import ctypes from fractions import Fraction import pytest import gmpy2 from gmpy2 import (acos, acosh, asin, asinh, atan, atan2, atanh, bincoef, c_div, c_div_2exp, c_divmod, c_divmod_2exp, c_mod, c_mod_2exp, can_round, check_range, comb, context, copy_sign, cos, cosh, cot, coth, csc, csch, degrees, divexact, divm, double_fac, f2q, f_div, f_div_2exp, f_divmod, f_divmod_2exp, f_mod, f_mod_2exp, fac, fib, fib2, fma, fmma, fmms, fms, free_cache, from_binary, gcd, gcdext, get_context, get_emax_max, get_emin_min, get_exp, ieee, inf, invert, iroot, iroot_rem, is_bpsw_prp, is_euler_prp, is_extra_strong_lucas_prp, is_fermat_prp, is_fibonacci_prp, is_finite, is_infinite, is_integer, is_lessgreater, is_lucas_prp, is_nan, is_regular, is_selfridge_prp, is_signed, is_strong_bpsw_prp, is_strong_lucas_prp, is_strong_prp, is_strong_selfridge_prp, is_unordered, is_zero, isqrt, isqrt_rem, jacobi, kronecker, lcm, legendre, lucas, lucas2, maxnum, minnum, mpc, mpfr, mpfr_from_old_binary, mpq, mpq_from_old_binary, mpz, mpz_from_old_binary, multi_fac, nan, next_prime, norm, phase, polar, powmod, powmod_sec, primorial, proj, radians, rect, remove, root, root_of_unity, rootn, sec, sech, set_context, set_exp, set_sign, sign, sin, sin_cos, sinh, sinh_cosh, t_div, t_div_2exp, t_divmod, t_divmod_2exp, t_mod, t_mod_2exp, tan, tanh, zero) def test_exp(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 ctx = gmpy2.get_context() assert ctx.exp(10.5) == mpfr('36315.502674246636') assert gmpy2.exp(mpfr(1)) == mpfr('2.7182818284590451') assert gmpy2.exp2(r) == mpfr('48.502930128332729') assert gmpy2.exp10(r) == mpfr('398107.17055349692') assert gmpy2.exp2(r2) == mpfr('42.224253144732629') assert gmpy2.exp10(r2) == mpfr('251188.6431509582') assert gmpy2.exp2(f) == mpfr('1.515716566510398') assert gmpy2.exp10(f) == mpfr('3.9810717055349722') assert gmpy2.expm1(r) == mpfr('269.42640742615254') assert gmpy2.expm1(r2) == mpfr('220.40641620418717') assert gmpy2.expm1(f) == mpfr('0.82211880039050889') assert gmpy2.eint(r) == mpfr('63.101785974299247') def test_log(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 ctx = gmpy2.get_context() assert ctx.log(mpfr(2)) == mpfr('0.69314718055994529') assert ctx.log(mpfr(1)) == mpfr('0.0') assert gmpy2.log10(mpfr(10)) == mpfr('1.0') assert gmpy2.log2(r) == mpfr('2.4854268271702415') assert gmpy2.log2(r2) == mpfr('2.4329594072761065') assert gmpy2.log2(f) == mpfr('-0.73696559416620622') assert gmpy2.log1p(r) == mpfr('1.8870696490323797') assert gmpy2.log1p(r2) == mpfr('1.8562979903656263') assert gmpy2.log1p(f) == mpfr('0.47000362924573552') def test_root(): assert root(zero(1), 2) == mpfr('0.0') assert root(zero(-1), 2) == mpfr('-0.0') assert root(zero(-1), 3) == mpfr('-0.0') assert root(zero(-1), 4) == mpfr('-0.0') assert root(zero(-1), 5) == mpfr('-0.0') assert root(zero(-1), 6) == mpfr('-0.0') assert root(2, 2) == mpfr('1.4142135623730951') assert root(mpz(2), 2) == mpfr('1.4142135623730951') assert root(mpq(2), 2) == mpfr('1.4142135623730951') assert root(mpfr(2), 2) == mpfr('1.4142135623730951') pytest.raises(TypeError, lambda: root(mpc(2), 2)) assert is_nan(root(-2, 2)) pytest.raises(OverflowError, lambda: root(2, -2)) pytest.raises(TypeError, lambda: root(2, 0.5)) ctx = gmpy2.get_context() pytest.raises(TypeError, lambda: ctx.root(mpfr(25))) def test_rootn(): assert rootn(zero(1), 2) == mpfr('0.0') assert rootn(zero(-1), 2) == mpfr('0.0') assert rootn(zero(-1), 3) == mpfr('-0.0') assert rootn(zero(-1), 4) == mpfr('0.0') assert rootn(zero(-1), 5) == mpfr('-0.0') assert rootn(zero(-1), 6) == mpfr('0.0') ctx = gmpy2.get_context() pytest.raises(TypeError, lambda: ctx.rootn(5.5)) pytest.raises(TypeError, lambda: ctx.rootn(mpc(4,1), 4)) assert ctx.rootn(mpfr(25), 4) == mpfr('2.2360679774997898') pytest.raises(TypeError, lambda: ctx.rootn(mpfr(25), 4.0)) def test_sqrt(): ctx = gmpy2.get_context() assert gmpy2.sqrt(float(25)) == mpfr('5.0') assert 19.5 ** 2 == 380.25 assert ctx.sqrt(mpfr(380.25)) == mpfr('19.5') ctx.allow_complex = True assert ctx.sqrt(mpfr(-380.25)) == mpc('0.0+19.5j') ctx.allow_complex = False assert is_nan(ctx.sqrt(mpfr(-380.25))) assert ctx.sqrt(complex(16,4)) == mpc('4.0306589103067649+0.4961967868047123j') assert ctx.sqrt(mpc(16,4)) == mpc('4.0306589103067649+0.4961967868047123j') assert gmpy2.rec_sqrt(mpfr('380.25')) == mpfr('0.05128205128205128') def test_maxnum(): a = mpfr("12.34") b = mpfr("45.67") nan = mpfr("nan") inf = mpfr("inf") assert maxnum(a, b) == mpfr('45.670000000000002') assert maxnum(b, a) == mpfr('45.670000000000002') assert maxnum(a, -b) == mpfr('12.34') assert maxnum(a, 123456) == mpfr('123456.0') assert maxnum(12345678901234567890, a) == mpfr('1.2345678901234567e+19') assert maxnum(0, -1) == mpfr('0.0') assert maxnum(1, inf) == mpfr('inf') assert maxnum(1, -inf) == mpfr('1.0') assert maxnum(nan, a) == mpfr('12.34') assert maxnum(a, nan) == mpfr('12.34') assert maxnum(nan, inf) == mpfr('inf') assert maxnum(nan, -inf) == mpfr('-inf') assert is_nan(maxnum(nan, nan)) def test_minnum(): a = mpfr("12.34") b = mpfr("45.67") nan = mpfr("nan") inf = mpfr("inf") minf = mpfr("-inf") assert minnum(a, b) == mpfr('12.34') assert minnum(b, a) == mpfr('12.34') assert minnum(1, inf) == mpfr('1.0') assert minnum(minf, a) == mpfr('-inf') assert minnum(nan, inf) == mpfr('inf') assert is_nan(minnum(nan, nan)) def test_fused(): assert fma(2,3,4) == mpz(10) assert fma(2,3,-4) == mpz(2) assert fma(2.0,3,-4) == mpfr('2.0') assert fma(2,3.0,-4) == mpfr('2.0') assert fma(2,3,-4.0) == mpfr('2.0') assert fma(2,mpfr(3),-4.0) == mpfr('2.0') assert fma(mpc(2),mpfr(3),-4.0) == mpc('2.0+0.0j') assert fms(2,3,4) == mpz(2) assert fms(2,3,-4) == mpz(10) assert ieee(128).fma(7,1/7,-1) == mpfr('-5.55111512312578270211815834045410156e-17',113) assert ieee(128).fma(7,mpq(1,7),-1) == mpq(0,1) pytest.raises(TypeError, lambda: fma(1,2,"r")) assert fma(1,2,mpq(3,4)) == mpq(11,4) assert fms(1,2,mpq(3,4)) == mpq(5,4) assert fms(1,mpfr(2),3) == mpfr('-1.0') assert fms(1,mpc(2),3) == mpc('-1.0+0.0j') assert fmma(2,3,4,5) == mpz(26) assert fmma(2,3,-4,5) == mpz(-14) assert fmma(2.0,3,-4, mpq(5)) == mpfr('-14.0') assert fmma(2,3.0,-4,5) == mpfr('-14.0') assert fmma(2,3,-4.0,5) == mpfr('-14.0') assert fmma(2,mpfr(3),-4.0,5) == mpfr('-14.0') pytest.raises(TypeError, lambda: fmma(mpc(2),mpfr(3),-4.0,5)) assert