[libc-commits] [libc] [libc][math][c23] Add acosf16() function (PR #127731)

[via libc-commits]

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@@ -0,0 +1,147 @@
+//===-- Half-precision acosf16(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/acosf16.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/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, SG, RN);
+// > round(pi, SG, RN);
+static constexpr float PI_2 = 0x1.921fb6p0f;
+static constexpr float PI = 0x1.921fb6p1f;
+
+static constexpr size_t N_EXCEPTS = 2;
+
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    {0xacaf, 0x3e93, 1, 0, 0},
+    {0xb874, 0x4052, 1, 0, 1},
+}};
+
+LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  uint16_t x_sign = x_u >> 15;
+
+  // |x| > 0x1p0, |x| > 1, or x is NaN.
+  if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+    // acosf16(NaN) = NaN
+    if (xbits.is_nan()) {
+      if (xbits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+
+      return x;
+    }
+
+    // 1 < |x| <= +/-inf
+    fputil::raise_except_if_required(FE_INVALID);
+    fputil::set_errno_if_required(EDOM);
+
+    return FPBits::quiet_nan().get_val();
+  }
+
+  float xf = x;
+
+  // Handle exceptional values
+  if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // |x| == 0x1p0, x is 1 or -1
+  // if x is (-)1, return pi, else
+  // if x is (+)1, return 0
+  if (LIBC_UNLIKELY(x_abs == 0x3c00))
+    return fputil::cast<float16>(x_sign ? PI : 0.0f);
+
+  float xsq = xf * xf;
+
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    // if x is 0, return pi/2
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return fputil::cast<float16>(PI_2);
+
+    // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+    // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+    // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+    float interm =
+        fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+                         0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+    return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_2));
+  }
+
+  // When |x| > 0.5, assume that 0.5 < |x| <= 1
+  //
+  // Step-by-step range-reduction proof:
+  // 1:  Let y = asin(x), such that, x = sin(y)
+  // 2:  From complimentary angle identity:
+  //       x = sin(y) = cos(pi/2 - y)
+  // 3:  Let z = pi/2 - y, such that x = cos(z)
+  // 4:  From double angle formula; cos(2A) = 1 - sin^2(A):
+  //       z = 2A, z/2 = A
+  //       cos(z) = 1 - 2 * sin*2(z/2)
----------------
overmighty wrote:

```suggestion
  // 4:  From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
  //       z = 2A, z/2 = A
  //       cos(z) = 1 - 2 * sin^2(z/2)
```

https://github.com/llvm/llvm-project/pull/127731