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Three word location

From Rosetta Code
Three word location is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

If one were to enter the words: 'softly affiliate activation' at the what3words.com site, the response would be a location in Walt Disney World. The latitude and longitude for that spot is 28.3852 -81.5638. Using that service enables anyone to specify any place on the Earth with three words.

Task: Provide a similar solution - Display a location on the Earth with three words derived from a latitude longitude pair.

For: latitude = 28.3852 longitude = -81.5638 Display: W18497 W11324 W01322

Implementation:

Build an array of 28126, 6 character words in the form W00000 thru W28125.

Convert latitude and longitude into positive integers.

Build a 43 bit integer containing latitude (21 bits) and longitude (22 bits).

Isolate most significant 15 bits for word 1 index.

Isolate next 14 bits for word 2 index.

Isolate next 14 bits for word 3 index.

Fetch each word from the word array.

Display the words.

Reverse the procedure and display the original latitude and longitude.

Extra credit: Find a way to populate the word array with actual words.


C[edit]

Translation of: Go
#include <stdio.h>
#include <stdlib.h>
 
typedef long long int64;
 
void to_word(char *ws, int64 w) {
sprintf(ws, "W%05lld", w);
}
 
int64 from_word(char *ws) {
return atoi(++ws);
}
 
int main() {
double lat, lon;
int64 latlon, ilat, ilon, w1, w2, w3;
char w1s[7], w2s[7], w3s[7];
printf("Starting figures:\n");
lat = 28.3852;
lon = -81.5638;
printf(" latitude = %0.4f, longitude = %0.4f\n", lat, lon);
 
// convert lat and lon to positive integers
ilat = (int64)(lat*10000 + 900000);
ilon = (int64)(lon*10000 + 1800000);
 
// build 43 bit BigInt comprising 21 bits (lat) and 22 bits (lon)
latlon = (ilat << 22) + ilon;
 
// isolate relevant bits
w1 = (latlon >> 28) & 0x7fff;
w2 = (latlon >> 14) & 0x3fff;
w3 = latlon & 0x3fff;
 
// convert to word format
to_word(w1s, w1);
to_word(w2s, w2);
to_word(w3s, w3);
 
// and print the results
printf("\nThree word location is:\n");
printf("  %s %s %s\n", w1s, w2s, w3s);
 
/* now reverse the procedure */
w1 = from_word(w1s);
w2 = from_word(w2s);
w3 = from_word(w3s);
 
latlon = (w1 << 28) | (w2 << 14) | w3;
ilat = latlon >> 22;
ilon = latlon & 0x3fffff;
lat = (double)(ilat-900000) / 10000;
lon = (double)(ilon-1800000) / 10000;
 
// and print the results
printf("\nAfter reversing the procedure:\n");
printf(" latitude = %0.4f, longitude = %0.4f\n", lat, lon);
return 0;
}
Output:
Starting figures:
  latitude = 28.3852, longitude = -81.5638

Three word location is:
  W18497 W11324 W01322

After reversing the procedure:
  latitude = 28.3852, longitude = -81.5638

Delphi[edit]

Translation of: Go
 
program Three_word_location;
 
{$APPTYPE CONSOLE}
 
{$R *.res}
 
uses
System.SysUtils;
 
type
TThreeWordLocation = array of string;
 
TGlobalPosition = record
private
FLatitude: Double;
FLongitude: Double;
FWs: TThreeWordLocation;
class function toWord(w: int64): string; static;
class function fromWord(ws: string): int64; static;
procedure SetLatitude(const Value: Double);
procedure SetLongitude(const Value: Double);
procedure Recalculate;
function GetTWLocationAsStr: string;
public
constructor Create(_lat, _lon: Double); overload;
constructor Create(Ws: TThreeWordLocation); overload;
procedure Assign(Ws: TThreeWordLocation);
property Latitude: Double read FLatitude write SetLatitude;
property Longitude: Double read FLongitude write SetLongitude;
property TWLocation: TThreeWordLocation read FWs;
property TWLocationAsStr: string read GetTWLocationAsStr;
end;
 
