[libc][math] Implement double precision cos correctly rounded to all rounding modes. (#96591)

Sharing the same algorithm as double precision sin:
https://github.com/llvm/llvm-project/pull/95736

3 files changed, 146 insertions, 13 deletions

diff --git a/libc/test/src/math/cos_test.cpp b/libc/test/src/math/cos_test.cpp
index 9a39616..e12e9a8 100644
--- a/libc/test/src/math/cos_test.cpp
+++ b/libc/test/src/math/cos_test.cpp
@@ -6,27 +6,124 @@
 //
 //===----------------------------------------------------------------------===//
 
+#include "src/__support/FPUtil/FPBits.h"
 #include "src/math/cos.h"
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"
 #include "utils/MPFRWrapper/MPFRUtils.h"
 
-#include "hdr/math_macros.h"
-
 using LlvmLibcCosTest = LIBC_NAMESPACE::testing::FPTest<double>;
 
 namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
 
-TEST_F(LlvmLibcCosTest, Range) {
-  static constexpr double _2pi = 6.283185307179586;
-  constexpr StorageType COUNT = 100'000;
-  constexpr StorageType STEP = STORAGE_MAX / COUNT;
-  for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
-    double x = FPBits(v).get_val();
-    // TODO: Expand the range of testing after range reduction is implemented.
-    if (isnan(x) || isinf(x) || x > _2pi || x < -_2pi)
-      continue;
-
-    ASSERT_MPFR_MATCH(mpfr::Operation::Cos, x, LIBC_NAMESPACE::cos(x), 1.0);
+using LIBC_NAMESPACE::testing::tlog;
+
+TEST_F(LlvmLibcCosTest, TrickyInputs) {
+  constexpr double INPUTS[] = {
+      0x1.8000000000009p-23,    0x1.8000000000024p-22,
+      0x1.800000000009p-21,     0x1.20000000000f3p-20,
+      0x1.800000000024p-20,     0x1.e0000000001c2p-20,
+      0x1.940c877fb7dacp-7,     -0x1.f42fb19b5b9b2p-6,
+      -0x1.0285070f9f1bcp-5,    0x1.23f40dccdef72p+0,
+      0x1.43cf16358c9d7p+0,     0x1.addf3b9722265p+0,
+      0x1.ae78d360afa15p+0,     0x1.e31b55306f22cp+2,
+      0x1.e639103a05997p+2,     -0x1.f7898d5a756ddp+2,
+      0x1.1685973506319p+3,     0x1.5f09cad750ab1p+3,
+      -0x1.aaf85537ea4c7p+3,    0x1.4f2b874135d27p+4,
+      0x1.13114266f9764p+4,     0x1.a211877de55dbp+4,
+      -0x1.a5eece87e8606p+4,    0x1.a65d441ea6dcep+4,
+      0x1.1ffb509f3db15p+5,     0x1.2345d1e090529p+5,
+      0x1.c96e28eb679f8p+5,     0x1.be886d9c2324dp+6,
+      -0x1.ab514bfc61c76p+7,    -0x1.14823229799c2p+7,
+      0x1.48ff1782ca91dp+8,     0x1.dcbfda0c7559ep+8,
+      0x1.dcbfda0c7559ep+8,     0x1.2e566149bf5fdp+9,
+      0x1.cb996c60f437ep+9,     0x1.ae945054939c2p+10,
+      -0x1.119471e9216cdp+10,   0x1.ae945054939c2p+10,
+      0x1.fffffffffdb6p+24,     0x1.fd4da4ef37075p+29,
+      0x1.55202aefde314p+31,    0x1.b951f1572eba5p+31,
+      0x1.7776c2343ba4ep+101,   0x1.85fc0f04c0128p+101,
+      0x1.678309fa50d58p+110,   0x1.fffffffffef4ep+199,
+      0x1.3eec5912ea7cdp+331,   -0x1.3eec5912ea7cdp+331,
+      -0x1.6deb37da81129p+205,  0x1.08087e9aad90bp+887,
+      -0x1.08087e9aad90bp+887,  -0x1.8bb5847d49973p+845,
+      0x1.6ac5b262ca1ffp+849,   0x1.f08b14e1c4d0fp+890,
+      0x1.2b5fe88a9d8d5p+903,   0x1.f6d7518808571p+1023,
+      -0x1.a880417b7b119p+1023, 0x1.00a33764a0a83p-7,
+      0x1.fe81868fc47fep+1,     0x1.0da8cc189b47dp-10,
+      0x1.da1838053b866p+5,
+
+  };
+  constexpr int N = sizeof(INPUTS) / sizeof(INPUTS[0]);
+
+  for (int i = 0; i < N; ++i) {
+    double x = INPUTS[i];
+    ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cos, x,
+                                   LIBC_NAMESPACE::cos(x), 0.5);
   }
 }
+
