I am done

rl/Lib/site-packages/sympy/codegen/tests/test_abstract_nodes.py

@@ -0,0 +1,14 @@
+from sympy.core.symbol import symbols
+from sympy.codegen.abstract_nodes import List
+
+
+def test_List():
+    l = List(2, 3, 4)
+    assert l == List(2, 3, 4)
+    assert str(l) == "[2, 3, 4]"
+    x, y, z = symbols('x y z')
+    l = List(x**2,y**3,z**4)
+    # contrary to python's built-in list, we can call e.g. "replace" on List.
+    m = l.replace(lambda arg: arg.is_Pow and arg.exp>2, lambda p: p.base-p.exp)
+    assert m == [x**2, y-3, z-4]
+    hash(m)

rl/Lib/site-packages/sympy/codegen/tests/test_algorithms.py

@@ -0,0 +1,179 @@
+import tempfile
+from sympy import log, Min, Max, sqrt
+from sympy.core.numbers import Float
+from sympy.core.symbol import Symbol, symbols
+from sympy.functions.elementary.trigonometric import cos
+from sympy.codegen.ast import Assignment, Raise, RuntimeError_, QuotedString
+from sympy.codegen.algorithms import newtons_method, newtons_method_function
+from sympy.codegen.cfunctions import expm1
+from sympy.codegen.fnodes import bind_C
+from sympy.codegen.futils import render_as_module as f_module
+from sympy.codegen.pyutils import render_as_module as py_module
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.utilities._compilation import compile_link_import_strings, has_c, has_fortran
+from sympy.utilities._compilation.util import may_xfail
+from sympy.testing.pytest import skip, raises
+
+cython = import_module('cython')
+wurlitzer = import_module('wurlitzer')
+
+def test_newtons_method():
+    x, dx, atol = symbols('x dx atol')
+    expr = cos(x) - x**3
+    algo = newtons_method(expr, x, atol, dx)
+    assert algo.has(Assignment(dx, -expr/expr.diff(x)))
+
+
+@may_xfail
+def test_newtons_method_function__ccode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x)
+
+    if not cython:
+        skip("cython not installed.")
+    if not has_c():
+        skip("No C compiler found.")
+
+    compile_kw = {"std": 'c99'}
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton.c', ('#include <math.h>\n'
+                          '#include <stdio.h>\n') + ccode(func)),
+            ('_newton.pyx', ("#cython: language_level={}\n".format("3") +
+                             "cdef extern double newton(double)\n"
+                             "def py_newton(x):\n"
+                             "    return newton(x)\n"))
+        ], build_dir=folder, compile_kwargs=compile_kw)
+        assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
+
+
+@may_xfail
+def test_newtons_method_function__fcode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x, attrs=[bind_C(name='newton')])
+
+    if not cython:
+        skip("cython not installed.")
+    if not has_fortran():
+        skip("No Fortran compiler found.")
+
+    f_mod = f_module([func], 'mod_newton')
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton.f90', f_mod),
+            ('_newton.pyx', ("#cython: language_level={}\n".format("3") +
+                             "cdef extern double newton(double*)\n"
+                             "def py_newton(double x):\n"
+                             "    return newton(&x)\n"))
+        ], build_dir=folder)
+        assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
+
+
+def test_newtons_method_function__pycode():
+    x = Symbol('x', real=True)
+    expr = cos(x) - x**3
+    func = newtons_method_function(expr, x)
+    py_mod = py_module(func)
+    namespace = {}
+    exec(py_mod, namespace, namespace)
+    res = eval('newton(0.5)', namespace)
+    assert abs(res - 0.865474033102) < 1e-12
+
+
+@may_xfail
+def test_newtons_method_function__ccode_parameters():
+    args = x, A, k, p = symbols('x A k p')
+    expr = A*cos(k*x) - p*x**3
+    raises(ValueError, lambda: newtons_method_function(expr, x))
+    use_wurlitzer = wurlitzer
+
+    func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
+
+    if not has_c():
+        skip("No C compiler found.")
+    if not cython:
+        skip("cython not installed.")
+
+    compile_kw = {"std": 'c99'}
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('newton_par.c', ('#include <math.h>\n'
+                          '#include <stdio.h>\n') + ccode(func)),
+            ('_newton_par.pyx', ("#cython: language_level={}\n".format("3") +
+                                 "cdef extern double newton(double, double, double, double)\n"
+                             "def py_newton(x, A=1, k=1, p=1):\n"
+                             "    return newton(x, A, k, p)\n"))
+        ], compile_kwargs=compile_kw, build_dir=folder)
+
+        if use_wurlitzer:
+            with wurlitzer.pipes() as (out, err):
+                result = mod.py_newton(0.5)
+        else:
+            result = mod.py_newton(0.5)
+
+        assert abs(result - 0.865474033102) < 1e-12
+
+        if not use_wurlitzer:
+            skip("C-level output only tested when package 'wurlitzer' is available.")
+
+        out, err = out.read(), err.read()
+        assert err == ''
+        assert out == """\
+x=         0.5
+x=      1.1121 d_x=     0.61214
+x=     0.90967 d_x=    -0.20247
+x=     0.86726 d_x=   -0.042409
+x=     0.86548 d_x=  -0.0017867
+x=     0.86547 d_x= -3.1022e-06
+x=     0.86547 d_x= -9.3421e-12
+x=     0.86547 d_x=  3.6902e-17
+"""  # try to run tests with LC_ALL=C if this assertion fails
+
+
+def test_newtons_method_function__rtol_cse_nan():
+    a, b, c, N_geo, N_tot = symbols('a b c N_geo N_tot', real=True, nonnegative=True)
+    i = Symbol('i', integer=True, nonnegative=True)
+    N_ari = N_tot - N_geo - 1
+    delta_ari = (c-b)/N_ari
+    ln_delta_geo = log(b) + log(-expm1((log(a)-log(b))/N_geo))
+    eqb_log = ln_delta_geo - log(delta_ari)
+
+    def _clamp(low, expr, high):
+        return Min(Max(low, expr), high)
+
+    meth_kw = {
+        'clamped_newton': {'delta_fn': lambda e, x: _clamp(
+            (sqrt(a*x)-x)*0.99,
+            -e/e.diff(x),
+            (sqrt(c*x)-x)*0.99
+        )},
+        'halley': {'delta_fn': lambda e, x: (-2*(e*e.diff(x))/(2*e.diff(x)**2 - e*e.diff(x, 2)))},
+        'halley_alt': {'delta_fn': lambda e, x: (-e/e.diff(x)/(1-e/e.diff(x)*e.diff(x,2)/2/e.diff(x)))},
+    }
+    args = eqb_log, b
+    for use_cse in [False, True]:
+        kwargs = {
+            'params': (b, a, c, N_geo, N_tot), 'itermax': 60, 'debug': True, 'cse': use_cse,
+            'counter': i, 'atol': 1e-100, 'rtol': 2e-16, 'bounds': (a,c),
+            'handle_nan': Raise(RuntimeError_(QuotedString("encountered NaN.")))
+        }
+        func = {k: newtons_method_function(*args, func_name=f"{k}_b", **dict(kwargs, **kw)) for k, kw in meth_kw.items()}
+        py_mod = {k: py_module(v) for k, v in func.items()}
+        namespace = {}
+        root_find_b = {}
+        for k, v in py_mod.items():
+            ns = namespace[k] = {}
+            exec(v, ns, ns)
+            root_find_b[k] = ns[f'{k}_b']
+        ref = Float('13.2261515064168768938151923226496')
+        reftol = {'clamped_newton': 2e-16, 'halley': 2e-16, 'halley_alt': 3e-16}
+        guess = 4.0
+        for meth, func in root_find_b.items():
+            result = func(guess, 1e-2, 1e2, 50, 100)
+            req = ref*reftol[meth]
+            if use_cse:
+                req *= 2
+            assert abs(result - ref) < req

rl/Lib/site-packages/sympy/codegen/tests/test_applications.py

@@ -0,0 +1,57 @@
+# This file contains tests that exercise multiple AST nodes
+
+import tempfile
+
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.utilities._compilation import compile_link_import_strings, has_c
+from sympy.utilities._compilation.util import may_xfail
+from sympy.testing.pytest import skip
+from sympy.codegen.ast import (
+    FunctionDefinition, FunctionPrototype, Variable, Pointer, real, Assignment,
+    integer, CodeBlock, While
+)
+from sympy.codegen.cnodes import void, PreIncrement
+from sympy.codegen.cutils import render_as_source_file
+
+cython = import_module('cython')
+np = import_module('numpy')
+
+def _mk_func1():
+    declars = n, inp, out = Variable('n', integer), Pointer('inp', real), Pointer('out', real)
+    i = Variable('i', integer)
+    whl = While(i<n, [Assignment(out[i], inp[i]), PreIncrement(i)])
+    body = CodeBlock(i.as_Declaration(value=0), whl)
+    return FunctionDefinition(void, 'our_test_function', declars, body)
+
+
+def _render_compile_import(funcdef, build_dir):
+    code_str = render_as_source_file(funcdef, settings={"contract": False})
+    declar = ccode(FunctionPrototype.from_FunctionDefinition(funcdef))
+    return compile_link_import_strings([
+        ('our_test_func.c', code_str),
+        ('_our_test_func.pyx', ("#cython: language_level={}\n".format("3") +
+                                "cdef extern {declar}\n"
+                                "def _{fname}({typ}[:] inp, {typ}[:] out):\n"
+                                "    {fname}(inp.size, &inp[0], &out[0])").format(
+                                    declar=declar, fname=funcdef.name, typ='double'
+                                ))
+    ], build_dir=build_dir)
+
+
+@may_xfail
+def test_copying_function():
+    if not np:
+        skip("numpy not installed.")
+    if not has_c():
+        skip("No C compiler found.")
+    if not cython:
+        skip("Cython not found.")
+
+    info = None
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = _render_compile_import(_mk_func1(), build_dir=folder)
+        inp = np.arange(10.0)
+        out = np.empty_like(inp)
+        mod._our_test_function(inp, out)
+        assert np.allclose(inp, out)