{ TGlobalPosition }
 
constructor TGlobalPosition.Create(_lat, _lon: Double);
begin
FLatitude := _lat;
FLongitude := _lon;
Recalculate;
end;
 
constructor TGlobalPosition.Create(ws: TThreeWordLocation);
begin
Assign(ws);
end;
 
class function TGlobalPosition.fromWord(ws: string): int64;
begin
Result := StrToInt(ws.Substring(1));
end;
 
function TGlobalPosition.GetTWLocationAsStr: string;
var
i: Integer;
begin
Result := '';
for i := 0 to 2 do
Result := Result + ' ' + FWs[i];
Result := Result.Trim;
end;
 
procedure TGlobalPosition.Recalculate;
var
i: Integer;
w: array[0..2] of int64;
ilat, ilon, latlon: Int64;
begin
SetLength(FWs, 3);
 
// convert lat and lon to positive integers
ilat := Round(FLatitude * 10000 + 900000);
ilon := Round(FLongitude * 10000 + 1800000);
 
// build 43 bit BigInt comprising 21 bits (lat) and 22 bits (lon)
latlon := (ilat shl 22) + ilon;
 
// isolate relevant bits
w[0] := (latlon shr 28) and $7fff;
w[1] := (latlon shr 14) and $3fff;
w[2] := latlon and $3fff;
 
// convert to word format
for i := 0 to 2 do
FWs[i] := toWord(w[i]);
end;
 
procedure TGlobalPosition.SetLatitude(const Value: Double);
begin
FLatitude := Value;
Recalculate;
end;
 
procedure TGlobalPosition.SetLongitude(const Value: Double);
begin
FLongitude := Value;
Recalculate;
end;
 
class function TGlobalPosition.toWord(w: int64): string;
begin
result := format('W%.5d', [w]);
end;
 
procedure TGlobalPosition.Assign(Ws: TThreeWordLocation);
var
i: Integer;
w: array[0..2] of int64;
ilat, ilon, latlon: Int64;
begin
SetLength(FWs, 3);
for i := 0 to 2 do
begin
FWs[i] := Ws[i];
w[i] := fromWord(Ws[i]);
end;
 
latlon := (w[0] shl 28) or (w[1] shl 14) or w[2];
ilat := latlon shr 22;
ilon := latlon and $3fffff;
FLatitude := (ilat - 900000) / 10000;
FLongitude := (ilon - 1800000) / 10000;
end;
 
var
pos: TGlobalPosition;
 
begin
pos.Create(28.3852, -81.5638);
 
Writeln('Starting figures:');
Writeln(Format(' latitude = %0.4f, longitude = %0.4f', [pos.Latitude, pos.Longitude]));
 
Writeln(#10'Three word location is:');
Writeln(' ', pos.TWLocationAsStr);
 
Writeln(#10'After reversing the procedure:');
 
// pos.Create(['W18497','W11324','W01322']);
pos.Create(pos.TWLocation);
Writeln(Format(' latitude = %0.4f, longitude = %0.4f', [pos.Latitude, pos.Longitude]));
 
Readln;
end.
 
 
Output:
Starting figures:
  latitude = 28,3852, longitude = -81,5638

Three word location is:
  W18497 W11324 W01322

After reversing the procedure:
  latitude = 28,3852, longitude = -81,5638


Go[edit]

Translation of: Wren

Though no need for big integers as we have int64 built in.

package main
 
import (
"fmt"
"strconv"
)
 
func toWord(w int64) string { return fmt.Sprintf("W%05d", w) }
 
func fromWord(ws string) int64 {
var u, _ = strconv.ParseUint(ws[1:], 10, 64)
return int64(u)
}
 
func main() {
fmt.Println("Starting figures:")
lat := 28.3852
lon := -81.5638
fmt.Printf(" latitude = %0.4f, longitude = %0.4f\n", lat, lon)
 
// convert lat and lon to positive integers
ilat := int64(lat*10000 + 900000)
ilon := int64(lon*10000 + 1800000)
 
// build 43 bit BigInt comprising 21 bits (lat) and 22 bits (lon)
latlon := (ilat << 22) + ilon
 
// isolate relevant bits
w1 := (latlon >> 28) & 0x7fff
w2 := (latlon >> 14) & 0x3fff
w3 := latlon & 0x3fff
 
// convert to word format
w1s := toWord(w1)
w2s := toWord(w2)
w3s := toWord(w3)
 
