[libc][math] Fix fast path with small inputs for double precision sin/cos. by lntue · Pull Request #221012 · llvm/llvm-project

lntue · 2026-09-03T18:05:43Z

#201748 added a fast branch for small inputs to double precision sin/cos,
but the Ziv error bounds were too tight.

Fixes in this PR:

Updating the Ziv error bounds to accommodate rounding errors.
Copy binary64 sin/cos hard-to-round cases from the CORE-MATH project.
Add python tool to convert textual hard to round cases to binary files, and add those binary files.
Add hard-to-round tests for double precision sin/cos in the exhaustive test folder.

Fixes #220934.

Assisted-by: Gemini is used to generate the worst-case text-to-binary tool.

…/cos.

lntue · 2026-09-03T18:06:49Z

@yklcs @zimmermann6: PTAL. Thanks!

llvmorg-github-actions · 2026-09-03T18:07:45Z

@llvm/pr-subscribers-github-workflow

@llvm/pr-subscribers-libc

Author: lntue

Changes

#201748 added a fast branch for small inputs to double precision sin/cos,
but the Ziv error bounds were too tight.

Fixes in this PR:

Updating the Ziv error bounds to accommodate rounding errors.
Copy binary64 sin/cos hard-to-round cases from the CORE-MATH project.
Add python tool to convert textual hard to round cases to binary files, and add those binary files.
Add hard-to-round tests for double precision sin/cos in the exhaustive test folder.

Fixes #220934.

Assisted-by: Gemini is used to generate the worst-case text-to-binary tool.

Patch is 49.58 MiB, truncated to 20.00 KiB below, full version: https://github.com/llvm/llvm-project/pull/221012.diff

11 Files Affected:

(modified) libc/src/__support/math/cos.h (+3-2)
(modified) libc/src/__support/math/sin.h (+2-2)
(modified) libc/test/src/math/exhaustive/CMakeLists.txt (+44)
(added) libc/test/src/math/exhaustive/cos.bin ()
(added) libc/test/src/math/exhaustive/cos.wc (+1090178)
(added) libc/test/src/math/exhaustive/cos_test.cpp (+21)
(added) libc/test/src/math/exhaustive/sin.bin ()
(added) libc/test/src/math/exhaustive/sin.wc (+1091085)
(added) libc/test/src/math/exhaustive/sin_test.cpp (+21)
(added) libc/test/src/math/exhaustive/worst_case_test.h (+335)
(added) libc/utils/mathtools/wc_to_bin.py (+302)

diff --git a/libc/src/__support/math/cos.h b/libc/src/__support/math/cos.h
index 427132454a2e3..ec88f02a499fe 100644
--- a/libc/src/__support/math/cos.h
+++ b/libc/src/__support/math/cos.h
@@ -116,8 +116,9 @@ LIBC_INLINE double cos(double x) {
 #ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
       return 1.0 + r_lo;
 #else
-      // Overall errors <= ulp(x^2/2) + 2^-69.
-      double err = fputil::multiply_add(x_sq, 0x1.0p-53, 0x1.0p-69);
+      // Overall errors <= 1.0 * ulp(x^2) + 2^-69 for default rounding mode
+      //                <= 2.0 * ulp(x^2) + 2^-69 for directed rounding mode.
+      double err = fputil::multiply_add(x_sq, 0x1.0p-51, 0x1.0p-69);
       double r_lo_u = r_lo + err;
       double r_lo_l = r_lo - err;
       double r_upper = 1.0 + r_lo_u;
diff --git a/libc/src/__support/math/sin.h b/libc/src/__support/math/sin.h
index 0c8933c10fd31..8c16a9ac66d9b 100644
--- a/libc/src/__support/math/sin.h
+++ b/libc/src/__support/math/sin.h
@@ -127,8 +127,8 @@ LIBC_INLINE double sin(double x) {
 #ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
       return x + r_lo;
 #else
-      // Overall errors <= 2 * ulp(x^3/6) + |x| * 2^-68.
-      double err = fputil::multiply_add(x_sq, 0x1.0p-53, 0x1.0p-68);
+      // Overall errors <= ulp(x^3) + |x| * 2^-68.
+      double err = fputil::multiply_add(x_sq, 0x1.0p-52, 0x1.0p-68);
       double r_lo_u = fputil::multiply_add(x, err, r_lo);
       double r_lo_l = fputil::multiply_add(-x, err, r_lo);
       double r_upper = x + r_lo_u;
diff --git a/libc/test/src/math/exhaustive/CMakeLists.txt b/libc/test/src/math/exhaustive/CMakeLists.txt
index 46b5b138cfb11..0c338425a59df 100644
--- a/libc/test/src/math/exhaustive/CMakeLists.txt
+++ b/libc/test/src/math/exhaustive/CMakeLists.txt
@@ -20,6 +20,16 @@ add_header_library(
     libc.src.__support.macros.properties.types
 )
 