rl/Lib/site-packages/sympy/codegen/tests/test_approximations.py

@@ -0,0 +1,53 @@
+import math
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.codegen.rewriting import optimize
+from sympy.codegen.approximations import SumApprox, SeriesApprox
+
+
+def test_SumApprox_trivial():
+    x = symbols('x')
+    expr1 = 1 + x
+    sum_approx = SumApprox(bounds={x: (-1e-20, 1e-20)}, reltol=1e-16)
+    apx1 = optimize(expr1, [sum_approx])
+    assert apx1 - 1 == 0
+
+
+def test_SumApprox_monotone_terms():
+    x, y, z = symbols('x y z')
+    expr1 = exp(z)*(x**2 + y**2 + 1)
+    bnds1 = {x: (0, 1e-3), y: (100, 1000)}
+    sum_approx_m2 = SumApprox(bounds=bnds1, reltol=1e-2)
+    sum_approx_m5 = SumApprox(bounds=bnds1, reltol=1e-5)
+    sum_approx_m11 = SumApprox(bounds=bnds1, reltol=1e-11)
+    assert (optimize(expr1, [sum_approx_m2])/exp(z) - (y**2)).simplify() == 0
+    assert (optimize(expr1, [sum_approx_m5])/exp(z) - (y**2 + 1)).simplify() == 0
+    assert (optimize(expr1, [sum_approx_m11])/exp(z) - (y**2 + 1 + x**2)).simplify() == 0
+
+
+def test_SeriesApprox_trivial():
+    x, z = symbols('x z')
+    for factor in [1, exp(z)]:
+        x = symbols('x')
+        expr1 = exp(x)*factor
+        bnds1 = {x: (-1, 1)}
+        series_approx_50 = SeriesApprox(bounds=bnds1, reltol=0.50)
+        series_approx_10 = SeriesApprox(bounds=bnds1, reltol=0.10)
+        series_approx_05 = SeriesApprox(bounds=bnds1, reltol=0.05)
+        c = (bnds1[x][1] + bnds1[x][0])/2  # 0.0
+        f0 = math.exp(c)  # 1.0
+
+        ref_50 = f0 + x + x**2/2
+        ref_10 = f0 + x + x**2/2 + x**3/6
+        ref_05 = f0 + x + x**2/2 + x**3/6 + x**4/24
+
+        res_50 = optimize(expr1, [series_approx_50])
+        res_10 = optimize(expr1, [series_approx_10])
+        res_05 = optimize(expr1, [series_approx_05])
+
+        assert (res_50/factor - ref_50).simplify() == 0
+        assert (res_10/factor - ref_10).simplify() == 0
+        assert (res_05/factor - ref_05).simplify() == 0
+
+        max_ord3 = SeriesApprox(bounds=bnds1, reltol=0.05, max_order=3)
+        assert optimize(expr1, [max_ord3]) == expr1

