Four is magic
You are encouraged to solve this task according to the task description, using any language you may know.
 Task
Write a subroutine, function, whatever it may be called in your language, that takes an integer number and returns an English text sequence starting with the English cardinal representation of that integer, the word 'is' and then the English cardinal representation of the count of characters that made up the first word, followed by a comma.
Continue the sequence by using the previous count word as the first word of the next phrase, append 'is' and the cardinal count of the letters in that word.
Continue until you reach four. Since four has four characters, finish by adding the words 'four is magic' and a period. All integers will eventually wind up at four.
For instance, suppose your are given the integer 3. Convert 3 to Three, add is , then the cardinal character count of three, or five, with a comma to separate if from the next phrase. Continue the sequence five is four, (five has four letters), and finally, four is magic.
Three is five, five is four, four is magic.
For reference, here are outputs for 0 through 9.
Zero is four, four is magic. One is three, three is five, five is four, four is magic. Two is three, three is five, five is four, four is magic. Three is five, five is four, four is magic. Four is magic. Five is four, four is magic. Six is three, three is five, five is four, four is magic. Seven is five, five is four, four is magic. Eight is five, five is four, four is magic. Nine is four, four is magic.
 Some task guidelines

 You may assume the input will only contain integer numbers.
 Cardinal numbers between 20 and 100 may use either hyphens or spaces as word separators but they must use a word separator. (23 is twenty three or twentythree not twentythree.)
 Cardinal number conversions should follow the English short scale. (billion is 1e9, trillion is 1e12, etc.)
 Cardinal numbers should not include commas. (20140 is twenty thousand one hundred forty not twenty thousand, one hundred forty.)
 When converted to a string, 100 should be one hundred, not a hundred or hundred, 1000 should be one thousand, not a thousand or thousand.
 When converted to a string, there should be no and in the cardinal string. 130 should be one hundred thirty not one hundred and thirty.
 When counting characters, count all of the characters in the cardinal number including spaces and hyphens. One hundred fiftyone should be 21 not 18.
 The output should follow the format "N is K, K is M, M is ... four is magic." (unless the input is 4, in which case the output should simply be "four is magic.")
 The output can either be the return value from the function, or be displayed from within the function.
 You are encouraged, though not mandated to use proper sentence capitalization.
 You may optionally support negative numbers. 7 is negative seven.
 Show the output here for a small representative sample of values, at least 5 but no more than 25. You are free to choose which which numbers to use for output demonstration.
You can choose to use a library, (module, external routine, whatever) to do the cardinal conversions as long as the code is easily and freely available to the public.
If you roll your own, make the routine accept at minimum any integer from 0 up to 999999. If you use a premade library, support at least up to unsigned 64 bit integers. (or the largest integer supported in your language if it is less.)
Four is magic is a popular codegolf task. This is not code golf. Write legible, idiomatic and well formatted code.
 Related tasks
Contents
AWK[edit]
# syntax: GAWK f FOUR_IS_MAGIC.AWK
BEGIN {
init_numtowords()
n = split("1 0 1 2 3 4 5 6 7 8 9 11 21 1995 1000000 1234567890 1100100100100",arr," ")
for (i=1; i<=n; i++) {
a = arr[i]
printf("%s: ",a)
do {
if (a == 4) {
break
}
a = numtowords(a)
b = numtowords(length(a))
printf("%s is %s, ",a,b)
a = length(a)
} while (b !~ /^four$/)
printf("four is magic.\n")
}
exit(0)
}
# source: The AWK Programming Language, page 75
function numtowords(n, minus,str) {
if (n < 0) {
n = n * 1
minus = "minus "
}
if (n == 0) {
str = "zero"
}
else {
str = intowords(n)
}
gsub(/ /," ",str)
gsub(/ $/,"",str)
return(minus str)
}
function intowords(n) {
n = int(n)
if (n >= 1000000000000) {
return intowords(n/1000000000000) " trillion " intowords(n%1000000000000)
}
if (n >= 1000000000) {
return intowords(n/1000000000) " billion " intowords(n%1000000000)
}
if (n >= 1000000) {
return intowords(n/1000000) " million " intowords(n%1000000)
}
if (n >= 1000) {
return intowords(n/1000) " thousand " intowords(n%1000)
}
if (n >= 100) {
return intowords(n/100) " hundred " intowords(n%100)
}
if (n >= 20) {
return tens[int(n/10)] " " intowords(n%10)
}
return(nums[n])
}
function init_numtowords() {
split("one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen",nums," ")
split("ten twenty thirty forty fifty sixty seventy eighty ninety",tens," ")
}
 Output:
1: minus one is nine, nine is four, four is magic. 0: zero is four, four is magic. 1: one is three, three is five, five is four, four is magic. 2: two is three, three is five, five is four, four is magic. 3: three is five, five is four, four is magic. 4: four is magic. 5: five is four, four is magic. 6: six is three, three is five, five is four, four is magic. 7: seven is five, five is four, four is magic. 8: eight is five, five is four, four is magic. 9: nine is four, four is magic. 11: eleven is six, six is three, three is five, five is four, four is magic. 21: twenty one is ten, ten is three, three is five, five is four, four is magic. 1995: one thousand nine hundred ninety five is thirty seven, thirty seven is twelve, twelve is six, six is three, three is five, five is four, four is magic. 1000000: one million is eleven, eleven is six, six is three, three is five, five is four, four is magic. 1234567890: one billion two hundred thirty four million five hundred sixty seven thousand eight hundred ninety is ninety eight, ninety eight is twelve, twelve is six, six is three, three is five, five is four, four is magic. 1100100100100: one trillion one hundred billion one hundred million one hundred thousand one hundred is eighty five, eighty five is eleven, eleven is six, six is three, three is five, five is four, four is magic.