// and print the results
fmt.Println("\nThree word location is:")
fmt.Printf("  %s %s %s\n", w1s, w2s, w3s)
 
/* now reverse the procedure */
w1 = fromWord(w1s)
w2 = fromWord(w2s)
w3 = fromWord(w3s)
 
latlon = (w1 << 28) | (w2 << 14) | w3
ilat = latlon >> 22
ilon = latlon & 0x3fffff
lat = float64(ilat-900000) / 10000
lon = float64(ilon-1800000) / 10000
 
// and print the results
fmt.Println("\nAfter reversing the procedure:")
fmt.Printf(" latitude = %0.4f, longitude = %0.4f\n", lat, lon)
}
Output:
Starting figures:
  latitude = 28.3852, longitude = -81.5638

Three word location is:
  W18497 W11324 W01322

After reversing the procedure:
  latitude = 28.3852, longitude = -81.5638

Julia[edit]

Direct translation from the SymSyn example given by the task creator, though note that idiomatic Julia would usually code this as two small encode() and decode() functions.

 
# Three Word Location - convert latitude and longitude to three words
LAT = 28.3852
LON = -81.5638
 
# build word array W00000 ... W28125
wordarray = ["W" * string(x, pad=5) for x in 0:28125]
 
# make latitude and longitude positive integers
ILAT = Int(LAT * 10000 + 900000)
ILON = Int(LON * 10000 + 1800000)
 
# build 43 bit integer containing latitude (21 bits) and longitude (22 bits)
LATLON = (ILAT << 22) + ILON
 
# isolate most significant 15 bits for word 1 index
# next 14 bits for word 2 index
# next 14 bits for word 3 index
W1 = (LATLON >> 28) & 0x7fff
W2 = (LATLON >> 14) & 0x3fff
W3 = LATLON & 0x3fff
 
# fetch each word from word array
w1 = wordarray[W1 + 1]
w2 = wordarray[W2 + 1]
w3 = wordarray[W3 + 1]
 
# display words
println("$w1 $w2 $w3")
 
 
# reverse the procedure
 
# look up each word
(w1index, w2index, w3index) = indexin([w1, w2, w3], wordarray) .- 1
 
# build the latlon integer from the word indexes
latlon = (w1index << 28) | (w2index << 14) | w3index
 
 
# isolate the latitude and longitude
ilon = latlon & 0xfffff
ilat = latlon >> 22
 
# convert back to floating point values
lon = (ilon - 1800000) / 10000
lat = (ilat - 900000) / 10000
 
# display values
println("latitude = $lat longitude = $lon")
 
Output:
W18497 W11324 W01322
latitude = 28.3852 longitude = -81.5638

Idiomatic version with scrambling[edit]

using Random
 
const LAT = 28.3852
const LON = -81.5638
 
# build word array W00000 ... W28125
const wordarray = ["W" * string(x, pad=5) for x in 0:28125]
 
function threewordencode(lat, lon, seed=0) # returns vector of 3 strings
arr = wordarray
if seed != 0
rng = MersenneTwister(seed)
arr = shuffle(rng, deepcopy(wordarray))
end
i = (Int(lat * 10000 + 900000) << 22) | Int(lon * 10000 + 1800000)
return map(x -> arr[x + 1], [(i >> 28) & 0x7fff, (i >> 14) & 0x3fff, i & 0x3fff])
end
 
function threeworddecode(w1, w2, w3, seed=0) # returns pair of Float64
arr = wordarray
if seed != 0
rng = MersenneTwister(seed)
arr = shuffle(rng, deepcopy(wordarray))
end
(i1, i2, i3) = indexin([w1, w2, w3], arr) .- 1
latlon = (i1 << 28) | (i2 << 14) | i3
ilon, ilat = latlon & 0xfffff, latlon >> 22
return (ilon - 1800000) / 10000, (ilat - 900000) / 10000
end
 
words = threewordencode(LAT, LON)
println(join(words, " "))
 
lat, lon = threeworddecode(words...)
println("latitude = $lat longitude = $lon")
 
println("\nWith scramble using key 12345678:")
words = threewordencode(LAT, LON, 12345678)
println(join(words, " "))
lat, lon = threeworddecode(words..., 12345678)
println("latitude = $lat longitude = $lon")
 
