Square form factorization: Difference between revisions
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1537228672809128917 0 fail
4611686018427387877 343242169 13435662733
</pre>
=={{header|Wren}}==
{{libheader|Wren-long}}
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
This is based on the C code in the Wikipedia article and the FreeBASIC entry examples.
'0' is not actually an example here but is used by FreeBASIC to mark the end of the 'data' statement list so I've ignored that.
As Wren doesn't natively support unsigned 64-bit arithmetic, I've used the ULong class in the first above named for this task.
Even so, there are two examples which fail (1000000000000000127 and 1537228672809128917) because the code is unable to process enough 'multipliers' before an overflow situation is encountered. To deal with this, the program automatically switches to BigInt to process such cases.
This is still 6 times faster than processing the whole lot using BigInt.
<lang ecmascript>import "/long" for ULong
import "/big" for BigInt
import "/fmt" for Fmt
var multiplier = [
1, 3, 5, 7, 11, 3*5, 3*7, 3*11, 5*7, 5*11, 7*11, 3*5*7, 3*5*11, 3*7*11, 5*7*11, 3*5*7*11
]
var squfof = Fn.new { |N|
var s = N.isqrt
if (s*s == N) return s
for (k in 0...multiplier.count) {
var T = ULong
var n = N
if (n > T.largest/multiplier[k]) {
T = BigInt
n = BigInt.new(n.toString)
}
var D = n * multiplier[k]
var P = D.isqrt
var Pprev = P
var Po = Pprev
var Qprev = T.one
var Q = D - Po*Po
var L = ((s * 2).isqrt * 2).toSmall
var B = 3 * L
var i = 2
var b = T.zero
var q = T.zero
var r = T.zero
while (i < B) {
b = (Po + P) / Q
P = b * Q - P
q = Q
Q = Qprev + b * (Pprev - P)
r = Q.isqrt
if ((i & 1) == 0 && r*r == Q) break
Qprev = q
Pprev = P
i = i + 1
}
if (i < B) {
b = (Po - P) / r
Pprev = P = b*r + P
Qprev = r
Q = (D - Pprev*Pprev) / Qprev
i = 0
while (true) {
b = (Po + P) / Q
Pprev = P
P = b * Q - P
q = Q
Q = Qprev + b * (Pprev - P)
Qprev = q
i = i + 1
if (P == Pprev) break
}
r = T.gcd(n, Qprev)
if (r != T.one && r != n) return (r is ULong) ? r : ULong.new(r.toString)
}
}
return ULong.zero
}
var examples = [
"2501",
"12851",
"13289",
"75301",
"120787",
"967009",
"997417",
"7091569",
"13290059",
"42854447",
"223553581",
"2027651281",
"11111111111",
"100895598169",
"1002742628021",
"60012462237239",
"287129523414791",
"9007199254740931",
"11111111111111111",
"314159265358979323",
"384307168202281507",
"419244183493398773",
"658812288346769681",
"922337203685477563",
"1000000000000000127",
"1152921505680588799",
"1537228672809128917",
"4611686018427387877"
]
System.print("Integer Factor Quotient")
System.print("------------------------------------------")
for (example in examples) {
var N = ULong.new(example)
var fact = squfof.call(N)
var quot = (fact.isZero) ? "fail" : (N / fact).toString
Fmt.print("$-20s $-10s $s", N, fact, quot)
}</lang>
{{out}}
<pre>
Integer Factor Quotient
------------------------------------------
2501 61 41
12851 71 181
13289 137 97
75301 293 257
120787 43 2809
967009 1609 601
997417 257 3881
7091569 2663 2663
13290059 3119 4261
42854447 9689 4423
223553581 11213 19937
2027651281 46061 44021
11111111111 21649 513239
100895598169 112303 898423
1002742628021 0 fail
60012462237239 6862753 8744663
287129523414791 6059887 47381993
9007199254740931 10624181 847801751
11111111111111111 2071723 5363222357
314159265358979323 317213509 990371647
384307168202281507 415718707 924440401
419244183493398773 48009977 8732438749
658812288346769681 62222119 10588072199
922337203685477563 110075821 8379108103
1000000000000000127 111756107 8948056861
1152921505680588799 139001459 8294312261
1537228672809128917 26675843 57626245319
4611686018427387877 343242169 13435662733
</pre>
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