F#[edit]
The Function[edit]
//Express an Integer in English Language. Nigel Galloway: September 19th., 2018
let fN=[["";"one";"two";"three";"four";"five";"six";"seven";"eight";"nine"];
["ten";"eleven";"twelve";"thirteen";"fourteen";"fifteen";"sixteen";"seventeen";"eighteen";"nineteen"];
["";"";"twenty";"thirty";"fourty";"fifty";"sixty";"seventy";"eighty";"ninety"]]
let rec I2α α β=match α with α when α<20 >β+fN.[α/10].[α%10]
α when α<100 >I2α (α%10) (β+fN.[2].[α/10]+if α%10>0 then " " else "")
α when α<1000 >I2α (α(α/100)*100) (β+fN.[0].[α/100]+" hunred"+if α%100>0 then " and " else "")
α when α<1000000>I2α (α%1000) (β+(I2α (α/1000) "")+" thousand"+if α%100=0 then "" else if (α(α/1000)*1000)<100 then " and " else " ")
The Task[edit]
let rec printI2α=function 0>printf "naught>"; printI2α 6
4>printfn "four is magic"
n when n<0>let g = I2α n "minus " in printf "%s>" g; printI2α (g.Length)
n >let g = I2α n "" in printf "%s>" g; printI2α (g.Length)
let N=System.Random()
List.init 25 (fun _>N.Next 999999) > List.iter printI2α
 Output:
seven hundred and fifty thousand nine hundred and eighty eight>sixty>five>four is magic nine hundred and fifty four thousand two hundred and twenty two>sixty one>nine>four is magic three hundred and seventy two thousand nine hundred and thirty one>sixty four>ten>three>five>four is magic six hundred and three thousand six hundred and eighteen>fifty three>eleven>six>three>five>four is magic two hundred and forty nine thousand three hundred and eighty eight>sixty five>ten>three>five>four is magic four hundred and sixty two thousand four hundred and ninety nine>sixty two>nine>four is magic six hundred and fifty thousand eight hundred and seventy five>fifty nine>ten>three>five>four is magic six hundred and ninety three thousand two hundred and seventy nine>sixty four>ten>three>five>four is magic one hundred and thirty three thousand four hundred and seventy six>sixty four>ten>three>five>four is magic seven hundred and thirty two thousand nine hundred and fifteen>sixty>five>four is magic seven hundred and seven thousand five hundred and forty one>fifty eight>eleven>six>three>five>four is magic twenty five thousand six hundred and two>thirty nine>eleven>six>three>five>four is magic seven hundred and sixty nine thousand two hundred and sixty four>sixty two>nine>four is magic eight hundred and ninety five thousand eight hundred and two>fifty eight>eleven>six>three>five>four is magic four hundred and eleven thousand one hundred and four>fifty one>nine>four is magic four hundred and ninety five thousand eight hundred and eighty one>sixty four>ten>three>five>four is magic six hundred and fifty six thousand one hundred and eighty seven>sixty one>nine>four is magic five hundred and twenty two thousand seven hundred and fifty>fifty eight>eleven>six>three>five>four is magic three hundred and forty four thousand and ninety two>fifty two>nine>four is magic three hundred and forty one thousand seven hundred and forty four>sixty five>ten>three>five>four is magic eight hundred and eighty four thousand two hundred and fifty>fifty eight>eleven>six>three>five>four is magic six hundred and forty thousand seven hundred and sixteen>fifty five>ten>three>five>four is magic six hundred and eight thousand three hundred and five>fifty one>nine>four is magic three hundred and ninety nine thousand two hundred and sixty eight>sixty four>ten>three>five>four is magic six hundred and ninety two thousand two hundred and seventy five>sixty two>nine>four is magic
Some particular values:
printI2α 0 > naught>six>three>five>four is magic printI2α 4 > four is magic printI2α 999999 > nine hundred and ninety nine thousand nine hundred and ninety nine>sixty four>ten>three>five>four is magic printI2α 23 > minus twenty three>eighteen>eight>five>four is magic
Factor[edit]
Factor's math.text.english
vocabulary does most of the heavy lifting. Since number>text
produces " and " and "," in its output, they are removed with a regular expression.
USING: ascii formatting io kernel make math.text.english regexp
sequences ;
IN: rosettacode.fourismagic
! Strip " and " and "," from the output of Factor's number>text
! word with a regular expression.
: number>english ( n  str )
number>text R/ and ,/ "" rereplace ;
! Return the length of the input integer's text form.
! e.g. 1 > 3
: nextlen ( n  m ) number>english length ;
! Given a starting integer, return the sequence of lengths
! terminating with 4.
! e.g. 1 > { 1 3 5 4 }
: lenchain ( n  seq )
[ [ dup 4 = ] [ dup , nextlen ] until , ] { } make ;
! Convert a nonfour number to its phrase form.
! e.g. 6 > "six is three, "
: nonfour ( n  str )
number>english dup length number>english
"%s is %s, " sprintf ;
! Convert any number to its phrase form.
! e.g. 4 > "four is magic."
: phrase ( n  str )
dup 4 = [ drop "four is magic." ] [ nonfour ] if ;
: saymagic ( n  )
lenchain [ phrase ] map concat capitalize print ;
{ 1 4 11 100 112719908181724 612312 } [ saymagic ] each
 Output:
One is three, three is five, five is four, four is magic. Four is magic. Negative eleven is fifteen, fifteen is seven, seven is five, five is four, four is magic. One hundred is eleven, eleven is six, six is three, three is five, five is four, four is magic. One hundred twelve trillion seven hundred nineteen billion nine hundred eight million one hundred eightyone thousand seven hundred twentyfour is one hundred fortythree, one hundred fortythree is twentythree, twentythree is twelve, twelve is six, six is three, three is five, five is four, four is magic. Negative six hundred twelve thousand three hundred twelve is fiftyseven, fiftyseven is eleven, eleven is six, six is three, three is five, five is four, four is magic.
