[libc-commits] [libc] [libc][math][c23] implement C23 math function asinpif16 (PR #146226)

[via libc-commits]

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+//===-- Half-precision asinpif16(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/asinpif16.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 {
+
+static constexpr float16 ONE_OVER_TWO = 0.5f16;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_ASINPIF16_EXCEPTS = 3;
+
+static constexpr fputil::ExceptValues<float16, N_ASINPIF16_EXCEPTS>
+    ASINPIF16_EXCEPTS{{
+        // (input_hex, RZ_output_hex, RU_offset, RD_offset, RN_offset)
+        // x = 0.0, asinfpi(0.0) = 0.0
+        {0x0000, 0x0000, 0, 0, 0},
+
+        // x = 1.0, asinfpi(1) = 1/2
+        {(fputil::FPBits<float16>(1.0f16)).uintval(),
+         (fputil::FPBits<float16>(ONE_OVER_TWO)).uintval(), 0, 0, 0},
+
+        // x = -1.0, asinfpi(-1.0) = -1/2
+        {(fputil::FPBits<float16>(-1.0f16)).uintval(),
+         (fputil::FPBits<float16>(-ONE_OVER_TWO)).uintval(), 0, 0, 0},
+    }};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+
+  FPBits xbits(x);
+  uint16_t x_uint = xbits.uintval();
+  bool is_neg = static_cast<bool>(x_uint >> 15);
+  float16 x_abs = is_neg ? -x : x;
+
+  auto signed_result = [is_neg](auto r) -> auto { return is_neg ? -r : r; };
+
+  if (LIBC_UNLIKELY(x_abs > 1.0f16)) {
+    // aspinf16(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();
+  }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  // exceptional values
+  if (auto r = ASINPIF16_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  // the coefficients for the polynomial approximation of asin(x)/pi in the
+  // range [0, 0.5] extracted using python-sympy
+  //
+  // Python code to generate the coefficients:
+  //  > from sympy import *
+  //  > import math
+  //  > x = symbols('x')
+  //  > print(series(asin(x)/math.pi, x, 0, 21))
+  //
+  // OUTPUT:
+  //
+  // 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 +
+  // 0.0142102627760621*x**7 + 0.00967087327815336*x**9 +
+  // 0.00712127941391293*x**11 + 0.00552355646848375*x**13 +
+  // 0.00444514782463692*x**15 + 0.00367705242846804*x**17 +
+  // 0.00310721681820837*x**19 + O(x**21)
+  //
+  // it's very accurate in the range [0, 0.5] and has a maximum error of
+  // 0.0000000000000001 in the range [0, 0.5].
+  static constexpr double POLY_COEFFS[10] = {
+      0.318309886183791,   // x^1
+      0.0530516476972984,  // x^3
+      0.0238732414637843,  // x^5
+      0.0142102627760621,  // x^7
+      0.00967087327815336, // x^9
+      0.00712127941391293, // x^11
+      0.00552355646848375, // x^13
+      0.00444514782463692, // x^15
+      0.00367705242846804, // x^17
+      0.00310721681820837  // x^19
+  };
+
+  // polynomial evaluation using horner's method
+  // work only for |x| in [0, 0.5]
+  auto asinpi_polyeval = [](double xsq) -> double {
+    return fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
+                            POLY_COEFFS[3], POLY_COEFFS[4], POLY_COEFFS[5],
+                            POLY_COEFFS[6], POLY_COEFFS[7], POLY_COEFFS[8],
+                            POLY_COEFFS[9]);
+  };
+
+  // if |x| <= 0.5:
+  if (LIBC_UNLIKELY(x_abs <= ONE_OVER_TWO)) {
+    // Use polynomial approximation of asin(x)/pi in the range [0, 0.5]
+    double xd = static_cast<double>(x);
+    double xsq = xd * xd;
+    double result = xd * asinpi_polyeval(xsq);
+    return fputil::cast<float16>(signed_result(result));
+  }
+
+  // If |x| > 0.5, we need to use the range reduction method:
+  //    y = asin(x) => x = sin(y)
+  //      because: sin(a) = cos(pi/2 - a)
+  //      therefore:
+  //    x = cos(pi/2 - y)
+  //      let z = pi/2 - y,
+  //    x = cos(z)
+  //      becuase: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2
----------------
lntue wrote:

typo: `because`

https://github.com/llvm/llvm-project/pull/146226