fmms(2,3,4,5) == mpz(-14) assert fmms(2,3,-4,5) == mpz(26) assert fmms(2, 3, mpq(1, 2), 5) == mpq(7,2) assert fmms(2, 3, mpfr(1.2), 1) == mpfr('4.7999999999999998') assert ieee(128).fmma(7,1/7,-1,3/11) == mpfr('0.727272727272727237401994671017746441',113) assert ieee(128).fmma(7,mpq(1,7),-1,mpq(3,11)) == mpq(8,11) def test_trigonometric(): assert gmpy2.acos(mpc(0.2, 0.2)) == mpc('1.3735541886535356-0.20256635782456389j') assert gmpy2.acos(mpc(0.2, 0.2)) == gmpy2.acos(complex(0.2, 0.2)) assert gmpy2.asin(mpc(0.2,0.2)) == mpc('0.1972421381413611+0.20256635782456389j') assert gmpy2.asin(mpc(2.0,0.2)) == mpc('1.4560834209500821+1.3245636864399635j') assert gmpy2.asin(mpc(0.2,0.2)) == gmpy2.asin(complex(0.2,0.2)) assert gmpy2.atan(mpc(2.0, 2.0)) == mpc('1.311223269671635+0.23887786125685909j') assert gmpy2.atan(mpc(2.0, 2.0)) == gmpy2.atan(complex(2.0, 2.0)) c = mpc(2,3) assert gmpy2.cos(c) == mpc('-4.189625690968807-9.109227893755337j') assert gmpy2.sin(c) == mpc('9.1544991469114301-4.1689069599665647j') assert gmpy2.sin_cos(c) == (mpc('9.1544991469114301-4.1689069599665647j'), mpc('-4.189625690968807-9.109227893755337j')) assert gmpy2.sin_cos(c) == gmpy2.sin_cos(complex(2,3)) assert gmpy2.sin_cos(c) == (gmpy2.sin(c), gmpy2.cos(c)) assert gmpy2.tan(mpc(4,5)) == mpc('8.9834776469715613e-05+1.0000132074347847j') assert gmpy2.atanh(mpc(2.0, 3.0)) == mpc('0.14694666622552977+1.3389725222944935j') assert gmpy2.atanh(mpc(2.0, 3.0)) == gmpy2.atanh(complex(2, 3)) assert gmpy2.tanh(mpc(4,5)) == mpc('1.0005630461157933-0.00036520305451130409j') def test_get_exp(): ctx = gmpy2.get_context() ctx.trap_erange = True pytest.raises(gmpy2.RangeError, lambda: get_exp(mpfr('inf'))) gmpy2.set_context(context()) assert get_exp(mpfr(5.232)) == 3 pytest.raises(TypeError, lambda: get_exp(0)) assert get_exp(mpfr('inf')) == 0 assert get_exp(mpfr(0)) == 0 def test_set_exp(): pytest.raises(ValueError, lambda: set_exp(mpfr('1.0'), int(fac(100)))) gmpy2.set_context(gmpy2.ieee(32)) ctx = gmpy2.get_context() ctx.trap_erange = True pytest.raises(gmpy2.RangeError, lambda: set_exp(mpfr('1.0'), 1000)) ctx.trap_erange = False assert set_exp(mpfr('1.0'), 1000) == mpfr('1.0') r = mpfr(4.55) assert set_exp(r, 4) == mpfr('9.0999999999999996') pytest.raises(TypeError, lambda: set_exp(r, mpz(4))) def test_can_round(): pytest.raises(TypeError, lambda: can_round(mpfr('1.1'), 10, "spam")) pytest.raises(ValueError, lambda: can_round(mpfr('1.1'), 10, 111, 111, 111)) pytest.raises(ValueError, lambda: can_round(mpfr('1.1'), 10, 1, 111, 111)) pytest.raises(ValueError, lambda: can_round(mpfr('1.1'), 10, 1, 1, -111)) x = mpfr('-1.112') assert can_round(x, 10, 1, 1, 1) assert not can_round(x, 10, 1, 1, 10) def test_powmod(): z1, z2 = mpz(5), mpz(2) q = mpq(2,3) assert powmod(z1, z2, 4) == pow(z1, z2, 4) pytest.raises(TypeError, lambda: powmod(z1)) pytest.raises(TypeError, lambda: powmod(z1, q, 4)) def test_powmod_sec(): assert powmod_sec(3,3,7) == mpz(6) assert powmod_sec(-3,3,7) == mpz(1) assert powmod(-3,3,7) == mpz(1) assert powmod(3,-3,7) == mpz(6) pytest.raises(TypeError, lambda: powmod_sec(1,2)) pytest.raises(TypeError, lambda: powmod_sec(1.2,3,4)) pytest.raises(TypeError, lambda: powmod_sec(1,2.3,4)) pytest.raises(TypeError, lambda: powmod_sec(1,2,3.4)) pytest.raises(ValueError, lambda: powmod_sec(3,-3,7)) pytest.raises(ValueError, lambda: powmod_sec(3,4,8)) def test_is_fermat_prp(): assert is_fermat_prp(12345,2) is False assert is_fermat_prp(113,2) assert is_fermat_prp(1234,2) is False pytest.raises(TypeError, lambda: is_fermat_prp(1234,'a')) pytest.raises(TypeError, lambda: is_fermat_prp(1234, 2, 3)) pytest.raises(ValueError, lambda: is_fermat_prp(113, 1)) pytest.raises(ValueError, lambda: is_fermat_prp(-113, 3)) pytest.raises(ValueError, lambda: is_fermat_prp(339, 3)) assert is_fermat_prp(mpz(12345),2) is False assert is_fermat_prp(113,mpz(2)) def test_is_euler_prp(): assert is_euler_prp(12345,2) is False assert is_euler_prp(113,2) assert is_euler_prp(1234,2) is False pytest.raises(TypeError, lambda: is_euler_prp(1234,'a')) pytest.raises(TypeError, lambda: is_euler_prp(1234, 2, 3)) pytest.raises(ValueError, lambda: is_euler_prp(113, 1)) pytest.raises(ValueError, lambda: is_euler_prp(-113, 3)) pytest.raises(ValueError, lambda: is_euler_prp(339, 3)) assert is_euler_prp(mpz(12345),2) is False assert is_euler_prp(113,mpz(2)) def test_is_strong_prp(): assert is_strong_prp(12345,2) is False assert is_strong_prp(113,2) assert is_strong_prp(1234,2) is False pytest.raises(TypeError, lambda: is_strong_prp(1234,'a')) pytest.raises(TypeError, lambda: is_strong_prp(1234, 2, 3)) pytest.raises(ValueError, lambda: is_strong_prp(113, 1)) pytest.raises(ValueError, lambda: is_strong_prp(-113, 3)) pytest.raises(ValueError, lambda: is_strong_prp(339, 3)) assert is_strong_prp(mpz(12345),2) is False assert is_strong_prp(113,mpz(2)) def test_is_fibonacci_prp(): assert is_fibonacci_prp(12345, 3, 1) is False assert is_fibonacci_prp(113, 3, 1) assert is_fibonacci_prp(12345, 3, -1) is False assert is_fibonacci_prp(113, 3, -1) pytest.raises(ValueError, lambda: is_fibonacci_prp(113, 3, 2)) pytest.raises(TypeError, lambda: is_fibonacci_prp('a', 3, 2)) pytest.raises(ValueError, lambda: is_fibonacci_prp(113, 2, 1)) assert is_fibonacci_prp(113, 2, -1) def test_is_lucas_prp(): assert is_lucas_prp(12345, 5, 2) is False assert is_lucas_prp(113, 5, 2) pytest.raises(ValueError, lambda: is_lucas_prp(12345, 3, 5)) def test_is_is_stronglucas_prp(): assert is_strong_lucas_prp(12345, 5, 2) is False assert is_strong_lucas_prp(113, 5, 2) pytest.raises(ValueError, lambda: is_strong_lucas_prp(12345, 3, 5)) def test_is_extra_strong_lucas_prp(): assert is_extra_strong_lucas_prp(12345, 9) is False assert is_extra_strong_lucas_prp(113, 5) pytest.raises(ValueError, lambda: is_extra_strong_lucas_prp(12345, 3)) def test_is_selfridge_prp(): assert is_selfridge_prp(12345) is False assert is_selfridge_prp(113) def test_is_strong_selfridge_prp(): assert is_strong_selfridge_prp(12345) is False assert is_strong_selfridge_prp(113) def test_is_bpsw_prp(): assert is_bpsw_prp(12345) is False assert is_bpsw_prp(113) def test_is_strong_bpsw_prp(): assert is_strong_bpsw_prp(12345) is False assert is_strong_bpsw_prp(113) def test_mpz_from_old_binary(): assert gmpy2.mpz_from_old_binary(b'\x15\xcd[\x07') == mpz(123456789) assert