[libc-commits] [libc] [libc][math][c23] Add cospif16 function (PR #113001)

via libc-commits libc-commits at lists.llvm.org
Fri Oct 18 16:54:26 PDT 2024


https://github.com/wldfngrs updated https://github.com/llvm/llvm-project/pull/113001

>From 0d59443daf39e994757f372d9aeb30fb4c22418b Mon Sep 17 00:00:00 2001
From: wldfngrs <wldfngrs at gmail.com>
Date: Sat, 19 Oct 2024 00:14:59 +0100
Subject: [PATCH 1/4] Add cospif16 function

---
 libc/config/linux/aarch64/entrypoints.txt  |   1 +
 libc/config/linux/x86_64/entrypoints.txt   |   1 +
 libc/newhdrgen/yaml/math.yaml              |   7 +
 libc/src/math/CMakeLists.txt               |   1 +
 libc/src/math/cospif16.h                   |  21 +++
 libc/src/math/generic/CMakeLists.txt       |  20 +++
 libc/src/math/generic/cospif16.cpp         | 141 +++++++++++++++++++++
 libc/test/src/math/CMakeLists.txt          |  11 ++
 libc/test/src/math/cospif16_test.cpp       |  38 ++++++
 libc/test/src/math/smoke/CMakeLists.txt    |  11 ++
 libc/test/src/math/smoke/cospif16_test.cpp |  44 +++++++
 11 files changed, 296 insertions(+)
 create mode 100644 libc/src/math/cospif16.h
 create mode 100644 libc/src/math/generic/cospif16.cpp
 create mode 100644 libc/test/src/math/cospif16_test.cpp
 create mode 100644 libc/test/src/math/smoke/cospif16_test.cpp

diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 885827d304efe3..85bb5df358ec3a 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -607,6 +607,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.canonicalizef16
     libc.src.math.ceilf16
     libc.src.math.copysignf16
+    libc.src.math.cospif16
     # TODO: aarch64 bug
     # Please see https://github.com/llvm/llvm-project/pull/100632#issuecomment-2258772681
     # libc.src.math.expf16
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 06ea7bba81f345..f40d752840b85a 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -611,6 +611,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.ceilf16
     libc.src.math.copysignf16
     libc.src.math.coshf16
+    libc.src.math.cospif16
     libc.src.math.exp10f16
     libc.src.math.exp10m1f16
     libc.src.math.exp2f16
diff --git a/libc/newhdrgen/yaml/math.yaml b/libc/newhdrgen/yaml/math.yaml
index 98ea1a0d25fbb7..e0986f00a3b464 100644
--- a/libc/newhdrgen/yaml/math.yaml
+++ b/libc/newhdrgen/yaml/math.yaml
@@ -206,6 +206,13 @@ functions:
     return_type: float
     arguments:
       - type: float
+  - name: cospif16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: ddivl
     standards:
       - stdc
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 516bed499b1941..3836d6562a0748 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -95,6 +95,7 @@ add_math_entrypoint_object(coshf)
 add_math_entrypoint_object(coshf16)
 
 add_math_entrypoint_object(cospif)
+add_math_entrypoint_object(cospif16)
 
 add_math_entrypoint_object(daddl)
 add_math_entrypoint_object(daddf128)
diff --git a/libc/src/math/cospif16.h b/libc/src/math/cospif16.h
new file mode 100644
index 00000000000000..6779e67cdccae6
--- /dev/null
+++ b/libc/src/math/cospif16.h
@@ -0,0 +1,21 @@
+//===-- Implementation header for cospif16 ---------------------*- 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_COSPIF16_H
+#define LLVM_LIBC_SRC_MATH_COSPIF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 cospif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_SINPIF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index d7c7a3431d3d95..e535c9e50b9b86 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -422,6 +422,26 @@ add_entrypoint_object(
     -O3
 )
 
