'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2021, 2023 Caleb Bell Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ''' import pytest from fluids.numerics import assert_close, assert_close1d from fluids.numerics.doubledouble import ( add_dd, add_imag_dd, cbrt_dd, cbrt_imag_dd, cube_dd, div_dd, div_imag_dd, eq_dd, exp_dd, ge_dd, gt_dd, imag_inv_dd, intpow_dd, le_dd, log_dd, lt_dd, mul_dd, mul_imag_dd, mul_imag_noerrors_dd, mul_noerrors_dd, neq_dd, pow_dd, sqrt_dd, sqrt_imag_dd, square_dd, ) try: import mpmath as mp has_mpmath = True mp.mp.dps=100 except: has_mpmath = False def mark_mpmath(f): f = pytest.mark.mpmath(f) f = pytest.mark.skipif(not has_mpmath, reason='missing mpmath')(f) return f def test_cube_dd(): ans = cube_dd(2.718281828459045, 1.4456468917292502e-16) assert_close1d(ans, (20.085536923187668, -1.8275625525512858e-16), rtol=1e-14) def test_div_imag_dd(): mp_ans = (-6221711.561975023 - 2.5074521914349666e-10j)/(1247.1686953729213 +2160.157819988352j) ans = div_imag_dd(-6221711.561975023, 0.0, - 2.5074521914349666e-10, 0.0, 1247.1686953729213, 0.0, 2160.157819988352, 0.0) assert_close1d(ans, (-1247.168695372921, -7.085386715133776e-14, 2160.1578199883515, -1.7404258749820416e-14), rtol=1e-13) def test_add_dd(): ans = add_dd(2.718281828459045, 1.4456468917292502e-16, -3.141592653589793, -1.2246467991473532e-16) assert_close1d(ans, (-0.423310825130748, 2.2100009258189695e-17), rtol=1e-13) @mark_mpmath def test_add_dd_mp(): ans = add_dd(2.718281828459045, 1.4456468917292502e-16, -3.141592653589793, -1.2246467991473532e-16) assert abs(mp.e-mp.pi - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 @mark_mpmath def test_mul_dd_mp(): ans = mul_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (8.539734222673568, -6.773815290502423e-16), rtol=1e-13) assert abs(mp.e*mp.pi - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 def test_div_dd(): ans = div_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (0.8652559794322651, 2.1741459631779752e-17), rtol=1e-13) @mark_mpmath def test_div_dd_mp(): ans = div_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert abs(mp.e/mp.pi - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 def test_sqrt_dd(): ans = sqrt_dd(2.718281828459045, 1.4456468917292502e-16) assert_close1d(ans, (1.6487212707001282, -4.731568479435833e-17), rtol=1e-13) @mark_mpmath def test_sqrt_dd_mp(): ans = sqrt_dd(2.718281828459045, 1.4456468917292502e-16) assert abs(mp.sqrt(mp.e) - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 def test_mul_noerrors_dd(): ans = mul_noerrors_dd(2.718281828, 3.1415926) assert_close1d(ans, (8.539734075559272, 6.111502792870851e-16), rtol=1e-13) assert_close1d(ans, mul_dd(2.718281828, 0.0, 3.1415926, 0.0), rtol=1e-13) def test_square_dd(): ans = square_dd(2.718281828459045, 1.4456468917292502e-16) assert_close1d(ans, (7.38905609893065, -1.7971139497839148e-16), rtol=1e-13) @mark_mpmath def test_square_dd_mp(): ans = square_dd(2.718281828459045, 1.4456468917292502e-16) assert abs(mp.e**2 - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 def test_mul_imag_dd(): ans = mul_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (-2.4805483021587085, 8.193747384776261e-17, 17.079468445347135, -1.3547630581004847e-15), rtol=1e-14) ans = mul_imag_dd(1.11, 0.00, .027, 0.0, -1.2, 0.0, .2995, 0.0) assert_close1d(ans, (-1.3400865, -1.0926552718171222e-16, 0.300045, 1.1863843241144421e-17), rtol=1e-14) @mark_mpmath def test_mul_imag_dd_mp(): ans = mul_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) mp_ans = (mp.e + mp.pi*1j)*(mp.e + mp.pi*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_mul_imag_noerrors_dd(): ans = mul_imag_noerrors_dd(1.11, .027, -1.2, .2995) assert_close1d(ans, (-1.3400865, -1.0926552718171222e-16, 0.300045, 1.1863843241144421e-17), rtol=1e-14) def test_sqrt_imag_dd(): ans = sqrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (1.853730863795006, 1.8197550334075816e-17, 0.8473702183385572, 4.942630438677856e-17)) ans = sqrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 0, 0) assert_close1d(ans, (1.6487212707001282, -4.731568479435833e-17, 0.0, 0.0)) @mark_mpmath def test_sqrt_imag_dd(): ans = sqrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) mp_ans = mp.sqrt(mp.e + mp.pi*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 ans = sqrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 0, 0) mp_ans = mp.sqrt(mp.e) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_add_imag_dd(): ans = add_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16) assert_close1d(ans, (5.859874482048839, -1.770598407624023e-16, 5.859874482048839, -1.770598407624023e-16)) @mark_mpmath def test_add_imag_dd_mp(): ans = add_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16) mp_ans = (mp.e + mp.pi*1j) + (mp.pi + mp.e*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_div_imag_dd(): ans = div_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16) assert_close1d(ans, (0.9896172675351794, -2.57625629153772e-17, 0.14372774191576643, 1.174077497180584e-17), rtol=1e-13) @mark_mpmath def test_div_imag_dd_mp(): ans = div_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16, 3.141592653589793, 1.2246467991473532e-16, 2.718281828459045, 1.4456468917292502e-16) mp_ans = (mp.e + mp.pi*1j)/(mp.pi + mp.e*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_imag_inv_dd(): ans = imag_inv_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (0.15750247989731844, -3.9415361951446925e-18, -0.18202992367722576, -5.408691854671257e-18), rtol=1e-13) @mark_mpmath def test_imag_inv_dd_mp(): ans = imag_inv_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) mp_ans = 1/(mp.e + mp.pi*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_cbrt_imag_dd(): ans = cbrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) assert_close1d(ans, (1.5423370526780396, 8.764992916723807e-17, 0.45326965450036827, 2.105896617565284e-17), rtol=1e-14) @mark_mpmath def test_cbrt_imag_dd_mp(): ans = cbrt_imag_dd(2.718281828459045, 1.4456468917292502e-16, 3.141592653589793, 1.2246467991473532e-16) mp_ans = mp.cbrt(mp.e + mp.pi*1j) assert abs(mp_ans.real - (mp.mpf(ans[0]) + mp.mpf(ans[1]) )) < 1e-30 assert abs(mp_ans.imag - (mp.mpf(ans[2]) + mp.mpf(ans[3]) )) < 1e-30 def test_cbrt_dd(): ans = cbrt_dd(3, 0.0) assert_close1d(ans, (1.4422495703074083, 8.054912676113696e-17), rtol=1e-13) ans = cbrt_dd(1.4422495703074083, 8.054912676113696e-17) assert_close1d(ans, (1.129830963909753, 1.601807086137469e-17), rtol=1e-13) @mark_mpmath def test_cbrt_dd_mp(): ans = cbrt_dd(3, 0.0) assert abs(mp.mpf(3)**(mp.mpf(1)/mp.mpf(3)) - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 ans = cbrt_dd(1.4422495703074083, 8.054912676113696e-17) assert abs((mp.mpf(3)**(mp.mpf(1)/mp.mpf(3)))**(mp.mpf(1)/mp.mpf(3)) - (mp.mpf(ans[0]) + mp.mpf(ans[1]))) < 1e-30 def test_eq_dd(): assert eq_dd(1, 0, 1, 0) assert not eq_dd(1, 0, 1, .1) assert not eq_dd(1, 0, 0, 0) assert not eq_dd(1, 1, 1, 0) assert not eq_dd(0, 0, 1, 0) def test_neq_dd(): assert not neq_dd(1, 0, 1, 0) assert neq_dd(1, 0, 1, .1) assert neq_dd(1, 0, 0, 0) assert neq_dd(1, 1, 1, 0) assert neq_dd(0, 0, 1, 0) def test_lt_dd(): assert not lt_dd(1, 0, 1, 0) assert not lt_dd(1, 1e-10, 1, 1e-10) assert lt_dd(.9, 0, 1, 0) assert not lt_dd(1, 1e-10, 1, 0) assert lt_dd(1, 0, 1, 1e-10) def test_gt_dd(): assert not gt_dd(1, 0, 1, 0) assert not gt_dd(1, 1e-10, 1, 1e-10) assert not gt_dd(.9, 0, 1, 0) assert gt_dd(1, 1e-10, 1, 0) assert not gt_dd(1, 0, 1, 1e-10) def test_le_dd(): assert le_dd(1, 0, 1, 0) assert le_dd(1, 1e-10, 1, 1e-10) assert le_dd(.9, 0, 1, 0) assert not le_dd(1, 1e-10, 1, 0) assert le_dd(1, 0, 1, 1e-10) def test_ge_dd(): assert ge_dd(1, 0, 1, 0) assert ge_dd(1, 1e-10, 1, 1e-10) assert not ge_dd(.9, 0, 1, 0) assert ge_dd(1, 1e-10, 1, 0) assert not ge_dd(1, 0, 1, 1e-10) @mark_mpmath def test_intpow_dd(): ar, ae = 0.6931471805599453, 2.3190468138462996e-17 for n in range(-7, 4): outr, oute = intpow_dd(ar, ae, n=n) mp_ans = (mp.mpf(ar) + mp.mpf(ae))**n ans_as_mp = mp.mpf(outr) + mp.mpf(oute) err = abs(1.0 - ans_as_mp/mp_ans) assert err < 1e-30 def test_exp_dd(): ar, ae = 0.6931471805599453, 2.3190468138462996e-17 outr, oute = exp_dd(ar, ae) assert outr == 2 assert_close(oute, 0, atol=1e-30) def test_log_dd(): a, b = log_dd(0.6931471805599453, 2.3190468138462996e-17) assert_close(a, -0.36651292058166435, rtol=1e-14) assert_close(b, 2.0606571710351483e-17, rtol=1e-14) def test_pow_dd(): for n in range(-3, 4): assert pow_dd(0.6931471805599453, 2.3190468138462996e-17, n, 0) == intpow_dd(0.6931471805599453, 2.3190468138462996e-17, n) a, b = pow_dd(0.6931471805599453, 2.3190468138462996e-17, 0.6931471805599453, 2.3190468138462996e-17) assert_close(a, 0.7756550370345752, rtol=1e-14) assert_close(b, 3.1024007879879916e-17, rtol=1e-14)