gmpy2.mpz_from_old_binary(b'\x15\xcd[\x07\xff') == mpz(-123456789) pytest.raises(TypeError, lambda: mpz_from_old_binary(1)) def test_mpq_from_old_binary(): assert mpq_from_old_binary(b'\x01\x00\x00\x00)\x98') == mpq(41,152) assert mpq_from_old_binary(b'\x01\x00\x00\x80)\x98') == mpq(-41,152) pytest.raises(TypeError, lambda: mpq_from_old_binary(1)) pytest.raises(ValueError, lambda: mpq_from_old_binary(b'aa')) pytest.raises(ValueError, lambda: mpq_from_old_binary(b'aaaaaaaaa')) def test_mpfr_from_old_binary(): assert mpfr_from_old_binary(b'\x085\x00\x00\x00\x02\x00\x00\x0009\xac\xcc\xcc\xcc\xcc\xcc\xd0') == mpfr('12345.674999999999') assert mpfr_from_old_binary(b'\t5\x00\x00\x00\x02\x00\x00\x0009\xac\xcc\xcc\xcc\xcc\xcc\xd0') == mpfr('-12345.674999999999') assert mpfr_from_old_binary(b'\n5\x00\x00\x00\x06\x00\x00\x00\x01\x14\xb3\x7fKQ\xf7\x0en') == mpfr('1.5e-17') pytest.raises(TypeError, lambda: mpfr_from_old_binary(1)) pytest.raises(ValueError, lambda: mpfr_from_old_binary(b'aaaaa')) assert mpfr_from_old_binary(b'\x04') == mpfr('0.0') def test_from_binary(): pytest.raises(TypeError, lambda: from_binary(1)) pytest.raises(ValueError, lambda: from_binary(b'a')) def test_phase(): pytest.raises(TypeError, lambda: phase()) pytest.raises(TypeError, lambda: phase(3)) assert phase(mpc(4,5)) == mpfr('0.89605538457134393') assert ieee(64).phase(mpc(4,5)) == mpfr('0.89605538457134393') def test_root_of_unity(): assert root_of_unity(1,1) == mpc('1.0+0.0j') assert root_of_unity(1,2) == mpc('1.0+0.0j') assert root_of_unity(2,1) == mpc('-1.0+0.0j') assert root_of_unity(3,1) == mpc('-0.5+0.8660254037844386j') assert root_of_unity(3,2) == mpc('-0.5-0.8660254037844386j') assert root_of_unity(3,3) == mpc('1.0+0.0j') assert ieee(128).root_of_unity(3,1) == mpc('-0.5+0.866025403784438646763723170752936161j',(113,113)) pytest.raises(TypeError, lambda: ieee(128).root_of_unity()) pytest.raises(TypeError, lambda: ieee(128).root_of_unity('a','b')) def test_norm(): pytest.raises(TypeError, lambda: norm()) pytest.raises(TypeError, lambda: norm(2)) assert norm(mpc(1,2)) == mpfr('5.0') assert ieee(32).norm(mpc(1,2)) == mpfr('5.0',24) def test_polar(): pytest.raises(TypeError, lambda: polar()) pytest.raises(TypeError, lambda: polar(5)) assert polar(mpc(1,1)) == (mpfr('1.4142135623730951'), mpfr('0.78539816339744828')) def test_rect(): pytest.raises(TypeError, lambda: rect()) pytest.raises(TypeError, lambda: rect(1)) assert rect(1,1) == mpc('0.54030230586813977+0.8414709848078965j') def test_proj(): pytest.raises(TypeError, lambda: proj()) pytest.raises(TypeError, lambda: proj(1)) assert proj(mpc(1,1)) == mpc('1.0+1.0j') assert proj(mpc(1,2)) == mpc('1.0+2.0j') def test_is_zero(): assert is_zero(mpc("0+0j")) assert is_zero(mpc("1+0j")) is False assert is_zero(mpc("1+1j")) is False assert is_zero(mpc("0+1j")) is False ctx = gmpy2.get_context() pynan = float('nan') pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') assert is_zero(float(0)) assert is_zero(mpfr(0)) assert not is_zero(pynan) assert not is_zero(rinf) assert not is_zero(mpfr(5)) assert not gmpy2.is_zero(float(5)) pytest.raises(TypeError, lambda: is_zero(None)) assert ctx.is_zero(float(0)) assert ctx.is_zero(mpfr(0)) assert not ctx.is_zero(pynan) assert not ctx.is_zero(rinf) assert not ctx.is_zero(mpfr(5)) assert not ctx.is_zero(float(5)) assert not ctx.is_zero(mpc(4,4)) assert not ctx.is_zero(mpc(0,4)) assert ctx.is_zero(mpc(0,0)) assert ctx.is_zero(complex(0,0)) assert not ctx.is_zero(complex(0,5)) assert mpfr(0).is_zero() assert not rinf.is_zero() assert not mpfr(-5).is_zero() assert mpc(0, 0).is_zero() assert not mpc(0, 4).is_zero() def test_is_nan(): assert is_nan(mpc("nan+1j")) assert is_nan(mpc("1+nanj")) assert is_nan(mpc("nan+nanj")) assert is_nan(mpc("1+1j")) is False ctx = gmpy2.get_context() pynan = float('nan') pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') r = mpfr(4) assert not r.is_nan() assert rnan.is_nan() assert not is_nan(r) assert is_nan(rnan) assert not ctx.is_nan(r) assert ctx.is_nan(rnan) assert ctx.is_nan(pynan) assert not ctx.is_nan(pyinf) assert mpc(rnan).is_nan() assert not mpc('4.0').is_nan() assert ctx.is_nan(complex(pynan)) def test_is_infinite(): assert is_infinite(mpc("inf+1j")) assert is_infinite(mpc("-inf+1j")) assert is_infinite(mpc("1+infj")) assert is_infinite(mpc("1-infj")) assert is_infinite(mpc("inf-infj")) assert is_infinite(mpc("1+1j")) is False ctx = gmpy2.get_context() pynan = float('nan') pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') z5 = mpz(5) assert not is_infinite(5) assert not is_infinite(z5) assert is_infinite(rinf) assert is_infinite(pyinf) assert is_infinite(complex(pyinf)) assert ctx.is_infinite(rinf) assert ctx.is_infinite(pyinf) assert not ctx.is_infinite(pynan) assert not ctx.is_infinite(rnan) assert not rnan.is_infinite() assert rinf.is_infinite() assert mpc(pyinf).is_infinite() assert not mpc(3, 4).is_infinite() def test_is_finite(): assert is_finite(mpc("0+0j")) assert is_finite(mpc("nan+0j")) is False assert is_finite(mpc("0+nanj")) is False assert is_finite(mpc("0+infj")) is False assert is_finite(mpc("inf+3j")) is False ctx = gmpy2.get_context() pynan = float('nan') pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') z5 = mpz(5) assert is_finite(5) assert is_finite(z5) assert not is_finite(rinf) assert not is_finite(pyinf) assert not is_finite(complex(pyinf)) assert not ctx.is_finite(rinf) assert not ctx.is_finite(pyinf) assert not ctx.is_finite(pynan) assert not ctx.is_finite(rnan) assert not rnan.is_finite() assert not rinf.is_finite() q = mpq(2,3) assert ctx.is_finite(q) assert not mpc(pyinf).is_finite() assert mpc(3, 4).is_finite() def test_is_signed(): rnan = mpfr('nan') rinf = mpfr('inf') assert not rinf.is_signed() assert not rnan.is_signed() assert mpfr(-5).is_signed() assert not mpfr(0).is_signed() assert not is_signed(5) assert is_signed(-5) assert not is_signed(float(5)) assert not is_signed(mpfr(5)) def test_is_regular(): ctx = gmpy2.get_context() pynan = float('nan') pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') z5 = mpz(5) assert not is_regular(rnan) assert not is_regular(rinf) assert not is_regular(mpfr(0)) assert not is_regular(pyinf) assert is_regular(mpfr(5)) assert is_regular(z5) assert is_regular(-0.6) assert not is_regular(pynan) assert not ctx.is_regular(rnan) assert