Go[edit]
Uses the say
function from the
Number names task.
package main
import (
"fmt"
"math"
"strings"
)
func main() {
for _, n := range [...]int64{
0, 4, 6, 11, 13, 75, 100, 337, 164,
math.MaxInt64,
} {
fmt.Println(fourIsMagic(n))
}
}
func fourIsMagic(n int64) string {
s := say(n)
s = strings.ToUpper(s[:1]) + s[1:]
t := s
for n != 4 {
n = int64(len(s))
s = say(n)
t += " is " + s + ", " + s
}
t += " is magic."
return t
}
// Following is from https://rosettacode.org/wiki/Number_names#Go
var small = [...]string{"zero", "one", "two", "three", "four", "five", "six",
"seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen",
"fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"}
var tens = [...]string{"", "", "twenty", "thirty", "forty",
"fifty", "sixty", "seventy", "eighty", "ninety"}
var illions = [...]string{"", " thousand", " million", " billion",
" trillion", " quadrillion", " quintillion"}
func say(n int64) string {
var t string
if n < 0 {
t = "negative "
// Note, for math.MinInt64 this leaves n negative.
n = n
}
switch {
case n < 20:
t += small[n]
case n < 100:
t += tens[n/10]
s := n % 10
if s > 0 {
t += "" + small[s]
}
case n < 1000:
t += small[n/100] + " hundred"
s := n % 100
if s > 0 {
t += " " + say(s)
}
default:
// work righttoleft
sx := ""
for i := 0; n > 0; i++ {
p := n % 1000
n /= 1000
if p > 0 {
ix := say(p) + illions[i]
if sx != "" {
ix += " " + sx
}
sx = ix
}
}
t += sx
}
return t
}
 Output:
Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. One hundred is eleven, eleven is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Nine quintillion two hundred twentythree quadrillion three hundred seventytwo trillion thirtysix billion eight hundred fiftyfour million seven hundred seventyfive thousand eight hundred seven is one hundred ninetysix, one hundred ninetysix is twentytwo, twentytwo is ten, ten is three, three is five, five is four, four is magic.
J[edit]
names =. 'one';'two';'three';'four';'five';'six';'seven';'eight';'nine';'ten';'eleven';'twelve';'thirteen';'fourteen';'fifteen';'sixteen';'seventeen';'eighteen';'nineteen'
tens =. '';'twenty';'thirty';'forty';'fifty';'sixty';'seventy';'eighty';'ninety'
NB. selects the xth element from list y
lookup =: >@{:@{.
NB. string formatting
addspace =: ((' '"_, ]) ` ]) @. (<&0 @ {: @ $)
NB. numbers in range 1 to 19
s1 =: lookup&names
NB. numbers in range 20 to 99
s2d=: (lookup&tens @ <. @ %&10) , addspace @ (s1 @ (10&))
NB. numbers in range 100 to 999
s3d =: s1 @ (<[email protected]%&100), ' hundred', addspace @ s2d @ (100&)
NB. numbers in range 1 to 999
s123d =: s1 ` s2d ` s3d @. (>& 19 + >&99)
NB. numbers in range 1000 to 999999
s456d =: (s123d @<[email protected]%&1000), ' thousand', addspace @ s123d @ (1000&)
NB. stringify numbers in range 1 to 999999
stringify =: s123d ` s456d @. (>&999)
NB. takes an int and returns an int of the length of the string of the input
lengthify =: {: @ $ @ stringify
NB. determines the string that should go after ' is '
what =: ((stringify @ lengthify), (', '"_)) ` ('magic'"_) @. (=&4)
runonce =: stringify , ' is ', what
run =: runonce, ((run @ lengthify) ` (''"_) @. (=&4))
doall =: run"0
inputs =: 4 8 16 25 89 365 2586 25865 369854
doall inputs
 Output:
four is magic eight is five, five is four, four is magic sixteen is seven, seven is five, five is four, four is magic twenty five is eleven, eleven is six, six is three, three is five, five is four, four is magic eighty nine is eleven, eleven is six, six is three, three is five, five is four, four is magic three hundred sixty five is twenty four, twenty four is eleven, eleven is six, six is three, three is five, five is four, four is magic two thousand five hundred eighty six is thirty six, thirty six is ten, ten is three, three is five, five is four, four is magic twenty five thousand eight hundred sixty five is forty five, forty five is ten, ten is three, three is five, five is four, four is magic three hundred sixty nine thousand eight hundred fifty four is fifty eight, fifty eight is eleven, eleven is six, six is three, three is five, five is four, four is magic
Kotlin[edit]
This uses the code I wrote for the Number names task, appropriately adjusted to deal with this task. Input is limited to signed 64 bit integers as Kotlin doesn't currently support unsigned types.
