1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
// Copyright (c) 2011 jnml. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build ignore
// Let QRN be the number of quadratic residues of N. Let Q be QRN/N. From a
// sorted list of primorial products < 2^32 find "record breakers". "Record
// breaker" is N with new lowest Q.
//
// There are only 49 "record breakers" < 2^32.
//
// To run the example $ go run main.go
package main
import (
"fmt"
"math"
"sort"
"time"
"modernc.org/mathutil"
"modernc.org/sortutil"
)
func main() {
pp := mathutil.PrimorialProductsUint32(0, math.MaxUint32, 32)
sort.Sort(sortutil.Uint32Slice(pp))
var bestN, bestD uint32 = 1, 1
order, checks := 0, 0
var ixDirty uint32
m := make([]byte, math.MaxUint32>>3)
for _, n := range pp {
for i := range m[:ixDirty+1] {
m[i] = 0
}
ixDirty = 0
checks++
limit0 := mathutil.QScaleUint32(n, bestN, bestD)
if limit0 > math.MaxUint32 {
panic(0)
}
limit := uint32(limit0)
n64 := uint64(n)
hi := n64 >> 1
hits := uint32(0)
check := true
fmt.Printf("\r%10d %d/%d", n, checks, len(pp))
t0 := time.Now()
for i := uint64(0); i < hi; i++ {
sq := uint32(i * i % n64)
ix := sq >> 3
msk := byte(1 << (sq & 7))
if m[ix]&msk == 0 {
hits++
if hits >= limit {
check = false
break
}
}
m[ix] |= msk
if ix > ixDirty {
ixDirty = ix
}
}
adjPrime := ".." // Composite before
if mathutil.IsPrime(n - 1) {
adjPrime = "P." // Prime before
}
switch mathutil.IsPrime(n + 1) {
case true:
adjPrime += "P" // Prime after
case false:
adjPrime += "." // Composite after
}
if check && mathutil.QCmpUint32(hits, n, bestN, bestD) < 0 {
order++
d := time.Since(t0)
bestN, bestD = hits, n
q := float64(hits) / float64(n)
fmt.Printf(
"\r%2s #%03d %d %d %.2f %.2E %s %s %v\n",
adjPrime, order, n, hits,
1/q, q, d, time.Now().Format("15:04:05"), mathutil.FactorInt(n),
)
}
}
}
|
