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Improved lucas.cal vt tables and arg checking

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This commit is contained in:
Landon Curt Noll
2017-06-09 15:44:48 -07:00
parent f91bfaab70
commit 0145883396
5 changed files with 114 additions and 41 deletions
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12
CHANGES
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@@ -1,4 +1,13 @@
The following are the changes from calc version 2.12.6.0 to date:
The following are the changes from calc version 2.12.6.1 to date:
Improved gen_v1(h,n) in lucas.cal to use an even faster search method.
Improved are checking in lucas.cal. In particular both h and n must be
integers >= 1. In the case of both rodseth_xhn(x, h, n) and gen_v1(h, n)
h must be odd.
The following are the changes from calc version 2.12.6.0 to 2.12.6.0:
Added the makefile variable ${COMMON_ADD} that will add flags
to all compile and link commands. The ${COMMON_ADD} flags are
@@ -68,7 +77,6 @@ The following are the changes from calc version 2.12.6.0 to date:
Fixed a number of typos in the CHANGES file.
The following are the changes from calc version 2.12.5.4 to 2.12.5.6:
Recompile to match current RHEL7.2 libc and friends.

2
Makefile.ship
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@@ -990,7 +990,7 @@ EXT=
# The default calc versions
#
VERSION= 2.12.6.0
VERSION= 2.12.6.1
# Names of shared libraries with versions
#