// version 1.1.43
val names = mapOf(
1 to "one",
2 to "two",
3 to "three",
4 to "four",
5 to "five",
6 to "six",
7 to "seven",
8 to "eight",
9 to "nine",
10 to "ten",
11 to "eleven",
12 to "twelve",
13 to "thirteen",
14 to "fourteen",
15 to "fifteen",
16 to "sixteen",
17 to "seventeen",
18 to "eighteen",
19 to "nineteen",
20 to "twenty",
30 to "thirty",
40 to "forty",
50 to "fifty",
60 to "sixty",
70 to "seventy",
80 to "eighty",
90 to "ninety"
)
val bigNames = mapOf(
1_000L to "thousand",
1_000_000L to "million",
1_000_000_000L to "billion",
1_000_000_000_000L to "trillion",
1_000_000_000_000_000L to "quadrillion",
1_000_000_000_000_000_000L to "quintillion"
)
fun numToText(n: Long): String {
if (n == 0L) return "zero"
val neg = n < 0L
val maxNeg = n == Long.MIN_VALUE
var nn = if (maxNeg) (n + 1) else if (neg) n else n
val digits3 = IntArray(7)
for (i in 0..6) { // split number into groups of 3 digits from the right
digits3[i] = (nn % 1000).toInt()
nn /= 1000
}
fun threeDigitsToText(number: Int) : String {
val sb = StringBuilder()
if (number == 0) return ""
val hundreds = number / 100
val remainder = number % 100
if (hundreds > 0) {
sb.append(names[hundreds], " hundred")
if (remainder > 0) sb.append(" ")
}
if (remainder > 0) {
val tens = remainder / 10
val units = remainder % 10
if (tens > 1) {
sb.append(names[tens * 10])
if (units > 0) sb.append("", names[units])
}
else sb.append(names[remainder])
}
return sb.toString()
}
val strings = Array<String>(7) { threeDigitsToText(digits3[it]) }
var text = strings[0]
var big = 1000L
for (i in 1..6) {
if (digits3[i] > 0) {
var text2 = strings[i] + " " + bigNames[big]
if (text.length > 0) text2 += " "
text = text2 + text
}
big *= 1000
}
if (maxNeg) text = text.dropLast(5) + "eight"
if (neg) text = "negative " + text
return text
}
fun fourIsMagic(n: Long): String {
if (n == 4L) return "Four is magic."
var text = numToText(n).capitalize()
val sb = StringBuilder()
while (true) {
val len = text.length.toLong()
if (len == 4L) return sb.append("$text is four, four is magic.").toString()
val text2 = numToText(len)
sb.append("$text is $text2, ")
text = text2
}
}
fun main(args: Array<String>) {
val la = longArrayOf(0, 4, 6, 11, 13, 75, 100, 337, 164, 9_223_372_036_854_775_807L)
for (i in la) {
println(fourIsMagic(i))
println()
}
}
 Output:
Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. One hundred is eleven, eleven is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Nine quintillion two hundred twentythree quadrillion three hundred seventytwo trillion thirtysix billion eight hundred fiftyfour million seven hundred seventyfive thousand eight hundred seven is one hundred ninetysix, one hundred ninetysix is twentytwo, twentytwo is ten, ten is three, three is five, five is four, four is magic.
Perl[edit]
use Lingua::EN::Numbers qw(num2en);
sub cardinal {
my($n) = @_;
(my $en = num2en($n)) =~ s/\ and,//g;
$en;
}
sub magic {
my($int) = @_;
my $str;
while () {
$str .= cardinal($int) . " is ";
if ($int == 4) {
$str .= "magic.\n";
last
} else {
$int = length cardinal($int);
$str .= cardinal($int) . ", ";
}
}
ucfirst $str;
}
print magic($_) for 0, 4, 6, 11, 13, 75, 337, 164, 9_876_543_209;
 Output:
Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Nine billion eight hundred seventysix million five hundred fortythree thousand two hundred nine is ninetyseven, ninetyseven is twelve, twelve is six, six is three, three is five, five is four, four is magic.
Perl 6[edit]
Lingua::EN::Numbers::Cardinal module available from the Perl 6 ecosystem.
use Lingua::EN::Numbers::Cardinal;
sub card ($n) { cardinal($n).subst(/','/, '', :g) }
sub magic (Int $int is copy) {
my $string;
loop {
$string ~= "{ card($int) } is ";
if $int = ($int == 4) ?? 0 !! card($int).chars {
$string ~= "{ card($int) }, "
} else {
$string ~= "magic.\n";
last
}
}
$string.tc
}
.&magic.say for 0, 4, 6, 11, 13, 75, 337, 164, 9876543209, 2**256;
 Output:
Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Nine billion eight hundred seventysix million five hundred fortythree thousand two hundred nine is ninetyseven, ninetyseven is twelve, twelve is six, six is three, three is five, five is four, four is magic. One hundred fifteen quattuorvigintillion seven hundred ninetytwo trevigintillion eightynine duovigintillion two hundred thirtyseven unvigintillion three hundred sixteen vigintillion one hundred ninetyfive novemdecillion four hundred twentythree octodecillion five hundred seventy septendecillion nine hundred eightyfive sexdecillion eight quindecillion six hundred eightyseven quattuordecillion nine hundred seven tredecillion eight hundred fiftythree duodecillion two hundred sixtynine undecillion nine hundred eightyfour decillion six hundred sixtyfive nonillion six hundred forty octillion five hundred sixtyfour septillion thirtynine sextillion four hundred fiftyseven quintillion five hundred eightyfour quadrillion seven trillion nine hundred thirteen billion one hundred twentynine million six hundred thirtynine thousand nine hundred thirtysix is eight hundred sixtynine, eight hundred sixtynine is twentyfour, twentyfour is eleven, eleven is six, six is three, three is five, five is four, four is magic.
Phix[edit]
Note that on 32bit Phix integers/atoms are only accurate to 9,007,199,254,740,992 (a hardware limit of 64bit floating point registers) so if you need more than that this will need to be reworked to use bigatoms.