not ctx.is_regular(rinf) assert not ctx.is_regular(mpfr(0)) assert not ctx.is_regular(pyinf) assert ctx.is_regular(mpfr(5)) assert ctx.is_regular(z5) assert ctx.is_regular(-0.6) assert not ctx.is_regular(pynan) assert mpfr(-0.6).is_regular() def test_is_integer(): ctx = gmpy2.get_context() pyinf = float('inf') rnan = mpfr('nan') rinf = mpfr('inf') assert not rinf.is_integer() assert not rnan.is_integer() assert mpfr(0).is_integer() assert mpfr(-42).is_integer() assert not mpfr(-42.65).is_integer() assert not is_integer(pyinf) assert is_integer(5) assert not is_integer(5.6) assert not is_integer(float(5.6)) assert ctx.is_integer(mpfr(5)) assert not ctx.is_integer(mpfr('5.6')) def test_is_lessgreater(): pynan = float('nan') rnan = mpfr('nan') assert not is_lessgreater(rnan, pynan) assert not is_lessgreater(rnan, 5) assert not is_lessgreater(5, pynan) assert not is_lessgreater(5, 5) assert not is_lessgreater(5, mpq(5/1)) assert not is_lessgreater(-5, float(-5)) assert is_lessgreater(-5, mpfr(4)) pytest.raises(TypeError, lambda: is_lessgreater(mpfr(0), mpc(4,1))) class Spam: def __mpfr__(self): return pytest.raises(TypeError, lambda: is_lessgreater(2, Spam())) def test_is_unordered(): pynan = float('nan') rnan = mpfr('nan') rinf = mpfr('inf') assert not is_unordered(-5, float(-5)) pytest.raises(TypeError, lambda: is_unordered(mpfr(0), mpc(4,1))) assert not is_unordered(-rinf, 0.0) assert is_unordered(rnan, pynan) assert is_unordered(rnan, 5) assert is_unordered(5, pynan) class Spam: def __mpfr__(self): return pytest.raises(TypeError, lambda: is_unordered(2, Spam())) def test_f2q(): a = mpfr('123.456') pytest.raises(TypeError, lambda: f2q('a')) pytest.raises(TypeError, lambda: f2q(1,2,3,4)) assert f2q(a,0.1) == mpz(123) assert f2q(a,0.01) == mpz(123) assert f2q(a,0.001) == mpq(247,2) assert f2q(a,0.0001) == mpq(1358,11) assert f2q(a,0.00001) == mpq(7037,57) assert f2q(a,0.000001) == mpq(15432,125) assert f2q(a,0.0000001) == mpq(15432,125) assert f2q(a) == mpq(15432,125) assert f2q(2.50000000000008) == mpq(15637498706148,6254999482459) assert f2q(2.5000000000000) == mpq(5,2) assert f2q(2.50000000000008, 0.001) == mpq(5,2) assert f2q(2.50000000000008, -50) == mpq(15637498706148,6254999482459) assert f2q(mpfr('0.500000011'), 1e-4) == mpq(1,2) assert f2q(mpfr('0.500000011'), 1e-5) == mpq(1,2) assert f2q(mpfr('0.500000011'), 1e-6) == mpq(1,2) assert f2q(mpfr('0.500000011'), 1e-7) == mpq(1,2) assert f2q(mpfr('0.500000011'), 1e-8) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-9) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-10) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-11) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-12) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-13) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-14) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-15) == mpq(22727273,45454545) assert f2q(mpfr('0.500000011'), 1e-16) == mpq(204545458,409090907) assert f2q(mpfr('0.500000011'), 1e-17) == mpq(204545458,409090907) def test_get_emin_min(): assert get_emin_min() in (-4611686018427387903, -1073741823) def test_get_emax_max(): assert get_emax_max() in (4611686018427387903, 1073741823) def test_set_sign(): r = mpfr(4.55) assert set_sign(r, False) == mpfr('4.5499999999999998') assert set_sign(r, True) == mpfr('-4.5499999999999998') pytest.raises(TypeError, lambda: set_sign(mpz(5), True)) pytest.raises(TypeError, lambda: set_sign(r, 'oiio')) def test_copy_sign(): assert copy_sign(mpfr(4), mpfr(-2)) == mpfr('-4.0') pytest.raises(TypeError, lambda: copy_sign(mpfr(4), True)) def test_nan(): x = nan() assert is_nan(x) def test_inf(): assert inf() == mpfr('inf') assert inf(-5) == mpfr('-inf') assert inf(mpz(-30)) == mpfr('-inf') pytest.raises(TypeError, lambda: inf(mpfr(30))) def test_check_range(): r = mpfr(4.55) assert check_range(r) == mpfr('4.5499999999999998') ctx = gmpy2.get_context() assert ctx.check_range(r) == mpfr('4.5499999999999998') pytest.raises(TypeError, lambda: ctx.check_range(mpz(5))) def test_sign(): a = mpq(3,11) assert sign(a) == 1 assert sign(-a) == -1 assert sign(mpq(0,5)) == 0 pytest.raises(TypeError, lambda: sign('str')) a = mpfr("12.34") assert sign(-1.5) == -1 assert sign(a) == 1 assert sign(mpfr(0)) == 0 assert sign(mpfr('inf')) == 1 assert sign(mpfr('-inf')) == -1 assert sign(mpfr('nan')) == 0 a = mpz(123) b = mpz(456) assert sign(b-a) == 1 assert sign(b-b) == 0 assert sign(a-b) == -1 assert sign(a) == 1 assert sign(-a) == -1 def test_acos(): assert acos(mpfr("0.2")).as_integer_ratio() == (mpz(6167402294989009), mpz(4503599627370496)) pytest.raises(TypeError, lambda: acos()) pytest.raises(TypeError, lambda: acos("a")) pytest.raises(TypeError, lambda: acos(0,0)) assert acos(0) == mpfr('1.5707963267948966') assert acos(mpz(0)) == mpfr('1.5707963267948966') assert acos(mpq(1,2)) == mpfr('1.0471975511965979') assert acos(Fraction(1,2)) == mpfr('1.0471975511965979') assert is_nan(acos(mpfr("nan"))) assert is_nan(acos(mpfr("inf"))) assert is_nan(acos(mpfr("-inf"))) set_context(context(trap_invalid=True)) pytest.raises(gmpy2.InvalidOperationError, lambda: acos(mpfr("nan"))) pytest.raises(gmpy2.InvalidOperationError, lambda: acos(mpfr("inf"))) pytest.raises(gmpy2.InvalidOperationError, lambda: acos(mpfr("-inf"))) set_context(context(precision=100)) assert acos(mpfr("0.2")) == mpfr('1.3694384060045658277761961394221',100) assert get_context().precision == 100 assert get_context().inexact def test_asin(): assert gmpy2.asin(mpfr("0.2")).as_integer_ratio() == (mpz(7254683656315453), mpz(36028797018963968)) pytest.raises(TypeError, lambda: asin()) pytest.raises(TypeError, lambda: asin("a")) pytest.raises(TypeError, lambda: asin(0,0)) assert asin(0) == mpfr('0.0') assert asin(mpz(0)) == mpfr('0.0') assert asin(mpq(1,2)) == mpfr('0.52359877559829893') assert asin(Fraction(1,2)) == mpfr('0.52359877559829893') assert is_nan(asin(mpfr("nan"))) assert is_nan(asin(mpfr("inf"))) assert is_nan(asin(mpfr("-inf"))) set_context(context(trap_invalid=True)) pytest.raises(gmpy2.InvalidOperationError, lambda: asin(mpfr("nan"))) pytest.raises(gmpy2.InvalidOperationError, lambda: asin(mpfr("inf"))) pytest.raises(gmpy2.InvalidOperationError, lambda: asin(mpfr("-inf"))) set_context(context(precision=100)) assert asin(mpfr("0.2")) == mpfr('0.20135792079033079145512555221757',100) assert