import math
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
 
def calc_e_small(x):
    n = 10
    f = np.arange(1, n+1).cumprod()
    b = np.array([x]*n).cumprod()
    return np.sum(b / f) + 1
 
def calc_e(x):
    reverse = False
    if x < 0:                           #处理负数
        x = -x
        reverse = True
    ln2 = 0.69314718055994530941723212145818
    c = x / ln2
    a = int(c + 0.5)
    b = x - a * ln2
    y = (2 ** a) * calc_e_small(b)
    if reverse:
        return 1 / y
    return y
 
if __name__ == "__main__":
    t1 = np.linspace(-2, 0, 10, endpoint= False)
    t2 = np.linspace(0, 2, 20)
    t = np.concatenate((t1, t2))
    print(t1)
    print(t2)
    print(t)                             #横轴数据
    y = np.empty_like(t)
    for i, x in enumerate(t):
        y[i] = calc_e(x)
        print( 'e^', x, '=', y[i], '(近似值)\t', math.exp(x))
        # print '误差' , y[i] - math.exp(x)
 
    mpl.rcParams['font.sans-serif'] = [u'SimHei']
    mpl.rcParams['axes.unicode_minus'] = False
    plt.plot(t, y, 'r-', t, y, 'go', linewidth = 2)
    plt.title(u'Taylor展式的应用', fontsize = 18)
    plt.xlabel('x', fontsize = 15)
    plt.ylabel('exp(x)', fontsize = 15)
    plt.grid(True)
    plt.show()