<adapted from demo\rosetta\number_names.exw, which alas outputs ",", "and", uses "minus" instead of "negative", etc...>
constant twenties = {"zero","one","two","three","four","five","six","seven","eight","nine","ten",
"eleven","twelve","thirteen","fourteen","fifteen","sixteen","seventeen","eighteen","nineteen"},
decades = {"twenty","thirty","forty","fifty","sixty","seventy","eighty","ninety"}
function hundred(integer n)
if n<20 then
return twenties[mod(n,20)+1]
elsif mod(n,10)=0 then
return decades[mod(floor(n/10),10)1]
end if
return decades[mod(floor(n/10),10)1] & '' & twenties[mod(n,10)+1]
end function
function thousand(integer n)
if n<100 then
return hundred(n)
elsif mod(n,100)=0 then
return twenties[mod(floor(n/100),20)+1]&" hundred"
end if
return twenties[mod(floor(n/100),20)+1] & " hundred " & hundred(mod(n,100))
end function
constant orders = {{power(10,12),"trillion"},
{power(10,9),"billion"},
{power(10,6),"million"},
{power(10,3),"thousand"}}
function triplet(integer n)
atom order, high, low
string name, res = ""
for i=1 to length(orders) do
{order,name} = orders[i]
high = floor(n/order)
low = mod(n,order)
if high!=0 then
res &= thousand(high)&' '&name
end if
n = low
if low=0 then exit end if
if length(res) and high!=0 then
res &= " "
end if
end for
if n!=0 or res="" then
res &= thousand(floor(n))
end if
return res
end function
function spell(integer n)
string res = ""
if n<0 then
res = "negative "
n = n
end if
res &= triplet(n)
return res
end function
</adapted from number_names.exw>
function fourIsMagic(atom n)
string s = spell(n)
s[1] = upper(s[1])
string t = s
while n!=4 do
n = length(s)
s = spell(n)
t &= " is " & s & ", " & s
end while
t &= " is magic.\n"
return t
end function
constant tests = {7, 1, 0, 1, 2, 3, 4, 23, 1e9, 20140, 100, 130, 151, 999999}
for i=1 to length(tests) do
puts(1,fourIsMagic(tests[i]))
end for
 Output:
Negative seven is fourteen, fourteen is eight, eight is five, five is four, four is magic. Negative one is twelve, twelve is six, six is three, three is five, five is four, four is magic. Zero is four, four is magic. One is three, three is five, five is four, four is magic. Two is three, three is five, five is four, four is magic. Three is five, five is four, four is magic. Four is magic. Twentythree is twelve, twelve is six, six is three, three is five, five is four, four is magic. One billion is eleven, eleven is six, six is three, three is five, five is four, four is magic. Twenty thousand one hundred forty is thirtythree, thirtythree is twelve, twelve is six, six is three, three is five, five is four, four is magic. One hundred is eleven, eleven is six, six is three, three is five, five is four, four is magic. One hundred thirty is eighteen, eighteen is eight, eight is five, five is four, four is magic. One hundred fiftyone is twentyone, twentyone is ten, ten is three, three is five, five is four, four is magic. Nine hundred ninetynine thousand nine hundred ninetynine is fiftyeight, fiftyeight is eleven, eleven is six, six is three, three is five, five is four, four is magic.
Python[edit]
Python 3 version. Should work for integers up to at least 10^3003. It can be extended easily to arbitrary integers by adding to the numbers dict.
import random
from collections import OrderedDict
numbers = { # taken from https://en.wikipedia.org/wiki/Names_of_large_numbers#cite_refa_143
1: 'one',
2: 'two',
3: 'three',
4: 'four',
5: 'five',
6: 'six',
7: 'seven',
8: 'eight',
9: 'nine',
10: 'ten',
11: 'eleven',
12: 'twelve',
13: 'thirteen',
14: 'fourteen',
15: 'fifteen',
16: 'sixteen',
17: 'seventeen',
18: 'eighteen',
19: 'nineteen',
20: 'twenty',
30: 'thirty',
40: 'forty',
50: 'fifty',
60: 'sixty',
70: 'seventy',
80: 'eighty',
90: 'ninety',
100: 'hundred',
1000: 'thousand',
10 ** 6: 'million',
10 ** 9: 'billion',
10 ** 12: 'trillion',
10 ** 15: 'quadrillion',
10 ** 18: 'quintillion',
10 ** 21: 'sextillion',
10 ** 24: 'septillion',
10 ** 27: 'octillion',
10 ** 30: 'nonillion',
10 ** 33: 'decillion',
10 ** 36: 'undecillion',
10 ** 39: 'duodecillion',
10 ** 42: 'tredecillion',
10 ** 45: 'quattuordecillion',
10 ** 48: 'quinquadecillion',
10 ** 51: 'sedecillion',
10 ** 54: 'septendecillion',
10 ** 57: 'octodecillion',
10 ** 60: 'novendecillion',
10 ** 63: 'vigintillion',
10 ** 66: 'unvigintillion',
10 ** 69: 'duovigintillion',
10 ** 72: 'tresvigintillion',
10 ** 75: 'quattuorvigintillion',
10 ** 78: 'quinquavigintillion',
10 ** 81: 'sesvigintillion',
10 ** 84: 'septemvigintillion',
10 ** 87: 'octovigintillion',
10 ** 90: 'novemvigintillion',
10 ** 93: 'trigintillion',
10 ** 96: 'untrigintillion',
10 ** 99: 'duotrigintillion',
10 ** 102: 'trestrigintillion',
10 ** 105: 'quattuortrigintillion',
10 ** 108: 'quinquatrigintillion',
10 ** 111: 'sestrigintillion',
10 ** 114: 'septentrigintillion',
10 ** 117: 'octotrigintillion',
10 ** 120: 'noventrigintillion',
10 ** 123: 'quadragintillion',
10 ** 153: 'quinquagintillion',
10 ** 183: 'sexagintillion',
10 ** 213: 'septuagintillion',
10 ** 243: 'octogintillion',
