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  1. #!/usr/bin/env python
  2.  
  3. import numpy as np
  4.  
  5. def poly_eval(x, a):
  6.     return sum([an*x**n for n,an in enumerate(a)])
  7.  
  8. def sqrt_1px(x):
  9.     a = [1.0, 
  10.          0.49959804148061, 
  11.          -0.12047308243453, 
  12.          0.04585425015501, 
  13.          -0.01076564682800 ]
  14.     return poly_eval(x, a)
  15.  
  16. def log2_1px(x):
  17.     a = [0.0,
  18.          1.44254494359510,
  19.          -0.7181452567504,
  20.          0.45754919692582,
  21.          -0.27790534462866,
  22.          0.121797910687826,
  23.          -0.02584144982967 ]
  24.     return poly_eval(x, a)
  25.  
  26. def pow2x(x):
  27.     a = [ 1.0,
  28.         0.69303212081966 ,
  29.         0.24137976293709,
  30.         0.05203236900844,
  31.         0.01355574723481 ]
  32.     return poly_eval(x,a)
  33.  
  34. def sin_pi2x(x):
  35.     a = [ 0.0,
  36.          1.57079632679490,
  37.          0.0,
  38.          -0.64596406188166,
  39.          0.0,
  40.          0.07969158490912,
  41.          0.0,
  42.          -0.00467687997706,
  43.          0.0,
  44.          0.00015303015470 ]
  45.     return poly_eval(x, a)
  46.  
  47. def cos_pix(x):
  48.     return 1 - 2*sin_pi2x(x)**2
  49.  
  50. if __name__ == '__main__':
  51.     xp = np.linspace(0, 1, 1001)
  52.     xn = np.linspace(-1, 0, 1001)
  53.     x  = np.linspace(-1, 1, 2001)
  54.  
  55.     # sqrt(1+x)
  56.     mae = np.max(np.abs(sqrt_1px(xp)-np.sqrt(1+xp)))
  57.     print "sqrt(1+x)\nMaximum Absolute Error: %e\n" % mae
  58.  
  59.     # log2(1+x)
  60.     mae = np.max(np.abs(log2_1px(xp) - np.log2(1+xp)))
  61.     print "log2(1+x)\nMaximum Absolute Error: %e\n" % mae
  62.  
  63.     # 2^x
  64.     mae = np.max(np.abs(pow2x(xp) - 2**xp))
  65.     print "2^x\nMaximum Absolute Error: %e\n" % mae
  66.  
  67.     # sin(pi/2*x)
  68.     mae = np.max(np.abs(sin_pi2x(x) - np.sin(np.pi/2*x)))
  69.     print "sin(pi/2*x)\nMaximum Absolute Error: %e\n" % mae    
  70.  
  71.     # cos(pi*x)
  72.     mae = np.max(np.abs(cos_pix(x) - np.cos(np.pi*x)))
  73.     print "cos(pi*x)\nMaximum Absolute Error: %e\n" % mae
  74.  
Success #stdin #stdout 0.12s 24184KB
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sqrt(1+x)
Maximum Absolute Error: 1.489434e-05

log2(1+x)
Maximum Absolute Error: 2.216198e-06

2^x
Maximum Absolute Error: 6.312298e-06

sin(pi/2*x)
Maximum Absolute Error: 2.410459e-08

cos(pi*x)
Maximum Absolute Error: 9.613158e-08
https://ideone.com/BwcT47
language:
Python (cpython 2.7.16)
created:
10 years ago
visibility:
public

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