[libc][math][c23] Add acospif16() function (#134664)

Addresses #132211  #132754
Part of #95250

4 files changed, 176 insertions, 0 deletions

diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index d177ff79141c..5161b2b61aa9 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -48,6 +48,8 @@ add_math_entrypoint_object(acosh)
 add_math_entrypoint_object(acoshf)
 add_math_entrypoint_object(acoshf16)
 
+add_math_entrypoint_object(acospif16)
+ 
 add_math_entrypoint_object(asin)
 add_math_entrypoint_object(asinf)
 add_math_entrypoint_object(asinf16)
diff --git a/libc/src/math/acospif16.h b/libc/src/math/acospif16.h
new file mode 100644
index 000000000000..e94a35bdf6fb
--- /dev/null
+++ b/libc/src/math/acospif16.h
@@ -0,0 +1,21 @@
+//===-- 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_MATH_ACOSPIF16_H
+#define LLVM_LIBC_SRC_MATH_ACOSPIF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 acospif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSPIF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index adbed5b2de48..25f583035fbc 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4112,6 +4112,25 @@ add_entrypoint_object(
     libc.src.__support.macros.properties.types  
 )
 
+add_entrypoint_object(
+  acospif16
+  SRCS
+    acospif16.cpp
+  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  
+)
+
 add_header_library(
   atan_utils
   HDRS
diff --git a/libc/src/math/generic/acospif16.cpp b/libc/src/math/generic/acospif16.cpp
new file mode 100644
index 000000000000..bfdf1694e3ba
--- /dev/null
+++ b/libc/src/math/generic/acospif16.cpp
@@ -0,0 +1,134 @@
+//===-- Half-precision acospi 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/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"
+
+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);
+}
+} // namespace LIBC_NAMESPACE_DECL