import math

def sin(x):
    if isinstance(x, Dual):
        return Dual(sin(x.x), cos(x.x) * x.dx)
    return math.sin(x)

def cos(x):
    if isinstance(x, Dual):
        return Dual(cos(x.x), -1 * sin(x.x) * x.dx)
    return math.cos(x)

class Dual:
    def __init__(self, x, dx):
        self.x = x
        self.dx = dx

    def __add__(self, r):
        assert isinstance(r, Dual)
        return Dual(self.x + r.x, self.dx + r.dx)

    def __mul__(self, r):
        if isinstance(r, Dual):
            return Dual(self.x * r.x, self.x * r.dx + r.x * self.dx)
        assert isinstance(r, float)
        return Dual(self.x * r, r * self.dx)

    def __rmul__(self, r):
        return self * r

    def __repr__(self):
        return repr((self.x, self.dx))

class Raw:
    def __mul__(self, r):
        assert isinstance(r, float)
        return Raw()

    def __rmul__(self, r):
        return self * r

    def __add__(self, r):
        assert isinstance(r, Raw)
        return Raw()

    def __repr__(self):
        return repr(())

def f(x, y):
    return sin(x) * y, sin(y) + x

print("raw:")
print(f(Dual(1.0, Raw()), Dual(2.0, Raw())))

print("forward mode:")
print(f(Dual(1.0, 1.0), Dual(2.0, 0.0)))
print(f(Dual(1.0, 0.0), Dual(2.0, 1.0)))

class Ref:
    def __init__(self, v):
        self.v = v

class WithBP:
    def __init__(self, rdx, bp):
        self.rdx = rdx
        self.bp = bp

    def __mul__(self, rhs):
        assert isinstance(rhs, float)
        r = Ref(0.0)
        bpv = self.bp.v
        def new_bp():
            self.rdx.v = self.rdx.v + r.v * rhs
            bpv()
        self.bp.v = new_bp
        return WithBP(r, self.bp)

    def __rmul__(self, rhs):
        return self * rhs

    def __add__(self, rhs):
        assert isinstance(rhs, WithBP)
        r = Ref(0.0)
        bpv = self.bp.v
        def new_bp():
            self.rdx.v = self.rdx.v + r.v
            rhs.rdx.v = rhs.rdx.v + r.v
            bpv()
        self.bp.v = new_bp
        return WithBP(r, self.bp)

print("reverse mode:")
bp = Ref(lambda: ())
x = WithBP(Ref(0.0), bp)
y = WithBP(Ref(0.0), bp)

a, b = f(Dual(1.0, x), Dual(2.0, y))
a.dx.rdx.v = 1.0
a.dx.bp.v()
print((x.rdx.v, y.rdx.v))

bp.v = lambda: ()
x = WithBP(Ref(0.0), bp)
y = WithBP(Ref(0.0), bp)

a, b = f(Dual(1.0, x), Dual(2.0, y))
b.dx.rdx.v = 1.0
bp.v()
print((x.rdx.v, y.rdx.v))

class Batched:
    def __init__(self, *l):
        self.l = l

    def __mul__(self, rhs):
        assert isinstance(rhs, float)
        return Batched(*[x * rhs for x in self.l])

    def __add__(self, rhs):
        assert isinstance(rhs, Batched)
        assert len(self.l) == len(rhs.l)
        return Batched(*[self.l[i] + rhs.l[i] for i in range(len(self.l))])

    def __rmul__(self, rhs):
        return self * rhs

    def __repr__(self):
        return repr(self.l)

print("batched forward mode:")
print(f(Dual(1.0, Batched(1.0, 0.0)), Dual(2.0, Batched(0.0, 1.0))))

print("batched reverse mode:")
bp = Ref(lambda: ())
ax = WithBP(Ref(0.0), bp)
bx = WithBP(Ref(0.0), bp)
ay = WithBP(Ref(0.0), bp)
by = WithBP(Ref(0.0), bp)
a, b = f(Dual(1.0, Batched(ax, bx)), Dual(2.0, Batched(ay, by)))
a.dx.l[0].rdx.v = 1.0
b.dx.l[1].rdx.v = 1.0
bp.v()
print((ax.rdx.v, bx.rdx.v, ay.rdx.v, by.rdx.v))