+
+add_entrypoint_object(
+  cospif16
+  SRCS
+    cospif16.cpp
+  HDRS
+    ../cospif16.h
+  DEPENDS
+    libc.src.__support.common
+    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.nearest_integer
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.macros.properties.types
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   sin
   SRCS
diff --git a/libc/src/math/generic/cospif16.cpp b/libc/src/math/generic/cospif16.cpp
new file mode 100644
index 00000000000000..779aab781b9f07
--- /dev/null
+++ b/libc/src/math/generic/cospif16.cpp
@@ -0,0 +1,141 @@
+//===-- Half-precision cospif 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/cospif16.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/nearest_integer.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
+// Table is generated with Sollya as follows:
+// > display = hexadecimal;
+// > for k from 0 to 63 do { round(sin(k * pi/32), SG, RN); };
+static constexpr float SIN_K_PI_OVER_32[64] = {
+    0x0.0p0,        0x1.917a6cp-4,  0x1.8f8b84p-3,  0x1.294062p-2,
+    0x1.87de2ap-2,  0x1.e2b5d4p-2,  0x1.1c73b4p-1,  0x1.44cf32p-1,
+    0x1.6a09e6p-1,  0x1.8bc806p-1,  0x1.a9b662p-1,  0x1.c38b3p-1,
+    0x1.d906bcp-1,  0x1.e9f416p-1,  0x1.f6297cp-1,  0x1.fd88dap-1,
+    0x1p0,          0x1.fd88dap-1,  0x1.f6297cp-1,  0x1.e9f416p-1,
+    0x1.d906bcp-1,  0x1.c38b3p-1,   0x1.a9b662p-1,  0x1.8bc806p-1,
+    0x1.6a09e6p-1,  0x1.44cf32p-1,  0x1.1c73b4p-1,  0x1.e2b5d4p-2,
+    0x1.87de2ap-2,  0x1.294062p-2,  0x1.8f8b84p-3,  0x1.917a6cp-4,
+    0x0.0p0,        -0x1.917a6cp-4, -0x1.8f8b84p-3, -0x1.294062p-2,
+    -0x1.87de2ap-2, -0x1.e2b5d4p-2, -0x1.1c73b4p-1, -0x1.44cf32p-1,
+    -0x1.6a09e6p-1, -0x1.8bc806p-1, -0x1.a9b662p-1, -0x1.c38b3p-1,
+    -0x1.d906bcp-1, -0x1.e9f416p-1, -0x1.f6297ep-1, -0x1.fd88dap-1,
+    -0x1p0,         -0x1.fd88dap-1, -0x1.f6297cp-1, -0x1.e9f416p-1,
+    -0x1.d906bcp-1, -0x1.c38b3p-1,  -0x1.a9b662p-1, -0x1.8bc806p-1,
+    -0x1.6a09e6p-1, -0x1.44cf32p-1, -0x1.1c73b4p-1, -0x1.e2b5d4p-2,
+    -0x1.87de2ap-2, -0x1.294062p-2, -0x1.8f8b84p-3, -0x1.917a6cp-4};
+
+static LIBC_INLINE int32_t range_reduction(float x, float &y) {
+  float kf = fputil::nearest_integer(x * 32);
+  y = fputil::multiply_add<float>(x, 32.0, -kf);
+
+  return static_cast<int32_t>(kf);
+}
+
+LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
+  using FPBits = typename fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+
+  // Range reduction:
+  // For |x| > 1/32, we perform range reduction as follows:
+  // Find k and y such that:
+  //   x = (k + y) * 1/32
+  //   k is an integer
+  //   |y| < 0.5
+  //
+  // This is done by performing:
+  //   k = round(x * 32)
+  //   y = x * 32 - k
+  //
+  // Once k and y are computed, we then deduce the answer by the sine of sum
+  // formula:
+  //   sin(x * pi) = sin((k + y) * pi/32)
+  //           = sin(k * pi/32) * cos(y * pi/32) + sin (y * pi/32) * cos (k *
+  //           pi/32)
+  // The values of sin(k * pi/32) and cos (k * pi/32) for k = 0...63 are
+  // precomputed and stored using a vector of 64 single precision floats. sin(y
+  // * pi/32) and cos(y * pi/32) are computed using degree-9 chebyshev
+  // polynomials generated by Sollya.
+
+  // For signed zeros
+  if (LIBC_UNLIKELY(x_abs == 0U)) return fputil::cast<float16>(1.0f);
+
+  // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
+  if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
+    if (LIBC_UNLIKELY(x_abs <= 0x67FF)) {
+      return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f); 
+    }
+     
+    // Check for NaN or infintiy values
+    if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
+      // If value is equal to infinity
+      if (x_abs == 0x7c00) {
+        fputil::set_errno_if_required(EDOM);
+	fputil::raise_except_if_required(FE_INVALID);
+      }
+
+      return x + FPBits::quiet_nan().get_val();
+    }
+    
+    return fputil::cast<float16>(1.0f); 
+  }
+  
+
+  float f32 = x;
+  float y;
+  int32_t k = range_reduction(f32, y);
+
+  float sin_k = SIN_K_PI_OVER_32[k & 63];
+  float cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
+
+  // Recall;
+  // cos(x * pi/32) = cos((k + y) * pi/32)
+  // 		    = cos(y * pi/32) * cos(k * pi/32) 
+  // 		      - sin(y * pi/32) * sin(k * pi/32) 
+  // Recall, after range reduction, -0.5 <= y <= 0.5. For very small
+  // values of y, calculating sin(y * p/32) can be inaccurate. Generating a
+  // polynomial for sin(y * p/32)/y instead significantly reduces the relative
+  // errors.
+  float ysq = y * y;
+
+  // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
+  // with: 
+  // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
+  float sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
+                                     0x1.a03354p-21f, -0x1.ad02d2p-20f);
+
+  // Note that cosm1_y = cos(y*pi/32) - 1 = cos_y - 1
+  // Derivation:
+  // cos(x * pi) = cos((k + y) * pi/32)
+  //             = cos_k * cos_y + sin_k * sin_y
+  //             = cos_k * (1 + cos_y - 1) + sin_k * sin_y
+  // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
+  // > P = fpminimax(cos(y*pi/32), [|0, 2, 4, 6|],[|1, SG...|], [0, 0.5]);
+  float cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3ccp-8f, 0x1.03a61ap-18f,
+                                         0x1.a6f7a2p-29f);
+
+  if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0))
+    return fputil::cast<float16>(0.0f);
+
+  // Since, cosm1_y = cos_y - 1, therefore:
+  // 	cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y
+  return fputil::cast<float16>(fputil::multiply_add(cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
+}
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 24a5abec898a89..c0209a13287028 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -45,6 +45,17 @@ add_fp_unittest(
 )
 
