Comments (6)
casevh
commented on July 29, 2024
gmpy2.gamma() has a similar behavior. I vaguely recollect another report of this issue and it was a limitation of the MPFR library. I haven't found the details but I'll keep looking.
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casevh
commented on July 29, 2024
I found this comment in MPFR's gamma.c:
if (u < 44787929UL && bits_fac (u - 1) <= p + (rnd_mode == MPFR_RNDN))
/* bits_fac: lower bound on the number of bits of m,
where gamma(x) = (u-1)! = m*2^e with m odd. */
return mpfr_fac_ui (gamma, u - 1, rnd_mode);
/* if bits_fac(...) > p (resp. p+1 for rounding to nearest),
then gamma(x) cannot be exact in precision p (resp. p+1).
FIXME: remove the test u < 44787929UL after changing bits_fac
to return a mpz_t or mpfr_t. */
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wjamesjr
commented on July 29, 2024
Yep, that looks like the issue. Strange number to set as a cutoff! I will fall back to a python factorial algorithm with some bit slicing. Thanks for the quick response!
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wjamesjr
commented on July 29, 2024
Looks like the issue runs deeper than just gamma(). The below code computing a mpz factorial fails as well, with result inf. 44787927 still works. Is there some trick to converting very large mpz values to mpfr??
n = 44787928
gmpy2.get_context().emin = gmpy2.get_emin_min()
gmpy2.get_context().emax = gmpy2.get_emax_max()
print("emin", gmpy2.get_context().emin)
print("emax", gmpy2.get_context().emax)
print("max precision", gmpy2.get_max_precision())
gmpy2.get_context().precision = 100
print("precision set to", gmpy2.get_context().precision)
factn = gmpy2.fac(n)
print(factn.num_digits())
factn2 = mpfr(factn)
print(factn2)
exit(0)
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wjamesjr
commented on July 29, 2024
Looks like I have a hard limit on size of mpz that will convert to mpfr. The below code works. Change 2 ** 29 to 2 ** 30 and it goes to inf again. Should mpfr be limited in bit size?? I thought that's what precision provided.
gmpy2.get_context().emin = gmpy2.get_emin_min()
gmpy2.get_context().emax = gmpy2.get_emax_max()
print("emin", gmpy2.get_context().emin)
print("emax", gmpy2.get_context().emax)
print("max precision", gmpy2.get_max_precision())
gmpy2.get_context().precision = 100
print("precision set to", gmpy2.get_context().precision)
t1 = mpz(1) << (2 ** 29)
t2 = mpfr(t1)
print(t2)
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casevh
commented on July 29, 2024
It looks like a deeper issue:
>> t1=mpz(1) << (2**27)
>> mpfr(t1)
mpfr('1.196380724997376356710237763087067030291123782412927478906332372851427131104587e+40403562',256)
>> _*_
mpfr('1.431326839145247872477712623353078898059627334067519357500412952958814141885275e+80807124',256)
>> _*_
mpfr('2.048696520457526277391095958728021868321933030871131210018127684872659300422929e+161614248',256)
>> _*_
mpfr('inf')
and
>> mpfr(123456.789)**63483756.2
mpfr('3.15691251903978272292764153590394795083483376196033776445078487109637376386208e+323228495',256)
>> mpfr(123456.789)**63483756.3
mpfr('1.019562878429473795214570128278084403612032953011088359304266502177487364234525e+323228496',256)
>> mpfr(123456.789)**63483756.4
mpfr('inf')
For reference
> gmpy2.get_context()
context(precision=256, real_prec=Default, imag_prec=Default,
round=RoundToNearest, real_round=Default, imag_round=Default,
emax=4611686018427387903, emin=-4611686018427387903,
subnormalize=False,
trap_underflow=False, underflow=False,
trap_overflow=False, overflow=True,
trap_inexact=False, inexact=True,
trap_invalid=False, invalid=False,
trap_erange=False, erange=False,
trap_divzero=False, divzero=False,
allow_complex=False,
rational_division=False,
allow_release_gil=False)
Time to dig into the MPFR source code.
…On Fri, Jan 5, 2024 at 8:11 AM Bill James ***@***.***> wrote:
Looks like I have a hard limit on size of mpz that will convert to mpfr.
The below code works. Change 2 ** 29 to 2 ** 30 and it goes to *inf*
again. Should mpfr be limited in bit size?? I thought that's what precision
provided.
gmpy2.get_context().emin = gmpy2.get_emin_min()
gmpy2.get_context().emax = gmpy2.get_emax_max()
print("emin", gmpy2.get_context().emin)
print("emax", gmpy2.get_context().emax)
print("max precision", gmpy2.get_max_precision())
gmpy2.get_context().precision = 100
print("precision set to", gmpy2.get_context().precision)
t1 = mpz(1) << (2 ** 29)
t2 = mpfr(t1)
print(t2)
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