rl/Lib/site-packages/sympy/codegen/tests/test_ast.py

@@ -0,0 +1,661 @@
+import math
+from sympy.core.containers import Tuple
+from sympy.core.numbers import nan, oo, Float, Integer
+from sympy.core.relational import Lt
+from sympy.core.symbol import symbols, Symbol
+from sympy.functions.elementary.trigonometric import sin
+from sympy.matrices.dense import Matrix
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.sets.fancysets import Range
+from sympy.tensor.indexed import Idx, IndexedBase
+from sympy.testing.pytest import raises
+
+
+from sympy.codegen.ast import (
+    Assignment, Attribute, aug_assign, CodeBlock, For, Type, Variable, Pointer, Declaration,
+    AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment,
+    DivAugmentedAssignment, ModAugmentedAssignment, value_const, pointer_const,
+    integer, real, complex_, int8, uint8, float16 as f16, float32 as f32,
+    float64 as f64, float80 as f80, float128 as f128, complex64 as c64, complex128 as c128,
+    While, Scope, String, Print, QuotedString, FunctionPrototype, FunctionDefinition, Return,
+    FunctionCall, untyped, IntBaseType, intc, Node, none, NoneToken, Token, Comment
+)
+
+x, y, z, t, x0, x1, x2, a, b = symbols("x, y, z, t, x0, x1, x2, a, b")
+n = symbols("n", integer=True)
+A = MatrixSymbol('A', 3, 1)
+mat = Matrix([1, 2, 3])
+B = IndexedBase('B')
+i = Idx("i", n)
+A22 = MatrixSymbol('A22',2,2)
+B22 = MatrixSymbol('B22',2,2)
+
+
+def test_Assignment():
+    # Here we just do things to show they don't error
+    Assignment(x, y)
+    Assignment(x, 0)
+    Assignment(A, mat)
+    Assignment(A[1,0], 0)
+    Assignment(A[1,0], x)
+    Assignment(B[i], x)
+    Assignment(B[i], 0)
+    a = Assignment(x, y)
+    assert a.func(*a.args) == a
+    assert a.op == ':='
+    # Here we test things to show that they error
+    # Matrix to scalar
+    raises(ValueError, lambda: Assignment(B[i], A))
+    raises(ValueError, lambda: Assignment(B[i], mat))
+    raises(ValueError, lambda: Assignment(x, mat))
+    raises(ValueError, lambda: Assignment(x, A))
+    raises(ValueError, lambda: Assignment(A[1,0], mat))
+    # Scalar to matrix
+    raises(ValueError, lambda: Assignment(A, x))
+    raises(ValueError, lambda: Assignment(A, 0))
+    # Non-atomic lhs
+    raises(TypeError, lambda: Assignment(mat, A))
+    raises(TypeError, lambda: Assignment(0, x))
+    raises(TypeError, lambda: Assignment(x*x, 1))
+    raises(TypeError, lambda: Assignment(A + A, mat))
+    raises(TypeError, lambda: Assignment(B, 0))
+
+
+def test_AugAssign():
+    # Here we just do things to show they don't error
+    aug_assign(x, '+', y)
+    aug_assign(x, '+', 0)
+    aug_assign(A, '+', mat)
+    aug_assign(A[1, 0], '+', 0)
+    aug_assign(A[1, 0], '+', x)
+    aug_assign(B[i], '+', x)
+    aug_assign(B[i], '+', 0)
+
+    # Check creation via aug_assign vs constructor
+    for binop, cls in [
+            ('+', AddAugmentedAssignment),
+            ('-', SubAugmentedAssignment),
+            ('*', MulAugmentedAssignment),
+            ('/', DivAugmentedAssignment),
+            ('%', ModAugmentedAssignment),
+        ]:
+        a = aug_assign(x, binop, y)
+        b = cls(x, y)
+        assert a.func(*a.args) == a == b
+        assert a.binop == binop
+        assert a.op == binop + '='
+
+    # Here we test things to show that they error
+    # Matrix to scalar
+    raises(ValueError, lambda: aug_assign(B[i], '+', A))
+    raises(ValueError, lambda: aug_assign(B[i], '+', mat))
+    raises(ValueError, lambda: aug_assign(x, '+', mat))
+    raises(ValueError, lambda: aug_assign(x, '+', A))
+    raises(ValueError, lambda: aug_assign(A[1, 0], '+', mat))
+    # Scalar to matrix
+    raises(ValueError, lambda: aug_assign(A, '+', x))
+    raises(ValueError, lambda: aug_assign(A, '+', 0))
+    # Non-atomic lhs
+    raises(TypeError, lambda: aug_assign(mat, '+', A))
+    raises(TypeError, lambda: aug_assign(0, '+', x))
+    raises(TypeError, lambda: aug_assign(x * x, '+', 1))
+    raises(TypeError, lambda: aug_assign(A + A, '+', mat))
+    raises(TypeError, lambda: aug_assign(B, '+', 0))
+
+
+def test_Assignment_printing():
+    assignment_classes = [
+        Assignment,
+        AddAugmentedAssignment,
+        SubAugmentedAssignment,
+        MulAugmentedAssignment,
+        DivAugmentedAssignment,
+        ModAugmentedAssignment,
+    ]
+    pairs = [
+        (x, 2 * y + 2),
+        (B[i], x),
+        (A22, B22),
+        (A[0, 0], x),
+    ]
+
+    for cls in assignment_classes:
+        for lhs, rhs in pairs:
+            a = cls(lhs, rhs)
+            assert repr(a) == '%s(%s, %s)' % (cls.__name__, repr(lhs), repr(rhs))
+
+
+def test_CodeBlock():
+    c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1))
+    assert c.func(*c.args) == c
+
+    assert c.left_hand_sides == Tuple(x, y)
+    assert c.right_hand_sides == Tuple(1, x + 1)
+
+def test_CodeBlock_topological_sort():
+    assignments = [
+        Assignment(x, y + z),
+        Assignment(z, 1),
+        Assignment(t, x),
+        Assignment(y, 2),
+        ]
+
+    ordered_assignments = [
+        # Note that the unrelated z=1 and y=2 are kept in that order
+        Assignment(z, 1),
+        Assignment(y, 2),
+        Assignment(x, y + z),
+        Assignment(t, x),
+        ]
+    c1 = CodeBlock.topological_sort(assignments)
+    assert c1 == CodeBlock(*ordered_assignments)
+
+    # Cycle
+    invalid_assignments = [
+        Assignment(x, y + z),
+        Assignment(z, 1),
+        Assignment(y, x),
+        Assignment(y, 2),
+        ]
+
+    raises(ValueError, lambda: CodeBlock.topological_sort(invalid_assignments))
+
+    # Free symbols
+    free_assignments = [
+        Assignment(x, y + z),
+        Assignment(z, a * b),
+        Assignment(t, x),
+        Assignment(y, b + 3),
+        ]
+
+    free_assignments_ordered = [
+        Assignment(z, a * b),
+        Assignment(y, b + 3),
+        Assignment(x, y + z),
+        Assignment(t, x),
+        ]
+
+    c2 = CodeBlock.topological_sort(free_assignments)
+    assert c2 == CodeBlock(*free_assignments_ordered)
+
+def test_CodeBlock_free_symbols():
+    c1 = CodeBlock(
+        Assignment(x, y + z),
+        Assignment(z, 1),
+        Assignment(t, x),
+        Assignment(y, 2),
+        )
+    assert c1.free_symbols == set()
+
+    c2 = CodeBlock(
+        Assignment(x, y + z),
+        Assignment(z, a * b),
+        Assignment(t, x),
+        Assignment(y, b + 3),
+    )
+    assert c2.free_symbols == {a, b}
+
+def test_CodeBlock_cse():
+    c1 = CodeBlock(
+        Assignment(y, 1),
+        Assignment(x, sin(y)),
+        Assignment(z, sin(y)),
+        Assignment(t, x*z),
+        )
+    assert c1.cse() == CodeBlock(
+        Assignment(y, 1),
+        Assignment(x0, sin(y)),
+        Assignment(x, x0),
+        Assignment(z, x0),
+        Assignment(t, x*z),
+    )
+
+    # Multiple assignments to same symbol not supported
+    raises(NotImplementedError, lambda: CodeBlock(
+        Assignment(x, 1),
+        Assignment(y, 1), Assignment(y, 2)
+    ).cse())
+
+    # Check auto-generated symbols do not collide with existing ones
+    c2 = CodeBlock(
+        Assignment(x0, sin(y) + 1),
+        Assignment(x1, 2 * sin(y)),
+        Assignment(z, x * y),
+        )
+    assert c2.cse() == CodeBlock(
+        Assignment(x2, sin(y)),
+        Assignment(x0, x2 + 1),
+        Assignment(x1, 2 * x2),
+        Assignment(z, x * y),
+        )
+
+
+def test_CodeBlock_cse__issue_14118():
+    # see https://github.com/sympy/sympy/issues/14118
+    c = CodeBlock(
+        Assignment(A22, Matrix([[x, sin(y)],[3, 4]])),
+        Assignment(B22, Matrix([[sin(y), 2*sin(y)], [sin(y)**2, 7]]))
+    )
+    assert c.cse() == CodeBlock(
+        Assignment(x0, sin(y)),
+        Assignment(A22, Matrix([[x, x0],[3, 4]])),
+        Assignment(B22, Matrix([[x0, 2*x0], [x0**2, 7]]))
+    )
+
+def test_For():
+    f = For(n, Range(0, 3), (Assignment(A[n, 0], x + n), aug_assign(x, '+', y)))
+    f = For(n, (1, 2, 3, 4, 5), (Assignment(A[n, 0], x + n),))
+    assert f.func(*f.args) == f
+    raises(TypeError, lambda: For(n, x, (x + y,)))
+
+
+def test_none():
+    assert none.is_Atom
+    assert none == none
+    class Foo(Token):
+        pass
+    foo = Foo()
+    assert foo != none
+    assert none == None
+    assert none == NoneToken()
+    assert none.func(*none.args) == none
+
+
+def test_String():
+    st = String('foobar')
+    assert st.is_Atom
+    assert st == String('foobar')
+    assert st.text == 'foobar'
+    assert st.func(**st.kwargs()) == st
+    assert st.func(*st.args) == st
+
+
+    class Signifier(String):
+        pass
+
+    si = Signifier('foobar')
+    assert si != st
+    assert si.text == st.text
+    s = String('foo')
+    assert str(s) == 'foo'
+    assert repr(s) == "String('foo')"
+
+def test_Comment():
+    c = Comment('foobar')
+    assert c.text == 'foobar'
+    assert str(c) == 'foobar'
+
+def test_Node():
+    n = Node()
+    assert n == Node()
+    assert n.func(*n.args) == n
+
+
+def test_Type():
+    t = Type('MyType')
+    assert len(t.args) == 1
+    assert t.name == String('MyType')
+    assert str(t) == 'MyType'
+    assert repr(t) == "Type(String('MyType'))"
+    assert Type(t) == t
+    assert t.func(*t.args) == t
+    t1 = Type('t1')
+    t2 = Type('t2')
+    assert t1 != t2
+    assert t1 == t1 and t2 == t2
+    t1b = Type('t1')
+    assert t1 == t1b
+    assert t2 != t1b
+
+
+def test_Type__from_expr():
+    assert Type.from_expr(i) == integer
+    u = symbols('u', real=True)
+    assert Type.from_expr(u) == real
+    assert Type.from_expr(n) == integer
+    assert Type.from_expr(3) == integer
+    assert Type.from_expr(3.0) == real
+    assert Type.from_expr(3+1j) == complex_
+    raises(ValueError, lambda: Type.from_expr(sum))
+
+
+def test_Type__cast_check__integers():
+    # Rounding
+    raises(ValueError, lambda: integer.cast_check(3.5))
+    assert integer.cast_check('3') == 3
+    assert integer.cast_check(Float('3.0000000000000000000')) == 3
+    assert integer.cast_check(Float('3.0000000000000000001')) == 3  # unintuitive maybe?
+
+    # Range
+    assert int8.cast_check(127.0) == 127
+    raises(ValueError, lambda: int8.cast_check(128))
+    assert int8.cast_check(-128) == -128
+    raises(ValueError, lambda: int8.cast_check(-129))
+
+    assert uint8.cast_check(0) == 0
+    assert uint8.cast_check(128) == 128
+    raises(ValueError, lambda: uint8.cast_check(256.0))
+    raises(ValueError, lambda: uint8.cast_check(-1))
+
+def test_Attribute():
+    noexcept = Attribute('noexcept')
+    assert noexcept == Attribute('noexcept')
+    alignas16 = Attribute('alignas', [16])
+    alignas32 = Attribute('alignas', [32])
+    assert alignas16 != alignas32
+    assert alignas16.func(*alignas16.args) == alignas16
+
+
+def test_Variable():
+    v = Variable(x, type=real)
+    assert v == Variable(v)
+    assert v == Variable('x', type=real)
+    assert v.symbol == x
+    assert v.type == real
+    assert value_const not in v.attrs
+    assert v.func(*v.args) == v
+    assert str(v) == 'Variable(x, type=real)'
+
+    w = Variable(y, f32, attrs={value_const})
+    assert w.symbol == y
+    assert w.type == f32
+    assert value_const in w.attrs
+    assert w.func(*w.args) == w
+
+    v_n = Variable(n, type=Type.from_expr(n))
+    assert v_n.type == integer
+    assert v_n.func(*v_n.args) == v_n
+    v_i = Variable(i, type=Type.from_expr(n))
+    assert v_i.type == integer
+    assert v_i != v_n
+
+    a_i = Variable.deduced(i)
+    assert a_i.type == integer
+    assert Variable.deduced(Symbol('x', real=True)).type == real
+    assert a_i.func(*a_i.args) == a_i
+
+    v_n2 = Variable.deduced(n, value=3.5, cast_check=False)
+    assert v_n2.func(*v_n2.args) == v_n2
+    assert abs(v_n2.value - 3.5) < 1e-15
+    raises(ValueError, lambda: Variable.deduced(n, value=3.5, cast_check=True))
+
+    v_n3 = Variable.deduced(n)
+    assert v_n3.type == integer
+    assert str(v_n3) == 'Variable(n, type=integer)'
+    assert Variable.deduced(z, value=3).type == integer
+    assert Variable.deduced(z, value=3.0).type == real
+    assert Variable.deduced(z, value=3.0+1j).type == complex_
+
+
+def test_Pointer():
+    p = Pointer(x)
+    assert p.symbol == x
+    assert p.type == untyped
+    assert value_const not in p.attrs
+    assert pointer_const not in p.attrs
+    assert p.func(*p.args) == p
+
+    u = symbols('u', real=True)
+    pu = Pointer(u, type=Type.from_expr(u), attrs={value_const, pointer_const})
+    assert pu.symbol is u
+    assert pu.type == real
+    assert value_const in pu.attrs
+    assert pointer_const in pu.attrs
+    assert pu.func(*pu.args) == pu
+
+    i = symbols('i', integer=True)
+    deref = pu[i]
+    assert deref.indices == (i,)
+
+
+def test_Declaration():
+    u = symbols('u', real=True)
+    vu = Variable(u, type=Type.from_expr(u))
+    assert Declaration(vu).variable.type == real
+    vn = Variable(n, type=Type.from_expr(n))
+    assert Declaration(vn).variable.type == integer
+
+    # PR 19107, does not allow comparison between expressions and Basic
+    # lt = StrictLessThan(vu, vn)
+    # assert isinstance(lt, StrictLessThan)
+
+    vuc = Variable(u, Type.from_expr(u), value=3.0, attrs={value_const})
+    assert value_const in vuc.attrs
+    assert pointer_const not in vuc.attrs
+    decl = Declaration(vuc)
+    assert decl.variable == vuc
+    assert isinstance(decl.variable.value, Float)
+    assert decl.variable.value == 3.0
+    assert decl.func(*decl.args) == decl
+    assert vuc.as_Declaration() == decl
+    assert vuc.as_Declaration(value=None, attrs=None) == Declaration(vu)
+
+    vy = Variable(y, type=integer, value=3)
+    decl2 = Declaration(vy)
+    assert decl2.variable == vy
+    assert decl2.variable.value == Integer(3)
+
+    vi = Variable(i, type=Type.from_expr(i), value=3.0)
+    decl3 = Declaration(vi)
+    assert decl3.variable.type == integer
+    assert decl3.variable.value == 3.0
+
+    raises(ValueError, lambda: Declaration(vi, 42))
+
+
+def test_IntBaseType():
+    assert intc.name == String('intc')
+    assert intc.args == (intc.name,)
+    assert str(IntBaseType('a').name) == 'a'
+
+
+def test_FloatType():
+    assert f16.dig == 3
+    assert f32.dig == 6
+    assert f64.dig == 15
+    assert f80.dig == 18
+    assert f128.dig == 33
+
+    assert f16.decimal_dig == 5
+    assert f32.decimal_dig == 9
+    assert f64.decimal_dig == 17
+    assert f80.decimal_dig == 21
+    assert f128.decimal_dig == 36
+
+    assert f16.max_exponent == 16
+    assert f32.max_exponent == 128
+    assert f64.max_exponent == 1024
+    assert f80.max_exponent == 16384
+    assert f128.max_exponent == 16384
+
+    assert f16.min_exponent == -13
+    assert f32.min_exponent == -125
+    assert f64.min_exponent == -1021
+    assert f80.min_exponent == -16381
+    assert f128.min_exponent == -16381
+
+    assert abs(f16.eps / Float('0.00097656', precision=16) - 1) < 0.1*10**-f16.dig
+    assert abs(f32.eps / Float('1.1920929e-07', precision=32) - 1) < 0.1*10**-f32.dig
+    assert abs(f64.eps / Float('2.2204460492503131e-16', precision=64) - 1) < 0.1*10**-f64.dig
+    assert abs(f80.eps / Float('1.08420217248550443401e-19', precision=80) - 1) < 0.1*10**-f80.dig
+    assert abs(f128.eps / Float(' 1.92592994438723585305597794258492732e-34', precision=128) - 1) < 0.1*10**-f128.dig
+
+    assert abs(f16.max / Float('65504', precision=16) - 1) < .1*10**-f16.dig
+    assert abs(f32.max / Float('3.40282347e+38', precision=32) - 1) < 0.1*10**-f32.dig
+    assert abs(f64.max / Float('1.79769313486231571e+308', precision=64) - 1) < 0.1*10**-f64.dig  # cf. np.finfo(np.float64).max
+    assert abs(f80.max / Float('1.18973149535723176502e+4932', precision=80) - 1) < 0.1*10**-f80.dig
+    assert abs(f128.max / Float('1.18973149535723176508575932662800702e+4932', precision=128) - 1) < 0.1*10**-f128.dig
+
+    # cf. np.finfo(np.float32).tiny
+    assert abs(f16.tiny / Float('6.1035e-05', precision=16) - 1) < 0.1*10**-f16.dig
+    assert abs(f32.tiny / Float('1.17549435e-38', precision=32) - 1) < 0.1*10**-f32.dig
+    assert abs(f64.tiny / Float('2.22507385850720138e-308', precision=64) - 1) < 0.1*10**-f64.dig
+    assert abs(f80.tiny / Float('3.36210314311209350626e-4932', precision=80) - 1) < 0.1*10**-f80.dig
+    assert abs(f128.tiny / Float('3.3621031431120935062626778173217526e-4932', precision=128) - 1) < 0.1*10**-f128.dig
+
+    assert f64.cast_check(0.5) == Float(0.5, 17)
+    assert abs(f64.cast_check(3.7) - 3.7) < 3e-17
+    assert isinstance(f64.cast_check(3), (Float, float))
+
+    assert f64.cast_nocheck(oo) == float('inf')
+    assert f64.cast_nocheck(-oo) == float('-inf')
+    assert f64.cast_nocheck(float(oo)) == float('inf')
+    assert f64.cast_nocheck(float(-oo)) == float('-inf')
+    assert math.isnan(f64.cast_nocheck(nan))
+
+    assert f32 != f64
+    assert f64 == f64.func(*f64.args)
+
+
+def test_Type__cast_check__floating_point():
+    raises(ValueError, lambda: f32.cast_check(123.45678949))
+    raises(ValueError, lambda: f32.cast_check(12.345678949))
+    raises(ValueError, lambda: f32.cast_check(1.2345678949))
+    raises(ValueError, lambda: f32.cast_check(.12345678949))
+    assert abs(123.456789049 - f32.cast_check(123.456789049) - 4.9e-8) < 1e-8
+    assert abs(0.12345678904 - f32.cast_check(0.12345678904) - 4e-11) < 1e-11
+
+    dcm21 = Float('0.123456789012345670499')  # 21 decimals
+    assert abs(dcm21 - f64.cast_check(dcm21) - 4.99e-19) < 1e-19
+
+    f80.cast_check(Float('0.12345678901234567890103', precision=88))
+    raises(ValueError, lambda: f80.cast_check(Float('0.12345678901234567890149', precision=88)))
+
+    v10 = 12345.67894
+    raises(ValueError, lambda: f32.cast_check(v10))
+    assert abs(Float(str(v10), precision=64+8) - f64.cast_check(v10)) < v10*1e-16
+
+    assert abs(f32.cast_check(2147483647) - 2147483650) < 1
+
+
+def test_Type__cast_check__complex_floating_point():
+    val9_11 = 123.456789049 + 0.123456789049j
+    raises(ValueError, lambda: c64.cast_check(.12345678949 + .12345678949j))
+    assert abs(val9_11 - c64.cast_check(val9_11) - 4.9e-8) < 1e-8
+
+    dcm21 = Float('0.123456789012345670499') + 1e-20j  # 21 decimals
+    assert abs(dcm21 - c128.cast_check(dcm21) - 4.99e-19) < 1e-19
+    v19 = Float('0.1234567890123456749') + 1j*Float('0.1234567890123456749')
+    raises(ValueError, lambda: c128.cast_check(v19))
+
+
+def test_While():
+    xpp = AddAugmentedAssignment(x, 1)
+    whl1 = While(x < 2, [xpp])
+    assert whl1.condition.args[0] == x
+    assert whl1.condition.args[1] == 2
+    assert whl1.condition == Lt(x, 2, evaluate=False)
+    assert whl1.body.args == (xpp,)
+    assert whl1.func(*whl1.args) == whl1
+
+    cblk = CodeBlock(AddAugmentedAssignment(x, 1))
+    whl2 = While(x < 2, cblk)
+    assert whl1 == whl2
+    assert whl1 != While(x < 3, [xpp])
+
+
+def test_Scope():
+    assign = Assignment(x, y)
+    incr = AddAugmentedAssignment(x, 1)
+    scp = Scope([assign, incr])
+    cblk = CodeBlock(assign, incr)
+    assert scp.body == cblk
+    assert scp == Scope(cblk)
+    assert scp != Scope([incr, assign])
+    assert scp.func(*scp.args) == scp
+
+
+def test_Print():
+    fmt = "%d %.3f"
+    ps = Print([n, x], fmt)
+    assert str(ps.format_string) == fmt
+    assert ps.print_args == Tuple(n, x)
+    assert ps.args == (Tuple(n, x), QuotedString(fmt), none)
+    assert ps == Print((n, x), fmt)
+    assert ps != Print([x, n], fmt)
+    assert ps.func(*ps.args) == ps
+
+    ps2 = Print([n, x])
+    assert ps2 == Print([n, x])
+    assert ps2 != ps
+    assert ps2.format_string == None
+
+
+def test_FunctionPrototype_and_FunctionDefinition():
+    vx = Variable(x, type=real)
+    vn = Variable(n, type=integer)
+    fp1 = FunctionPrototype(real, 'power', [vx, vn])
+    assert fp1.return_type == real
+    assert fp1.name == String('power')
+    assert fp1.parameters == Tuple(vx, vn)
+    assert fp1 == FunctionPrototype(real, 'power', [vx, vn])
+    assert fp1 != FunctionPrototype(real, 'power', [vn, vx])
+    assert fp1.func(*fp1.args) == fp1
+
+
+    body = [Assignment(x, x**n), Return(x)]
+    fd1 = FunctionDefinition(real, 'power', [vx, vn], body)
+    assert fd1.return_type == real
+    assert str(fd1.name) == 'power'
+    assert fd1.parameters == Tuple(vx, vn)
+    assert fd1.body == CodeBlock(*body)
+    assert fd1 == FunctionDefinition(real, 'power', [vx, vn], body)
+    assert fd1 != FunctionDefinition(real, 'power', [vx, vn], body[::-1])
+    assert fd1.func(*fd1.args) == fd1
+
+    fp2 = FunctionPrototype.from_FunctionDefinition(fd1)
+    assert fp2 == fp1
+
+    fd2 = FunctionDefinition.from_FunctionPrototype(fp1, body)
+    assert fd2 == fd1
+
+
+def test_Return():
+    rs = Return(x)
+    assert rs.args == (x,)
+    assert rs == Return(x)
+    assert rs != Return(y)
+    assert rs.func(*rs.args) == rs
+
+
+def test_FunctionCall():
+    fc = FunctionCall('power', (x, 3))
+    assert fc.function_args[0] == x
+    assert fc.function_args[1] == 3
+    assert len(fc.function_args) == 2
+    assert isinstance(fc.function_args[1], Integer)
+    assert fc == FunctionCall('power', (x, 3))
+    assert fc != FunctionCall('power', (3, x))
+    assert fc != FunctionCall('Power', (x, 3))
+    assert fc.func(*fc.args) == fc
+
+    fc2 = FunctionCall('fma', [2, 3, 4])
+    assert len(fc2.function_args) == 3
+    assert fc2.function_args[0] == 2
+    assert fc2.function_args[1] == 3
+    assert fc2.function_args[2] == 4
+    assert str(fc2) in ( # not sure if QuotedString is a better default...
+        'FunctionCall(fma, function_args=(2, 3, 4))',
+        'FunctionCall("fma", function_args=(2, 3, 4))',
+    )
+
+def test_ast_replace():
+    x = Variable('x', real)
+    y = Variable('y', real)
+    n = Variable('n', integer)
+
+    pwer = FunctionDefinition(real, 'pwer', [x, n], [pow(x.symbol, n.symbol)])
+    pname = pwer.name
+    pcall = FunctionCall('pwer', [y, 3])
+
+    tree1 = CodeBlock(pwer, pcall)
+    assert str(tree1.args[0].name) == 'pwer'
+    assert str(tree1.args[1].name) == 'pwer'
+    for a, b in zip(tree1, [pwer, pcall]):
+        assert a == b
+
+    tree2 = tree1.replace(pname, String('power'))
+    assert str(tree1.args[0].name) == 'pwer'
+    assert str(tree1.args[1].name) == 'pwer'
+    assert str(tree2.args[0].name) == 'power'
+    assert str(tree2.args[1].name) == 'power'

