Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with
or
.
Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

116 lines (99 sloc) 3.605 kB
# Generate test cases for a bignum implementation.
import sys
# integer square roots
def sqrt(n):
d = long(n)
a = 0L
# b must start off as a power of 4 at least as large as n
ndigits = len(hex(long(n)))
b = 1L << (ndigits*4)
while 1:
a = a >> 1
di = 2*a + b
if di <= d:
d = d - di
a = a + b
b = b >> 2
if b == 0: break
return a
# continued fraction convergents of a rational
def confrac(n, d):
coeffs = [(1,0),(0,1)]
while d != 0:
i = n / d
n, d = d, n % d
coeffs.append((coeffs[-2][0]-i*coeffs[-1][0],
coeffs[-2][1]-i*coeffs[-1][1]))
return coeffs
def findprod(target, dir = +1, ratio=(1,1)):
# Return two numbers whose product is as close as we can get to
# 'target', with any deviation having the sign of 'dir', and in
# the same approximate ratio as 'ratio'.
r = sqrt(target * ratio[0] * ratio[1])
a = r / ratio[1]
b = r / ratio[0]
if a*b * dir < target * dir:
a = a + 1
b = b + 1
assert a*b * dir >= target * dir
best = (a,b,a*b)
while 1:
improved = 0
a, b = best[:2]
coeffs = confrac(a, b)
for c in coeffs:
# a*c[0]+b*c[1] is as close as we can get it to zero. So
# if we replace a and b with a+c[1] and b+c[0], then that
# will be added to our product, along with c[0]*c[1].
da, db = c[1], c[0]
# Flip signs as appropriate.
if (a+da) * (b+db) * dir < target * dir:
da, db = -da, -db
# Multiply up. We want to get as close as we can to a
# solution of the quadratic equation in n
#
# (a + n da) (b + n db) = target
# => n^2 da db + n (b da + a db) + (a b - target) = 0
A,B,C = da*db, b*da+a*db, a*b-target
discrim = B^2-4*A*C
if discrim > 0 and A != 0:
root = sqrt(discrim)
vals = []
vals.append((-B + root) / (2*A))
vals.append((-B - root) / (2*A))
if root * root != discrim:
root = root + 1
vals.append((-B + root) / (2*A))
vals.append((-B - root) / (2*A))
for n in vals:
ap = a + da*n
bp = b + db*n
pp = ap*bp
if pp * dir >= target * dir and pp * dir < best[2]*dir:
best = (ap, bp, pp)
improved = 1
if not improved:
break
return best
def hexstr(n):
s = hex(n)
if s[:2] == "0x": s = s[2:]
if s[-1:] == "L": s = s[:-1]
return s
# Tests of multiplication which exercise the propagation of the last
# carry to the very top of the number.
for i in range(1,4200):
a, b, p = findprod((1<<i)+1, +1, (i, i*i+1))
print "mul", hexstr(a), hexstr(b), hexstr(p)
a, b, p = findprod((1<<i)+1, +1, (i, i+1))
print "mul", hexstr(a), hexstr(b), hexstr(p)
# Simple tests of modpow.
for i in range(64, 4097, 63):
modulus = sqrt(1<<(2*i-1)) | 1
base = sqrt(3*modulus*modulus) % modulus
expt = sqrt(modulus*modulus*2/5)
print "pow", hexstr(base), hexstr(expt), hexstr(modulus), hexstr(pow(base, expt, modulus))
if i <= 1024:
# Test even moduli, which can't be done by Montgomery.
modulus = modulus - 1
print "pow", hexstr(base), hexstr(expt), hexstr(modulus), hexstr(pow(base, expt, modulus))
Jump to Line
Something went wrong with that request. Please try again.