get_context().precision == 100 assert get_context().inexact def test_atan(): assert atan(mpfr("0.2")).as_integer_ratio() == (mpz(1777981139569027), mpz(9007199254740992)) assert atan(mpfr("100")).as_integer_ratio() == (mpz(3514601628432273), mpz(2251799813685248)) pytest.raises(TypeError, lambda: atan()) pytest.raises(TypeError, lambda: atan("a")) pytest.raises(TypeError, lambda: atan(0,0)) assert atan(0) == mpfr('0.0') assert atan(mpz(0)) == mpfr('0.0') assert atan(mpq(1,2)) == mpfr('0.46364760900080609') assert atan(Fraction(1,2)) == mpfr('0.46364760900080609') assert is_nan(gmpy2.atan(mpfr("nan"))) assert atan(mpfr("inf")) == mpfr('1.5707963267948966') assert atan(mpfr("-inf")) == mpfr('-1.5707963267948966') set_context(context(trap_invalid=True)) pytest.raises(gmpy2.InvalidOperationError, lambda: atan(mpfr("nan"))) set_context(context(precision=100)) assert gmpy2.atan(mpfr("0.2")) == mpfr('0.19739555984988075837004976519484',100) assert get_context().precision == 100 assert get_context().inexact def test_atan2(): assert atan2(1,2).as_integer_ratio() == (mpz(8352332796509007), mpz(18014398509481984)) assert atan2(-1,2).as_integer_ratio() == (mpz(-8352332796509007), mpz(18014398509481984)) assert atan2(1,-2).as_integer_ratio() == (mpz(3015098076232407), mpz(1125899906842624)) assert atan2(-1,-2).as_integer_ratio() == (mpz(-3015098076232407), mpz(1125899906842624)) assert atan2(float("0"),float("0")).as_integer_ratio() == (mpz(0), mpz(1)) assert atan2(float("-0"),float("0")).as_integer_ratio() == (mpz(0), mpz(1)) assert atan2(float("0"),float("-0")).as_integer_ratio() == (mpz(884279719003555), mpz(281474976710656)) assert atan2(float("-0"),float("-0")).as_integer_ratio() == (mpz(-884279719003555), mpz(281474976710656)) assert atan2(float("inf"),float("inf")).as_integer_ratio() == (mpz(884279719003555), mpz(1125899906842624)) assert atan2(float("-inf"),float("inf")).as_integer_ratio() == (mpz(-884279719003555), mpz(1125899906842624)) assert atan2(float("inf"),float("-inf")).as_integer_ratio() == (mpz(2652839157010665), mpz(1125899906842624)) assert atan2(float("-inf"),float("-inf")).as_integer_ratio() == (mpz(-2652839157010665), mpz(1125899906842624)) def test_cos(): assert cos(mpfr("0.2")).as_integer_ratio() == (mpz(4413827474764093), mpz(4503599627370496)) assert cos(mpfr("20")).as_integer_ratio() == (mpz(7351352886077503), mpz(18014398509481984)) or (sys.platform == 'win32') assert cos(mpfr("2000")).as_integer_ratio() == (mpz(-3309781376808469), mpz(9007199254740992)) pytest.raises(TypeError, lambda: cos()) pytest.raises(TypeError, lambda: cos("a")) pytest.raises(TypeError, lambda: cos(0,0)) assert cos(0) == mpfr('1.0') assert cos(mpz(0)) == mpfr('1.0') assert cos(mpq(1,2)) == mpfr('0.87758256189037276') assert cos(Fraction(1,2)) == mpfr('0.87758256189037276') assert is_nan(cos(mpfr("nan"))) assert is_nan(cos(mpfr("inf"))) assert is_nan(cos(mpfr("-inf"))) set_context(context(trap_invalid=True)) pytest.raises(gmpy2.InvalidOperationError, lambda: cos(mpfr("nan"))) pytest.raises(gmpy2.InvalidOperationError, lambda: cos(mpfr("inf"))) pytest.raises(gmpy2.InvalidOperationError, lambda: cos(mpfr("-inf"))) set_context(context(precision=100)) assert cos(mpfr("0.2")) == mpfr('0.98006657784124163112419651674809',100) assert get_context().precision == 100 assert get_context().inexact def test_cot(): assert cot(mpfr("0.2")).as_integer_ratio() == (mpz(173569956714485), mpz(35184372088832)) assert cot(gmpy2.const_pi()).as_integer_ratio() == (mpz(-8165619676597685), mpz(1)) assert cot(1) == mpfr('0.64209261593433076') assert cot(float('0')) == mpfr('inf') assert cot(float('-0')) == mpfr('-inf') assert cot(mpfr('0')) == mpfr('inf') assert cot(mpfr('-0')) == mpfr('-inf') def test_csc(): r2 = mpfr('5.6') assert csc(r2) == mpfr('-1.5841166632383596') def test_sec(): r2 = mpfr('5.6') assert sec(r2) == mpfr('1.2893811186238056') def test_sin(): r = mpfr(5.6) assert sin(r) == mpfr('-0.63126663787232162') assert sin(r) == sin(5.6) def test_sin_cos(): r = mpfr(5.6) assert sin_cos(r) == (mpfr('-0.63126663787232162'), mpfr('0.77556587851024961')) assert sin_cos(r) == sin_cos(5.6) assert sin_cos(r) == (sin(r), cos(r)) def test_tan(): r = mpfr(5.6) assert tan(r) == mpfr('-0.8139432836897027') def test_acosh(): r = mpfr(5.6) assert acosh(r) == mpfr('2.4078447868719399') def test_asinh(): r = mpfr(5.6) assert asinh(r) == mpfr('2.4237920435875173') def test_atanh(): assert atanh(mpfr(0.365)) == mpfr('0.38264235436318422') assert atanh(mpfr(0.365)) == atanh(0.365) def test_cosh(): r = mpfr(5.6) assert cosh(r) == mpfr('135.2150526449345') assert cosh(r) == cosh(5.6) def test_coth(): r = mpfr(5.6) assert coth(r) == mpfr('1.0000273487661038') def test_csch(): r = mpfr(5.6) assert csch(r) == mpfr('0.0073958285649757295') def test_degrees(): rad = mpfr(1.57) ctx = get_context() assert ctx.degrees(rad) == mpfr('89.954373835539243') assert degrees(rad) == mpfr('89.954373835539243') assert degrees(1) == mpfr('57.295779513082323') def test_radians(): deg = mpfr(90) ctx = get_context() assert ctx.radians(deg) == mpfr('1.5707963267948966') assert radians(deg) == mpfr('1.5707963267948966') assert radians(45) == mpfr('0.78539816339744828') assert radians(mpz(20)) == mpfr('0.3490658503988659') assert radians(mpfr('inf')) == mpfr('inf') assert is_nan(radians(mpfr('nan'))) def test_sech(): r = mpfr(5.6) assert sech(r) == mpfr('0.0073956263037217584') def test_sinh(): r = mpfr(5.6) assert sinh(r) == mpfr('135.21135478121803') assert sinh(r) == gmpy2.sinh(5.6) def test_sinh_cosh(): r = mpfr(5.6) assert sinh_cosh(r) == (mpfr('135.21135478121803'), mpfr('135.2150526449345')) assert sinh_cosh(r) == sinh_cosh(5.6) assert sinh_cosh(r) == (sinh(r), cosh(r)) def test_tanh(): r = mpfr(5.6) assert tanh(r) == mpfr('0.99997265198183083') def test_c_divmod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: c_divmod(1)) pytest.raises(TypeError, lambda: c_divmod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: c_divmod(a,0)) assert c_divmod(b,a) == (mpz(4), mpz(-36)) assert c_divmod(b,-a) == (mpz(-3), mpz(87)) assert c_divmod(-b,a) == (mpz(-3), mpz(-87)) assert c_divmod(-b,-a) == (mpz(4), mpz(36)) def test_c_divmod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: c_divmod_2exp(1)) pytest.raises(TypeError, lambda: c_divmod_2exp(1, 