[libc-commits] [libc] [libc][math][c23] Add acospif16() function (PR #132754)

[via libc-commits]

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@@ -0,0 +1,146 @@
+//===-- Half-precision acospif16(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/acospif16.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" // remove unnecessary includes
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya using the following command:
+// > round(2/pi, SG, RN);
+// > round(1/pi, SG, RN);
+static constexpr float TWO_DIV_PI = 0x1.45f306p-1f;
+static constexpr float PI_INV = 0x1.45f306p-2f;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 2;
+
+LLVM_LIBC_FUNCTION(float16, acospif16, (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)) {
+    // acospif16(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();
+  }
+
+  // TODO: handling for exception values
+
+  // |x| == 0x1p0, x is 1 or -1
+  // if x is (-)1, return 1
+  // if x is (+)1, return 0
+  if (LIBC_UNLIKELY(x_abs == 0x3c00))
+    return fputil::cast<float16>(x_sign ? 1.0f : 0.0f);
+
+  float xf = x;
+  float xsq = xf * xf;
+
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    // if x is 0, return 0.5
+    if (LIBC_UNLIKELY(x_abs == 0))
+      return fputil::cast<float16>(0.5f);
+
+    // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then
+    //            acospi(x) = 0.5 - asin(x)*(INVERSE_PI)
+    // 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]);
----------------
amemov wrote:

Thank you @Intue. I initially did that, but then started overthinking that it might not be correct mathematically and couldn't verify that my original idea was on the right track. 

https://github.com/llvm/llvm-project/pull/132754