doc: Minor fixes in safegcd_implementation.md
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@ -569,8 +569,14 @@ bits efficiently, which is possible on most platforms; it is abstracted here as
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```python
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```python
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def count_trailing_zeros(v):
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def count_trailing_zeros(v):
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"""For a non-zero value v, find z such that v=(d<<z) for some odd d."""
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"""
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return (v & -v).bit_length() - 1
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When v is zero, consider all N zero bits as "trailing".
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For a non-zero value v, find z such that v=(d<<z) for some odd d.
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"""
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if v == 0:
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return N
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else:
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return (v & -v).bit_length() - 1
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i = N # divsteps left to do
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i = N # divsteps left to do
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while True:
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while True:
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@ -601,7 +607,7 @@ becomes negative, or when *i* reaches *0*. Combined, this is equivalent to addin
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It is easy to find what that multiple is: we want a number *w* such that *g+w f* has a few bottom
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It is easy to find what that multiple is: we want a number *w* such that *g+w f* has a few bottom
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zero bits. If that number of bits is *L*, we want *g+w f mod 2<sup>L</sup> = 0*, or *w = -g/f mod 2<sup>L</sup>*. Since *f*
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zero bits. If that number of bits is *L*, we want *g+w f mod 2<sup>L</sup> = 0*, or *w = -g/f mod 2<sup>L</sup>*. Since *f*
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is odd, such a *w* exists for any *L*. *L* cannot be more than *i* steps (as we'd finish the loop before
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is odd, such a *w* exists for any *L*. *L* cannot be more than *i* steps (as we'd finish the loop before
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doing more) or more than *η+1* steps (as we'd run `eta, f, g = -eta, g, f` at that point), but
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doing more) or more than *η+1* steps (as we'd run `eta, f, g = -eta, g, -f` at that point), but
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apart from that, we're only limited by the complexity of computing *w*.
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apart from that, we're only limited by the complexity of computing *w*.
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This code demonstrates how to cancel up to 4 bits per step:
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This code demonstrates how to cancel up to 4 bits per step:
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@ -618,7 +624,7 @@ while True:
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break
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break
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# We know g is odd now
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# We know g is odd now
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if eta < 0:
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if eta < 0:
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eta, f, g = -eta, g, f
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eta, f, g = -eta, g, -f
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# Compute limit on number of bits to cancel
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# Compute limit on number of bits to cancel
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limit = min(min(eta + 1, i), 4)
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limit = min(min(eta + 1, i), 4)
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# Compute w = -g/f mod 2**limit, using the table value for -1/f mod 2**4. Note that f is
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# Compute w = -g/f mod 2**limit, using the table value for -1/f mod 2**4. Note that f is
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