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| 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 | |