[libc-commits] [libc] [libc][math][c23] Add acoshf16 C23 math function. (PR #130588)

[Harrison Hao via libc-commits]

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@@ -74,16 +66,29 @@ LLVM_LIBC_FUNCTION(float16, acoshf16, (float16 x)) {
   // ([1, 1.25)).
   //
   // Brief derivation:
-  // 1. Start from the definition: acosh(x) = y means x = cosh(y).
-  // 2. Set x = 1 + delta. For small delta, y ≈ sqrt(2 * delta).
-  // 3. Expand acosh(1 + delta) using Taylor series around delta=0:
+  // 1. Expand acosh(1 + delta) using Taylor series around delta=0:
   //    acosh(1 + delta) ≈ sqrt(2 * delta) * [1 - delta/12 + 3*delta^2/160
   //                     - 5*delta^3/896 + 35*delta^4/18432 + ...]
-  // 4. Truncate the series to fit accurately for delta in [0, 0.25].
-  // 5. Polynomial coefficients (from sollya) used here are:
+  // 2. Truncate the series to fit accurately for delta in [0, 0.25].
+  // 3. Polynomial coefficients (from sollya) used here are:
   //    P(delta) ≈ 1 - 0x1.555556p-4 * delta + 0x1.333334p-6 * delta^2
   //               - 0x1.6db6dcp-8 * delta^3 + 0x1.f1c71cp-10 * delta^4
-  if (LIBC_UNLIKELY(xf < 1.25f)) {
+  // 4. The Sollya commands used to generate these coefficients were:
+  //      > display = hexadecimal;
+  //      > round(1/12, SG, RN);
+  //      > round(3/160, SG, RN);
+  //      > round(5/896, SG, RN);
+  //      > round(35/18432, SG, RN);
+  //      With hexadecimal display mode enabled, the outputs were:
+  //      0x1.555556p-4
+  //      0x1.333334p-6
+  //      0x1.6db6dcp-8
+  //      0x1.f1c71cp-10
+  // 5. The maximum absolute error, estimated using:
+  //      dirtyinfnorm(acosh(1 + x) - sqrt(2*x) * P(x), [0, 0.25])
+  //    is:
+  //      0x1.d84281p-22
+  if (LIBC_UNLIKELY(x_u < 1.25f)) {
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harrisonGPU wrote:

Okay, I have updated it. @lntue  :-)

https://github.com/llvm/llvm-project/pull/130588