def FPDiv(a, b, k, f, kappa, simplex_flag=False):
"""
Goldschmidt method as presented in Catrina10,
"""
theta = int(ceil(log(k/3.5) / log(2)))
alpha = two_power(2*f)
w = AppRcr(b, k, f, kappa, simplex_flag)
x = alpha - b * w
y = a * w
y = TruncPr(y, 2*k, f, kappa)
for i in range(theta):
y = y * (alpha + x)
x = x * x
y = TruncPr(y, 2*k, 2*f, kappa)
x = TruncPr(x, 2*k, 2*f, kappa)
y = y * (alpha + x)
y = TruncPr(y, 2*k, 2*f, kappa)
return y
def AppRcr(b, k, f, kappa, simplex_flag=False):
"""
Approximate reciprocal of [b]:
Given [b], compute [1/b]
"""
alpha = cint(int(2.9142 * 2**k))
c, v = Norm(b, k, f, kappa, simplex_flag)
#v should be 2**{k - m} where m is the length of the bitwise repr of [b]
d = alpha - 2 * c
w = d * v
w = TruncPr(w, 2 * k, 2 * (k - f))
# now w * 2 ^ {-f} should be an initial approximation of 1/b
return w
def block(i):
A[i] = TruncPr(A[i - 1] * W[i - 1], 2*k, f, kappa)
temp = (B[i - 1] * W[i - 1]) >> f
# no reading and writing to the same variable in a for loop.
W[i] = two - temp
B[i] = temp