'a')) pytest.raises(TypeError, lambda: c_divmod_2exp('a', 16)) pytest.raises(OverflowError, lambda: c_divmod_2exp(a,-16)) assert c_divmod_2exp(a,0) == (mpz(123456), mpz(0)) assert c_divmod_2exp(a,16) == (mpz(2), mpz(-7616)) assert c_divmod_2exp(-a,16) == (mpz(-1), mpz(-57920)) def test_c_div(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: c_div(1)) pytest.raises(TypeError, lambda: c_div(1, 'a')) pytest.raises(ZeroDivisionError, lambda: c_div(a,0)) assert c_div(b,a) == mpz(4) assert c_div(b,-a) == mpz(-3) assert c_div(-b,a) == mpz(-3) assert c_div(-b,-a) == mpz(4) def test_c_div_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: c_div_2exp(1)) pytest.raises(TypeError, lambda: c_div_2exp(1, 'a')) pytest.raises(TypeError, lambda: c_div_2exp('a', 16)) pytest.raises(OverflowError, lambda: c_div_2exp(a, -16)) assert c_div_2exp(a,0) == mpz(123456) assert c_div_2exp(a,16) == mpz(2) assert c_div_2exp(-a,16) == mpz(-1) def test_c_mod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: c_mod(1)) pytest.raises(TypeError, lambda: c_mod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: c_mod(a,0)) assert c_mod(b,a) == mpz(-36) assert c_mod(b,-a) == mpz(87) assert c_mod(-b,a) == mpz(-87) assert c_mod(-b,-a) == mpz(36) def test_c_mod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: c_mod_2exp(1)) pytest.raises(TypeError, lambda: c_mod_2exp(1, 'a')) pytest.raises(TypeError, lambda: c_mod_2exp('a', 16)) pytest.raises(OverflowError, lambda: c_mod_2exp(a, -16)) assert c_mod_2exp(a,0) == mpz(0) assert c_mod_2exp(a,16) == mpz(-7616) assert c_mod_2exp(-a,16) == mpz(-57920) def test_f_divmod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: f_divmod(1)) pytest.raises(TypeError, lambda: f_divmod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: f_divmod(a,0)) assert f_divmod(b,a) == (mpz(3), mpz(87)) assert f_divmod(b,-a) == (mpz(-4), mpz(-36)) assert f_divmod(-b,a) == (mpz(-4), mpz(36)) assert f_divmod(-b,-a) == (mpz(3), mpz(-87)) def test_f_divmod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: f_divmod_2exp(1)) pytest.raises(TypeError, lambda: f_divmod_2exp(1, 'a')) pytest.raises(TypeError, lambda: f_divmod_2exp('a', 16)) pytest.raises(OverflowError, lambda: f_divmod_2exp(a,-16)) assert f_divmod_2exp(a,0) == (mpz(123456), mpz(0)) assert f_divmod_2exp(a,16) == (mpz(1), mpz(57920)) assert f_divmod_2exp(-a,16) == (mpz(-2), mpz(7616)) def test_f_div(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: f_div(1)) pytest.raises(TypeError, lambda: f_div(1, 'a')) pytest.raises(ZeroDivisionError, lambda: f_div(a,0)) assert f_div(b,a) == mpz(3) assert f_div(b,-a) == mpz(-4) assert f_div(-b,a) == mpz(-4) assert f_div(-b,-a) == mpz(3) def test_f_div_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: f_div_2exp(1)) pytest.raises(TypeError, lambda: f_div_2exp(1, 'a')) pytest.raises(TypeError, lambda: f_div_2exp('a', 16)) pytest.raises(OverflowError, lambda: f_div_2exp(a, -16)) assert f_div_2exp(a,0) == mpz(123456) assert f_div_2exp(a,16) == mpz(1) assert f_div_2exp(-a,16) == mpz(-2) def test_f_mod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: f_mod(1)) pytest.raises(TypeError, lambda: f_mod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: f_mod(a,0)) assert f_mod(b,a) == mpz(87) assert f_mod(b,-a) == mpz(-36) assert f_mod(-b,a) == mpz(36) assert f_mod(-b,-a) == mpz(-87) def test_f_mod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: f_mod_2exp(1)) pytest.raises(TypeError, lambda: f_mod_2exp(1, 'a')) pytest.raises(TypeError, lambda: f_mod_2exp('a', 16)) pytest.raises(OverflowError, lambda: f_mod_2exp(a, -16)) assert f_mod_2exp(a,0) == mpz(0) assert f_mod_2exp(a,16) == mpz(57920) assert f_mod_2exp(-a,16) == mpz(7616) def test_t_divmod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: t_divmod(1)) pytest.raises(TypeError, lambda: t_divmod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: t_divmod(a,0)) assert t_divmod(b,a) == (mpz(3), mpz(87)) assert t_divmod(b,-a) == (mpz(-3), mpz(87)) assert t_divmod(-b,a) == (mpz(-3), mpz(-87)) assert t_divmod(-b,-a) == (mpz(3), mpz(-87)) def test_t_divmod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: t_divmod_2exp(1)) pytest.raises(TypeError, lambda: t_divmod_2exp(1, 'a')) pytest.raises(TypeError, lambda: t_divmod_2exp('a', 16)) pytest.raises(OverflowError, lambda: t_divmod_2exp(a,-16)) assert t_divmod_2exp(a,0) == (mpz(123456), mpz(0)) assert t_divmod_2exp(a,16) == (mpz(1), mpz(57920)) assert t_divmod_2exp(-a,16) == (mpz(-1), mpz(-57920)) def test_t_div(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: t_div(1)) pytest.raises(TypeError, lambda: t_div(1, 'a')) pytest.raises(ZeroDivisionError, lambda: t_div(a,0)) assert t_div(b,a) == mpz(3) assert t_div(b,-a) == mpz(-3) assert t_div(-b,a) == mpz(-3) assert t_div(-b,-a) == mpz(3) def test_t_div_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: t_div_2exp(1)) pytest.raises(TypeError, lambda: t_div_2exp(1, 'a')) pytest.raises(TypeError, lambda: t_div_2exp('a', 16)) pytest.raises(OverflowError, lambda: t_div_2exp(a, -16)) assert t_div_2exp(a,0) == mpz(123456) assert t_div_2exp(a,16) == mpz(1) assert t_div_2exp(-a,16) == mpz(-1) def test_t_mod(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: t_mod(1)) pytest.raises(TypeError, lambda: t_mod(1, 'a')) pytest.raises(ZeroDivisionError, lambda: t_mod(a,0)) assert t_mod(b,a) == mpz(87) assert t_mod(b,-a) == mpz(87) assert t_mod(-b,a) == mpz(-87) assert t_mod(-b,-a) == mpz(-87) def test_t_mod_2exp(): a = mpz(123456) pytest.raises(TypeError, lambda: t_mod_2exp(1)) pytest.raises(TypeError, lambda: t_mod_2exp(1, 'a')) pytest.raises(TypeError, lambda: t_mod_2exp('a', 16)) pytest.raises(OverflowError, lambda: t_mod_2exp(a, -16)) assert t_mod_2exp(a,0) == mpz(0) assert t_mod_2exp(a,16) == mpz(57920) assert t_mod_2exp(-a,16) == mpz(-57920) def test_get_max_precision(): assert gmpy2.get_max_precision() > 53 def test_free_cache(): assert free_cache() is None def test_gcd(): a = mpz(123) b = mpz(456) assert gcd(1,2,3) == mpz(1) assert gcd(2, 4, 6) == mpz(2) pytest.raises(TypeError, lambda: gcd(1,'a')) assert gcd(123,456) == mpz(3) assert gcd(a,b) == mpz(3) def test_lcm(): a = mpz(123) b = mpz(456) assert lcm(1,2,3) == mpz(6) assert lcm(2, 3, 4) == mpz(12) pytest.raises(TypeError, lambda: lcm(1,'a')) assert lcm(a,b) == mpz(18696) assert