[libre-riscv-dev] FP unit testing (was Re: [isa-dev] FP reciprocal sqrt extension proposal)

[lkcl]

On Sunday, July 14, 2019 at 8:39:48 AM UTC+1, Jacob Lifshay wrote:
>
> On Sun, Jul 14, 2019 at 12:26 AM lkcl <luke.l... at gmail.com <javascript:>> 
> wrote: 
> > using bigfloat to perform the reciprocal-square-root in a much higher 
> precision will cover the requirement to provide accurate FPSQRT.  however 
> the corner-cases (at the extreme limits of the exponent, and when the 
> mantissa's MSB is zero) are going to be a bundle of fun. 
> > 
> Note that mpfr has code to emulate fixed-size floating point numbers, 
> including handling denormal numbers. It also has mostly (see caveats) 
> the same special-case semantics (+-0, +-Inf, NaN) as IEEE 754, so that 
> should make it a lot easier to use. 
>

https://pythonhosted.org/bigfloat/reference/index.html#bigfloat.Context

that's interesting.  some IEEE754-like contexts are provided.
  

>
> MPFR is used in gcc to evaluate floating-point expressions at compile 
> time, so it is well-tested and likely to be correct.
>

excellent
 

>
> mpfr does, however, have some notable caveats: see 
> https://www.mpfr.org/mpfr-current/mpfr.html#MPFR-and-the-IEEE-754-Standard 
>

under-normalisation not supported, because, obviously, with an 
arbitrary-sized exponent you don't need to lose accuracy in the mantissa.

>>> from bigfloat import BigFloat
>>> b = BigFloat(1.0)
>>> b
BigFloat.exact('1.0000000000000000', precision=53)
>>> b.hex()
'0x0.80000000000000p+1'
>>> b._exponent()
1
>>> b._format_to_fixed_precision(1)
(False, '10', -1)
>>> b = BigFloat(52.39)
>>> b._format_to_fixed_precision(24)
(False, '52390000000000000568434189', -24)
>>> b.hex()
'0x0.d18f5c28f5c290p+6'

ah ha!  perfect!  that's exactly what we need.  and there's a 
"BigFloat.fromhex()" function as well, so it will be possible to transfer 
numbers in and out of bigfloat, in order to perform conversions to (full) 
IEEE754 FP16/32/64 format.

i am still puzzled as to how a *soft* FP rsqrt implementation may be 
verified and found to be a correct implementation of the IEEE754  standard.

l.