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Improved how lucas.cal pre-verifies numbers

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Landon Curt Noll
2018-02-21 12:36:21 -08:00
parent c585d7aa78
commit 83c898cc2b
1 changed files with 52 additions and 18 deletions
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70
cal/lucas.cal
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@@ -1,7 +1,7 @@
/*
* lucas - perform a Lucas primality test on h*2^n-1
*
* Copyright (C) 1999,2017 Landon Curt Noll
* Copyright (C) 1999,2017,2018 Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
@@ -373,41 +373,53 @@ lucas(h, n)
return 1; /* 239 is prime */
}
/*
* Verify that h*2^n-1 is not a multiple of 3
*
* The case for h*2^n-1 == 3 is handled above.
*/
if (((h % 3 == 1) && (n % 2 == 0)) || ((h % 3 == 2) && (n % 2 == 1))) {
/* no need to test h*2^n-1, it is a multiple of 3 */
ldebug("lucas","not-prime: != 3 and is a multiple of 3");
return 0;
}
/*
* Avoid any numbers divisible by small primes
*/
/*
* check for 3 <= prime factors < 29
* pfact(28)/2 = 111546435
* check for 5 <= prime factors < 31
* pfact(30)/6 = 1078282205
*/
testval = h*2^n - 1;
if (gcd(testval, 111546435) > 1) {
/* a small 3 <= prime < 29 divides h*2^n-1 */
ldebug("lucas","not-prime: 3<=prime<29 divides h*2^n-1");
if (gcd(testval, 1078282205) > 1) {
/* a small 5 <= prime < 31 divides h*2^n-1 */
ldebug("lucas",\
"not-prime: a small 5<=prime<31 divides h*2^n-1");
return 0;
}
/*
* check for 29 <= prime factors < 47
* pfact(46)/pfact(28) = 5864229
* check for 31 <= prime factors < 53
* pfact(52)/pfact(30) = 95041567
*/
if (gcd(testval, 58642669) > 1) {
/* a small 29 <= prime < 47 divides h*2^n-1 */
ldebug("lucas","not-prime: 29<=prime<47 divides h*2^n-1");
if (gcd(testval, 95041567) > 1) {
/* a small 31 <= prime < 53 divides h*2^n-1 */
ldebug("lucas","not-prime: 31<=prime<53 divides h*2^n-1");
return 0;
}
/*
* check for prime 47 <= factors < 257, if h*2^n-1 is large
* 2^282 > pfact(256)/pfact(46) > 2^281
* check for prime 53 <= factors < 257, if h*2^n-1 is large
* 2^276 > pfact(256)/pfact(52) > 2^275
*/
bits = highbit(testval);
if (bits >= 281) {
if (bits >= 275) {
if (pprod256 <= 0) {
pprod256 = pfact(256)/pfact(46);
pprod256 = pfact(256)/pfact(52);
}
if (gcd(testval, pprod256) > 1) {
/* a small 47 <= prime < 257 divides h*2^n-1 */
/* a small 53 <= prime < 257 divides h*2^n-1 */
ldebug("lucas",\
"not-prime: 47<=prime<257 divides h*2^n-1");
"not-prime: 53<=prime<257 divides h*2^n-1");
return 0;
}
}
@@ -423,7 +435,9 @@ lucas(h, n)
* generate a test for h*2^n-1. The legacy function,
* legacy_gen_v1() used by the Amdahl 6 could have returned
* -1. The new gen_v1() based on the method outlined in Ref4
* will never return -1.
* will never return -1 if h*2^n-1 is not a multiple of 3.
* Because the "multiple of 3" case is handled above, the
* call below to gen_v1() will never return -1.
*/
v1 = gen_v1(h, n);
if (v1 < 0) {
@@ -1172,6 +1186,26 @@ gen_v1(h, n)
return -1;
}
/*
* Common Mersenne number case:
*
* For Mersenne numbers:
*
* 2^n-1
*
* we can use, 40% of the time, v(1) == 3. However nearly all code that
* implements the Lucas-Lehmer test uses v(1) == 4. Whenever for
* h != 0 mod 3, and particular the Mersenne number case of when h == 1:
*
* 1*2^n-1
*
* v(1) == 4 always works. For this reason, we return 4 when h == 1.
*/
if (h == 1) {
/* v(1) == 4 always works for the Mersenne number case */
return 4;
}
/*
* check for Case 1: (h mod 3 != 0)
*/