10 ** 273: 'nonagintillion',
10 ** 303: 'centillion',
10 ** 306: 'uncentillion',
10 ** 309: 'duocentillion',
10 ** 312: 'trescentillion',
10 ** 333: 'decicentillion',
10 ** 336: 'undecicentillion',
10 ** 363: 'viginticentillion',
10 ** 366: 'unviginticentillion',
10 ** 393: 'trigintacentillion',
10 ** 423: 'quadragintacentillion',
10 ** 453: 'quinquagintacentillion',
10 ** 483: 'sexagintacentillion',
10 ** 513: 'septuagintacentillion',
10 ** 543: 'octogintacentillion',
10 ** 573: 'nonagintacentillion',
10 ** 603: 'ducentillion',
10 ** 903: 'trecentillion',
10 ** 1203: 'quadringentillion',
10 ** 1503: 'quingentillion',
10 ** 1803: 'sescentillion',
10 ** 2103: 'septingentillion',
10 ** 2403: 'octingentillion',
10 ** 2703: 'nongentillion',
10 ** 3003: 'millinillion'
}
numbers = OrderedDict(sorted(numbers.items(), key=lambda t: t[0], reverse=True))
def string_representation(i: int) > str:
"""
Return the english string representation of an integer
"""
if i == 0:
return 'zero'
words = ['negative'] if i < 0 else []
working_copy = abs(i)
for key, value in numbers.items():
if key <= working_copy:
times = int(working_copy / key)
if key >= 100:
words.append(string_representation(times))
words.append(value)
working_copy = times * key
if working_copy == 0:
break
return ' '.join(words)
def next_phrase(i: int):
"""
Generate all the phrases
"""
while not i == 4: # Generate phrases until four is reached
str_i = string_representation(i)
len_i = len(str_i)
yield str_i, 'is', string_representation(len_i)
i = len_i
# the last phrase
yield string_representation(i), 'is', 'magic'
def magic(i: int) > str:
phrases = []
for phrase in next_phrase(i):
phrases.append(' '.join(phrase))
return f'{", ".join(phrases)}.'.capitalize()
if __name__ == '__main__':
for j in (random.randint(0, 10 ** 3) for i in range(5)):
print(j, ':\n', magic(j), '\n')
for j in (random.randint(10 ** 24, 10 ** 24) for i in range(2)):
print(j, ':\n', magic(j), '\n')
 Output:
475 : Four hundred seventy five is twenty five, twenty five is eleven, eleven is six, six is three, three is five, five is four, four is magic. 968 : Nine hundred sixty eight is twenty four, twenty four is eleven, eleven is six, six is three, three is five, five is four, four is magic. 304 : Three hundred four is eighteen, eighteen is eight, eight is five, five is four, four is magic. 544 : Five hundred forty four is twenty three, twenty three is twelve, twelve is six, six is three, three is five, five is four, four is magic. 394 : Three hundred ninety four is twenty five, twenty five is eleven, eleven is six, six is three, three is five, five is four, four is magic. 49587779907680717664396 : Negative forty nine sextillion five hundred eighty seven quintillion seven hundred seventy nine quadrillion nine hundred seven trillion six hundred eighty billion seven hundred seventeen million six hundred sixty four thousand three hundred ninety six is two hundred fifty one, two hundred fifty one is twenty one, twenty one is ten, ten is three, three is five, five is four, four is magic. 874143425855745733896030 : Eight hundred seventy four sextillion one hundred forty three quintillion four hundred twenty five quadrillion eight hundred fifty five trillion seven hundred forty five billion seven hundred thirty three million eight hundred ninety six thousand thirty is two hundred fifty three, two hundred fifty three is twenty three, twenty three is twelve, twelve is six, six is three, three is five, five is four, four is magic.
Racket[edit]
#lang racket
(define numbernames
(list "zero" "one" "two" "three" "four" "five" "six" "seven" "eight" "nine" "ten" "eleven" "twelve"
"thirteen" "fourteen" "fifteen" "sixteen" "seventeen" "eighteen" "nineteen"))
(define numbersalist
'((20 . twenty)
(30 . thirty)
(40 . forty)
(50 . fifty)
(60 . sixty)
(70 . seventy)
(80 . eighty)
(90 . ninety)
(100 . hundred)
(1000 . thousand)
(#e1E6 . million)
(#e1E9 . billion)
(#e1E12 . trillion)
(#e1E15 . quadrillion)
(#e1E18 . quintillion)
(#e1E21 . sextillion)
(#e1E24 . septillion)
(#e1E27 . octillion)
(#e1E30 . nonillion)
(#e1E33 . decillion)
(#e1E36 . undecillion)
(#e1E39 . duodecillion)
(#e1E42 . tredecillion)
(#e1E45 . quattuordecillion)
(#e1E48 . quinquadecillion)
(#e1E51 . sedecillion)
(#e1E54 . septendecillion)
(#e1E57 . octodecillion)
(#e1E60 . novendecillion)
(#e1E63 . vigintillion)
(#e1E66 . unvigintillion)
(#e1E69 . duovigintillion)
(#e1E72 . tresvigintillion)
(#e1E75 . quattuorvigintillion)
(#e1E78 . quinquavigintillion)
(#e1E81 . sesvigintillion)
(#e1E84 . septemvigintillion)
(#e1E87 . octovigintillion)
(#e1E90 . novemvigintillion)
(#e1E93 . trigintillion)
(#e1E96 . untrigintillion)
(#e1E99 . duotrigintillion)
(#e1E102 . trestrigintillion)
(#e1E105 . quattuortrigintillion)
(#e1E108 . quinquatrigintillion)
(#e1E111 . sestrigintillion)
(#e1E114 . septentrigintillion)
(#e1E117 . octotrigintillion)
(#e1E120 . noventrigintillion)
(#e1E123 . quadragintillion)
(#e1E153 . quinquagintillion)
(#e1E183 . sexagintillion)
(#e1E213 . septuagintillion)
