Coverage for local/lib/python2.7/site-packages/sage/libs/mpmath/ext_libmp.pyx : 79%

""" 

Faster versions of some key functions in mpmath.libmp. 

""" 

from __future__ import print_function, absolute_import 

from .ext_impl cimport * 

from sage.libs.gmp.all cimport * 

from sage.rings.integer cimport Integer 

from .ext_impl import exp_fixed, cos_sin_fixed, log_int_fixed 

# Note: not thread-safe 

cdef MPF tmp1 

cdef MPF tmp2 

MPF_init(&tmp1) 

MPF_init(&tmp2) 

def mpf_add(tuple x, tuple y, int prec=0, str rnd='d'): 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

MPF_set_tuple(&tmp2, y) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_add(&tmp1, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_sub(tuple x, tuple y, int prec=0, str rnd='d'): 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

MPF_set_tuple(&tmp2, y) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_sub(&tmp1, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_mul(tuple x, tuple y, int prec=0, str rnd='d'): 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

MPF_set_tuple(&tmp2, y) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_mul(&tmp1, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_div(tuple x, tuple y, int prec, str rnd='d'): 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

MPF_set_tuple(&tmp2, y) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_div(&tmp1, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_sqrt(tuple x, int prec, str rnd='d'): 

""" 

Computes sqrt(x) with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_sqrt, from_float, to_float 

sage: x = from_float(2) 

sage: y = mpf_sqrt(x, 53, 'n') 

sage: to_float(y) 

1.4142135623730951 

""" 

if x[0]: 

import mpmath.libmp as libmp 

raise libmp.ComplexResult("square root of a negative number") 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_sqrt(&tmp1, &tmp1, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_log(tuple x, int prec, str rnd='d'): 

""" 

Computes log(x) with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_log, from_float, to_float 

sage: x = from_float(2) 

sage: y = mpf_log(x, 53, 'n') 

sage: to_float(y) 

0.6931471805599453 

""" 

if x[0]: 

import mpmath.libmp as libmp 

raise libmp.ComplexResult("logarithm of a negative number") 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_log(&tmp1, &tmp1, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_exp(tuple x, int prec, str rnd='d'): 

""" 

Computes exp(x) with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_exp, from_float, to_float 

sage: x = from_float(2) 

sage: z = mpf_exp(x, 53, 'n') 

sage: to_float(z) 

7.38905609893065 

""" 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_exp(&tmp1, &tmp1, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_cos(tuple x, int prec, str rnd='d'): 

""" 

Computes cos(x) with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_cos, from_float, to_float 

sage: x = from_float(1) 

sage: y = mpf_cos(x, 53, 'n') 

sage: to_float(y) 

0.5403023058681398 

""" 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_cos(&tmp1, &tmp1, opts) 

return MPF_to_tuple(&tmp1) 

def mpf_sin(tuple x, int prec, str rnd='d'): 

""" 

Computes sin(x) with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_sin, from_float, to_float 

sage: x = from_float(1) 

sage: y = mpf_sin(x, 53, 'n') 

sage: to_float(y) 

0.8414709848078965 

""" 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_sin(&tmp1, &tmp1, opts) 

return MPF_to_tuple(&tmp1) 

def mpc_sqrt(tuple z, int prec, str rnd='d'): 

""" 

Computes sqrt(z) with mpc value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpc_sqrt, from_float, to_float 

sage: z = from_float(-2), from_float(0) 

sage: re, im = mpc_sqrt(z, 53, 'n') 

sage: to_float(re), to_float(im) 

(0.0, 1.4142135623730951) 

""" 

cdef tuple a, b 

cdef MPopts opts 

a, b = z 

MPF_set_tuple(&tmp1, a) 

MPF_set_tuple(&tmp2, b) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_complex_sqrt(&tmp1, &tmp2, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1), MPF_to_tuple(&tmp2) 

def mpc_exp(tuple z, int prec, str rnd='d'): 

""" 

Computes exp(z) with mpc value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpc_exp, from_float, to_float 

sage: z = from_float(0), from_float(1) 

sage: re, im = mpc_exp(z, 53, 'n') 

sage: to_float(re), to_float(im) 

(0.5403023058681398, 0.8414709848078965) 

""" 

cdef tuple a, b 

cdef MPopts opts 

a, b = z 

MPF_set_tuple(&tmp1, a) 

MPF_set_tuple(&tmp2, b) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

MPF_complex_exp(&tmp1, &tmp2, &tmp1, &tmp2, opts) 

return MPF_to_tuple(&tmp1), MPF_to_tuple(&tmp2) 

def mpf_pow(tuple x, tuple y, int prec, str rnd='d'): 

""" 

Computes x ^ y with mpf value tuples. 

EXAMPLES:: 

sage: from mpmath.libmp import mpf_pow, from_float, to_float 

sage: x = from_float(2) 

sage: y = from_float(3) 

sage: z = mpf_pow(x, y, 53, 'n') 

sage: to_float(z) 

8.0 

""" 

cdef MPopts opts 

MPF_set_tuple(&tmp1, x) 

MPF_set_tuple(&tmp2, y) 

opts.rounding = rndmode_from_python(rnd) 

opts.prec = prec 

if MPF_pow(&tmp1, &tmp1, &tmp2, opts): 

import mpmath.libmp as libmp 

raise libmp.ComplexResult("negative number raised to a fractional power") 

return MPF_to_tuple(&tmp1)