Specify the reduced-interval accuracy of trigonometric polynomials

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调研方向

Start with std/math/trig.wave:69, the reported small-angle probes, and the related large-angle work in #600. Before changing code, discuss the proposed absolute, relative, and ULP contract with @LunaStev, including behavior near zeros and poles. Done means the bounds are agreed, independent high-precision fixtures cover interval and quadrant boundaries, the reduced-interval approximation meets the contract, and the #600 regressions plus separate f32 wrapper checks still pass.

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描述

discussion enhancement help wanted

Motivation

Small-angle testing avoids the large-angle reduction problem fixed in #600. At x=0.75, sin_f64 is 92 ULP from a 100-digit nearest reference; near pi/4 it is 184 ULP. cos differs by 4/10 ULP for those inputs. No correct-rounding contract is currently promised.

Starting point: std/math/trig.wave:69.

Validation

Audited canonical Wave 540728c2eb6cc12f5c69c3fb3fdb96e07ba059a4 (0.0.1-alpha-dev), whose tree matches the local checkout. Validation: Executed exact-bit small-angle probes and high-precision oracle; independent of huge-argument phase loss. Executed compiler probes use the matching checkout-built compiler and std on Linux amd64 (Rust 1.89.0 / LLVM 21.1.8). Source/header or mocked checks are not native execution on another OS.

Scope

Set an explicit error envelope for the reduced-interval sin/cos polynomial and resulting tan behavior. Improve the approximation only to meet that agreed goal; do not reopen the already replaced large-angle reduction algorithm as the same defect.

Related: #600. These links do not claim those broader or completed scopes are unfinished.

Design discussion required

This issue records a proposal or an unresolved contract; it is not approval to choose new semantics. Please mention @LunaStev to discuss the design before starting implementation.

Completion criteria

  • Define small/reduced-interval absolute/relative/ULP bounds and behavior near zeros/poles.
  • Use independent high-precision fixtures at interval/quadrant boundaries.
  • Retain #600 large-angle and non-finite regressions; verify f32 wrappers separately.
主要语言
Rust
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20 小时 49 分钟
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从这里开始

  1. 先读完整个 Issue,再读项目的贡献指南。
  2. 在 Issue 下留言说明你要接手 —— 这能避免两个人做同样的事。
  3. Fork 仓库,在一个分支上完成修改。
  4. 提交 Pull Request,并在描述里引用这个 Issue 编号。

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