(#e1E243 . octogintillion)
(#e1E273 . nonagintillion)
(#e1E303 . centillion)
(#e1E306 . uncentillion)
(#e1E309 . duocentillion)
(#e1E312 . trescentillion)
(#e1E333 . decicentillion)
(#e1E336 . undecicentillion)
(#e1E363 . viginticentillion)
(#e1E366 . unviginticentillion)
(#e1E393 . trigintacentillion)
(#e1E423 . quadragintacentillion)
(#e1E453 . quinquagintacentillion)
(#e1E483 . sexagintacentillion)
(#e1E513 . septuagintacentillion)
(#e1E543 . octogintacentillion)
(#e1E573 . nonagintacentillion)
(#e1E603 . ducentillion)
(#e1E903 . trecentillion)
(#e1E1203 . quadringentillion)
(#e1E1503 . quingentillion)
(#e1E1803 . sescentillion)
(#e1E2103 . septingentillion)
(#e1E2403 . octingentillion)
(#e1E2703 . nongentillion)
(#e1E3003 . millinillion)))
(define (number>words n)
(define (n>list n acc)
(define (nameof n) (symbol>string(cdr (assoc n numbersalist))))
(define (consname n) (cons (nameof n) acc))
(cond
[(and (zero? n) (pair? acc)) (reverse acc)]
[(< n 20) (reverse (list (listref numbernames n)))]
[(< n 100) (letvalues (([q r] (quotient/remainder n 10))) (n>list r (consname (* q 10))))]
[else (let*values
(([val] (argmax values (filtermap (compose (λ (val) (and (< val n) val)) car) numbersalist)))
([q r] (quotient/remainder n val)))
(n>list r (append (cons (nameof val) (reverse (n>list q null))) acc)))]))
(stringjoin (n>list n null)))
(define (firstcap s)
(stringappend (stringupcase (substring s 0 1)) (substring s 1)))
(define (numbermagic n)
(firstcap (magic (number>words n) null)))
(define (magic word accumulator)
(if (equal? word "four")
(stringjoin (reverse (cons "four is magic." accumulator)) ", ")
(let ((wordlen (stringlength word)))
(magic (number>words wordlen)
(cons (stringappend word " is " (number>words wordlen)) accumulator)))))
(module+ test
(define testnumbers
(append (range 11) '(23 172 20140 100 130 876000000 874143425855745733896030)))
(foreach (λ (n) (displayln (numbermagic n))) testnumbers))
 Output:
Zero is four, four is magic. One is three, three is five, five is four, four is magic. Two is three, three is five, five is four, four is magic. Three is five, five is four, four is magic. Four is magic. Five is four, four is magic. Six is three, three is five, five is four, four is magic. Seven is five, five is four, four is magic. Eight is five, five is four, four is magic. Nine is four, four is magic. Ten is three, three is five, five is four, four is magic. Three is five, five is four, four is magic. Two is three, three is five, five is four, four is magic. Twenty thousand one hundred forty is three, three is five, five is four, four is magic. Ten is three, three is five, five is four, four is magic. One hundred thirty is eighteen, eighteen is eight, eight is five, five is four, four is magic. Six million is eleven, eleven is six, six is three, three is five, five is four, four is magic. Four sextillion three quintillion five quadrillion five trillion five billion three million six thousand thirty is eleven, eleven is six, six is three, three is five, five is four, four is magic.
REXX[edit]
The numbers used for the default were taken from the Kotlin example.
Numbers are limited to 3,003 decimal digits, the maximum number that the $SPELL# REXX program will handle.
/*REXX pgm converts a # to English into the phrase: a is b, b is c, ... four is magic. */
numeric digits 3003 /*be able to handle gihugic numbers. */
parse arg x /*obtain optional numbers from the C.L.*/
if x='' then x=164 0 4 6 11 13 75 100 337 9223372036854775807 /*use these defaults?*/
@.=. /*stemmed array used for memoization. */
do j=1 for words(x) /*process each of the numbers in list. */
say 4_is( word(x, j) ) /*display phrase that'll be returned. */
say /*display a blank line between outputs.*/
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
4_is: procedure expose @.; parse arg #,,$ /*obtain the start number.*/
if #\==4 then do until L==4 /*Not 4? Process number.*/
@.#=$spell#(# 'quiet minus negative') /*spell number in English.*/
#[email protected].#; L=length(#) /*get the length of spelt#*/
if @.L==. then @.L=$spell#(L 'quiet') /*¬spelt before? Spell it.*/
$=$ # "is" @.L',' /*add phrase to the answer*/
#=L /*use the new number, ··· */
end /*until*/ /* ··· which will be spelt*/
$=strip($ 'four is magic.') /*finish the sentence with the finale. */
parse var $ first 2 other; upper first /*capitalize the first letter of output*/
return first  other /*return the sentence to the invoker. */
The $SPELL#.REX routine can be found here ───► $SPELL#.REX.
 output when using the default inputs:
Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. One hundred is eleven, eleven is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Nine quintillion two hundred twentythree quadrillion three hundred seventytwo trillion thirtysix billion eight hundred fiftyfour million seven hundred seventyfive thousand eight hundred seven is one hundred ninetysix, one hundred ninetysix is twentytwo, twentytwo is ten, ten is three, three is five, five is four, four is magic.
