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

[via libc-commits]

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@@ -0,0 +1,102 @@
+//===-- Half-precision acosh(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/acoshf16.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/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.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> ACOSHF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.6dcp+1, acoshf16(x) = 0x1.b6p+0 (RZ)
+    {0x41B7, 0x3ED8, 1, 0, 0},
+    // x = 0x1.39p+0, acoshf16(x) = 0x1.4f8p-1 (RZ)
+    {0x3CE4, 0x393E, 1, 0, 1},
+}};
+
+LLVM_LIBC_FUNCTION(float16, acoshf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+
+  // Check for NaN input first.
+  if (LIBC_UNLIKELY(xbits.is_nan())) {
+    if (xbits.is_signaling_nan()) {
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    return x;
+  }
+
+  // Check for infinite inputs.
+  if (LIBC_UNLIKELY(xbits.is_inf())) {
+    if (xbits.is_neg()) {
+      fputil::set_errno_if_required(EDOM);
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    return x;
+  }
+
+  // Domain error for inputs less than 1.0.
+  if (LIBC_UNLIKELY(x_abs < 0x3c00U)) {
+    fputil::set_errno_if_required(EDOM);
+    fputil::raise_except_if_required(FE_INVALID);
+    return FPBits::quiet_nan().get_val();
+  }
+
+  // acosh(1.0) exactly equals 0.0
+  if (LIBC_UNLIKELY(x_u == 0x3c00U))
+    return FPBits::zero().get_val();
+
+  if (auto r = ACOSHF16_EXCEPTS.lookup(xbits.uintval());
+      LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  float xf = x;
+  // High-precision polynomial approximation for inputs close to 1.0
+  // ([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:
+  //    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:
+  //    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)) {
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lntue wrote:

You can change this condition to use the bit pattern of `x` instead:  `x_u < ...`.

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