rl/Lib/site-packages/sympy/codegen/tests/test_cfunctions.py

@@ -0,0 +1,165 @@
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.codegen.cfunctions import (
+    expm1, log1p, exp2, log2, fma, log10, Sqrt, Cbrt, hypot
+)
+from sympy.core.function import expand_log
+
+
+def test_expm1():
+    # Eval
+    assert expm1(0) == 0
+
+    x = Symbol('x', real=True)
+
+    # Expand and rewrite
+    assert expm1(x).expand(func=True) - exp(x) == -1
+    assert expm1(x).rewrite('tractable') - exp(x) == -1
+    assert expm1(x).rewrite('exp') - exp(x) == -1
+
+    # Precision
+    assert not ((exp(1e-10).evalf() - 1) - 1e-10 - 5e-21) < 1e-22  # for comparison
+    assert abs(expm1(1e-10).evalf() - 1e-10 - 5e-21) < 1e-22
+
+    # Properties
+    assert expm1(x).is_real
+    assert expm1(x).is_finite
+
+    # Diff
+    assert expm1(42*x).diff(x) - 42*exp(42*x) == 0
+    assert expm1(42*x).diff(x) - expm1(42*x).expand(func=True).diff(x) == 0
+
+
+def test_log1p():
+    # Eval
+    assert log1p(0) == 0
+    d = S(10)
+    assert expand_log(log1p(d**-1000) - log(d**1000 + 1) + log(d**1000)) == 0
+
+    x = Symbol('x', real=True)
+
+    # Expand and rewrite
+    assert log1p(x).expand(func=True) - log(x + 1) == 0
+    assert log1p(x).rewrite('tractable') - log(x + 1) == 0
+    assert log1p(x).rewrite('log') - log(x + 1) == 0
+
+    # Precision
+    assert not abs(log(1e-99 + 1).evalf() - 1e-99) < 1e-100  # for comparison
+    assert abs(expand_log(log1p(1e-99)).evalf() - 1e-99) < 1e-100
+
+    # Properties
+    assert log1p(-2**Rational(-1, 2)).is_real
+
+    assert not log1p(-1).is_finite
+    assert log1p(pi).is_finite
+
+    assert not log1p(x).is_positive
+    assert log1p(Symbol('y', positive=True)).is_positive
+
+    assert not log1p(x).is_zero
+    assert log1p(Symbol('z', zero=True)).is_zero
+
+    assert not log1p(x).is_nonnegative
+    assert log1p(Symbol('o', nonnegative=True)).is_nonnegative
+
+    # Diff
+    assert log1p(42*x).diff(x) - 42/(42*x + 1) == 0
+    assert log1p(42*x).diff(x) - log1p(42*x).expand(func=True).diff(x) == 0
+
+
+def test_exp2():
+    # Eval
+    assert exp2(2) == 4
+
+    x = Symbol('x', real=True)
+
+    # Expand
+    assert exp2(x).expand(func=True) - 2**x == 0
+
+    # Diff
+    assert exp2(42*x).diff(x) - 42*exp2(42*x)*log(2) == 0
+    assert exp2(42*x).diff(x) - exp2(42*x).diff(x) == 0
+
+
+def test_log2():
+    # Eval
+    assert log2(8) == 3
+    assert log2(pi) != log(pi)/log(2)  # log2 should *save* (CPU) instructions
+
+    x = Symbol('x', real=True)
+    assert log2(x) != log(x)/log(2)
+    assert log2(2**x) == x
+
+    # Expand
+    assert log2(x).expand(func=True) - log(x)/log(2) == 0
+
+    # Diff
+    assert log2(42*x).diff() - 1/(log(2)*x) == 0
+    assert log2(42*x).diff() - log2(42*x).expand(func=True).diff(x) == 0
+
+
+def test_fma():
+    x, y, z = symbols('x y z')
+
+    # Expand
+    assert fma(x, y, z).expand(func=True) - x*y - z == 0
+
+    expr = fma(17*x, 42*y, 101*z)
+
+    # Diff
+    assert expr.diff(x) - expr.expand(func=True).diff(x) == 0
+    assert expr.diff(y) - expr.expand(func=True).diff(y) == 0
+    assert expr.diff(z) - expr.expand(func=True).diff(z) == 0
+
+    assert expr.diff(x) - 17*42*y == 0
+    assert expr.diff(y) - 17*42*x == 0
+    assert expr.diff(z) - 101 == 0
+
+
+def test_log10():
+    x = Symbol('x')
+
+    # Expand
+    assert log10(x).expand(func=True) - log(x)/log(10) == 0
+
+    # Diff
+    assert log10(42*x).diff(x) - 1/(log(10)*x) == 0
+    assert log10(42*x).diff(x) - log10(42*x).expand(func=True).diff(x) == 0
+
+
+def test_Cbrt():
+    x = Symbol('x')
+
+    # Expand
+    assert Cbrt(x).expand(func=True) - x**Rational(1, 3) == 0
+
+    # Diff
+    assert Cbrt(42*x).diff(x) - 42*(42*x)**(Rational(1, 3) - 1)/3 == 0
+    assert Cbrt(42*x).diff(x) - Cbrt(42*x).expand(func=True).diff(x) == 0
+
+
+def test_Sqrt():
+    x = Symbol('x')
+
+    # Expand
+    assert Sqrt(x).expand(func=True) - x**S.Half == 0
+
+    # Diff
+    assert Sqrt(42*x).diff(x) - 42*(42*x)**(S.Half - 1)/2 == 0
+    assert Sqrt(42*x).diff(x) - Sqrt(42*x).expand(func=True).diff(x) == 0
+
+
+def test_hypot():
+    x, y = symbols('x y')
+
+    # Expand
+    assert hypot(x, y).expand(func=True) - (x**2 + y**2)**S.Half == 0
+
+    # Diff
+    assert hypot(17*x, 42*y).diff(x).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(x) == 0
+    assert hypot(17*x, 42*y).diff(y).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(y) == 0
+
+    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
+    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

