[libc][math] Refactor acospif16 implementation to header-only in src/__support/math folder.

libc/shared/math.h

@@ -16,6 +16,7 @@
 #include "math/acosf16.h"
 #include "math/acoshf.h"
 #include "math/acoshf16.h"
+#include "math/acospif16.h"
 #include "math/erff.h"
 #include "math/exp.h"
 #include "math/exp10.h"

libc/shared/math/acospif16.h

@@ -0,0 +1,29 @@
+//===-- Shared acospif16 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_ACOSPIF16_H
+#define LLVM_LIBC_SHARED_MATH_ACOSPIF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acospif16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acospif16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSPIF16_H

libc/src/__support/math/CMakeLists.txt

@@ -95,6 +95,21 @@ add_header_library(
     libc.src.__support.macros.optimization
 )
 
+add_header_library(
+  acospif16
+  HDRS
+    acospif16.h
+  DEPENDS
+    libc.src.__support.FPUtil.cast
+    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/acospif16.h

@@ -0,0 +1,147 @@
+//===-- Implementation header for acospif16 ---------------------*- 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_ACOSPIF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_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/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr 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();
+  }
+
+  // |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;
+
+  // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
+  // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
+  // 0.5]);
+  constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
+                                    0x1.897e36p-6f, 0x1.9efafcp-7f,
+                                    0x1.06d884p-6f};
+  // |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)/pi
+    float interm =
+        fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
+                         POLY_COEFFS[3], POLY_COEFFS[4]);
+
+    return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
+  }
+
+  // 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))
+  //       acospi(x) = 2 * (asin(sqrt(u)) / pi)
+  //
+  // 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)
+  //       acospi(x) = 1 - acos(-x)/pi
+  // 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);
+
+  float asin_sqrt_u =
+      sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
+                                POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
+
+  // Same as acos(x), but devided the expression with pi
+  return fputil::cast<float16>(
+      x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
+             : 2.0f * asin_sqrt_u);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H

libc/src/math/generic/CMakeLists.txt

@@ -4043,16 +4043,8 @@ add_entrypoint_object(
   HDRS
     ../acospif16.h
   DEPENDS
-    libc.hdr.errno_macros
-    libc.hdr.fenv_macros
-    libc.src.__support.FPUtil.cast
-    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.acospif16
+    libc.src.errno.errno
 )
 
 add_header_library(

libc/src/math/generic/acospif16.cpp

@@ -7,128 +7,12 @@
 //===----------------------------------------------------------------------===//
 
 #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/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/acospif16.h"
 
 namespace LIBC_NAMESPACE_DECL {
 
 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();
-  }
-
-  // |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;
-
-  // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
-  // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
-  // 0.5]);
-  constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
-                                    0x1.897e36p-6f, 0x1.9efafcp-7f,
-                                    0x1.06d884p-6f};
-  // |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)/pi
-    float interm =
-        fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
-                         POLY_COEFFS[3], POLY_COEFFS[4]);
-
-    return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
-  }
-
-  // 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))
-  //       acospi(x) = 2 * (asin(sqrt(u)) / pi)
-  //
-  // 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)
-  //       acospi(x) = 1 - acos(-x)/pi
-  // 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);
-
-  float asin_sqrt_u =
-      sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
-                                POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
-
-  // Same as acos(x), but devided the expression with pi
-  return fputil::cast<float16>(
-      x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
-             : 2.0f * asin_sqrt_u);
+  return math::acospif16(x);
 }
+
 } // namespace LIBC_NAMESPACE_DECL

libc/test/shared/CMakeLists.txt

@@ -12,6 +12,7 @@ add_fp_unittest(
     libc.src.__support.math.acosf16
     libc.src.__support.math.acoshf
     libc.src.__support.math.acoshf16
+    libc.src.__support.math.acospif16
     libc.src.__support.math.erff
     libc.src.__support.math.exp
     libc.src.__support.math.exp10

libc/test/shared/shared_math_test.cpp

@@ -8,13 +8,15 @@
 
 #include "shared/math.h"
 #include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
 
 #ifdef LIBC_TYPES_HAS_FLOAT16
 
 TEST(LlvmLibcSharedMathTest, AllFloat16) {
   int exponent;
 
   EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acoshf16(1.0f16));
+  EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acospif16(1.0f16));
 
   EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::exp10f16(0.0f16));