Ring[edit]
/* Checking numbers from 0 to 10 */
for c = 0 to 10
See checkmagic(c) + NL
next
/* The functions */
Func CheckMagic numb
CardinalN = ""
Result = ""
if isnumber(numb) = false or numb < 0 or numb > 999_999_999_999_999
Return "ERROR: Number entered is incorrect"
ok
if numb = 4
Result = "Four is magic."
else
While True
if CardinalN = "four"
Result += "four is magic"
exit
ok
strnumb = StringNumber(numb)
CardinalN = StringNumber(len(strnumb))
Result += strnumb + " is " + CardinalN + ", "
numb = len(strnumb)
End
Result += "."
Result = upper(Result[1]) + Right(Result, len(Result) 1)
ok
Return Result
Func StringNumber cnumb
NumStr = [:n0 = "zero", :n1 = "one", :n2 = "two", :n3 = "three", :n4 = "four", :n5 = "five",
:n6 = "six", :n7 = "seven", :n8 = "eight", :n9 = "nine", :n10 = "ten",
:n11 = "eleven", :n12 = "twelve", :n13 = "thirteen", :n14 = "fourteen", :n15 = "fifteen",
:n16 = "sixteen", :n17 = "seventeen", :n18 = "eighteen", :n19 = "nineteen",
:n20 = "twenty", :n30 = "thirty", :n40 = "fourty", :n50 = "fifty", :n60 = "sixty", :n70 = "seventy", :n80 = "eighty", :n90 = "ninety"]
numLev = [:l1 = "", :l2 = "thousand", :l3 = "million", :l4 = "billion", :l5 = "trillion"]
Result = ""
if cnumb > 0
decimals(0)
snumb = string((cnumb))
lnumb = [""]
fl = floor(len(snumb) / 3)
if fl > 0
for i = 1 to fl
lnumb[i] = right(snumb, 3)
snumb = left(snumb, len(snumb) 3)
lnumb + ""
next
if (len(snumb) % 3) > 0
lnumb[len(lnumb)] = snumb
else
del(lnumb, len(lnumb))
ok
else
lnumb[1] = snumb
ok
for l = len(lnumb) to 1 step 1
bnumb = lnumb[l]
bResult = ""
if number(bnumb) != 0
for n = len(bnumb) to 1 step 1
if (len(bnumb) = 3 and n = 2) or (len(bnumb) = 2 and n = 1)
if number(bnumb[n]) > 1
eval("bResult = NumStr[:n" + bnumb[n] + "0] + ' ' + bResult")
elseif number(bnumb[n]) = 1
eval("bResult = NumStr[:n" + bnumb[n] + bnumb[n+1] + "] + ' ' + bResult")
ok
else
if len(bnumb) = 3 and n = 1 and number(bnumb[1]) > 0
if trim(bResult) != ""
bResult = " " + bResult
ok
if number(bnumb[1]) > 1
bResult = "hundreds" + bResult
else
bResult = "hundred" + bResult
ok
if left(trim(bResult), 7) = "hundred"
bResult = bResult + " "
ok
ok
if (len(bnumb) = 3 and n = 1 and number(bnumb[1]) = 0) OR (len(bnumb) = n and number(bnumb[n]) = 0) OR (len(bnumb) = 3 and number(bnumb[2]) = 1) OR (len(bnumb) = 2 and number(bnumb[1]) = 1)
loop
ok
eval("bResult = NumStr[:n" + bnumb[n] + "] + ' ' + bResult")
ok
next
Result = Result + bResult
if l > 1
if number(bnumb) > 1
eval("Result = Result + numLev[:l" + l + "] + 's ' ")
else
eval("Result = Result + numLev[:l" + l + "] + ' ' ")
ok
ok
ok
next
else
Result = Result + NumStr[:n0]
ok
Return trim(Result)
Output:
Zero is four, four is magic. One is three, three is five, five is four, four is magic. Two is three, three is five, five is four, four is magic. Three is five, five is four, four is magic. Four is magic. Five is four, four is magic. Six is three, three is five, five is four, four is magic. Seven is five, five is four, four is magic. Eight is five, five is four, four is magic. Nine is four, four is magic. Ten is three, three is five, five is four, four is magic.
zkl[edit]
Limitiation: zkl only has 64 bit signed integars.
Uses the nth function from Spelling_of_ordinal_numbers#zkl
fcn fourIsMagic(int){
if(int==0) return("Zero is four, four is magic.");
string:="";
while(1){ c:=nth(int,False);
string+="%s is ".fmt(c);
if(int = ( if(int==4) 0 else c.len() )){
string+="%s, ".fmt(nth(int,False));
}else{
string+="magic.";
break;
}
}
string[0].toUpper() + string[1,*]
}
foreach n in (T(0,4,6,11,13,75,337,164,9876543209)){
println(fourIsMagic(n),"\n")
}
 Output:
Zero is four, four is magic. Four is magic. Six is three, three is five, five is four, four is magic. Eleven is six, six is three, three is five, five is four, four is magic. Thirteen is eight, eight is five, five is four, four is magic. Seventyfive is twelve, twelve is six, six is three, three is five, five is four, four is magic. Three hundred thirtyseven is twentysix, twentysix is ten, ten is three, three is five, five is four, four is magic. Negative one hundred sixtyfour is thirtyone, thirtyone is ten, ten is three, three is five, five is four, four is magic. Nine billion eight hundred seventysix million five hundred fortythree thousand two hundred nine is ninetyseven, ninetyseven is twelve, twelve is six, six is three, three is five, five is four, four is magic.