 
+add_fp_unittest(
+  cospif16_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    cospif16_test.cpp
+  DEPENDS
+    libc.src.math.cospif16
+)
+
 add_fp_unittest(
   daddl_test
   NEED_MPFR
diff --git a/libc/test/src/math/cospif16_test.cpp b/libc/test/src/math/cospif16_test.cpp
new file mode 100644
index 00000000000000..1ba70c31cc1519
--- /dev/null
+++ b/libc/test/src/math/cospif16_test.cpp
@@ -0,0 +1,38 @@
+//===-- Exhaustive test for cospif16 --------------------------------------===//
+//
+// 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/cospif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcCospif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+// Range: [0, Inf]
+static constexpr uint16_t POS_START = 0x0000U;
+static constexpr uint16_t POS_STOP = 0x7c00U;
+
+// Range: [-Inf, 0]
+static constexpr uint16_t NEG_START = 0x8000U;
+static constexpr uint16_t NEG_STOP = 0xfc00U;
+
+TEST_F(LlvmLibcCospif16Test, PositiveRange) {
+  for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x, LIBC_NAMESPACE::cospif16(x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcCospif16Test, NegativeRange) {
+  for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+    float16 x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x, LIBC_NAMESPACE::cospif16(x), 0.5);
+  }
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 3c077240356bd3..8bba7a083da4d7 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -25,6 +25,17 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  cospif16_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    cospif16_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.src.math.cospif16
+)
+
 add_fp_unittest(
   sinf_test
   SUITE
diff --git a/libc/test/src/math/smoke/cospif16_test.cpp b/libc/test/src/math/smoke/cospif16_test.cpp
new file mode 100644
index 00000000000000..7daa5d2956c10f
--- /dev/null
+++ b/libc/test/src/math/smoke/cospif16_test.cpp
@@ -0,0 +1,44 @@
+//===-- Unittests for sinpif16 --------------------------------------------===//
+//
+// 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/errno/libc_errno.h"
+#include "src/math/cospif16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcCospif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcCospif16Test, SpecialNumbers) {
+  LIBC_NAMESPACE::libc_errno = 0;
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(zero));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(neg_zero));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+}
+
+TEST_F(LlvmLibcCospif16Test, Integers) {
+  EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(-0x420));
+  EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(-0x1.4p+14));
+  EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::cospif16(0x421));
+  EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::cospif16(0x333));
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(-0x1.28p4));
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(-0x1.ffcp9));
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(0x1.01p7));
+  EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(0x1.f6cp9));
+}

