358,42 +358,63 @@ LLVM_LIBC_FUNCTION(double, pow, (double x, double y)) {
   // Then m_x = (1 + dx) / r, and
   //   log2(m_x) = log2( (1 + dx) / r )
   //             = log2(1 + dx) - log2(r).
-  // Perform exact range reduction
+
+  // In order for the overall computations x^y = 2^(y * log2(x)) to has relative
+  // errors < 2^-52 (1ULP), we will need evaluate the exponent part y * log2(x)
+  // with absolute errors < 2^52 (or better, 2^-53).  Since the whole exponent
+  // range for double precision is bounded by |y * log2(x)| < 1076 ~ 2^10, we
+  // need to evaluate log2(x) with absolute errors < 2^-53 * 2^-10 = 2^-63.
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lntue wrote:

Done.

https://github.com/llvm/llvm-project/pull/102098