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Beginnings of a test suite for the bignum code. The output of
testdata/bignum.py is twice the size of the rest of the PuTTY source put together, so I'm not checking it in. This reveals bugs in the new multiplication code, which I have yet to fix. [originally from svn r9097]
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,82 @@ | ||
| # Generate test cases for a bignum implementation. | ||
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| import sys | ||
| import mathlib | ||
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| 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'. | ||
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| r = mathlib.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 | ||
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| best = (a,b,a*b) | ||
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| while 1: | ||
| improved = 0 | ||
| a, b = best[:2] | ||
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| terms = mathlib.confracr(a, b, output=None) | ||
| coeffs = [(1,0),(0,1)] | ||
| for t in terms: | ||
| coeffs.append((coeffs[-2][0]-t*coeffs[-1][0], | ||
| coeffs[-2][1]-t*coeffs[-1][1])) | ||
| 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] | ||
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| # Flip signs as appropriate. | ||
| if (a+da) * (b+db) * dir < target * dir: | ||
| da, db = -da, -db | ||
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| # 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 = mathlib.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)) | ||
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| 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 | ||
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| if not improved: | ||
| break | ||
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| return best | ||
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| def hexstr(n): | ||
| s = hex(n) | ||
| if s[:2] == "0x": s = s[2:] | ||
| if s[-1:] == "L": s = s[:-1] | ||
| return s | ||
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| # 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 hexstr(a), hexstr(b), hexstr(p) | ||
| a, b, p = findprod((1<<i)+1, +1, (i, i+1)) | ||
| print hexstr(a), hexstr(b), hexstr(p) |