[libc-commits] [libc] [libc][math][c23] Add atanf16() function (PR #141612)

[via libc-commits]

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@@ -0,0 +1,108 @@
+//===-- Half-precision atanf16(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/atanf16.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 Solly using the following command:
+// > round(pi/2, D, RN);
+static constexpr float PI_2 = 0x1.921fb54442d18p0f;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 6;
+
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    {0x2745, 0x2744, 1, 0, 1},
+    {0x3099, 0x3090, 1, 0, 1},
+    {0x3c6c, 0x3aae, 1, 0, 1},
+    {0x466e, 0x3daa, 1, 0, 1},
+    {0x48ae, 0x3ddb, 1, 0, 0},
+    {0x5619, 0x3e3d, 1, 0, 1},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+LLVM_LIBC_FUNCTION(float16, atanf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  bool x_sign = x_u >> 15;
+  float sign = (x_sign ? -1.0 : 1.0);
+
+  // |x| >= +/-inf
+  if (LIBC_UNLIKELY(x_abs >= 0x7c00U)) {
+    if (xbits.is_nan()) {
+      if (xbits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+      return x;
+    }
+
+    // atanf16(+/-inf) = +/-pi/2
+    return fputil::cast<float16>(sign * PI_2);
+  }
+
+  float xf = x;
+  float xsq = xf * xf;
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  // Handle exceptional values
+  if (auto r = ATANF16_EXCEPTS.lookup_odd(x_abs, x_sign);
+      LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+#endif
+
+  // |x| <= 0x1p0, |x| <= 1
+  if (x_abs <= 0x3C00) {
+    // atanf16(+/-0) = +/-0
+    if (LIBC_UNLIKELY(x_abs == 0)) {
+      return x;
+    }
+
+    // Degree-14 minimax odd polynomial of atan(x) generated by Sollya with:
+    // > P = fpminimax(atan(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|SG...|],
+    // [0, 1]);
+    float result = fputil::polyeval(
+        xsq, 0x1.fffffcp-1f, -0x1.55519ep-2f, 0x1.98f6a8p-3f, -0x1.1f0a92p-3f,
+        0x1.95b654p-4f, -0x1.e65492p-5f, 0x1.8c0c36p-6f, -0x1.32316ep-8f);
+    return fputil::cast<float16>(xf * result);
+  }
+
+  // If |x| > 1
+  // y = atan(x) = sign(x) * atan(|x|)
+  // atan(|x|) = pi/2 - atan(1/|x|)
+  // Recall, 1/|x| < 1
+  float x_inv_sq = 1 / xsq;
----------------
overmighty wrote:

Nit:

```suggestion
  float x_inv_sq = 1.0f / xsq;
```

https://github.com/llvm/llvm-project/pull/141612