lcm(123,456) == mpz(18696) def test_gcdext(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: gcdext(1,2,3)) pytest.raises(TypeError, lambda: gcdext(1,'a')) temp = gcdext(a,b) assert temp[0] == a*temp[1] + b*temp[2] temp = gcdext(123,456) assert temp[0] == a*temp[1] + b*temp[2] def test_divm(): a = mpz(123) b = mpz(456) assert divm(b,a,20) == mpz(12) pytest.raises(TypeError, lambda: divm(a,b,100,5)) pytest.raises(TypeError, lambda: divm(a,b,'a')) pytest.raises(ZeroDivisionError, lambda: divm(a,b,100)) assert divm(6,12,14) == mpz(4) assert divm(0,1,2) == mpz(0) assert divm(4,8,20) == mpz(3) def test_fac(): pytest.raises(OverflowError, lambda: fac(-7)) pytest.raises(TypeError, lambda: fac('a')) assert fac(7) == mpz(5040) def test_double_fac(): pytest.raises(OverflowError, lambda: double_fac(-7)) pytest.raises(TypeError, lambda: double_fac('a')) assert double_fac(7) == mpz(105) assert double_fac(7) * gmpy2.double_fac(8) == mpz(40320) assert fac(8) == mpz(40320) def test_primorial(): pytest.raises(OverflowError, lambda: primorial(-7)) pytest.raises(TypeError, lambda: primorial('a')) assert primorial(7) == mpz(210) def test_multi_fac(): pytest.raises(TypeError, lambda: multi_fac(-7)) pytest.raises(TypeError, lambda: multi_fac(7,'a')) pytest.raises(OverflowError, lambda: multi_fac(7,-1)) pytest.raises(OverflowError, lambda: multi_fac(-7,1)) pytest.raises(TypeError, lambda: multi_fac('a')) pytest.raises(TypeError, lambda: multi_fac(10)) pytest.raises(TypeError, lambda: multi_fac(10,11,12)) assert multi_fac(17,4) == mpz(9945) def test_fib(): pytest.raises(OverflowError, lambda: fib(-2)) assert fib(17) == mpz(1597) def test_fib2(): pytest.raises(OverflowError, lambda: fib2(-2)) assert fib2(17) == (mpz(1597), mpz(987)) def test_lucas(): pytest.raises(OverflowError, lambda: lucas(-2)) assert lucas(17) == mpz(3571) def test_lucas2(): pytest.raises(OverflowError, lambda: lucas2(-2)) assert lucas2(17) == (mpz(3571), mpz(2207)) def test_bincoef(): pytest.raises(TypeError, lambda: bincoef(1)) pytest.raises(TypeError, lambda: bincoef(1,2,3)) assert [bincoef(10,i) for i in range(10)] == [1, 10, 45, 120, 210, 252, 210, 120, 45, 10] assert bincoef(1111111111111111111111, 2) == mpz(617283950617283950616604938271604938271605) def test_comb(): pytest.raises(OverflowError, lambda: comb(3,-1)) pytest.raises(TypeError, lambda: comb('a',4)) assert comb(8,4) == mpz(70) def test_isqrt(): a = mpz(123) assert isqrt(a) == 11 assert isqrt(123) == 11 pytest.raises(ValueError, lambda: isqrt(-1)) pytest.raises(ValueError, lambda: isqrt(mpz(-1))) pytest.raises(TypeError, lambda: isqrt('a')) def test_isqrt_rem(): a = mpz(123) b = mpz(456) assert isqrt_rem(a) == (mpz(11), mpz(2)) assert isqrt_rem(b) == (mpz(21), mpz(15)) pytest.raises(ValueError, lambda: isqrt_rem(-1)) pytest.raises(ValueError, lambda: isqrt_rem(mpz(-1))) pytest.raises(TypeError, lambda: isqrt_rem('a')) pytest.raises(ValueError, lambda: isqrt_rem(mpz(-1))) def test_remove(): a = mpz(123) b = mpz(456) assert remove(a,2) == (mpz(123), 0) assert remove(a,mpz(2)) == (mpz(123), 0) assert remove(a,3) == (mpz(41), 1) assert remove(b,2) == (mpz(57), 3) assert remove(b,3) == (mpz(152), 1) pytest.raises(ValueError, lambda: remove(b,1)) pytest.raises(ValueError, lambda: remove(b,mpz(1))) pytest.raises(ValueError, lambda: remove(b,0)) assert remove(b,789) == (mpz(456), 0) pytest.raises(ValueError, lambda: remove(b,-3)) pytest.raises(TypeError, lambda: remove(b,float('NaN'))) pytest.raises(ValueError, lambda: remove(3,-1)) pytest.raises(TypeError, lambda: remove(3)) pytest.raises(TypeError, lambda: remove()) def test_invert(): a = mpz(123) b = mpz(456) assert invert(a,100) == mpz(87) assert invert(a,mpz(100)) == mpz(87) pytest.raises(ZeroDivisionError, lambda: invert(b,mpz(100))) pytest.raises(ZeroDivisionError, lambda: invert(b,mpz(0))) pytest.raises(TypeError, lambda: invert(3)) pytest.raises(TypeError, lambda: invert()) pytest.raises(ZeroDivisionError, lambda: invert(456,0)) pytest.raises(TypeError, lambda: invert(456,'a')) pytest.raises(ZeroDivisionError, lambda: invert(456,100)) assert invert(123,100) == mpz(87) def test_divexact(): a = mpz(123) pytest.raises(TypeError, lambda: divexact(2)) pytest.raises(TypeError, lambda: divexact(2, 'a')) pytest.raises(ZeroDivisionError, lambda: divexact(a,0)) pytest.raises(ZeroDivisionError, lambda: divexact(a,mpz(0))) pytest.raises(ZeroDivisionError, lambda: divexact(123,0)) aa = mpz('1234567912345678912345679') bb = mpz('789789789789789789789789') cc = aa*bb assert divexact(cc,aa) == 789789789789789789789789 aa = 1234567912345678912345679 bb = 789789789789789789789789 cc = aa*bb assert divexact(cc,aa) == 789789789789789789789789 def test_next_prime(): pytest.raises(TypeError, lambda: next_prime('a')) assert next_prime(mpz(2)) == mpz(3) assert next_prime(2) == mpz(3) assert next_prime(1000000) == mpz(1000003) assert next_prime(2357*7069-1) != 2357*7069 def test_iroot(): a = mpz(123) b = mpz(456) pytest.raises(TypeError, lambda: iroot(1,2,3)) pytest.raises(ValueError, lambda: iroot(-9,2)) pytest.raises(ValueError, lambda: iroot(9,0)) assert [(iroot(a,i+1),gmpy2.iroot(b,i+1)) for i in range(5)] == [((mpz(123), True), (mpz(456), True)), ((mpz(11), False), (mpz(21), False)), ((mpz(4), False), (mpz(7), False)), ((mpz(3), False), (mpz(4), False)), ((mpz(2), False), (mpz(3), False))] assert iroot(9,2) == (mpz(3), True) ULONG_MAX = ctypes.c_ulong(-1).value assert iroot(4,ULONG_MAX) == (mpz(1), False) pytest.raises(OverflowError, lambda: iroot(4,ULONG_MAX+1)) def test_iroot_rem(): a = mpz(123) pytest.raises(TypeError, lambda: iroot_rem(1,2,3)) pytest.raises(ValueError, lambda: iroot_rem(-9,2)) pytest.raises(ValueError, lambda: iroot_rem(9,0)) assert iroot_rem(a,2) == (mpz(11), mpz(2)) assert iroot_rem(a,3) == (mpz(4), mpz(59)) assert iroot_rem(a*a,2) == (mpz(123), mpz(0)) def test_jacobi(): pytest.raises(TypeError, lambda: jacobi('a', 10)) pytest.raises(ValueError, lambda: jacobi(10,-3)) pytest.raises(TypeError, lambda: jacobi(3)) pytest.raises(TypeError, lambda: jacobi()) assert jacobi(10,3) == 1 def test_kronecker(): pytest.raises(TypeError, lambda: gmpy2.kronecker('a', 10)) assert kronecker(10,3) == 1 assert kronecker(10,-3) == 1 pytest.raises(TypeError, lambda: kronecker(3)) pytest.raises(TypeError, lambda: kronecker()) aaa = 10**20 bbb = aaa + 39 assert jacobi(aaa,bbb) == 