rl/Lib/site-packages/sympy/codegen/tests/test_cnodes.py

@@ -0,0 +1,112 @@
+from sympy.core.symbol import symbols
+from sympy.printing.codeprinter import ccode
+from sympy.codegen.ast import Declaration, Variable, float64, int64, String, CodeBlock
+from sympy.codegen.cnodes import (
+    alignof, CommaOperator, goto, Label, PreDecrement, PostDecrement, PreIncrement, PostIncrement,
+    sizeof, union, struct
+)
+
+x, y = symbols('x y')
+
+
+def test_alignof():
+    ax = alignof(x)
+    assert ccode(ax) == 'alignof(x)'
+    assert ax.func(*ax.args) == ax
+
+
+def test_CommaOperator():
+    expr = CommaOperator(PreIncrement(x), 2*x)
+    assert ccode(expr) == '(++(x), 2*x)'
+    assert expr.func(*expr.args) == expr
+
+
+def test_goto_Label():
+    s = 'early_exit'
+    g = goto(s)
+    assert g.func(*g.args) == g
+    assert g != goto('foobar')
+    assert ccode(g) == 'goto early_exit'
+
+    l1 = Label(s)
+    assert ccode(l1) == 'early_exit:'
+    assert l1 == Label('early_exit')
+    assert l1 != Label('foobar')
+
+    body = [PreIncrement(x)]
+    l2 = Label(s, body)
+    assert l2.name == String("early_exit")
+    assert l2.body == CodeBlock(PreIncrement(x))
+    assert ccode(l2) == ("early_exit:\n"
+        "++(x);")
+
+    body = [PreIncrement(x), PreDecrement(y)]
+    l2 = Label(s, body)
+    assert l2.name == String("early_exit")
+    assert l2.body == CodeBlock(PreIncrement(x), PreDecrement(y))
+    assert ccode(l2) == ("early_exit:\n"
+        "{\n   ++(x);\n   --(y);\n}")
+
+
+def test_PreDecrement():
+    p = PreDecrement(x)
+    assert p.func(*p.args) == p
+    assert ccode(p) == '--(x)'
+
+
+def test_PostDecrement():
+    p = PostDecrement(x)
+    assert p.func(*p.args) == p
+    assert ccode(p) == '(x)--'
+
+
+def test_PreIncrement():
+    p = PreIncrement(x)
+    assert p.func(*p.args) == p
+    assert ccode(p) == '++(x)'
+
+
+def test_PostIncrement():
+    p = PostIncrement(x)
+    assert p.func(*p.args) == p
+    assert ccode(p) == '(x)++'
+
+
+def test_sizeof():
+    typename = 'unsigned int'
+    sz = sizeof(typename)
+    assert ccode(sz) == 'sizeof(%s)' % typename
+    assert sz.func(*sz.args) == sz
+    assert not sz.is_Atom
+    assert sz.atoms() == {String('unsigned int'), String('sizeof')}
+
+
+def test_struct():
+    vx, vy = Variable(x, type=float64), Variable(y, type=float64)
+    s = struct('vec2', [vx, vy])
+    assert s.func(*s.args) == s
+    assert s == struct('vec2', (vx, vy))
+    assert s != struct('vec2', (vy, vx))
+    assert str(s.name) == 'vec2'
+    assert len(s.declarations) == 2
+    assert all(isinstance(arg, Declaration) for arg in s.declarations)
+    assert ccode(s) == (
+        "struct vec2 {\n"
+        "   double x;\n"
+        "   double y;\n"
+        "}")
+
+
+def test_union():
+    vx, vy = Variable(x, type=float64), Variable(y, type=int64)
+    u = union('dualuse', [vx, vy])
+    assert u.func(*u.args) == u
+    assert u == union('dualuse', (vx, vy))
+    assert str(u.name) == 'dualuse'
+    assert len(u.declarations) == 2
+    assert all(isinstance(arg, Declaration) for arg in u.declarations)
+    assert ccode(u) == (
+        "union dualuse {\n"
+        "   double x;\n"
+        "   int64_t y;\n"
+        "}")

rl/Lib/site-packages/sympy/codegen/tests/test_cxxnodes.py

@@ -0,0 +1,14 @@
+from sympy.core.symbol import Symbol
+from sympy.codegen.ast import Type
+from sympy.codegen.cxxnodes import using
+from sympy.printing.codeprinter import cxxcode
+
+x = Symbol('x')
+
+def test_using():
+    v = Type('std::vector')
+    u1 = using(v)
+    assert cxxcode(u1) == 'using std::vector'
+
+    u2 = using(v, 'vec')
+    assert cxxcode(u2) == 'using vec = std::vector'

rl/Lib/site-packages/sympy/codegen/tests/test_fnodes.py

@@ -0,0 +1,213 @@
+import os
+import tempfile
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.codegen.ast import (
+    Assignment, Print, Declaration, FunctionDefinition, Return, real,
+    FunctionCall, Variable, Element, integer
+)
+from sympy.codegen.fnodes import (
+    allocatable, ArrayConstructor, isign, dsign, cmplx, kind, literal_dp,
+    Program, Module, use, Subroutine, dimension, assumed_extent, ImpliedDoLoop,
+    intent_out, size, Do, SubroutineCall, sum_, array, bind_C
+)
+from sympy.codegen.futils import render_as_module
+from sympy.core.expr import unchanged
+from sympy.external import import_module
+from sympy.printing.codeprinter import fcode
+from sympy.utilities._compilation import has_fortran, compile_run_strings, compile_link_import_strings
+from sympy.utilities._compilation.util import may_xfail
+from sympy.testing.pytest import skip, XFAIL
+
+cython = import_module('cython')
+np = import_module('numpy')
+
+
+def test_size():
+    x = Symbol('x', real=True)
+    sx = size(x)
+    assert fcode(sx, source_format='free') == 'size(x)'
+
+
+@may_xfail
+def test_size_assumed_shape():
+    if not has_fortran():
+        skip("No fortran compiler found.")
+    a = Symbol('a', real=True)
+    body = [Return((sum_(a**2)/size(a))**.5)]
+    arr = array(a, dim=[':'], intent='in')
+    fd = FunctionDefinition(real, 'rms', [arr], body)
+    render_as_module([fd], 'mod_rms')
+
+    (stdout, stderr), info = compile_run_strings([
+        ('rms.f90', render_as_module([fd], 'mod_rms')),
+        ('main.f90', (
+            'program myprog\n'
+            'use mod_rms, only: rms\n'
+            'real*8, dimension(4), parameter :: x = [4, 2, 2, 2]\n'
+            'print *, dsqrt(7d0) - rms(x)\n'
+            'end program\n'
+        ))
+    ], clean=True)
+    assert '0.00000' in stdout
+    assert stderr == ''
+    assert info['exit_status'] == os.EX_OK
+
+
+@XFAIL  # https://github.com/sympy/sympy/issues/20265
+@may_xfail
+def test_ImpliedDoLoop():
+    if not has_fortran():
+        skip("No fortran compiler found.")
+
+    a, i = symbols('a i', integer=True)
+    idl = ImpliedDoLoop(i**3, i, -3, 3, 2)
+    ac = ArrayConstructor([-28, idl, 28])
+    a = array(a, dim=[':'], attrs=[allocatable])
+    prog = Program('idlprog', [
+        a.as_Declaration(),
+        Assignment(a, ac),
+        Print([a])
+    ])
+    fsrc = fcode(prog, standard=2003, source_format='free')
+    (stdout, stderr), info = compile_run_strings([('main.f90', fsrc)], clean=True)
+    for numstr in '-28 -27 -1 1 27 28'.split():
+        assert numstr in stdout
+    assert stderr == ''
+    assert info['exit_status'] == os.EX_OK
+
+
+@may_xfail
+def test_Program():
+    x = Symbol('x', real=True)
+    vx = Variable.deduced(x, 42)
+    decl = Declaration(vx)
+    prnt = Print([x, x+1])
+    prog = Program('foo', [decl, prnt])
+    if not has_fortran():
+        skip("No fortran compiler found.")
+
+    (stdout, stderr), info = compile_run_strings([('main.f90', fcode(prog, standard=90))], clean=True)
+    assert '42' in stdout
+    assert '43' in stdout
+    assert stderr == ''
+    assert info['exit_status'] == os.EX_OK
+
+
+@may_xfail
+def test_Module():
+    x = Symbol('x', real=True)
+    v_x = Variable.deduced(x)
+    sq = FunctionDefinition(real, 'sqr', [v_x], [Return(x**2)])
+    mod_sq = Module('mod_sq', [], [sq])
+    sq_call = FunctionCall('sqr', [42.])
+    prg_sq = Program('foobar', [
+        use('mod_sq', only=['sqr']),
+        Print(['"Square of 42 = "', sq_call])
+    ])
+    if not has_fortran():
+        skip("No fortran compiler found.")
+    (stdout, stderr), info = compile_run_strings([
+        ('mod_sq.f90', fcode(mod_sq, standard=90)),
+        ('main.f90', fcode(prg_sq, standard=90))
+    ], clean=True)
+    assert '42' in stdout
+    assert str(42**2) in stdout
+    assert stderr == ''
+
+
+@XFAIL  # https://github.com/sympy/sympy/issues/20265
+@may_xfail
+def test_Subroutine():
+    # Code to generate the subroutine in the example from
+    # http://www.fortran90.org/src/best-practices.html#arrays
+    r = Symbol('r', real=True)
+    i = Symbol('i', integer=True)
+    v_r = Variable.deduced(r, attrs=(dimension(assumed_extent), intent_out))
+    v_i = Variable.deduced(i)
+    v_n = Variable('n', integer)
+    do_loop = Do([
+        Assignment(Element(r, [i]), literal_dp(1)/i**2)
+    ], i, 1, v_n)
+    sub = Subroutine("f", [v_r], [
+        Declaration(v_n),
+        Declaration(v_i),
+        Assignment(v_n, size(r)),
+        do_loop
+    ])
+    x = Symbol('x', real=True)
+    v_x3 = Variable.deduced(x, attrs=[dimension(3)])
+    mod = Module('mymod', definitions=[sub])
+    prog = Program('foo', [
+        use(mod, only=[sub]),
+        Declaration(v_x3),
+        SubroutineCall(sub, [v_x3]),
+        Print([sum_(v_x3), v_x3])
+    ])
+
+    if not has_fortran():
+        skip("No fortran compiler found.")
+
+    (stdout, stderr), info = compile_run_strings([
+        ('a.f90', fcode(mod, standard=90)),
+        ('b.f90', fcode(prog, standard=90))
+    ], clean=True)
+    ref = [1.0/i**2 for i in range(1, 4)]
+    assert str(sum(ref))[:-3] in stdout
+    for _ in ref:
+        assert str(_)[:-3] in stdout
+    assert stderr == ''
+
+
+def test_isign():
+    x = Symbol('x', integer=True)
+    assert unchanged(isign, 1, x)
+    assert fcode(isign(1, x), standard=95, source_format='free') == 'isign(1, x)'
+
+
+def test_dsign():
+    x = Symbol('x')
+    assert unchanged(dsign, 1, x)
+    assert fcode(dsign(literal_dp(1), x), standard=95, source_format='free') == 'dsign(1d0, x)'
+
+
+def test_cmplx():
+    x = Symbol('x')
+    assert unchanged(cmplx, 1, x)
+
+
+def test_kind():
+    x = Symbol('x')
+    assert unchanged(kind, x)
+
+
+def test_literal_dp():
+    assert fcode(literal_dp(0), source_format='free') == '0d0'
+
+
+@may_xfail
+def test_bind_C():
+    if not has_fortran():
+        skip("No fortran compiler found.")
+    if not cython:
+        skip("Cython not found.")
+    if not np:
+        skip("NumPy not found.")
+
+    a = Symbol('a', real=True)
+    s = Symbol('s', integer=True)
+    body = [Return((sum_(a**2)/s)**.5)]
+    arr = array(a, dim=[s], intent='in')
+    fd = FunctionDefinition(real, 'rms', [arr, s], body, attrs=[bind_C('rms')])
+    f_mod = render_as_module([fd], 'mod_rms')
+
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings([
+            ('rms.f90', f_mod),
+            ('_rms.pyx', (
+                "#cython: language_level={}\n".format("3") +
+                "cdef extern double rms(double*, int*)\n"
+                "def py_rms(double[::1] x):\n"
+                "    cdef int s = x.size\n"
+                "    return rms(&x[0], &s)\n"))
+        ], build_dir=folder)
+        assert abs(mod.py_rms(np.array([2., 4., 2., 2.])) - 7**0.5) < 1e-14

