166 lines
4.5 KiB
Python
166 lines
4.5 KiB
Python
from sympy.core.numbers import (Rational, pi)
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from sympy.core.singleton import S
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.functions.elementary.exponential import (exp, log)
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from sympy.codegen.cfunctions import (
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expm1, log1p, exp2, log2, fma, log10, Sqrt, Cbrt, hypot
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)
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from sympy.core.function import expand_log
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def test_expm1():
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# Eval
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assert expm1(0) == 0
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x = Symbol('x', real=True)
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# Expand and rewrite
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assert expm1(x).expand(func=True) - exp(x) == -1
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assert expm1(x).rewrite('tractable') - exp(x) == -1
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assert expm1(x).rewrite('exp') - exp(x) == -1
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# Precision
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assert not ((exp(1e-10).evalf() - 1) - 1e-10 - 5e-21) < 1e-22 # for comparison
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assert abs(expm1(1e-10).evalf() - 1e-10 - 5e-21) < 1e-22
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# Properties
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assert expm1(x).is_real
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assert expm1(x).is_finite
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# Diff
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assert expm1(42*x).diff(x) - 42*exp(42*x) == 0
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assert expm1(42*x).diff(x) - expm1(42*x).expand(func=True).diff(x) == 0
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def test_log1p():
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# Eval
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assert log1p(0) == 0
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d = S(10)
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assert expand_log(log1p(d**-1000) - log(d**1000 + 1) + log(d**1000)) == 0
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x = Symbol('x', real=True)
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# Expand and rewrite
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assert log1p(x).expand(func=True) - log(x + 1) == 0
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assert log1p(x).rewrite('tractable') - log(x + 1) == 0
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assert log1p(x).rewrite('log') - log(x + 1) == 0
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# Precision
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assert not abs(log(1e-99 + 1).evalf() - 1e-99) < 1e-100 # for comparison
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assert abs(expand_log(log1p(1e-99)).evalf() - 1e-99) < 1e-100
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# Properties
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assert log1p(-2**Rational(-1, 2)).is_real
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assert not log1p(-1).is_finite
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assert log1p(pi).is_finite
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assert not log1p(x).is_positive
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assert log1p(Symbol('y', positive=True)).is_positive
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assert not log1p(x).is_zero
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assert log1p(Symbol('z', zero=True)).is_zero
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assert not log1p(x).is_nonnegative
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assert log1p(Symbol('o', nonnegative=True)).is_nonnegative
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# Diff
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assert log1p(42*x).diff(x) - 42/(42*x + 1) == 0
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assert log1p(42*x).diff(x) - log1p(42*x).expand(func=True).diff(x) == 0
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def test_exp2():
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# Eval
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assert exp2(2) == 4
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x = Symbol('x', real=True)
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# Expand
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assert exp2(x).expand(func=True) - 2**x == 0
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# Diff
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assert exp2(42*x).diff(x) - 42*exp2(42*x)*log(2) == 0
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assert exp2(42*x).diff(x) - exp2(42*x).diff(x) == 0
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def test_log2():
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# Eval
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assert log2(8) == 3
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assert log2(pi) != log(pi)/log(2) # log2 should *save* (CPU) instructions
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x = Symbol('x', real=True)
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assert log2(x) != log(x)/log(2)
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assert log2(2**x) == x
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# Expand
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assert log2(x).expand(func=True) - log(x)/log(2) == 0
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# Diff
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assert log2(42*x).diff() - 1/(log(2)*x) == 0
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assert log2(42*x).diff() - log2(42*x).expand(func=True).diff(x) == 0
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def test_fma():
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x, y, z = symbols('x y z')
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# Expand
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assert fma(x, y, z).expand(func=True) - x*y - z == 0
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expr = fma(17*x, 42*y, 101*z)
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# Diff
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assert expr.diff(x) - expr.expand(func=True).diff(x) == 0
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assert expr.diff(y) - expr.expand(func=True).diff(y) == 0
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assert expr.diff(z) - expr.expand(func=True).diff(z) == 0
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assert expr.diff(x) - 17*42*y == 0
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assert expr.diff(y) - 17*42*x == 0
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assert expr.diff(z) - 101 == 0
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def test_log10():
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x = Symbol('x')
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# Expand
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assert log10(x).expand(func=True) - log(x)/log(10) == 0
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# Diff
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assert log10(42*x).diff(x) - 1/(log(10)*x) == 0
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assert log10(42*x).diff(x) - log10(42*x).expand(func=True).diff(x) == 0
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def test_Cbrt():
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x = Symbol('x')
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# Expand
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assert Cbrt(x).expand(func=True) - x**Rational(1, 3) == 0
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# Diff
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assert Cbrt(42*x).diff(x) - 42*(42*x)**(Rational(1, 3) - 1)/3 == 0
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assert Cbrt(42*x).diff(x) - Cbrt(42*x).expand(func=True).diff(x) == 0
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def test_Sqrt():
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x = Symbol('x')
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# Expand
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assert Sqrt(x).expand(func=True) - x**S.Half == 0
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# Diff
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assert Sqrt(42*x).diff(x) - 42*(42*x)**(S.Half - 1)/2 == 0
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assert Sqrt(42*x).diff(x) - Sqrt(42*x).expand(func=True).diff(x) == 0
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def test_hypot():
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x, y = symbols('x y')
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# Expand
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assert hypot(x, y).expand(func=True) - (x**2 + y**2)**S.Half == 0
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# Diff
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assert hypot(17*x, 42*y).diff(x).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(x) == 0
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assert hypot(17*x, 42*y).diff(y).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(y) == 0
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assert hypot(17*x, 42*y).diff(x).expand(func=True) - 2*17*17*x*((17*x)**2 + (42*y)**2)**Rational(-1, 2)/2 == 0
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assert hypot(17*x, 42*y).diff(y).expand(func=True) - 2*42*42*y*((17*x)**2 + (42*y)**2)**Rational(-1, 2)/2 == 0
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