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from mpmath import *
from random import seed, randint, random
import math
# Test compatibility with Python floats, which are
# IEEE doubles (53-bit)
N = 5000
seed(1)
# Choosing exponents between roughly -140, 140 ensures that
# the Python floats don't overflow or underflow
xs = [(random()-1) * 10**randint(-140, 140) for x in range(N)]
ys = [(random()-1) * 10**randint(-140, 140) for x in range(N)]
# include some equal values
ys[int(N*0.8):] = xs[int(N*0.8):]
# Detect whether Python is compiled to use 80-bit floating-point
# instructions, in which case the double compatibility test breaks
uses_x87 = -4.1974624032366689e+117 / -8.4657370748010221e-47 \
== 4.9581771393902231e+163
def test_double_compatibility():
mp.prec = 53
for x, y in zip(xs, ys):
mpx = mpf(x)
mpy = mpf(y)
assert mpf(x) == x
assert (mpx < mpy) == (x < y)
assert (mpx > mpy) == (x > y)
assert (mpx == mpy) == (x == y)
assert (mpx != mpy) == (x != y)
assert (mpx <= mpy) == (x <= y)
assert (mpx >= mpy) == (x >= y)
assert mpx == mpx
if uses_x87:
mp.prec = 64
a = mpx + mpy
b = mpx * mpy
c = mpx / mpy
d = mpx % mpy
mp.prec = 53
assert +a == x + y
assert +b == x * y
assert +c == x / y
assert +d == x % y
else:
assert mpx + mpy == x + y
assert mpx * mpy == x * y
assert mpx / mpy == x / y
assert mpx % mpy == x % y
assert abs(mpx) == abs(x)
assert mpf(repr(x)) == x
assert ceil(mpx) == math.ceil(x)
assert floor(mpx) == math.floor(x)
def test_sqrt():
# this fails quite often. it appers to be float
# that rounds the wrong way, not mpf
fail = 0
mp.prec = 53
for x in xs:
x = abs(x)
mp.prec = 100
mp_high = mpf(x)**0.5
mp.prec = 53
mp_low = mpf(x)**0.5
fp = x**0.5
assert abs(mp_low-mp_high) <= abs(fp-mp_high)
fail += mp_low != fp
assert fail < N/10
def test_bugs():
# particular bugs
assert mpf(4.4408920985006262E-16) < mpf(1.7763568394002505E-15)
assert mpf(-4.4408920985006262E-16) > mpf(-1.7763568394002505E-15)
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