[libc-commits] [PATCH] D115828: [libc] Implement correctly rounded log2f based on RLIBM library.

[Paul Zimmermann via libc-commits]

       Dear Santosh,

> Here is a new polynomial that is generated using the exact output compensation in the patch. Tue suggested to use the FMA based poly eval as he was observing performance regressions with the SIMD instruction in x86-64.
> 
> Polynomial: y=1.4426950408936214387267682468518614768981933593750000000000000000000000e+00 x^(1) + -7.2134752892795794831926059487159363925457000732421875000000000000000000e-01 x^(2) + 4.8090233829603024062748772848863154649734497070312500000000000000000000e-01 x^(3) + -3.6137987525825709944626851211069151759147644042968750000000000000000000e-01 x^(4) + 3.2929554893140711158139311010017991065979003906250000000000000000000000e-01 x^(5)
> 
> Polynomial evaluation used is as follows:
> 
> double t1 = fma(x, a5, a4);
>  double t2 = fma(x, t1, a3);
>  double t3 = fma(x, t2, a2);
>  double t4 = fma(x, t3, a1);
> 
> final result = fma(d, t4, extra_factor)
> 
> Can you check if it produces correctly rounded results for all inputs and all rounding modes?

sure. If I converted the coefficients properly to hexadecimal values,
there is still one incorrectly rounded result for rounding towards zero
or down (same input x):

libm wrong by up to 1.01e+00 ulp(s) [1] for x=0x1.03a16ap+0
log2      gives 0x1.4cdc4ap-6
mpfr_log2 gives 0x1.4cdc4cp-6

Best regards,
Paul