algo: implement sine/cosine based on Intel SVML for single/double precision #1

seiko2plus · 2025-06-04T16:22:59Z

Add sin/cos functions with ≤1 ULP and ≤4 ULP accuracy variants
Support large argument ranges with proper range reduction
Standalone implementation doesn't require libm
Written using Google Highway
implemented for both float32 and float64 data types

- Add sin/cos functions with ≤1 ULP and ≤4 ULP accuracy variants - Support large argument ranges with proper range reduction - Standalone implementation doesn't require libm - Written using Google Highway for SIMD optimization - Optimize for both float32 and float64 data types

Copilot

Pull Request Overview

This PR implements highly accurate sine and cosine functions using Intel SVML techniques and extended precision range reduction, with separate implementations for small and large argument cases. Key changes include:

New implementations of sin/cos functions that guarantee ≤1 ULP (single precision) and ≤4 ULP (double precision) accuracy.
Support for large argument range reduction using multi-precision techniques based on a precomputed lookup table.
Integration with the Google Highway library for platform-specific SIMD optimizations.

Reviewed Changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
npsr/utils-inl.h	Adds utility functions with conditional compilation and lookup support.
npsr/trig/small-inl.h	Provides polynomial approximations for small-angle sin/cos calculations.
npsr/trig/lut-inl.h.py	Implements a Python script to generate lookup tables for trigonometric reductions and approximations.
npsr/trig/large-inl.h	Implements the extended precision algorithm for large argument reduction.
npsr/trig/inl.h	Integrates the small and large argument implementations into a unified sin/cos API.
npsr/npsr.h	Wraps the trigonometric headers ensuring single inclusion per target.
npsr/common.h	Provides common macros, type definitions, and an RAII class for floating‑point environment control.

Comments suppressed due to low confidence (2)

npsr/trig/small-inl.h:338

Cosine-specific adjustments are marked as TODO and not yet implemented. Please complete the phase adjustment logic (i.e. correctly apply the π/2 shift) to ensure cosine accuracy matches the sine pathway.

    // TODO: Implement cosine-specific adjustments

npsr/trig/large-inl.h:147

[nitpick] Consider adding more inline comments to explain the rationale behind the magic numbers used for fractional shifts to improve code clarity and maintainability.

constexpr int kFracMidShift = kIsSingle ? 18 : 24;

Copilot · 2025-06-06T15:50:05Z

npsr/common.h

+ *
+ * Precise precise = {kLowAccuracy, kNoSpecialCases, kNoLargeArgument};
+ * const ScalableTag<float> d;
+ * typename V = Vec<DFromV<SclableTag>>;


There is a typo in the documentation comment: 'SclableTag' should be corrected to 'ScalableTag'.

Suggested change

* typename V = Vec<DFromV<SclableTag>>;

* typename V = Vec<DFromV<ScalableTag>>;

Mousius

In general I think this is a good starting point. Do you want to land this with #if 0 and other various things incomplete @seiko2plus? We can be a bit relaxed as we setup the repo.

Mousius · 2025-06-05T11:48:59Z

npsr/utils-inl.h

+#ifdef NPSR_UTILS_INL_H_
+#undef NPSR_UTILS_INL_H_
+#else
+#define NPSR_UTILS_INL_H_


I think we should have a lut-inl.h, so we can haev LutX2, LutX4 etc?

A generic utils-inl.h is going to get pretty big I think.

I agree, mainly to optimize 128-bit simd extensions, transpose and shuffles to reduce cache/memory access

Mousius · 2025-06-05T11:50:07Z

npsr/common.h

+  struct _Zero {};
+  static constexpr auto kForce = _Force{};
+  static constexpr auto kNearest = _Nearest{};
+#if 0 // not used yet


Can we add these when we come across use cases for them?

sure, this good point .. I'm gonna remove them

Mousius · 2025-06-09T20:47:46Z

npsr/trig/inl.h

+
+namespace npsr::HWY_NAMESPACE::sincos {
+template <bool IS_COS, typename V, typename Prec>
+HWY_API V SinCos(Prec &prec, V x) {


Potentially worth creating a new macro for HWY_API so it doesn't change behaviour for Highway?

Suggest a name? HWY_API just combine HWY_ATTR and HWY_INLINE.

Mousius · 2025-06-09T21:05:12Z

npsr/trig/inl.h

+#include "npsr/sincos/small-inl.h"
+
+// clang-format off
+#if defined(NPSR_TRIG_INL_H_) == defined(HWY_TARGET_TOGGLE) // NOLINT


I think this should be trig-inl.h?