+add_header_library(
+  worst_case_test
+  HDRS
+    worst_case_test.h
+  DEPENDS
+    libc.src.__support.CPP.type_traits
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.macros.properties.types
+)
+
 add_fp_unittest(
   sqrtf_test
   NO_RUN_POSTBUILD
@@ -67,6 +77,23 @@ add_fp_unittest(
     -lpthread
 )
 
+add_fp_unittest(
+  sin_test
+  NEED_MPFR
+  SUITE
+    libc_math_exhaustive_tests
+  SRCS
+    sin_test.cpp
+  COMPILE_OPTIONS
+    "-DLIBC_MATH_EXHAUSTIVE_TEST_DIR=\"${CMAKE_CURRENT_SOURCE_DIR}\""
+  DEPENDS
+    .worst_case_test
+    libc.src.math.sin
+    libc.src.__support.FPUtil.fp_bits
+  LINK_LIBRARIES
+    -lpthread
+)
+
 add_fp_unittest(
   sinf_float_test
   NO_RUN_POSTBUILD
@@ -114,6 +141,23 @@ add_fp_unittest(
     -lpthread
 )
 
+add_fp_unittest(
+  cos_test
+  NEED_MPFR
+  SUITE
+    libc_math_exhaustive_tests
+  SRCS
+    cos_test.cpp
+  COMPILE_OPTIONS
+    "-DLIBC_MATH_EXHAUSTIVE_TEST_DIR=\"${CMAKE_CURRENT_SOURCE_DIR}\""
+  DEPENDS
+    .worst_case_test
+    libc.src.math.cos
+    libc.src.__support.FPUtil.fp_bits
+  LINK_LIBRARIES
+    -lpthread
+)
+
 add_fp_unittest(
   cosf_float_test
   NO_RUN_POSTBUILD
diff --git a/libc/test/src/math/exhaustive/cos.bin b/libc/test/src/math/exhaustive/cos.bin
new file mode 100644
index 0000000000000..adbe198eea018
Binary files /dev/null and b/libc/test/src/math/exhaustive/cos.bin differ
diff --git a/libc/test/src/math/exhaustive/cos.wc b/libc/test/src/math/exhaustive/cos.wc
new file mode 100644
index 0000000000000..b6cecad6daeaa
--- /dev/null
+++ b/libc/test/src/math/exhaustive/cos.wc
@@ -0,0 +1,1090178 @@
+# Copied from the CORE-MATH project:
+# Commit: 77792c2c3933e950ae6b058e65018376402f0692
+# Link: https://gitlab.inria.fr/core-math/core-math/-/blob/77792c2c3933e950ae6b058e65018376402f0692/src/binary64/cos/cos.wc
+#
+# worst cases from https://www.vinc17.net/research/testlibm/testlibm-data.xz
+# (update from 2020-11-27), from 0 to pi, with 46 to 54 identical bits after
+# the round bit
+0x1.0009effd4bedap-12
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[truncated]

github-actions · 2026-09-03T18:10:15Z

✅ With the latest revision this PR passed the Python code formatter.

yklcs · 2026-09-04T05:36:50Z

Thanks Tue, our tests are passing as well.
Guessing there's a reason why the new worst-case tests are placed under the exhaustive directory?

lntue · 2026-09-04T06:54:55Z

Thanks Tue, our tests are passing as well. Guessing there's a reason why the new worst-case tests are placed under the exhaustive directory?

I didn't know how long the tests will take in our limited power pre-commit CIs yet, so just in case it takes too long, we will have to make it build-only for precommit CIs, and only run it in our dedicated post commit CIs. So far looks like only our riscv64 qemu precommit CI bot struggle with it. I could imagine when we have many more of these tests, we might have to run all of them in our dedicated post commit CIs.

Also at the moment they mimic other single precision exhaustive test setup, so using quite many things from libc++ that we don't have coverage in LLVM libc yet.

yklcs · 2026-09-04T07:37:26Z

Thanks Tue, our tests are passing as well. Guessing there's a reason why the new worst-case tests are placed under the exhaustive directory?

I didn't know how long the tests will take in our limited power pre-commit CIs yet, so just in case it takes too long, we will have to make it build-only for precommit CIs, and only run it in our dedicated post commit CIs. So far looks like only our riscv64 qemu precommit CI bot struggle with it. I could imagine when we have many more of these tests, we might have to run all of them in our dedicated post commit CIs.

Also at the moment they mimic other single precision exhaustive test setup, so using quite many things from libc++ that we don't have coverage in LLVM libc yet.

Ah I see. Thanks for the quick fix!

[libc][math] Fix fast path with small inputs for double precision sin…

c2ca41a

…/cos.

lntue requested a review from a team as a code owner September 3, 2026 18:05

llvmorg-github-actions Bot added the libc label Sep 3, 2026

Add option to reduce concurrency for exhaustive tests, and fix format.

ca41249

llvmorg-github-actions Bot added the github:workflow label Sep 4, 2026

kaladron self-requested a review September 4, 2026 14:47

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[libc][math] Fix fast path with small inputs for double precision sin/cos. - #221012

[libc][math] Fix fast path with small inputs for double precision sin/cos.#221012
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llvmorg-github-actions Bot commented Sep 3, 2026 •

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