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Old 2011-09-08, 00:41   #3
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Oct 2004

2×3×19×31 Posts

A and B are treated as constants in your formula for the Murphy E score. The Murphy score computation in GGNFS and Msieve (the latter is deliberately chosen to produce comparable scores to the former) is given the polynomial skew S, chooses the sieving area (always 1e16), and sets A to sqrt(sieve_area * S) and B to sqrt(sieve_area / S). So A and B are still constants, but they depend on the skew of the sieving region. All the implementations out there compute the integral numerically (most use the midpoint rule, msieve uses a full numerical integrator).

Murphy's dissertation originally did not account for the actual length of the rays emanating from the origin. Even the current code does not increase the size of the sieve interval or the value of L1 and L2 for larger problems.
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