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/* This script is part of radix_info.
Copyright (C) 2023 Adrien Hopkins
This program is free software: you can redistribute it and/or modify
it under the terms of version 3 of the GNU General Public License
as published by the Free Software Foundation.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
*/
package main
import (
"aphopkins/radix_info/factors"
"fmt"
"io"
"math"
"sort"
)
// FactorInfo contains all of the information this program
// calculates about a radix.
type factorInfo struct {
// The radix this info is about
Radix uint
// A representation of this radix as a product of prime numbers.
// Most of the important info about radices is determined through this.
PrimeFactorization factors.PrimeFactorization
// The radix's factors, in sorted order.
Factors []uint
// An estimate of the utility of the radix's factors.
Score float64
// The number of digits that are totatives (numbers that share no
// factors with the radix - they are the worst kind of digits)
Totient uint
// The fraction of digits that are totatives (numbers that share no
// factors with the radix - they are the worst kind of digits)
TotativeRatio float64
// The totative digits of this radix. May be nil if this was not requested.
TotativeDigits []uint32
// A rank measuring how well the radix works with the most elementary
// numbers and ratios
BasicRank string
// Whether or not this radix is part of any special factor-related classes.
// This is not calculated if the radix is too large - in this case
// this field will be nil.
Type factors.CompositenessType
// An estimate of the complexity of the radix's multiplication table.
// This is not calculated if the radix is too large - in this case
// this field will be nil.
MTC *uint64
// The radix's natural logarithm. This determines the length of numbers
// in this radix - higher Ln means numbers take up fewer digits.
// If c = log(a)/log(b), then numbers in radix b will be around
// c times longer than numbers in radix a.
Ln float64
// Information about each digit's compatibility with the radix.
// This determines what kind of decimal expansion the digit's
// reciprocoal has and what patterns are in its row of the multiplication
// table.
DigitMap []factors.DigitType
}
const (
// The maximum radix that will always be treated as normal
// (i.e. radix type and exact MTC will be calculated)
maxNormal = 1 << 16
// The max radix that will be treated as normal with -l
// above this, MTC can exceed the size of a uint64
maxExtended = 1 << 32
)
func getFactorInfo(a args) *factorInfo {
radix := a.Radix
r_factors := factors.Factors(radix)
sort.Slice(r_factors, func(i, j int) bool {
return r_factors[i] < r_factors[j]
})
var totativeDigits []uint32 = nil
if a.TotativeDigits && radix < maxExtended {
totativeDigits = factors.TotativeDigits(uint32(radix))
}
var mtc_ptr *uint64 = nil
if radix < maxNormal || (a.ExactMTCLarge && radix < maxExtended) {
mtc := factors.MTC(uint32(radix))
mtc_ptr = &mtc
}
var digitMap []factors.DigitType
if a.FullMap {
digitMap = make([]factors.DigitType, maxSmallRadix)
for d := 0; d < maxSmallRadix; d++ {
digitMap[d] = factors.GetDigitType(uint(d), radix)
}
} else if radix <= maxSmallRadix {
digitMap = factors.DigitMap(radix)
} else {
digitMap = []factors.DigitType{}
}
totativeCount := factors.Totient(radix)
totativeRatio := float64(totativeCount) / float64(radix)
return &factorInfo{radix, factors.PrimeFactorize(radix),
r_factors, factors.Score(radix), totativeCount, totativeRatio,
totativeDigits, factors.BasicRank(radix), factors.Type(radix),
mtc_ptr, math.Log(float64(radix)), digitMap}
}
func (fi *factorInfo) writeTo(w io.Writer) {
fmt.Fprintln(w, fi.Radix, "=", fi.PrimeFactorization)
fmt.Fprintln(w, "Factors:", fi.Factors)
fmt.Fprintf(w, "Factor Utility Score: %.4f\n", fi.Score)
fmt.Fprintf(w, "Regular Utility Score: %.4f\n",
float64(fi.Radix)/float64(fi.Totient))
fmt.Fprintln(w, "2345 Rank:", fi.BasicRank)
if fi.TotativeDigits != nil {
fmt.Fprintf(w, "Totative Digits: %v (%.3f%%)\n",
fi.TotativeDigits, fi.TotativeRatio*100.0)
} else {
fmt.Fprintf(w, "Totative Digit Count: %d (%.3f%%)\n",
fi.Totient, fi.TotativeRatio*100.0)
}
writeTypeMessage(w, fi.Type)
if fi.MTC != nil {
fmt.Fprintln(w, "Multiplication Table Complexity:", *fi.MTC)
} else {
low_mtc_est := float64(fi.Radix) * float64(fi.Totient-2)
high_mtc_est := float64(fi.Radix) * float64(fi.Radix-2)
fmt.Fprintf(w,
"Multiplication Table Complexity is between %.6g and %.6g.\n",
low_mtc_est, high_mtc_est)
}
fmt.Fprintf(w, "Natural Logarithm: %.3f\n", fi.Ln)
if len(fi.DigitMap) > 0 {
writeDigitMap(w, fi.DigitMap)
}
}
func (fi *factorInfo) writeToCompact(w io.Writer) {
fmt.Fprintf(w, "%d = %s | σ(r)/r: %.2f | r/φ(r): %.2f\n",
fi.Radix, fi.PrimeFactorization, fi.Score, 1/fi.TotativeRatio)
fmt.Fprintf(w, "%s | ", typeAbbrev(fi.Type))
if fi.MTC != nil {
fmt.Fprintf(w, "MTC: %d | ", *fi.MTC)
} else {
low_mtc_est := float32(fi.Radix) * float32(fi.Totient-2)
high_mtc_est := float32(fi.Radix) * float32(fi.Radix-2)
fmt.Fprintf(w, "%.4g ≤ MTC ≤ %.4g | ", low_mtc_est, high_mtc_est)
}
fmt.Fprintf(w, "ln: %.2f", fi.Ln)
fmt.Fprintln(w)
if len(fi.DigitMap) > 0 {
writeDigitMapCompact(w, fi.DigitMap)
}
}
func writeTypeMessage(w io.Writer, t factors.CompositenessType) {
switch t {
case factors.ColossallyAbundant:
fmt.Fprintln(w, "This radix is colossally abundant!")
case factors.Superabundant:
fmt.Fprintln(w, "This radix is superabundant.")
case factors.OrderedExponent:
fmt.Fprintln(w, "This radix has ordered exponents.")
case factors.Practical:
fmt.Fprintln(w, "This radix is practical.")
}
}
func typeAbbrev(t factors.CompositenessType) string {
switch t {
case factors.ColossallyAbundant:
return "Colossally Abundant"
case factors.Superabundant:
return "Superabundant"
case factors.OrderedExponent:
return "Ordered Exponents"
case factors.Practical:
return "Practical"
case factors.None:
return "Not Practical"
default:
panic("Should not be possible to get here.")
}
}
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