137
cal/lucas.cal
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@@ -243,8 +243,8 @@ pprod256 = 0; /* product of "primes up to 256" / "primes up to 46" */
* do make this so.
*
* input:
* h the h as in h*2^n-1
* n the n as in h*2^n-1
* h h as in h*2^n-1 (must be >= 1)
* n n as in h*2^n-1 (must be >= 1)
*
* returns:
* 1 => h*2^n-1 is prime
@@ -267,13 +267,17 @@ lucas(h, n)
* check arg types
*/
if (!isint(h)) {
ldebug("lucas", "h is non-int");
quit "FATAL: bad args: h must be an integer";
}
if (h < 1) {
quit "FATAL: bad args: h must be an integer >= 1";
}
if (!isint(n)) {
ldebug("lucas", "n is non-int");
quit "FATAL: bad args: n must be an integer";
}
if (n < 1) {
quit "FATAL: bad args: n must be an integer >= 1";
}
/*
* reduce h if even
@@ -484,9 +488,9 @@ lucas(h, n)
* See the function gen_v1() for details on the value of v(1).
*
* input:
* h - h as in h*2^n-1
* n - n as in h*2^n-1
* v1 - gen_v1(h,n) (see function below)
* h - h as in h*2^n-1 (must be >= 1)
* n - n as in h*2^n-1 (must be >= 1)
* v1 - gen_v1(h,n) (must be >= 3) (see function below)
*
* returns:
* u(2) - initial value for Lucas test on h*2^n-1
@@ -499,6 +503,8 @@ gen_u2(h, n, v1)
local r; /* low value: v(n) */
local s; /* high value: v(n+1) */
local hbits; /* highest bit set in h */
local oldh; /* pre-reduced h */
local oldn; /* pre-reduced n */
local i;
/*
@@ -507,24 +513,45 @@ gen_u2(h, n, v1)
if (!isint(h)) {
quit "bad args: h must be an integer";
}
if (h < 0) {
quit "bad args: h must be an integer >= 1";
}
if (!isint(n)) {
quit "bad args: n must be an integer";
}
if (n < 1) {
quit "bad args: n must be an integer >= 1";
}
if (!isint(v1)) {
quit "bad args: v1 must be an integer";
}
if (v1 <= 0) {
quit "bogus arg: v1 is <= 0";
if (v1 < 3) {
quit "bogus arg: v1 must be an integer >= 3";
}
/*
* reduce h if even
*
* we will force h to be odd by moving powers of two over to 2^n
*/
oldh = h;
oldn = n;
shiftdown = fcnt(h,2); /* h % 2^shiftdown == 0, max shiftdown */
if (shiftdown > 0) {
h >>= shiftdown;
n += shiftdown;
}
/*
* enforce the h > 0 and n >= 2 rules
*/
if (h <= 0 || n < 1) {
print " ERROR: h=":oldh, "n=":oldn, "reduced h=":h, "n=":n;
quit "reduced args violate the rule: 0 < h < 2^n";
}
hbits = highbit(h);
if (hbits >= n) {
print " ERROR: h=":oldh, "n=":oldn, "reduced h=":h, "n=":n;
quit "reduced args violate the rule: 0 < h < 2^n";
}
@@ -599,8 +626,8 @@ gen_u2(h, n, v1)
* See the function gen_u2() for details.
*
* input:
* h - h as in h*2^n-1
* n - n as in h*2^n-1
* h - h as in h*2^n-1 (must be >= 1)
* n - n as in h*2^n-1 (must be >= 1)
* v1 - gen_v1(h,n) (see function below)
*
* returns:
@@ -638,9 +665,9 @@ gen_u0(h, n, v1)
* x > 2
*
* input:
* x - potential v(1) value
* h - h as in h*2^n-1
* n - n as in h*2^n-1
* x potential v(1) value
* h h as in h*2^n-1 (h must be odd >= 1)
* n n as in h*2^n-1 (must be >= 1)
*
* returns:
* 1 if v(1) == x for h*2^n-1
@@ -657,9 +684,18 @@ rodseth_xhn(x, h, n)
if (!isint(h)) {
quit "bad args: h must be an integer";
}
if (iseven(h)) {
quit "bad args: h must be an odd integer";
}
if (h < 1) {
quit "bad args: h must be an integer >= 1";
}
if (!isint(n)) {
quit "bad args: n must be an integer";
}
if (n < 1) {
quit "bad args: n must be an integer >= 1";
}
if (!isint(x)) {
quit "bad args: x must be an integer";
}
@@ -764,22 +800,31 @@ rodseth_xhn(x, h, n)
* 1 155
*
* The above distribution was found to hold fairly well over many values of
* odd h that are a multiple of 3 and for many values of n where h < 2^n.
* odd h that are also a multiple of 3 and for many values of n where h < 2^n.
*
* When h * 2^n-1 is prime and h is multiple of 3, a smallest v(1) that is
* even is extremely rate. Of the list of 127287 known primes of the form
* h*2^n-1 when h was a multiple of 3, none has an smallest v(1) that was even.
*
* About 1 out of 45000 cases when h is a multiple of 3 use v(1) > 99 as the
* smallest value of v(1).
*
