/usr/lib/python2.7/dist-packages/mpmath/tests/test_trig.py is in python-mpmath 0.19-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 | from mpmath import *
from mpmath.libmp import *
def test_trig_misc_hard():
mp.prec = 53
# Worst-case input for an IEEE double, from a paper by Kahan
x = ldexp(6381956970095103,797)
assert cos(x) == mpf('-4.6871659242546277e-19')
assert sin(x) == 1
mp.prec = 150
a = mpf(10**50)
mp.prec = 53
assert sin(a).ae(-0.7896724934293100827)
assert cos(a).ae(-0.6135286082336635622)
# Check relative accuracy close to x = zero
assert sin(1e-100) == 1e-100 # when rounding to nearest
assert sin(1e-6).ae(9.999999999998333e-007, rel_eps=2e-15, abs_eps=0)
assert sin(1e-6j).ae(1.0000000000001666e-006j, rel_eps=2e-15, abs_eps=0)
assert sin(-1e-6j).ae(-1.0000000000001666e-006j, rel_eps=2e-15, abs_eps=0)
assert cos(1e-100) == 1
assert cos(1e-6).ae(0.9999999999995)
assert cos(-1e-6j).ae(1.0000000000005)
assert tan(1e-100) == 1e-100
assert tan(1e-6).ae(1.0000000000003335e-006, rel_eps=2e-15, abs_eps=0)
assert tan(1e-6j).ae(9.9999999999966644e-007j, rel_eps=2e-15, abs_eps=0)
assert tan(-1e-6j).ae(-9.9999999999966644e-007j, rel_eps=2e-15, abs_eps=0)
def test_trig_near_zero():
mp.dps = 15
for r in [round_nearest, round_down, round_up, round_floor, round_ceiling]:
assert sin(0, rounding=r) == 0
assert cos(0, rounding=r) == 1
a = mpf('1e-100')
b = mpf('-1e-100')
assert sin(a, rounding=round_nearest) == a
assert sin(a, rounding=round_down) < a
assert sin(a, rounding=round_floor) < a
assert sin(a, rounding=round_up) >= a
assert sin(a, rounding=round_ceiling) >= a
assert sin(b, rounding=round_nearest) == b
assert sin(b, rounding=round_down) > b
assert sin(b, rounding=round_floor) <= b
assert sin(b, rounding=round_up) <= b
assert sin(b, rounding=round_ceiling) > b
assert cos(a, rounding=round_nearest) == 1
assert cos(a, rounding=round_down) < 1
assert cos(a, rounding=round_floor) < 1
assert cos(a, rounding=round_up) == 1
assert cos(a, rounding=round_ceiling) == 1
assert cos(b, rounding=round_nearest) == 1
assert cos(b, rounding=round_down) < 1
assert cos(b, rounding=round_floor) < 1
assert cos(b, rounding=round_up) == 1
assert cos(b, rounding=round_ceiling) == 1
def test_trig_near_n_pi():
mp.dps = 15
a = [n*pi for n in [1, 2, 6, 11, 100, 1001, 10000, 100001]]
mp.dps = 135
a.append(10**100 * pi)
mp.dps = 15
assert sin(a[0]) == mpf('1.2246467991473531772e-16')
assert sin(a[1]) == mpf('-2.4492935982947063545e-16')
assert sin(a[2]) == mpf('-7.3478807948841190634e-16')
assert sin(a[3]) == mpf('4.8998251578625894243e-15')
assert sin(a[4]) == mpf('1.9643867237284719452e-15')
assert sin(a[5]) == mpf('-8.8632615209684813458e-15')
assert sin(a[6]) == mpf('-4.8568235395684898392e-13')
assert sin(a[7]) == mpf('3.9087342299491231029e-11')
assert sin(a[8]) == mpf('-1.369235466754566993528e-36')
r = round_nearest
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) == 1
r = round_up
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) == 1
r = round_down
assert cos(a[0], rounding=r) > -1
assert cos(a[1], rounding=r) < 1
assert cos(a[2], rounding=r) < 1
assert cos(a[3], rounding=r) > -1
assert cos(a[4], rounding=r) < 1
assert cos(a[5], rounding=r) > -1
assert cos(a[6], rounding=r) < 1
assert cos(a[7], rounding=r) > -1
assert cos(a[8], rounding=r) < 1
r = round_floor
assert cos(a[0], rounding=r) == -1
assert cos(a[1], rounding=r) < 1
assert cos(a[2], rounding=r) < 1
assert cos(a[3], rounding=r) == -1
assert cos(a[4], rounding=r) < 1
assert cos(a[5], rounding=r) == -1
assert cos(a[6], rounding=r) < 1
assert cos(a[7], rounding=r) == -1
assert cos(a[8], rounding=r) < 1
r = round_ceiling
assert cos(a[0], rounding=r) > -1
assert cos(a[1], rounding=r) == 1
assert cos(a[2], rounding=r) == 1
assert cos(a[3], rounding=r) > -1
assert cos(a[4], rounding=r) == 1
assert cos(a[5], rounding=r) > -1
assert cos(a[6], rounding=r) == 1
assert cos(a[7], rounding=r) > -1
assert cos(a[8], rounding=r) == 1
mp.dps = 15
if __name__ == '__main__':
for f in globals().keys():
if f.startswith("test_"):
print(f)
globals()[f]()
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