rl/Lib/site-packages/sympy/codegen/tests/test_matrix_nodes.py

@@ -0,0 +1,50 @@
+from sympy.core.symbol import symbols
+from sympy.core.function import Function
+from sympy.matrices.dense import Matrix
+from sympy.matrices.dense import zeros
+from sympy.simplify.simplify import simplify
+from sympy.codegen.matrix_nodes import MatrixSolve
+from sympy.utilities.lambdify import lambdify
+from sympy.printing.numpy import NumPyPrinter
+from sympy.testing.pytest import skip
+from sympy.external import import_module
+
+
+def test_matrix_solve_issue_24862():
+    A = Matrix(3, 3, symbols('a:9'))
+    b = Matrix(3, 1, symbols('b:3'))
+    hash(MatrixSolve(A, b))
+
+
+def test_matrix_solve_derivative_exact():
+    q = symbols('q')
+    a11, a12, a21, a22, b1, b2 = (
+        f(q) for f in symbols('a11 a12 a21 a22 b1 b2', cls=Function))
+    A = Matrix([[a11, a12], [a21, a22]])
+    b = Matrix([b1, b2])
+    x_lu = A.LUsolve(b)
+    dxdq_lu = A.LUsolve(b.diff(q) - A.diff(q) * A.LUsolve(b))
+    assert simplify(x_lu.diff(q) - dxdq_lu) == zeros(2, 1)
+    # dxdq_ms is the MatrixSolve equivalent of dxdq_lu
+    dxdq_ms = MatrixSolve(A, b.diff(q) - A.diff(q) * MatrixSolve(A, b))
+    assert MatrixSolve(A, b).diff(q) == dxdq_ms
+
+
+def test_matrix_solve_derivative_numpy():
+    np = import_module('numpy')
+    if not np:
+        skip("numpy not installed.")
+    q = symbols('q')
+    a11, a12, a21, a22, b1, b2 = (
+        f(q) for f in symbols('a11 a12 a21 a22 b1 b2', cls=Function))
+    A = Matrix([[a11, a12], [a21, a22]])
+    b = Matrix([b1, b2])
+    dx_lu = A.LUsolve(b).diff(q)
+    subs = {a11.diff(q): 0.2, a12.diff(q): 0.3, a21.diff(q): 0.1,
+            a22.diff(q): 0.5, b1.diff(q): 0.4, b2.diff(q): 0.9,
+            a11: 1.3, a12: 0.5, a21: 1.2, a22: 4, b1: 6.2, b2: 3.5}
+    p, p_vals = zip(*subs.items())
+    dx_sm = MatrixSolve(A, b).diff(q)
+    np.testing.assert_allclose(
+        lambdify(p, dx_sm, printer=NumPyPrinter)(*p_vals),
+        lambdify(p, dx_lu, printer=NumPyPrinter)(*p_vals))

rl/Lib/site-packages/sympy/codegen/tests/test_numpy_nodes.py

@@ -0,0 +1,50 @@
+from itertools import product
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.printing.repr import srepr
+from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
+
+x, y, z = symbols('x y z')
+
+def test_logaddexp():
+    lae_xy = logaddexp(x, y)
+    ref_xy = log(exp(x) + exp(y))
+    for wrt, deriv_order in product([x, y, z], range(3)):
+        assert (
+            lae_xy.diff(wrt, deriv_order) -
+            ref_xy.diff(wrt, deriv_order)
+        ).rewrite(log).simplify() == 0
+
+    one_third_e = 1*exp(1)/3
+    two_thirds_e = 2*exp(1)/3
+    logThirdE = log(one_third_e)
+    logTwoThirdsE = log(two_thirds_e)
+    lae_sum_to_e = logaddexp(logThirdE, logTwoThirdsE)
+    assert lae_sum_to_e.rewrite(log) == 1
+    assert lae_sum_to_e.simplify() == 1
+    was = logaddexp(2, 3)
+    assert srepr(was) == srepr(was.simplify())  # cannot simplify with 2, 3
+
+
+def test_logaddexp2():
+    lae2_xy = logaddexp2(x, y)
+    ref2_xy = log(2**x + 2**y)/log(2)
+    for wrt, deriv_order in product([x, y, z], range(3)):
+        assert (
+            lae2_xy.diff(wrt, deriv_order) -
+            ref2_xy.diff(wrt, deriv_order)
+        ).rewrite(log).cancel() == 0
+
+    def lb(x):
+        return log(x)/log(2)
+
+    two_thirds = S.One*2/3
+    four_thirds = 2*two_thirds
+    lbTwoThirds = lb(two_thirds)
+    lbFourThirds = lb(four_thirds)
+    lae2_sum_to_2 = logaddexp2(lbTwoThirds, lbFourThirds)
+    assert lae2_sum_to_2.rewrite(log) == 1
+    assert lae2_sum_to_2.simplify() == 1
+    was = logaddexp2(x, y)
+    assert srepr(was) == srepr(was.simplify())  # cannot simplify with x, y

rl/Lib/site-packages/sympy/codegen/tests/test_pynodes.py

@@ -0,0 +1,13 @@
+from sympy.core.symbol import symbols
+from sympy.codegen.pynodes import List
+
+
+def test_List():
+    l = List(2, 3, 4)
+    assert l == List(2, 3, 4)
+    assert str(l) == "[2, 3, 4]"
+    x, y, z = symbols('x y z')
+    l = List(x**2,y**3,z**4)
+    # contrary to python's built-in list, we can call e.g. "replace" on List.
+    m = l.replace(lambda arg: arg.is_Pow and arg.exp>2, lambda p: p.base-p.exp)
+    assert m == [x**2, y-3, z-4]

rl/Lib/site-packages/sympy/codegen/tests/test_pyutils.py

@@ -0,0 +1,7 @@
+from sympy.codegen.ast import Print
+from sympy.codegen.pyutils import render_as_module
+
+def test_standard():
+    ast = Print('x y'.split(), r"coordinate: %12.5g %12.5g\n")
+    assert render_as_module(ast, standard='python3') == \
+        '\n\nprint("coordinate: %12.5g %12.5g\\n" % (x, y), end="")'

