[libc-commits] [libc] [libc][math][c23] Add asinf16() function (PR #124212)

[via libc-commits]

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@@ -0,0 +1,126 @@
+//===-- Half-precision asinf16(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/asinf16.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/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, D, RN);
+static constexpr float PI_2 = 0x1.921fb54442d18p0f;
+
+LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  float xf = x;
+
+  float xsq = xf * xf;
+
+  // |x| <= 0x1p-1, |x| <= 0.5
+  if (x_abs <= 0x3800) {
+    if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) {
+      // asinf16(+/-0) = +/-0
+      if (LIBC_UNLIKELY(x_abs == 0U)) {
+        return x;
+      }
+
+      // Exhaustive tests show that, when:
+      // x > 0, and rounding upward, or
+      // x < 0, and rounding downward, then,
+      // asin(x) = x * 2^-11 + x
+      // else, in other rounding modes,
+      // asin(x) = x
+      int rounding = fputil::quick_get_round();
+
+      if ((xbits.is_pos() && rounding == FE_UPWARD) ||
+          (xbits.is_neg() && rounding == FE_DOWNWARD)) {
+        return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf));
+      }
+      return x;
+    }
+
+    // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
+    // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+    float result =
+        fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+                         0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+    return fputil::cast<float16>(xf * result);
+  }
+
+  // |x| > 1, asinf16(x) = NaN
+  if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+    // |x| <= +/-inf
+    if (LIBC_UNLIKELY(x_abs <= 0x7c00)) {
+      fputil::set_errno_if_required(EDOM);
+      fputil::raise_except_if_required(FE_INVALID);
+    }
+
+    return FPBits::quiet_nan().get_val();
+  }
+
+  // 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)
+  // 5:  Make sin(z/2) subject of the formula:
+  //       sin(z/2) = sqrt((1 - cos(z))/2)
+  // 6:  Recall [3]; x = cos(z). Therefore:
+  //       sin(z/2) = sqrt((1 - x)/2)
+  // 7:  Let u = (1 - x)/2
+  // 8:  Therefore:
+  //       arcsin(sqrt(u)) = z/2
+  //       2 * arcsin(sqrt(u)) = z
+  // 9:  Recall [3], z = pi/2 - y. Therefore:
+  //       y = pi/2 - z
+  //       y = pi/2 - 2 * arcsin(sqrt(u))
+  // 10: Recall [1], y = asin(x). Therefore:
+  //       arcsin(x) = pi/2 - 2 * arcsin(sqrt(u))
+  //
+  // WHY?
+  // 11: Recall [7], u = (1 - x)/2
+  // 12: Since 0.5 < x <= 1, therefore:
+  //       0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
+  //
+  // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
+  // Step [10] as `sqrt(u)` is in range.
+
+  // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0
+  float xf_abs = (xf < 0 ? -xf : xf);
+  float sign = ((xbits.uintval() >> 15) == 1 ? -1.0 : 1.0);
----------------
overmighty wrote:

Nit: unnecessary parentheses.

https://github.com/llvm/llvm-project/pull/124212