Absolute value
==============

Test abs() and context.abs().

>>> import gmpy2
>>> from gmpy2 import mpz, xmpz, mpq, mpfr, mpc

>>> a=mpz(123)
>>> b=abs(a)
>>> a is b
True
>>> a=xmpz(123)
>>> b=abs(a)
>>> a is b
False
>>> a=mpz(-123)
>>> b=abs(a)
>>> b
mpz(123)
>>> a is b
False
>>> a
mpz(-123)
>>> a=mpq(12,7)
>>> b=abs(a)
>>> a is b
True
>>> a=mpq(-12,7)
>>> b=abs(a)
>>> b
mpq(12,7)
>>> a
mpq(-12,7)
>>> a=xmpz(-123)
>>> b=abs(a)
>>> b
>>> a
xmpz(123)
>>> b is None
True
>>> b = abs(a)
>>> b is None
True
>>> a=mpfr(1.0)
>>> b=abs(a)
>>> a is b
False
>>> abs(mpfr(1, precision=100))
mpfr('1.0')
>>> ctx = gmpy2.get_context()
>>> ctx.clear_flags()
>>> abs(mpfr('nan'))
mpfr('nan')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=True,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx.clear_flags()
>>> abs(mpfr('inf'))
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx.clear_flags()
>>> abs(mpfr('-inf'))
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> abs(mpc(-1,0))
mpfr('1.0')
>>> abs(-1+0j)
1.0
>>> abs(mpc(1,1))
mpfr('1.4142135623730951')
>>> ctx=gmpy2.get_context()
>>> ctx.clear_flags()
>>> mpc('nan+0j')
mpc('nan+0.0j')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=True,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> abs(mpc('nan+0j'))
mpfr('nan')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=True,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx.clear_flags()
>>> abs(mpc('nanj'))
mpfr('nan')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=True,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx.clear_flags()
>>> abs(mpc('inf+10j'))
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx.clear_flags()
>>> abs(mpc('-infj'))
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> a=mpc('nan+infj')
>>> ctx.clear_flags()
>>> abs(a)
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> a=mpc('-inf+nanj')
>>> ctx.clear_flags()
>>> abs(a)
mpfr('inf')
>>> ctx
context(precision=53, real_prec=Default, imag_prec=Default,
        round=RoundToNearest, real_round=Default, imag_round=Default,
        emax=1073741823, emin=-1073741823,
        subnormalize=False,
        trap_underflow=False, underflow=False,
        trap_overflow=False, overflow=False,
        trap_inexact=False, inexact=False,
        trap_invalid=False, invalid=False,
        trap_erange=False, erange=False,
        trap_divzero=False, divzero=False,
        allow_complex=False,
        rational_division=False,
        guard_bits=0,
        convert_exact=False,
        mpfr_divmod_exact=False)
>>> ctx=gmpy2.context()
>>> ctx.abs(-1)
mpz(1)
>>> ctx.abs(0)
mpz(0)
>>> ctx.abs(1)
mpz(1)
>>> ctx.abs(mpz(8))
mpz(8)
>>> ctx.abs(mpz(-8))
mpz(8)
>>> ctx.abs(-1.0)
mpfr('1.0')
>>> ctx.abs(mpfr(-2))
mpfr('2.0')
>>> ctx.abs(2+3j)
mpfr('3.6055512754639891')
>>> ctx.abs(mpc(2+3j))
mpfr('3.6055512754639891')