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fastmath: Increase precision of 2^x, needed for LC3 HR Precision tests

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This commit is contained in:
Antoine Soulier
2024-02-27 14:28:28 -08:00
parent e67bb2d07d
commit a01c060807
2 changed files with 53 additions and 26 deletions
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24
tables/fastmath.py
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@@ -19,25 +19,33 @@ import numpy as np
import matplotlib.pyplot as plt
def fast_exp2(x, p):
def fast_exp2(x, t, p):
p = p.astype(np.float32)
x = x.astype(np.float32)
y = (((((p[0]*x) + p[1])*x + p[2])*x + p[3])*x + p[4])*x + 1
m = ((x + 0.5/8) % (1/8)) - (0.5/8)
e = int((x - m) * 8)
return np.power(y.astype(np.float32), 16)
y = ((((p[0]*m) + p[1])*m + p[2])*m + p[3])*m + p[4]
y = y * 2**(e // 8) * t[e % 8]
return y.astype(np.float32)
def approx_exp2():
x = np.arange(-8, 8, step=1e-3)
x = np.arange(0, 1/8, step=1e-6)
p = np.polyfit(x, 2 ** x, 4)
t = [ 2**(i/8) for i in range(8) ]
x = np.arange(-10, 10, step=1e-3)
y = [ fast_exp2(x[i], t, p) for i in range(len(x)) ]
p = np.polyfit(x, ((2 ** (x/16)) - 1) / x, 4)
y = [ fast_exp2(x[i], p) for i in range(len(x)) ]
e = np.abs(y - 2**x) / (2 ** x)
print('{{ {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e} }}'
.format(p[0], p[1], p[2], p[3], p[4]))
print('{{ {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e}, \n'
' {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e}, '.format(*t))
print('{{ {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e}, {:14.8e} }}'.format(*p))
print('Max relative error: ', np.max(e))
print('Max RMS error: ', np.sqrt(np.mean(e ** 2)))