* Given this information, when odd h is a multiple of 3 we try, in order,
* these values of X:
*
* 3, 5, 9, 11, 15, 17, 21, 29, 20, 27, 35, 36, 39, 41, 45, 32, 51, 44,
* 56, 49, 59, 57, 65, 55, 69, 71, 77, 81, 66, 95, 80, 67, 84, 99, 72,
* 74, 87, 90, 104, 101, 105, 109, 116, 111, 92
* 3, 5, 9, 11, 15, 17, 21, 29, 27, 35, 39, 41, 45, 51, 49, 59, 57,
* 65, 55, 69, 71, 77, 81, 95, 67, 99, 87
*
* And stop on the first value of X where:
*
* jacobi(X-2, h*2^n-1) == 1
* jacobi(X+2, h*2^n-1) == -1
*
* If no value in that list works, we start simple search starting with X = 120
* and incrementing by 1 until a value of X is found.
* About 1 out of 45000 cases when h is a multiple of 3 use V(1) > 99 as
* the smallest value of v(1).
*
* If no value in that list works, we start simple search starting with X = 101
* and incrementing by 2 until a value of X is found.
*
* The x_tbl[] matrix contains those common values of X to try in order.
* If all x_tbl_len fail to satisfy Ref4 condition 1, then we begin a
@@ -794,14 +839,13 @@ rodseth_xhn(x, h, n)
* v(1) for a given n when h is a multiple of 3. Skipping
* rarely used v(1) will not doom gen_v1() to a long search.
*/
x_tbl_len = 45;
x_tbl_len = 27;
mat x_tbl[x_tbl_len];
x_tbl = {
3, 5, 9, 11, 15, 17, 21, 29, 20, 27, 35, 36, 39, 41, 45, 32, 51, 44,
56, 49, 59, 57, 65, 55, 69, 71, 77, 81, 66, 95, 80, 67, 84, 99, 72,
74, 87, 90, 104, 101, 105, 109, 116, 111, 92
3, 5, 9, 11, 15, 17, 21, 29, 27, 35, 39, 41, 45, 51, 49, 59, 57, 65,
55, 69, 71, 77, 81, 95, 67, 99, 87
};
next_x = 120;
next_x = 101;
/*
* gen_v1 - compute the v(1) for a given h*2^n-1 if we can
@@ -956,8 +1000,8 @@ next_x = 120;
***
*
* input:
* h h as in h*2^n-1
* n n as in h*2^n-1
* h h as in h*2^n-1 (h must be odd >= 1)
* n n as in h*2^n-1 (must be >= 1)
*
* output:
* returns v(1), or -1 is there is no quick way
@@ -974,9 +1018,18 @@ gen_v1(h, n)
if (!isint(h)) {
quit "bad args: h must be an integer";
}
if (iseven(h)) {
quit "bad args: h must be an odd integer";
}
if (h < 1) {
quit "bad args: h must be an integer >= 1";
}
if (!isint(n)) {
quit "bad args: n must be an integer";
}
if (n < 1) {
quit "bad args: n must be an integer >= 1";
}
/*
* check for Case 1: (h mod 3 != 0)
@@ -1015,17 +1068,13 @@ gen_v1(h, n)
}
/*
* We are in that rare case (about 1 in 2 300 000) where none of the
* We are in that rare case (about 1 in 45 000) where none of the
* common X values satisfy Ref4 condition 1. We start a linear search
* at next_x from here on.
*
* However, we also need to keep in mind that when x+2 >= 257, we
* need to verify that gcd(x-2, h*2^n-1) == 1 and
* and to verify that gcd(x+2, h*2^n-1) == 1.
* of odd vules at next_x from here on.
*/
x = next_x;
while (rodseth_xhn(x, h, n) != 1) {
++x;
x += 2;
}
/* finally found a v(1) value */
ldebug("gen_v1", "h= " + str(h) + " n= " + str(n) +
@@ -1457,8 +1506,8 @@ legacy_d_qval[7] = 19; legacy_v1_qval[7] = 74; /* a=38 b=1 r=2 */
***
*
* input:
* h h as in h*2^n-1
* n n as in h*2^n-1
* h h as in h*2^n-1 (must be >= 1)
* n n as in h*2^n-1 (must be >= 1)
*
* output:
* returns v(1), or -1 is there is no quick way
@@ -1470,6 +1519,22 @@ legacy_gen_v1(h, n)
local val_mod; /* h*2^n-1 mod 'D' */
local i;
/*
* check arg types
*/
if (!isint(h)) {
quit "bad args: h must be an integer";
}
if (h < 1) {
quit "bad args: h must be an integer >= 1";
}
if (!isint(n)) {
quit "bad args: n must be an integer";
}
if (n < 1) {
quit "bad args: n must be an integer >= 1";
}
/*
* check for case 1
*/

2
custom/Makefile
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@@ -348,7 +348,7 @@ EXT=
# The default calc versions
#
VERSION= 2.12.6.0
VERSION= 2.12.6.1
# Names of shared libraries with versions
#

2
custom/Makefile.head
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@@ -348,7 +348,7 @@ EXT=
# The default calc versions
#
VERSION= 2.12.6.0
VERSION= 2.12.6.1
# Names of shared libraries with versions
#