>From b6e0457809c4ce8033300f706802e3c79cbe8237 Mon Sep 17 00:00:00 2001
From: wldfngrs <wldfngrs at gmail.com>
Date: Sat, 19 Oct 2024 00:20:13 +0100
Subject: [PATCH 2/4] clang format

---
 libc/docs/math/index.rst             |  2 +-
 libc/src/math/generic/cospif16.cpp   | 23 ++++++++++++-----------
 libc/test/src/math/cospif16_test.cpp |  6 ++++--
 3 files changed, 17 insertions(+), 14 deletions(-)

diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 6591cbbdc15584..84ed0e4135eba6 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -280,7 +280,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | cosh      | |check|          |                 |                        | |check|              |                        | 7.12.5.4               | F.10.2.4                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| cospi     | |check|          |                 |                        |                      |                        | 7.12.4.12              | F.10.1.12                  |
+| cospi     | |check|          |                 |                        | |check|              |                        | 7.12.4.12              | F.10.1.12                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | dsqrt     | N/A              | N/A             |   |check|              | N/A                  |       |check|\*        | 7.12.14.6              | F.10.11                    |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/src/math/generic/cospif16.cpp b/libc/src/math/generic/cospif16.cpp
index 779aab781b9f07..90deb4a77dad90 100644
--- a/libc/src/math/generic/cospif16.cpp
+++ b/libc/src/math/generic/cospif16.cpp
@@ -75,28 +75,28 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
   // polynomials generated by Sollya.
 
   // For signed zeros
-  if (LIBC_UNLIKELY(x_abs == 0U)) return fputil::cast<float16>(1.0f);
+  if (LIBC_UNLIKELY(x_abs == 0U))
+    return fputil::cast<float16>(1.0f);
 
   // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
   if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
     if (LIBC_UNLIKELY(x_abs <= 0x67FF)) {
-      return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f); 
+      return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f);
     }
-     
+
     // Check for NaN or infintiy values
     if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
       // If value is equal to infinity
       if (x_abs == 0x7c00) {
         fputil::set_errno_if_required(EDOM);
-	fputil::raise_except_if_required(FE_INVALID);
+        fputil::raise_except_if_required(FE_INVALID);
       }
 
       return x + FPBits::quiet_nan().get_val();
     }
-    
-    return fputil::cast<float16>(1.0f); 
+
+    return fputil::cast<float16>(1.0f);
   }
-  
 
   float f32 = x;
   float y;
@@ -107,8 +107,8 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
 
   // Recall;
   // cos(x * pi/32) = cos((k + y) * pi/32)
-  // 		    = cos(y * pi/32) * cos(k * pi/32) 
-  // 		      - sin(y * pi/32) * sin(k * pi/32) 
+  // 		    = cos(y * pi/32) * cos(k * pi/32)
+  // 		      - sin(y * pi/32) * sin(k * pi/32)
   // Recall, after range reduction, -0.5 <= y <= 0.5. For very small
   // values of y, calculating sin(y * p/32) can be inaccurate. Generating a
   // polynomial for sin(y * p/32)/y instead significantly reduces the relative
@@ -116,7 +116,7 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
   float ysq = y * y;
 
   // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
-  // with: 
+  // with:
   // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
   float sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
                                      0x1.a03354p-21f, -0x1.ad02d2p-20f);
@@ -136,6 +136,7 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
 
