#!/usr/bin/env python
from random import random
from sympy import factor, I, Integer, pi, simplify, sin, sqrt, Symbol, sympify
from sympy.abc import x, y, z
from timeit import default_timer as clock


def bench_R1():
    "real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))"
    def f(z):
        return sqrt(Integer(1)/3)*z**2 + I/3
    f(f(f(f(f(f(f(f(f(f(I/2)))))))))).as_real_imag()[0]


def bench_R2():
    "Hermite polynomial hermite(15, y)"
    def hermite(n, y):
        if n == 1:
            return 2*y
        if n == 0:
            return 1
        return (2*y*hermite(n - 1, y) - 2*(n - 1)*hermite(n - 2, y)).expand()

    hermite(15, y)


def bench_R3():
    "a = [bool(f==f) for _ in range(10)]"
    f = x + y + z
    [bool(f == f) for _ in range(10)]


def bench_R4():
    # we don't have Tuples
    pass


def bench_R5():
    "blowup(L, 8); L=uniq(L)"
    def blowup(L, n):
        for i in range(n):
            L.append( (L[i] + L[i + 1]) * L[i + 2] )

    def uniq(x):
        v = set(x)
        return v
    L = [x, y, z]
    blowup(L, 8)
    L = uniq(L)


def bench_R6():
    "sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))"
    sum(simplify((x + sin(i))/x + (x - sin(i))/x) for i in range(100))


def bench_R7():
    "[f.subs(x, random()) for _ in range(10**4)]"
    f = x**24 + 34*x**12 + 45*x**3 + 9*x**18 + 34*x**10 + 32*x**21
    [f.subs(x, random()) for _ in range(10**4)]


def bench_R8():
    "right(x^2,0,5,10^4)"
    def right(f, a, b, n):
        a = sympify(a)
        b = sympify(b)
        n = sympify(n)
        x = f.atoms(Symbol).pop()
        Deltax = (b - a)/n
        c = a
        est = 0
        for i in range(n):
            c += Deltax
            est += f.subs(x, c)
        return est*Deltax

    right(x**2, 0, 5, 10**4)


def _bench_R9():
    "factor(x^20 - pi^5*y^20)"
    factor(x**20 - pi**5*y**20)


def bench_R10():
    "v = [-pi,-pi+1/10..,pi]"
    def srange(min, max, step):
        v = [min]
        while (max - v[-1]).evalf() > 0:
            v.append(v[-1] + step)
        return v[:-1]
    srange(-pi, pi, sympify(1)/10)


def bench_R11():
    "a = [random() + random()*I for w in [0..1000]]"
    [random() + random()*I for w in range(1000)]


def bench_S1():
    "e=(x+y+z+1)**7;f=e*(e+1);f.expand()"
    e = (x + y + z + 1)**7
    f = e*(e + 1)
    f.expand()


if __name__ == '__main__':
    benchmarks = [
        bench_R1,
        bench_R2,
        bench_R3,
        bench_R5,
        bench_R6,
        bench_R7,
        bench_R8,
        #_bench_R9,
        bench_R10,
        bench_R11,
        #bench_S1,
    ]

    report = []
    for b in benchmarks:
        t = clock()
        b()
        t = clock() - t
        print("%s%65s: %f" % (b.__name__, b.__doc__, t))