[libc-commits] [libc] [libc][math][c23] Add atanhf16 C23 math function. (PR #132612)

[Harrison Hao via libc-commits]

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@@ -0,0 +1,92 @@
+//===-- Half-precision atanh(x) function ----------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/atanhf16.h"
+#include "explogxf.h"
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+static constexpr size_t N_EXCEPTS = 2;
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANHF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.a5cp-4, atanhf16(x) = 0x1.a74p-4 (RZ)
+    {0x2E97, 0x2E9D, 1, 0, 0},
+    // x = -0x1.a5cp-4, atanhf16(x) = -0x1.a74p-4 (RZ)
+    {0xAE97, 0xAE9D, 0, 1, 0},
+}};
+
+LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+
+  FPBits xbits(x);
+  Sign sign = xbits.sign();
+  uint16_t x_abs = xbits.abs().uintval();
+
+  // |x| >= 1
+  if (LIBC_UNLIKELY(x_abs >= 0x3c00U)) {
+    if (xbits.is_nan())
+      return x;
+
+    // |x| == 1.0
+    if (x_abs == 0x3c00U) {
+      fputil::set_errno_if_required(ERANGE);
+      fputil::raise_except_if_required(FE_DIVBYZERO);
+      return FPBits::inf(sign).get_val();
+    }
+    // |x| > 1.0
+    fputil::set_errno_if_required(EDOM);
+    fputil::raise_except_if_required(FE_INVALID);
+    return FPBits::quiet_nan().get_val();
+  }
+
+  if (auto r = ATANHF16_EXCEPTS.lookup(xbits.uintval());
+      LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // For |x| less than approximately 0.10
+  if (LIBC_UNLIKELY(x_abs <= 0x2e66U)) {
+    // The Taylor expansion of atanh(x) is:
+    //    atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + x^11/11
+    //             = x * [1 + x^2/3 + x^4/5 + x^6/7 + x^8/9 + x^10/11]
+    // When |x| < 0x0100U, this can be approximated by:
+    //    atanh(x) ≈ x + (1/3)*x^3
+    if (LIBC_UNLIKELY(x_abs < 0x0100U)) {
+      return static_cast<float16>(
+          LIBC_UNLIKELY(x_abs == 0) ? x : (x + 0x1.555556p-2f * x * x * x));
+    }
+
+    // For 0x0100U <= |x| <= 0x2e66U:
+    //   Let t = x^2.
+    //   Define P(t) ≈ (1/3)*t + (1/5)*t^2 + (1/7)*t^3 + (1/9)*t^4 + (1/11)*t^5.
+    // Coefficients (from Sollya, RN, hexadecimal):
+    //  1/3 = 0x1.555556p-2, 1/5 = 0x1.99999ap-3, 1/7 = 0x1.24924ap-3,
+    //  1/9 = 0x1.c71c72p-4, 1/11 = 0x1.745d18p-4
+    // Thus, atanh(x) ≈ x * (1 + P(x^2)).
+    float xf = x;
+    float x2 = xf * xf;
+    float pe = fputil::polyeval(x2, 0.0f, 0x1.555556p-2f, 0x1.99999ap-3f,
+                                0x1.24924ap-3f, 0x1.c71c72p-4f, 0x1.745d18p-4f);
+    return fputil::cast<float16>(fputil::multiply_add(xf, pe, xf));
+  }
+
+  float xf = x;
+  return fputil::cast<float16>(0.5f * log_eval((xf + 1.0f) / (xf - 1.0f)));
----------------
harrisonGPU wrote:

Hi @overmighty , I have updated it, but I still don't understand why we don't change 0.5f to 0.5. Do you mean that even if I use 0.5f, log_eval will return a double value, thus automatically converting it to double and it is unnecessary to use 0.5f, right?

https://github.com/llvm/llvm-project/pull/132612