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Faster expected curves

Seth Troisi requested to merge faster_expected_curves into master

I verified none of the code in the middle depends on batch_s or batch_last_B1_used and ran make check

Currently you must wait (a non-trivial amount of time) to computing the batch product before # of expected curves are printed.

$ echo "2^997-1" | ecm -param 1 -v 1e8 1e9
GMP-ECM 7.0.4 [configured with GMP 6.2.99, --enable-asm-redc] [ECM]
Tuned for x86_64/k8/params.h
Running on five
Input number is 2^997-1 (301 digits)
Using MODMULN [mulredc:1, sqrredc:1]
Computing batch product (of 144266969 bits) of primes up to B1=100000000 took **3047ms**
Using B1=100000000, B2=1000000000, polynomial Dickson(6), sigma=1:4034180356
dF=4096, k=6, d=39270, d2=13, i0=2534
Expected number of curves to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
129	576	2910	16333	100627	674284	4876112	3.8e+07	3.1e+08	2.3e+09

Afterwards # of expected curves is printed near instantly.

$ echo "2^997-1" | timeout 0.1 ./ecm -param 1 -v 1e8 1e9
GMP-ECM 7.0.5-dev [configured with GMP 6.2.99, --enable-asm-redc, --enable-gpu, --enable-assert] [ECM]
Tuned for x86_64/k8/params.h
Running on five
Input number is 2^997-1 (301 digits)
Using MODMULN [mulredc:1, sqrredc:1]
Using B1=100000000, B2=1000000000, polynomial Dickson(6), sigma=1:522910088
dF=4096, k=6, d=39270, d2=13, i0=2534
Expected number of curves to find a factor of n digits (assuming one exists):
35	40	45	50	55	60	65	70	75	80
129	576	2910	16333	100627	674284	4876112	3.8e+07	3.1e+08	2.3e+09

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