Re: [RFC PATCH] riscv: add vectorized sin

Hi Paul,

On 2026/7/9 20:02, Paul Zimmermann wrote:
>> The worst-case error is <= 1 ULP.
> 
> great! Is that observed or do you have a proof of this bound?
> Did you try with inputs from [1] and [2]?
> 
> Note that it now exists some vector and correctly rounded implementations [3] and [4].
Thank you for the insightful questions. To be completely honest, the <= 
1 ULP bound was an observation rather than a proof. I arrived at this 
conclusion by testing the implementation with approximately 770,000 
samples (about 440,000 uniformly distributed random inputs across three 
code paths, plus roughly 300,000 random full-exponent-range bit 
patterns) against a 250-bit MPFR/mpmath reference. In those specific 
tests, no results exceeded 1 ULP.

However, after running the test cases you provided, I realized my 
initial assessment was incomplete. The maximum ULP errors are 0.931 and 
1.0 for trig.wc and sin.wc respectively. Specifically, 17 cases in 
sin.wc show a ULP error of exactly 1.0, and all of these cases fall into 
the slow path (where |x| >= 1e6).

Thank you also for sharing those papers; they serve as excellent 
references for improving my implementation. I have also noticed that 
some open-source libraries, such as SLEEF [1], claim to achieve <= 1 ULP 
accuracy. Before formally submitting the patch, I will continue to study 
these resources and further refine the accuracy of my implementation, 
while ensuring license compatibility.

Thank you very much for your valuable feedback and guidance.

BR,
Pincheng Wang

[1] https://sleef.org/