rl/Lib/site-packages/sympy/codegen/tests/test_rewriting.py

@@ -0,0 +1,479 @@
+import tempfile
+from sympy.core.numbers import pi, Rational
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.trigonometric import (cos, sin, sinc)
+from sympy.matrices.expressions.matexpr import MatrixSymbol
+from sympy.assumptions import assuming, Q
+from sympy.external import import_module
+from sympy.printing.codeprinter import ccode
+from sympy.codegen.matrix_nodes import MatrixSolve
+from sympy.codegen.cfunctions import log2, exp2, expm1, log1p
+from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
+from sympy.codegen.scipy_nodes import cosm1, powm1
+from sympy.codegen.rewriting import (
+    optimize, cosm1_opt, log2_opt, exp2_opt, expm1_opt, log1p_opt, powm1_opt, optims_c99,
+    create_expand_pow_optimization, matinv_opt, logaddexp_opt, logaddexp2_opt,
+    optims_numpy, optims_scipy, sinc_opts, FuncMinusOneOptim
+)
+from sympy.testing.pytest import XFAIL, skip
+from sympy.utilities import lambdify
+from sympy.utilities._compilation import compile_link_import_strings, has_c
+from sympy.utilities._compilation.util import may_xfail
+
+cython = import_module('cython')
+numpy = import_module('numpy')
+scipy = import_module('scipy')
+
+
+def test_log2_opt():
+    x = Symbol('x')
+    expr1 = 7*log(3*x + 5)/(log(2))
+    opt1 = optimize(expr1, [log2_opt])
+    assert opt1 == 7*log2(3*x + 5)
+    assert opt1.rewrite(log) == expr1
+
+    expr2 = 3*log(5*x + 7)/(13*log(2))
+    opt2 = optimize(expr2, [log2_opt])
+    assert opt2 == 3*log2(5*x + 7)/13
+    assert opt2.rewrite(log) == expr2
+
+    expr3 = log(x)/log(2)
+    opt3 = optimize(expr3, [log2_opt])
+    assert opt3 == log2(x)
+    assert opt3.rewrite(log) == expr3
+
+    expr4 = log(x)/log(2) + log(x+1)
+    opt4 = optimize(expr4, [log2_opt])
+    assert opt4 == log2(x) + log(2)*log2(x+1)
+    assert opt4.rewrite(log) == expr4
+
+    expr5 = log(17)
+    opt5 = optimize(expr5, [log2_opt])
+    assert opt5 == expr5
+
+    expr6 = log(x + 3)/log(2)
+    opt6 = optimize(expr6, [log2_opt])
+    assert str(opt6) == 'log2(x + 3)'
+    assert opt6.rewrite(log) == expr6
+
+
+def test_exp2_opt():
+    x = Symbol('x')
+    expr1 = 1 + 2**x
+    opt1 = optimize(expr1, [exp2_opt])
+    assert opt1 == 1 + exp2(x)
+    assert opt1.rewrite(Pow) == expr1
+
+    expr2 = 1 + 3**x
+    assert expr2 == optimize(expr2, [exp2_opt])
+
+
+def test_expm1_opt():
+    x = Symbol('x')
+
+    expr1 = exp(x) - 1
+    opt1 = optimize(expr1, [expm1_opt])
+    assert expm1(x) - opt1 == 0
+    assert opt1.rewrite(exp) == expr1
+
+    expr2 = 3*exp(x) - 3
+    opt2 = optimize(expr2, [expm1_opt])
+    assert 3*expm1(x) == opt2
+    assert opt2.rewrite(exp) == expr2
+
+    expr3 = 3*exp(x) - 5
+    opt3 = optimize(expr3, [expm1_opt])
+    assert 3*expm1(x) - 2 == opt3
+    assert opt3.rewrite(exp) == expr3
+    expm1_opt_non_opportunistic = FuncMinusOneOptim(exp, expm1, opportunistic=False)
+    assert expr3 == optimize(expr3, [expm1_opt_non_opportunistic])
+    assert opt1 == optimize(expr1, [expm1_opt_non_opportunistic])
+    assert opt2 == optimize(expr2, [expm1_opt_non_opportunistic])
+
+    expr4 = 3*exp(x) + log(x) - 3
+    opt4 = optimize(expr4, [expm1_opt])
+    assert 3*expm1(x) + log(x) == opt4
+    assert opt4.rewrite(exp) == expr4
+
+    expr5 = 3*exp(2*x) - 3
+    opt5 = optimize(expr5, [expm1_opt])
+    assert 3*expm1(2*x) == opt5
+    assert opt5.rewrite(exp) == expr5
+
+    expr6 = (2*exp(x) + 1)/(exp(x) + 1) + 1
+    opt6 = optimize(expr6, [expm1_opt])
+    assert opt6.count_ops() <= expr6.count_ops()
+
+    def ev(e):
+        return e.subs(x, 3).evalf()
+    assert abs(ev(expr6) - ev(opt6)) < 1e-15
+
+    y = Symbol('y')
+    expr7 = (2*exp(x) - 1)/(1 - exp(y)) - 1/(1-exp(y))
+    opt7 = optimize(expr7, [expm1_opt])
+    assert -2*expm1(x)/expm1(y) == opt7
+    assert (opt7.rewrite(exp) - expr7).factor() == 0
+
+    expr8 = (1+exp(x))**2 - 4
+    opt8 = optimize(expr8, [expm1_opt])
+    tgt8a = (exp(x) + 3)*expm1(x)
+    tgt8b = 2*expm1(x) + expm1(2*x)
+    # Both tgt8a & tgt8b seem to give full precision (~16 digits for double)
+    # for x=1e-7 (compare with expr8 which only achieves ~8 significant digits).
+    # If we can show that either tgt8a or tgt8b is preferable, we can
+    # change this test to ensure the preferable version is returned.
+    assert (tgt8a - tgt8b).rewrite(exp).factor() == 0
+    assert opt8 in (tgt8a, tgt8b)
+    assert (opt8.rewrite(exp) - expr8).factor() == 0
+
+    expr9 = sin(expr8)
+    opt9 = optimize(expr9, [expm1_opt])
+    tgt9a = sin(tgt8a)
+    tgt9b = sin(tgt8b)
+    assert opt9 in (tgt9a, tgt9b)
+    assert (opt9.rewrite(exp) - expr9.rewrite(exp)).factor().is_zero
+
+
+def test_expm1_two_exp_terms():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = exp(x) + exp(y) - 2
+    opt1 = optimize(expr1, [expm1_opt])
+    assert opt1 == expm1(x) + expm1(y)
+
+
+def test_cosm1_opt():
+    x = Symbol('x')
+
+    expr1 = cos(x) - 1
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert cosm1(x) - opt1 == 0
+    assert opt1.rewrite(cos) == expr1
+
+    expr2 = 3*cos(x) - 3
+    opt2 = optimize(expr2, [cosm1_opt])
+    assert 3*cosm1(x) == opt2
+    assert opt2.rewrite(cos) == expr2
+
+    expr3 = 3*cos(x) - 5
+    opt3 = optimize(expr3, [cosm1_opt])
+    assert 3*cosm1(x) - 2 == opt3
+    assert opt3.rewrite(cos) == expr3
+    cosm1_opt_non_opportunistic = FuncMinusOneOptim(cos, cosm1, opportunistic=False)
+    assert expr3 == optimize(expr3, [cosm1_opt_non_opportunistic])
+    assert opt1 == optimize(expr1, [cosm1_opt_non_opportunistic])
+    assert opt2 == optimize(expr2, [cosm1_opt_non_opportunistic])
+
+    expr4 = 3*cos(x) + log(x) - 3
+    opt4 = optimize(expr4, [cosm1_opt])
+    assert 3*cosm1(x) + log(x) == opt4
+    assert opt4.rewrite(cos) == expr4
+
+    expr5 = 3*cos(2*x) - 3
+    opt5 = optimize(expr5, [cosm1_opt])
+    assert 3*cosm1(2*x) == opt5
+    assert opt5.rewrite(cos) == expr5
+
+    expr6 = 2 - 2*cos(x)
+    opt6 = optimize(expr6, [cosm1_opt])
+    assert -2*cosm1(x) == opt6
+    assert opt6.rewrite(cos) == expr6
+
+
+def test_cosm1_two_cos_terms():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = cos(x) + cos(y) - 2
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert opt1 == cosm1(x) + cosm1(y)
+
+
+def test_expm1_cosm1_mixed():
+    x = Symbol('x')
+    expr1 = exp(x) + cos(x) - 2
+    opt1 = optimize(expr1, [expm1_opt, cosm1_opt])
+    assert opt1 == cosm1(x) + expm1(x)
+
+
+def _check_num_lambdify(expr, opt, val_subs, approx_ref, lambdify_kw=None, poorness=1e10):
+    """ poorness=1e10 signifies that `expr` loses precision of at least ten decimal digits. """
+    num_ref = expr.subs(val_subs).evalf()
+    eps = numpy.finfo(numpy.float64).eps
+    assert abs(num_ref - approx_ref) < approx_ref*eps
+    f1 = lambdify(list(val_subs.keys()), opt, **(lambdify_kw or {}))
+    args_float = tuple(map(float, val_subs.values()))
+    num_err1 = abs(f1(*args_float) - approx_ref)
+    assert num_err1 < abs(num_ref*eps)
+    f2 = lambdify(list(val_subs.keys()), expr, **(lambdify_kw or {}))
+    num_err2 = abs(f2(*args_float) - approx_ref)
+    assert num_err2 > abs(num_ref*eps*poorness)   # this only ensures that the *test* works as intended
+
+
+def test_cosm1_apart():
+    x = Symbol('x')
+
+    expr1 = 1/cos(x) - 1
+    opt1 = optimize(expr1, [cosm1_opt])
+    assert opt1 == -cosm1(x)/cos(x)
+    if scipy:
+        _check_num_lambdify(expr1, opt1, {x: S(10)**-30}, 5e-61, lambdify_kw={"modules": 'scipy'})
+
+    expr2 = 2/cos(x) - 2
+    opt2 = optimize(expr2, optims_scipy)
+    assert opt2 == -2*cosm1(x)/cos(x)
+    if scipy:
+        _check_num_lambdify(expr2, opt2, {x: S(10)**-30}, 1e-60, lambdify_kw={"modules": 'scipy'})
+
+    expr3 = pi/cos(3*x) - pi
+    opt3 = optimize(expr3, [cosm1_opt])
+    assert opt3 == -pi*cosm1(3*x)/cos(3*x)
+    if scipy:
+        _check_num_lambdify(expr3, opt3, {x: S(10)**-30/3}, float(5e-61*pi), lambdify_kw={"modules": 'scipy'})
+
+
+def test_powm1():
+    args = x, y = map(Symbol, "xy")
+
+    expr1 = x**y - 1
+    opt1 = optimize(expr1, [powm1_opt])
+    assert opt1 == powm1(x, y)
+    for arg in args:
+        assert expr1.diff(arg) == opt1.diff(arg)
+    if scipy and tuple(map(int, scipy.version.version.split('.')[:3])) >= (1, 10, 0):
+        subs1_a = {x: Rational(*(1.0+1e-13).as_integer_ratio()), y: pi}
+        ref1_f64_a = 3.139081648208105e-13
+        _check_num_lambdify(expr1, opt1, subs1_a, ref1_f64_a, lambdify_kw={"modules": 'scipy'}, poorness=10**11)
+
+        subs1_b = {x: pi, y: Rational(*(1e-10).as_integer_ratio())}
+        ref1_f64_b = 1.1447298859149205e-10
+        _check_num_lambdify(expr1, opt1, subs1_b, ref1_f64_b, lambdify_kw={"modules": 'scipy'}, poorness=10**9)
+
+
+def test_log1p_opt():
+    x = Symbol('x')
+    expr1 = log(x + 1)
+    opt1 = optimize(expr1, [log1p_opt])
+    assert log1p(x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+    expr2 = log(3*x + 3)
+    opt2 = optimize(expr2, [log1p_opt])
+    assert log1p(x) + log(3) == opt2
+    assert (opt2.rewrite(log) - expr2).simplify() == 0
+
+    expr3 = log(2*x + 1)
+    opt3 = optimize(expr3, [log1p_opt])
+    assert log1p(2*x) - opt3 == 0
+    assert opt3.rewrite(log) == expr3
+
+    expr4 = log(x+3)
+    opt4 = optimize(expr4, [log1p_opt])
+    assert str(opt4) == 'log(x + 3)'
+
+
+def test_optims_c99():
+    x = Symbol('x')
+
+    expr1 = 2**x + log(x)/log(2) + log(x + 1) + exp(x) - 1
+    opt1 = optimize(expr1, optims_c99).simplify()
+    assert opt1 == exp2(x) + log2(x) + log1p(x) + expm1(x)
+    assert opt1.rewrite(exp).rewrite(log).rewrite(Pow) == expr1
+
+    expr2 = log(x)/log(2) + log(x + 1)
+    opt2 = optimize(expr2, optims_c99)
+    assert opt2 == log2(x) + log1p(x)
+    assert opt2.rewrite(log) == expr2
+
+    expr3 = log(x)/log(2) + log(17*x + 17)
+    opt3 = optimize(expr3, optims_c99)
+    delta3 = opt3 - (log2(x) + log(17) + log1p(x))
+    assert delta3 == 0
+    assert (opt3.rewrite(log) - expr3).simplify() == 0
+
+    expr4 = 2**x + 3*log(5*x + 7)/(13*log(2)) + 11*exp(x) - 11 + log(17*x + 17)
+    opt4 = optimize(expr4, optims_c99).simplify()
+    delta4 = opt4 - (exp2(x) + 3*log2(5*x + 7)/13 + 11*expm1(x) + log(17) + log1p(x))
+    assert delta4 == 0
+    assert (opt4.rewrite(exp).rewrite(log).rewrite(Pow) - expr4).simplify() == 0
+
+    expr5 = 3*exp(2*x) - 3
+    opt5 = optimize(expr5, optims_c99)
+    delta5 = opt5 - 3*expm1(2*x)
+    assert delta5 == 0
+    assert opt5.rewrite(exp) == expr5
+
+    expr6 = exp(2*x) - 3
+    opt6 = optimize(expr6, optims_c99)
+    assert opt6 in (expm1(2*x) - 2, expr6)  # expm1(2*x) - 2 is not better or worse
+
+    expr7 = log(3*x + 3)
+    opt7 = optimize(expr7, optims_c99)
+    delta7 = opt7 - (log(3) + log1p(x))
+    assert delta7 == 0
+    assert (opt7.rewrite(log) - expr7).simplify() == 0
+
+    expr8 = log(2*x + 3)
+    opt8 = optimize(expr8, optims_c99)
+    assert opt8 == expr8
+
+
+def test_create_expand_pow_optimization():
+    cc = lambda x: ccode(
+        optimize(x, [create_expand_pow_optimization(4)]))
+    x = Symbol('x')
+    assert cc(x**4) == 'x*x*x*x'
+    assert cc(x**4 + x**2) == 'x*x + x*x*x*x'
+    assert cc(x**5 + x**4) == 'pow(x, 5) + x*x*x*x'
+    assert cc(sin(x)**4) == 'pow(sin(x), 4)'
+    # gh issue 15335
+    assert cc(x**(-4)) == '1.0/(x*x*x*x)'
+    assert cc(x**(-5)) == 'pow(x, -5)'
+    assert cc(-x**4) == '-(x*x*x*x)'
+    assert cc(x**4 - x**2) == '-(x*x) + x*x*x*x'
+    i = Symbol('i', integer=True)
+    assert cc(x**i - x**2) == 'pow(x, i) - (x*x)'
+    y = Symbol('y', real=True)
+    assert cc(Abs(exp(y**4))) == "exp(y*y*y*y)"
+
+    # gh issue 20753
+    cc2 = lambda x: ccode(optimize(x, [create_expand_pow_optimization(
+        4, base_req=lambda b: b.is_Function)]))
+    assert cc2(x**3 + sin(x)**3) == "pow(x, 3) + sin(x)*sin(x)*sin(x)"
+
+
+def test_matsolve():
+    n = Symbol('n', integer=True)
+    A = MatrixSymbol('A', n, n)
+    x = MatrixSymbol('x', n, 1)
+
+    with assuming(Q.fullrank(A)):
+        assert optimize(A**(-1) * x, [matinv_opt]) == MatrixSolve(A, x)
+        assert optimize(A**(-1) * x + x, [matinv_opt]) == MatrixSolve(A, x) + x
+
+
+def test_logaddexp_opt():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = log(exp(x) + exp(y))
+    opt1 = optimize(expr1, [logaddexp_opt])
+    assert logaddexp(x, y) - opt1 == 0
+    assert logaddexp(y, x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+
+def test_logaddexp2_opt():
+    x, y = map(Symbol, 'x y'.split())
+    expr1 = log(2**x + 2**y)/log(2)
+    opt1 = optimize(expr1, [logaddexp2_opt])
+    assert logaddexp2(x, y) - opt1 == 0
+    assert logaddexp2(y, x) - opt1 == 0
+    assert opt1.rewrite(log) == expr1
+
+
+def test_sinc_opts():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, sinc_opts) == v
+
+    x = Symbol('x')
+    check({
+        sin(x)/x       : sinc(x),
+        sin(2*x)/(2*x) : sinc(2*x),
+        sin(3*x)/x     : 3*sinc(3*x),
+        x*sin(x)       : x*sin(x)
+    })
+
+    y = Symbol('y')
+    check({
+        sin(x*y)/(x*y)       : sinc(x*y),
+        y*sin(x/y)/x         : sinc(x/y),
+        sin(sin(x))/sin(x)   : sinc(sin(x)),
+        sin(3*sin(x))/sin(x) : 3*sinc(3*sin(x)),
+        sin(x)/y             : sin(x)/y
+    })
+
+
+def test_optims_numpy():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, optims_numpy) == v
+
+    x = Symbol('x')
+    check({
+        sin(2*x)/(2*x) + exp(2*x) - 1: sinc(2*x) + expm1(2*x),
+        log(x+3)/log(2) + log(x**2 + 1): log1p(x**2) + log2(x+3)
+    })
+
+
+@XFAIL  # room for improvement, ideally this test case should pass.
+def test_optims_numpy_TODO():
+    def check(d):
+        for k, v in d.items():
+            assert optimize(k, optims_numpy) == v
+
+    x, y = map(Symbol, 'x y'.split())
+    check({
+        log(x*y)*sin(x*y)*log(x*y+1)/(log(2)*x*y): log2(x*y)*sinc(x*y)*log1p(x*y),
+        exp(x*sin(y)/y) - 1: expm1(x*sinc(y))
+    })
+
+
+@may_xfail
+def test_compiled_ccode_with_rewriting():
+    if not cython:
+        skip("cython not installed.")
+    if not has_c():
+        skip("No C compiler found.")
+
+    x = Symbol('x')
+    about_two = 2**(58/S(117))*3**(97/S(117))*5**(4/S(39))*7**(92/S(117))/S(30)*pi
+    # about_two: 1.999999999999581826
+    unchanged = 2*exp(x) - about_two
+    xval = S(10)**-11
+    ref = unchanged.subs(x, xval).n(19) # 2.0418173913673213e-11
+
+    rewritten = optimize(2*exp(x) - about_two, [expm1_opt])
+
+    # Unfortunately, we need to call ``.n()`` on our expressions before we hand them
+    # to ``ccode``, and we need to request a large number of significant digits.
+    # In this test, results converged for double precision when the following number
+    # of significant digits were chosen:
+    NUMBER_OF_DIGITS = 25   # TODO: this should ideally be automatically handled.
+
+    func_c = '''
+#include <math.h>
+
+double func_unchanged(double x) {
+    return %(unchanged)s;
+}
+double func_rewritten(double x) {
+    return %(rewritten)s;
+}
+''' % {"unchanged": ccode(unchanged.n(NUMBER_OF_DIGITS)),
+           "rewritten": ccode(rewritten.n(NUMBER_OF_DIGITS))}
+
+    func_pyx = '''
+#cython: language_level=3
+cdef extern double func_unchanged(double)
+cdef extern double func_rewritten(double)
+def py_unchanged(x):
+    return func_unchanged(x)
+def py_rewritten(x):
+    return func_rewritten(x)
+'''
+    with tempfile.TemporaryDirectory() as folder:
+        mod, info = compile_link_import_strings(
+            [('func.c', func_c), ('_func.pyx', func_pyx)],
+            build_dir=folder, compile_kwargs={"std": 'c99'}
+        )
+        err_rewritten = abs(mod.py_rewritten(1e-11) - ref)
+        err_unchanged = abs(mod.py_unchanged(1e-11) - ref)
+        assert 1e-27 < err_rewritten < 1e-25  # highly accurate.
+        assert 1e-19 < err_unchanged < 1e-16  # quite poor.
+
+    # Tolerances used above were determined as follows:
+    # >>> no_opt = unchanged.subs(x, xval.evalf()).evalf()
+    # >>> with_opt = rewritten.n(25).subs(x, 1e-11).evalf()
+    # >>> with_opt - ref, no_opt - ref
+    # (1.1536301877952077e-26, 1.6547074214222335e-18)