+TEST_F(LlvmLibcCosTest, InDoubleRange) {
+  constexpr uint64_t COUNT = 1'234'51;
+  uint64_t START = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p-50).uintval();
+  uint64_t STOP = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p200).uintval();
+  uint64_t STEP = (STOP - START) / COUNT;
+
+  auto test = [&](mpfr::RoundingMode rounding_mode) {
+    mpfr::ForceRoundingMode __r(rounding_mode);
+    if (!__r.success)
+      return;
+
+    uint64_t fails = 0;
+    uint64_t tested = 0;
+    uint64_t total = 0;
+    double worst_input, worst_output = 0.0;
+    double ulp = 0.5;
+
+    for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
+      double x = FPBits(v).get_val();
+      if (isnan(x) || isinf(x))
+        continue;
+
+      double result = LIBC_NAMESPACE::cos(x);
+      ++total;
+      if (isnan(result) || isinf(result))
+        continue;
+
+      ++tested;
+
+      if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Cos, x, result,
+                                             0.5, rounding_mode)) {
+        ++fails;
+        while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Cos, x,
+                                                  result, ulp, rounding_mode)) {
+          worst_input = x;
+          worst_output = result;
+
+          if (ulp > 1000.0)
+            break;
+
+          ulp *= 2.0;
+        }
+      }
+    }
+    if (fails) {
+      tlog << " Cos failed: " << fails << "/" << tested << "/" << total
+           << " tests.\n";
+      tlog << "   Max ULPs is at most: " << static_cast<uint64_t>(ulp) << ".\n";
+      EXPECT_MPFR_MATCH(mpfr::Operation::Cos, worst_input, worst_output, 0.5,
+                        rounding_mode);
+    }
+  };
+
+  tlog << " Test Rounding To Nearest...\n";
+  test(mpfr::RoundingMode::Nearest);
+
+  tlog << " Test Rounding Downward...\n";
+  test(mpfr::RoundingMode::Downward);
+
+  tlog << " Test Rounding Upward...\n";
+  test(mpfr::RoundingMode::Upward);
+
+  tlog << " Test Rounding Toward Zero...\n";
+  test(mpfr::RoundingMode::TowardZero);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index ee99fb9..d79e296 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3677,3 +3677,13 @@ add_fp_unittest(
   DEPENDS
     libc.src.math.sin
 )
+
+add_fp_unittest(
+  cos_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    cos_test.cpp
+  DEPENDS
+    libc.src.math.cos
+)
diff --git a/libc/test/src/math/smoke/cos_test.cpp b/libc/test/src/math/smoke/cos_test.cpp
new file mode 100644
index 0000000..81c8612
--- /dev/null
+++ b/libc/test/src/math/smoke/cos_test.cpp
@@ -0,0 +1,26 @@
+//===-- Unittests for cos -------------------------------------------------===//
+//
+// 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/cos.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcCosTest = LIBC_NAMESPACE::testing::FPTest<double>;
+
+using LIBC_NAMESPACE::testing::tlog;
+
+TEST_F(LlvmLibcCosTest, SpecialNumbers) {
+  EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(aNaN));
+  EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(inf));
+  EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(neg_inf));
+  EXPECT_FP_EQ_ALL_ROUNDING(1.0, LIBC_NAMESPACE::cos(zero));
+  EXPECT_FP_EQ_ALL_ROUNDING(1.0, LIBC_NAMESPACE::cos(neg_zero));
+  EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(0x1.0p-50));
+  EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(min_normal));
+  EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(min_denormal));
+}