   // Since, cosm1_y = cos_y - 1, therefore:
   // 	cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y
-  return fputil::cast<float16>(fputil::multiply_add(cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
+  return fputil::cast<float16>(fputil::multiply_add(
+      cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
 }
 } // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/src/math/cospif16_test.cpp b/libc/test/src/math/cospif16_test.cpp
index 1ba70c31cc1519..2c61086ef8735b 100644
--- a/libc/test/src/math/cospif16_test.cpp
+++ b/libc/test/src/math/cospif16_test.cpp
@@ -26,13 +26,15 @@ static constexpr uint16_t NEG_STOP = 0xfc00U;
 TEST_F(LlvmLibcCospif16Test, PositiveRange) {
   for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
     float16 x = FPBits(v).get_val();
-    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x, LIBC_NAMESPACE::cospif16(x), 0.5);
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x,
+                                   LIBC_NAMESPACE::cospif16(x), 0.5);
   }
 }
 
 TEST_F(LlvmLibcCospif16Test, NegativeRange) {
   for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
     float16 x = FPBits(v).get_val();
-    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x, LIBC_NAMESPACE::cospif16(x), 0.5);
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x,
+                                   LIBC_NAMESPACE::cospif16(x), 0.5);
   }
 }

>From 9a1e08becb07fc6a352c165bebc29825318e60fc Mon Sep 17 00:00:00 2001
From: wldfngrs <wldfngrs at gmail.com>
Date: Sat, 19 Oct 2024 00:51:49 +0100
Subject: [PATCH 3/4] doc update

---
 libc/src/math/generic/cospif16.cpp         | 6 +++---
 libc/test/src/math/smoke/cospif16_test.cpp | 2 +-
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/libc/src/math/generic/cospif16.cpp b/libc/src/math/generic/cospif16.cpp
index 90deb4a77dad90..662f1101862b91 100644
--- a/libc/src/math/generic/cospif16.cpp
+++ b/libc/src/math/generic/cospif16.cpp
@@ -66,9 +66,9 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
   //
   // Once k and y are computed, we then deduce the answer by the sine of sum
   // formula:
-  //   sin(x * pi) = sin((k + y) * pi/32)
-  //           = sin(k * pi/32) * cos(y * pi/32) + sin (y * pi/32) * cos (k *
-  //           pi/32)
+  //   cos(x * pi) = cos((k + y) * pi/32)
+  //           = cos(k * pi/32) * cos(y * pi/32) 
+  //           + sin(y * pi/32) * sin(k * pi/32)
   // The values of sin(k * pi/32) and cos (k * pi/32) for k = 0...63 are
   // precomputed and stored using a vector of 64 single precision floats. sin(y
   // * pi/32) and cos(y * pi/32) are computed using degree-9 chebyshev
diff --git a/libc/test/src/math/smoke/cospif16_test.cpp b/libc/test/src/math/smoke/cospif16_test.cpp
index 7daa5d2956c10f..f6d7483393191f 100644
--- a/libc/test/src/math/smoke/cospif16_test.cpp
+++ b/libc/test/src/math/smoke/cospif16_test.cpp
@@ -1,4 +1,4 @@
-//===-- Unittests for sinpif16 --------------------------------------------===//
+//===-- Unittests for cospif16 --------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.

>From bf93bb460dde909e5a0b13dc2b72ed17c4cb0989 Mon Sep 17 00:00:00 2001
From: wldfngrs <wldfngrs at gmail.com>
Date: Sat, 19 Oct 2024 00:53:45 +0100
Subject: [PATCH 4/4] clang-format

---
 libc/src/math/generic/cospif16.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libc/src/math/generic/cospif16.cpp b/libc/src/math/generic/cospif16.cpp
index 662f1101862b91..21c5722d244fa7 100644
--- a/libc/src/math/generic/cospif16.cpp
+++ b/libc/src/math/generic/cospif16.cpp
@@ -67,7 +67,7 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
   // Once k and y are computed, we then deduce the answer by the sine of sum
   // formula:
   //   cos(x * pi) = cos((k + y) * pi/32)
-  //           = cos(k * pi/32) * cos(y * pi/32) 
+  //           = cos(k * pi/32) * cos(y * pi/32)
   //           + sin(y * pi/32) * sin(k * pi/32)
   // The values of sin(k * pi/32) and cos (k * pi/32) for k = 0...63 are
   // precomputed and stored using a vector of 64 single precision floats. sin(y



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