[libc][math] Refactor acosf16 implementation to header-only in src/__support/math folder.

libc/shared/math.h

@@ -13,6 +13,7 @@
 
 #include "math/acos.h"
 #include "math/acosf.h"
+#include "math/acosf16.h"
 #include "math/exp.h"
 #include "math/exp10.h"
 #include "math/exp10f.h"

libc/shared/math/acosf16.h

@@ -0,0 +1,29 @@
+//===-- Shared acosf16 function ---------------------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ACOSF16_H
+#define LLVM_LIBC_SHARED_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acosf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acosf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSF16_H

libc/src/__support/math/CMakeLists.txt

@@ -31,6 +31,22 @@ add_header_library(
     libc.src.__support.macros.optimization
 )
 
+add_header_library(
+  acosf16
+  HDRS
+    acosf16.h
+  DEPENDS
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.sqrt
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.types
+)
+
 add_header_library(
   asin_utils
   HDRS

libc/src/__support/math/acos.h

@@ -26,7 +26,6 @@ namespace math {
 
 static constexpr double acos(double x) {
   using DoubleDouble = fputil::DoubleDouble;
-  using Float128 = fputil::DyadicFloat<128>;
   using namespace asin_internal;
   using FPBits = fputil::FPBits<double>;
 

libc/src/__support/math/acosf16.h

@@ -0,0 +1,164 @@
+//===-- Implementation header for acosf16 -----------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#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 {
+
+namespace math {
+
+static constexpr float16 acosf16(float16 x) {
+
+  // Generated by Sollya using the following command:
+  // > round(pi/2, SG, RN);
+  // > round(pi, SG, RN);
+  constexpr float PI_OVER_2 = 0x1.921fb6p0f;
+  constexpr float PI = 0x1.921fb6p1f;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  constexpr size_t N_EXCEPTS = 2;
+
+  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},
+  }};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  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;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  // Handle exceptional values
+  if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  // |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_OVER_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_OVER_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 - 2 * 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:
+  //       asin(sqrt(u)) = z/2
+  //       2 * asin(sqrt(u)) = z
+  // 9:  Recall [3]; z = pi/2 - y. Therefore:
+  //       y = pi/2 - z
+  //       y = pi/2 - 2 * asin(sqrt(u))
+  // 10: Recall [1], y = asin(x). Therefore:
+  //       asin(x) = pi/2 - 2 * asin(sqrt(u))
+  // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+  //     Therefore:
+  //       acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
+  //       acos(x) = 2 * asin(sqrt(u))
+  //
+  // THE RANGE REDUCTION, HOW?
+  // 12: Recall [7], u = (1 - x)/2
+  // 13: 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 [11] as `sqrt(u)` is in range.
+  // When -1 < x <= -0.5, the identity:
+  //       acos(x) = pi - acos(-x)
+  // allows us to compute for the negative x value (lhs)
+  // with a positive x value instead (rhs).
+
+  float xf_abs = (xf < 0 ? -xf : xf);
+  float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+  float sqrt_u = fputil::sqrt<float>(u);
+
+  // 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 asin_sqrt_u =
+      sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+                                0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+  return fputil::cast<float16>(
+      x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H

libc/src/math/generic/CMakeLists.txt

@@ -4040,17 +4040,8 @@ add_entrypoint_object(
   HDRS
     ../acosf16.h
   DEPENDS
-    libc.hdr.errno_macros
-    libc.hdr.fenv_macros
-    libc.src.__support.FPUtil.cast
-    libc.src.__support.FPUtil.except_value_utils
-    libc.src.__support.FPUtil.fenv_impl
-    libc.src.__support.FPUtil.fp_bits
-    libc.src.__support.FPUtil.multiply_add
-    libc.src.__support.FPUtil.polyeval
-    libc.src.__support.FPUtil.sqrt
-    libc.src.__support.macros.optimization
-    libc.src.__support.macros.properties.types
+    libc.src.__support.math.acosf16
+    libc.src.errno.errno
 )
 
 add_entrypoint_object(