- Add Python-based generator tool for creating C++ headers and Python templates - Include sollya wrapper for mathematical computations - Add utilities for formatting C/Python arrays and header generation - Include comprehensive .gitignore for Python/C++ development

- Configure spin commands for building, testing, and development - Add custom generate command for sollya-based file generation - Set up IPython integration with pre-imported numpy_sr module - Configure project metadata and build requirements

- Implement Python bindings for Highway SIMD intrinsics - Add type system for scalar/vector data with proper conversions - Create dynamic dispatch system for multiple SIMD targets - Include helper functions for ULP distance calculations - Set up pytest infrastructure for comprehensive testing

Match Highway library's code formatting conventions

Highway provides portable SIMD intrinsics required by the testing framework

Initialize build configuration for npsr module

- Generate test vectors using Sollya for high-precision reference values - Test challenging cases including large arguments, pi multiples, and edge cases - Cover both float32 and float64 precision with ULP accuracy validation - Include tests for standard and low-accuracy modes

Clean up empty PreciseBind function in preparation for proper implementation

Enable trigonometric functions in the Python testing framework

- Correct polynomial coefficients for double precision cosine - Fix table indexing and data layout for lookup tables - Improve accuracy for large argument range reduction

- Implement efficient SVML-style linear approximation for sin/cos - Fix precision issues in Cody-Waite range reduction - Add proper sign handling for both sine and cosine - Improve polynomial evaluation with correction terms - Document mathematical equivalence between traditional and optimized approaches

- Move Precise class and related types to npsr/precise.h - Add deduction guides for cleaner template instantiation - Improve modularity by separating precision control from common utilities

…ures - Change parameter order to Precise<Args...>, V for consistency - Update include paths from sincos/ to trig/ - Fix constant types and naming conventions (kException -> kExceptions)

Add meson configuration to include trigonometric test data in installation

Define Python dependencies for building and testing: - meson/meson-python for build system - ninja for compilation - spin for development workflow - pytest for test execution

seiko2plus · 2025-06-10T08:36:26Z

In general I think this is a good starting point. Do you want to land this with #if 0 and other various things incomplete @seiko2plus? We can be a bit relaxed as we setup the repo.

I was putting all my time into the testing unit, also improve luts generations.. so I left any extra optimizations off until I make sure that both functions sin/cos are well implemented.

seiko2plus · 2025-06-10T08:37:38Z

All stress tests passed localy on x86, just need a CI and nice cleanup and then it will be ready for review ... maybe I should split it up into multiple prs

Mousius · 2025-06-11T17:12:24Z

All stress tests passed localy on x86, just need a CI and nice cleanup and then it will be ready for review ... maybe I should split it up into multiple prs

Yep, this is unreviewable as-is, so incremental PRs would be much appreciated 😸

r-devulap · 2025-06-11T17:13:15Z

maybe I should split it up into multiple prs

Yes please, I am having a hard time reviewing this.

seiko2plus · 2025-06-11T17:29:47Z

Yep, this is unreviewable as-is, so incremental PRs would be much appreciated
Yes please, I am having a hard time reviewing this.

Working on it.

seiko2plus force-pushed the impl-sincos branch from 58a8ced to 2c6746f Compare June 4, 2025 16:25

BUG: Fix Precise options and doc comment for it

18d9307

seiko2plus force-pushed the impl-sincos branch from a3356f1 to 18d9307 Compare June 4, 2025 18:34

seiko2plus changed the title ~~algo: implement sine/cosine using Intel SVML for single/double precision~~ algo: implement sine/cosine based on Intel SVML for single/double precision Jun 4, 2025

r-devulap self-assigned this Jun 6, 2025

r-devulap requested a review from Copilot June 6, 2025 15:49

Copilot AI reviewed Jun 6, 2025

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Mousius mentioned this pull request Jun 9, 2025

Routines #2

Open

Mousius requested changes Jun 9, 2025

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Mousius reviewed Jun 9, 2025

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seiko2plus added 16 commits June 10, 2025 11:13

Add spin build system configuration

c8af54e

- Configure spin commands for building, testing, and development - Add custom generate command for sollya-based file generation - Set up IPython integration with pre-imported numpy_sr module - Configure project metadata and build requirements

replace sin/cos lut with the new generators

182c52c

Add clang-format configuration using Google style

424ab26

Match Highway library's code formatting conventions

Add Highway library as git submodule

21ac103

Highway provides portable SIMD intrinsics required by the testing framework

Add npsr meson build placeholder

7167b9f

Initialize build configuration for npsr module

Remove Sin/Cos bindings from precision template

cbfde16

Clean up empty PreciseBind function in preparation for proper implementation

Bind Sin/Cos intrinsics to Python interface

9039ab8

Enable trigonometric functions in the Python testing framework

Fix polynomial evaluation for large arguments in double precision

a672683

- Correct polynomial coefficients for double precision cosine - Fix table indexing and data layout for lookup tables - Improve accuracy for large argument range reduction

Refactor: Extract Precise class to separate header

afbf0c8

- Move Precise class and related types to npsr/precise.h - Add deduction guides for cleaner template instantiation - Improve modularity by separating precision control from common utilities

Refactor: Move Precise parameter to first position in function signat…

fe1d0f8

…ures - Change parameter order to Precise<Args...>, V for consistency - Update include paths from sincos/ to trig/ - Fix constant types and naming conventions (kException -> kExceptions)

Install sin/cos test cases in build system

43fb58b

Add meson configuration to include trigonometric test data in installation

Add test requirements file

c800ad8

Define Python dependencies for building and testing: - meson/meson-python for build system - ninja for compilation - spin for development workflow - pytest for test execution

seiko2plus mentioned this pull request Jun 10, 2025

Add cpp-linter action #3

Merged

seiko2plus mentioned this pull request Jun 11, 2025

SIMD, TST: Reimplment _simd unit testing in C++ numpy/numpy#24069

Closed

	* typename V = Vec<DFromV<SclableTag>>;
	* typename V = Vec<DFromV<ScalableTag>>;

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algo: implement sine/cosine based on Intel SVML for single/double precision #1

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