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

[Harrison Hao via libc-commits]

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@@ -0,0 +1,120 @@
+//===-- Half-precision acoshf16 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 "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"
+#include "src/math/generic/explogxf.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 = 0x1.6ep+1, acoshf16(x) = 0x1.dbp+0 (RZ)
+    {0x41B7, 0x3ED8, 1, 0, 0},
+    // x = 0x1.c8p+0, acoshf16(x) = 0x1.27cp-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 very close to 1.0
+  // Specifically, for inputs within the range [1, 1.25), we employ the
+  // following step-by-step Taylor expansion derivation to maintain numerical
+  // accuracy:
+  //
+  // Step-by-step derivation:
+  // 1. Define y = acosh(x), thus by definition x = cosh(y).
+  //
+  // 2. Expand cosh(y) using exponential identities:
+  //      cosh(y) = (e^y + e^{-y}) / 2
+  //      For small y, let us set y ≈ sqrt(2 * delta), thus:
+  //      x ≈ cosh(y) ≈ 1 + delta, for small delta
+  //      hence delta = x - 1.
+  //
+  // 3. Express y explicitly in terms of delta (for small delta):
+  //      y = acosh(1 + delta) ≈ sqrt(2 * delta) for very small delta.
+  //
+  // 4. Use Taylor expansion around delta = 0 to obtain a more accurate
+  // polynomial:
+  //      acosh(1 + delta) ≈ sqrt(2 * delta) * [1 - delta/12 + 3*delta^2/160 -
+  //      5*delta^3/896 + 35*delta^4/18432 + ...] For practical computation and
+  //      precision, truncate and fit the polynomial precisely in the range [0,
+  //      0.25].
+  //
+  // 5. The implemented polynomial approximation (coefficients obtained from
+  // careful numerical fitting) is:
+  //      P(delta) ≈ 1 - 0x1.55551ap-4 * delta + 0x1.33160cp-6 * delta^2 -
+  //      0x1.6890f4p-8 * delta^3 + 0x1.8f3a62p-10 * delta^4
+  //
+  // Since delta = x - 1, and 0 <= delta < 0.25, this approximation achieves
+  // high precision and numerical stability.
----------------
harrisonGPU wrote:

I used a Python script to compute the floating-point coefficients and then converted them into hexadecimal (0x) format. I did not use Sollya (before this patch, I had never used Sollya). I have updated it, please review again.

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