XCAS float precision

[Albert Chan]

I finally join the club, and downloaded XCas (for Windows 32-bits)

If XCas float default is IEEE double precision, I should get this:

Python: 3.141592653589794 - 3.141592653589793 => 8.88e-16

This is above in hex-float, where ULP = 2^-51 ~ 4.44e-16:
0x1.921fb54442d1aP1 - 0x1.921fb54442d18P1 = 2 ULP ~ 8.88e-16

Instead, I get something unexpected, suggesting XCas uses 54-bits float (or more)
(Also, returned float is not normalized, with a zero before decimal point)

XCAS: 3.141592653589794 - 3.141592653589793 => 0.111e-14 (2.5 ULP ?)

Just to confirm above with 54-bits float math (now, ULP = 2^-52)

0x1.921fb54442d1a0P+1 - 0x1.921fb54442d178P+1 = 5 ULP ~ 1.11E-15 (match above)

[parisse]

Xcas is using longfloats (via MPFR) for representation of floats having more than 14 digits.

[Albert Chan]

(10-04-2018 07:22 PM)parisse Wrote:  Xcas is using longfloats (via MPFR) for representation of floats having more than 14 digits.

Thanks you. It now make sense.

pibf := 3.141592653589793 // bigfloat
pi53 := 3.141592653 + 5.89793-10 // machine float

evalf(pibf, 20) => 3.1415926535897928940 // big float confirmed
evalf(pi53, 20) => 3.14159265359 // pi53 is 0.5 ULP bigger than pibf

It seems when big float mixed with machine float, big-float is "demoted".

evalf(pibf + 0.0, 20) => 3.14159265359
pibf - pi53 //==> 0.0

pibf == pi53 //==> true, big float demoted before comparison.

[parisse]

Indeed. Mixing floats and long floats will convert long float to float.