Possible incorrect calculations in subnormalize mode about gmpy HOT 2 CLOSED

I think it is the correct behavior.

Let's display both the decimal and binary values:

from gmpy2 import get_context, div_2exp, mpfr, next_below

get_context().precision = 2
get_context().emin = -2
get_context().emax = 3

get_context().subnormalize = False
a = div_2exp(mpfr(3), 4)
b = next_below(mpfr(0.25))

get_context().subnormalize = True
c = div_2exp(mpfr(3), 4)
d = next_below(mpfr(0.25))

a, a.__format__('b')
b, b.__format__('b')
c, c.__format__('b')
d, d.__format__('b')

The output is:

(mpfr('0.19',2), '1.1p-3')
(mpfr('0.19',2), '1.1p-3')
(mpfr('0.25',2), '1p-2')
(mpfr('0.12',2), '1p-3')

For 'a' and 'b', the binary output uses two bits ("1.1") but the exponent is -3 which is less than 'emin'. If the exponent is restricted to 'emin', the binary output for 'a' and 'b' would be '0.11p-2'. But this requires 3 bits ("0.11"). Subnormalize needs to round to 2 bits. div_2exp follows the honors the rounding mode (round ties to even) so '0.11' is rounded to '1.0' or '1p-2'. 'next_below' just uses the next smaller so '0.11' becomes '0.10' or '1p-3'.

I think I got the analysis correct. But the subtleties floating point representations never cease to surprise me.

from gmpy.

I am closing this issue as @casevh gave an accurate analysis of what is going on -- there does not seem to be a bug here.

from gmpy.