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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) | |