Re: doing radix conversions in floats

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Apr 15, 2025 at 11:42:11PM -0700, American Citizen wrote:
> Has anyone ever written a radix conversion program for converting decimal
> floats to other radixes such a base 16?
> 
> I wrote a dec2hex and hex2dec for integers which seems to work, if I
> stipulated that the output of the numbers in other bases than 10 is a
> delimited string "0xnnn".

In GP you can do
? strprintf("0x%x",7123456)
%89 = "0x6cb200"
? eval("0x6cb200")
%90 = 7123456

> I post the code for both below, but ask if anyone has come up with radix
> conversions to the right of the decimal point (and in the current working
> precision of gp-pari) ?
> 
> For example the square root of 2 to 39 digits is
> 1.41421356237309504880168872420969807857 but the equivalent base 16
> representation is 1.6a09e667f3bcc908b2fb1366ea957d3e3adec1751277509a when I
> make an attempt to have the equivalent hexadecimal number.

You can start with something like

d2h(x)=my(f=frac(x));strprintf("%x.%x",truncate(x-f),f*16^((bitprecision(f)+exponent(f))\4))
h2d(s)=my([a,b]=strsplit(s,"."));eval(Str("0x",a))+eval(Str("0x",b))/16^#b*bitprecision(1.,4*#b)

? d2h(sqrt(2))
%123 = "1.6a09e667f3bcc908b2fb1366ea957d3"
? h2d(%)
%124 = 1.4142135623730950488016887242096980785

Cheers,
Bill