rl/Lib/site-packages/sympy/codegen/tests/test_scipy_nodes.py

@@ -0,0 +1,44 @@
+from itertools import product
+from sympy.core.power import Pow
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.trigonometric import cos
+from sympy.core.numbers import pi
+from sympy.codegen.scipy_nodes import cosm1, powm1
+
+x, y, z = symbols('x y z')
+
+
+def test_cosm1():
+    cm1_xy = cosm1(x*y)
+    ref_xy = cos(x*y) - 1
+    for wrt, deriv_order in product([x, y, z], range(3)):
+        assert (
+            cm1_xy.diff(wrt, deriv_order) -
+            ref_xy.diff(wrt, deriv_order)
+        ).rewrite(cos).simplify() == 0
+
+    expr_minus2 = cosm1(pi)
+    assert expr_minus2.rewrite(cos) == -2
+    assert cosm1(3.14).simplify() == cosm1(3.14)  # cannot simplify with 3.14
+    assert cosm1(pi/2).simplify() == -1
+    assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0
+
+
+def test_powm1():
+    cases = {
+            powm1(x, y): x**y - 1,
+            powm1(x*y, z): (x*y)**z - 1,
+            powm1(x, y*z): x**(y*z)-1,
+            powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1
+    }
+    for pm1_e, ref_e in cases.items():
+        for wrt, deriv_order in product([x, y, z], range(3)):
+            der = pm1_e.diff(wrt, deriv_order)
+            ref = ref_e.diff(wrt, deriv_order)
+            delta = (der - ref).rewrite(Pow)
+            assert delta.simplify() == 0
+
+    eulers_constant_m1 = powm1(x, 1/log(x))
+    assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1
+    assert eulers_constant_m1.simplify() == exp(1) - 1