#!/usr/bin/env python
from sympy.core.random import random
from sympy.core.numbers import (I, Integer, pi)
from sympy.core.symbol import Symbol
from sympy.core.sympify import sympify
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.trigonometric import sin
from sympy.polys.polytools import factor
from sympy.simplify.simplify import simplify
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))