def full_lagrange(xs, fxs):
newxs = bytearray('')
for item in xs:
newxs.append(item)
newfxs = bytearray('')
for item in fxs:
newfxs.append(item)
return fastpolymath_c.full_lagrange(str(newxs), str(newfxs))
def full_lagrange(xs, fxs):
newxs = bytearray('')
for item in xs:
newxs.append(item)
newfxs = bytearray('')
for item in fxs:
newfxs.append(item)
return fastpolymath_c.full_lagrange(str(newxs), str(newfxs))
def _full_lagrange(xs, fxs):
assert (len(xs) == len(fxs))
if fastpolymath and SPEEDUP:
newxs = bytearray('')
for item in xs:
newxs.append(item)
newfxs = bytearray('')
for item in fxs:
newfxs.append(item)
return fastpolymath.full_lagrange(xs, fxs)
returnedcoefficients = []
# we need to compute:
# l_0 = (x - x_1) / (x_0 - x_1) * (x - x_2) / (x_0 - x_2) * ...
# l_1 = (x - x_0) / (x_1 - x_0) * (x - x_2) / (x_1 - x_2) * ...
for i in range(len(fxs)):
this_polynomial = [1]
# take the terms one at a time.
# I'm computing the denominator and using it to compute the polynomial.
for j in range(len(fxs)):
# skip the i = jth term because that's how Lagrange works...
if i == j:
continue
# I'm computing the denominator and using it to compute the polynomial.
denominator = _gf256_sub(xs[i], xs[j])
# denominator = xs[i]-xs[j]
# don't need to negate because -x = x in GF256
this_term = [
_gf256_div(xs[j], denominator),
_gf256_div(1, denominator)
]
# this_term = [-xs[j]/denominator, 1/denominator]
# let's build the polynomial...
this_polynomial = _multiply_polynomials(this_polynomial, this_term)
# okay, now I've gone and computed the polynomial. I need to multiply it
# by the result of f(x)
this_polynomial = _multiply_polynomials(this_polynomial, [fxs[i]])
# we've solved this polynomial. We should add to the others.
returnedcoefficients = _add_polynomials(returnedcoefficients,
this_polynomial)
return returnedcoefficients
def _full_lagrange(xs, fxs):
assert(len(xs) == len(fxs))
if fastpolymath and SPEEDUP:
newxs = bytearray('')
for item in xs:
newxs.append(item)
newfxs = bytearray('')
for item in fxs:
newfxs.append(item)
return fastpolymath.full_lagrange(xs, fxs)
returnedcoefficients = []
# we need to compute:
# l_0 = (x - x_1) / (x_0 - x_1) * (x - x_2) / (x_0 - x_2) * ...
# l_1 = (x - x_0) / (x_1 - x_0) * (x - x_2) / (x_1 - x_2) * ...
for i in range(len(fxs)):
this_polynomial = [1]
# take the terms one at a time.
# I'm computing the denominator and using it to compute the polynomial.
for j in range(len(fxs)):
# skip the i = jth term because that's how Lagrange works...
if i == j:
continue
# I'm computing the denominator and using it to compute the polynomial.
denominator = _gf256_sub(xs[i], xs[j])
# denominator = xs[i]-xs[j]
# don't need to negate because -x = x in GF256
this_term = [_gf256_div(xs[j], denominator), _gf256_div(1, denominator)]
# this_term = [-xs[j]/denominator, 1/denominator]
# let's build the polynomial...
this_polynomial = _multiply_polynomials(this_polynomial, this_term)
# okay, now I've gone and computed the polynomial. I need to multiply it
# by the result of f(x)
this_polynomial = _multiply_polynomials(this_polynomial, [fxs[i]])
# we've solved this polynomial. We should add to the others.
returnedcoefficients = _add_polynomials(returnedcoefficients, this_polynomial)
return returnedcoefficients
import fastpolymath_c print "[2,4,5] * [14,30,32] -> " x = fastpolymath_c.full_lagrange(chr(2)+chr(4)+chr(5),chr(14)+chr(30)+chr(32)) for c in x: print ord(c), print