1 assert legendre(aaa,bbb) == 1 assert kronecker(aaa,bbb) == 1 def test_legendre(): pytest.raises(TypeError, lambda: legendre('a', 10)) assert legendre(10,3) == 1 pytest.raises(ValueError, lambda: legendre(10,-3)) pytest.raises(TypeError, lambda: legendre(3)) pytest.raises(TypeError, lambda: legendre()) def test_fsum(): assert gmpy2.fsum([]) == mpfr('0.0') assert gmpy2.fsum([4, 5, 6]) == mpfr('15.0') assert gmpy2.fsum(range(13)) == mpfr('78.0') pytest.raises(TypeError, lambda: gmpy2.fsum(1)) def test_next_toward(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.next_toward()) pytest.raises(TypeError, lambda: gmpy2.next_toward(r)) assert gmpy2.next_toward(r, r2) == mpfr('5.5999999999999988') assert gmpy2.next_toward(r, f) == mpfr('5.5999999999999988') def test_next_above(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.next_above()) pytest.raises(TypeError, lambda: gmpy2.next_above(r, r2)) assert gmpy2.next_above(r) == mpfr('5.6000000000000005') assert gmpy2.next_above(r2) == mpfr('5.4000000000000012') assert gmpy2.next_above(f) == mpfr('0.60000000000000009') def test_factorial(): ctx = gmpy2.get_context() assert gmpy2.factorial(0) == mpfr('1.0') pytest.raises(TypeError, lambda: gmpy2.factorial(-0.0)) assert gmpy2.factorial(2) == mpfr('2.0') pytest.raises(TypeError, lambda: gmpy2.factorial('fred')) assert gmpy2.factorial(123) == mpfr('1.2146304367025329e+205') assert gmpy2.factorial(123456) == mpfr('2.6040699049291379e+574964') assert gmpy2.factorial(123456789) == mpfr('inf') pytest.raises(OverflowError, lambda: gmpy2.factorial(1234567899999999999999)) assert gmpy2.factorial(mpz(5)) == mpfr('120.0') assert ctx.factorial(4) == mpfr('24.0') def test_round2(): r = mpfr(1.65656565) assert gmpy2.round2(r, 2) == mpfr('1.5',2) assert gmpy2.round2(r, 5) == mpfr('1.69',5) assert gmpy2.round2(r) == mpfr('1.6565656499999999') assert gmpy2.round2(mpq('1/3')) == mpfr('0.33333333333333331') assert gmpy2.round2(mpq('1/3'), 30) == mpfr('0.33333333349',30) pytest.raises(ValueError, lambda: gmpy2.round2(r, -5)) pytest.raises(TypeError, lambda: gmpy2.round2(mpc(4, 4), 5)) assert gmpy2.round2(mpz(5), 5) == mpfr('5.0',5) pytest.raises(TypeError, lambda: gmpy2.round2(5, 6, 5)) pytest.raises(TypeError, lambda: gmpy2.round2()) def test_reldiff(): assert gmpy2.reldiff(mpfr(2.5), mpfr(17.5)) == mpfr('6.0') def test_modf(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.modf(r, r2)) assert gmpy2.modf(0.8) == (mpfr('0.0'), mpfr('0.80000000000000004')) assert gmpy2.modf(r) == (mpfr('5.0'), mpfr('0.59999999999999964')) assert gmpy2.modf(-r2) == (mpfr('-5.0'), mpfr('-0.40000000000000036')) assert gmpy2.fmod(mpfr(25), mpfr(2.5)) == mpfr('0.0') assert gmpy2.fmod(mpfr(25), 5.0) == mpfr('0.0') pytest.raises(TypeError, lambda: gmpy2.fmod(mpfr(25))) def test_remquo(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.remquo()) pytest.raises(TypeError, lambda: gmpy2.remquo(r)) assert gmpy2.remquo(r, f) == (mpfr('0.19999999999999984'), 9) assert gmpy2.remquo(r, r2) == (mpfr('0.19999999999999929'), 1) def test_frexp(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.frexp()) pytest.raises(TypeError, lambda: gmpy2.frexp(r, r2)) assert gmpy2.frexp(r) == (3, mpfr('0.69999999999999996')) assert gmpy2.frexp(r2) == (3, mpfr('0.67500000000000004')) assert gmpy2.frexp(f) == (0, mpfr('0.59999999999999998')) def test_rint(): r, r2 = mpfr('5.6'), mpfr(5.4) assert gmpy2.rint(r) == mpfr('6.0') assert gmpy2.rint(r2) == mpfr('5.0') def test_rint_ceil(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 assert gmpy2.rint_ceil(r) == mpfr('6.0') == gmpy2.ceil(r) assert gmpy2.rint_ceil(r2) == mpfr('6.0') == gmpy2.ceil(r2) assert gmpy2.rint_ceil(f) == mpfr('1.0') == gmpy2.ceil(f) def test_rint_floor(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 assert gmpy2.rint_floor(r) == mpfr('5.0') == gmpy2.floor(r) assert gmpy2.rint_floor(r2) == mpfr('5.0') == gmpy2.floor(r2) assert gmpy2.rint_floor(f) == mpfr('0.0') == gmpy2.floor(f) def test_rint_round(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 assert gmpy2.rint_round(r) == mpfr('6.0') assert gmpy2.rint_round(r2) == mpfr('5.0') assert gmpy2.rint_round(f) == mpfr('1.0') def test_rint_trunc(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 assert gmpy2.rint_trunc(r) == mpfr('5.0') == gmpy2.trunc(r) assert gmpy2.rint_trunc(r2) == mpfr('5.0') == gmpy2.trunc(r2) assert gmpy2.rint_trunc(f) == mpfr('0.0') == gmpy2.trunc(f) def test_round_away(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 assert gmpy2.round_away(r) == mpfr('6.0') assert gmpy2.round_away(r2) == mpfr('5.0') assert gmpy2.round_away(f) == mpfr('1.0') def test_gamma_funcs(): r, r2 = mpfr('5.6'), mpfr(5.4) assert gmpy2.gamma(r) == mpfr('61.55391500628923') assert gmpy2.lngamma(r) == mpfr('4.1199134575335288') assert gmpy2.digamma(r) == mpfr('1.6308319195144647') pytest.raises(TypeError, lambda: gmpy2.lgamma()) pytest.raises(TypeError, lambda: gmpy2.lgamma(r, r2)) assert gmpy2.lgamma(r) == (mpfr('4.1199134575335288'), 1) assert is_nan(gmpy2.lgamma(mpfr('nan'))[0]) assert gmpy2.lgamma(mpfr('inf')) == (mpfr('inf'), 1) def test_bessel_funcs(): r = mpfr('5.6') assert gmpy2.j0(r) == mpfr('0.026970884685114358') assert gmpy2.j1(r) == mpfr('-0.33433283629100752') assert gmpy2.y0(r) == mpfr('-0.33544418124531583') assert gmpy2.y1(r) == mpfr('-0.056805614399479849') assert gmpy2.jn(5, 43.2) == mpfr('-0.11672089168206982') pytest.raises(TypeError, lambda: gmpy2.jn(1.2,43.2)) assert gmpy2.yn(5,43.2) == mpfr('-0.034805474763124698') pytest.raises(TypeError, lambda: gmpy2.yn(43.2, 5.5)) def test_other_funcs(): r, r2 = mpfr('5.6'), mpfr(5.4) f = 0.6 pytest.raises(TypeError, lambda: gmpy2.agm(mpc(4,4), 5)) assert gmpy2.frac(r) == mpfr('0.59999999999999964') assert gmpy2.frac(r2) == mpfr('0.40000000000000036') assert gmpy2.frac(f) == mpfr('0.59999999999999998') assert gmpy2.cbrt(r) == mpfr('1.7758080034852013') assert gmpy2.cbrt(r2) == mpfr('1.7544106429277198') assert gmpy2.cbrt(f) == mpfr('0.84343266530174921') assert gmpy2.li2(r) == mpfr('1.6186578451141254') assert gmpy2.zeta(r) == mpfr('1.02337547922703') assert gmpy2.erf(r) == mpfr('0.99999999999999767') assert gmpy2.erfc(r) == mpfr('2.382836284583028e-15') assert gmpy2.ai(r) == mpfr('2.6500613296849995e-05') assert gmpy2.remainder(mpfr(5), mpfr(3.2)) == mpfr('-1.4000000000000004')