Output:
W18497 W11324 W01322
latitude = -81.5638 longitude = 28.3852

With scramble using key 12345678:
W20242 W23427 W16215
latitude = -81.5638 longitude = 28.3852

Phix[edit]

Translation of: Go
Requires 0.8.2+ - I used this task as an excuse to add << and >> bit shift operators,

alongside && and || as infix versions of and/or_bits(). Pre-0.8.2 code left in as comments.
Note the precedence of these ops is not yet finalised, they need extra parenthesis for now.

function toWord(integer w)
return sprintf("W%05d", w)
end function
 
function fromWord(string ws)
sequence r = scanf(ws,"W%05d")
integer res = r[1][1]
return res
end function
 
printf(1,"Starting figures:\n")
atom lat = 28.3852,
lon = -81.5638
printf(1," latitude = %0.4f, longitude = %0.4f\n", {lat, lon})
 
-- convert lat and lon to positive integers
integer ilat := floor((lat+90)*10000),
ilon := floor((lon+180)*10000)
 
-- build 43 bit BigInt comprising 21 bits (lat) and 22 bits (lon)
-- (Std phix atoms have 53/64 bits of precision on 32/64 bit, both plenty)
--atom latlon := ilat*power(2,22) + ilon -- (pre-0.8.2)
atom latlon := (ilat << 22) + ilon
 
-- isolate relevant bits
--integer w1 = and_bits(floor(latlon/power(2,28)),0x7fff), --("")
-- w2 = and_bits(floor(latlon/power(2,14)),0x3fff),
-- w3 = and_bits(latlon,0x3fff)
integer w1 = (latlon >> 28) && 0x7fff,
w2 = (latlon >> 14) && 0x3fff,
w3 = latlon && 0x3fff
 
-- convert to word format
string w1s = toWord(w1),
w2s = toWord(w2),
w3s = toWord(w3)
 
-- and print the results
printf(1,"\nThree word location is:\n")
printf(1,"  %s %s %s\n", {w1s, w2s, w3s})
 
-- now reverse the procedure
w1 = fromWord(w1s)
w2 = fromWord(w2s)
w3 = fromWord(w3s)
 
-- NB: or_bits (likewise ||), being expressly 32-bit, is NOT appropriate here...
--latlon = w1*power(2,28) + w2*power(2,14) + w3 -- (pre-0.8.2)
--ilat = floor(latlon/power(2,22))
--ilon = and_bits(latlon,0x3fffff)
latlon = (w1 << 28) + (w2 << 14) + w3
ilat = latlon >> 22
ilon = latlon && 0x3fffff
lat = ilat/10000 - 90
lon = ilon/10000 - 180
 
-- and print the results
printf(1,"\nAfter reversing the procedure:\n")
printf(1," latitude = %0.4f, longitude = %0.4f\n", {lat, lon})
Output:
Starting figures:
  latitude = 28.3852, longitude = -81.5638

Three word location is:
  W18497 W11324 W01322

After reversing the procedure:
  latitude = 28.3852, longitude = -81.5638

Raku[edit]

Works with: Rakudo version 2020.07

The task[edit]

In large part due to the complete lack of specification, reference implementation, or guidance from the task creator, came up with my own bespoke synthetic word list.

Words always consist of a series of consonant/vowel pairs. Uses a cut down alphabet to reduce possible confusion from overlapping pronunciation.

Some letters with overlapping pronunciation are removed: c: confusable with k or s, g: overlaps with j, x: overlaps with z, q: just because, v: similar to w and we have way more than enough characters anyway.

As it is, with this alphabet we can form 512000 different 6 character "words"; 28126 is a drop in the bucket. To spread out the the words a bit, add a bit of randomness. 28126 fits into 512000 18 and a bit times. Add a random multiple of 28126 to the encoder then modulus it back out on decode. Will get different results on different runs.

We don't bother to pre-calculate and store the words, just generate them on the fly.

Official pronunciation guide:

  • a - long a (say may day)
  • e - long e (he me see)
  • i - long i (hi sigh die)
  • o - long o (go so low)
  • u - long u (due boo moo)
# SYNTHETICS HANDLING
my @synth = flat < b d f h j k l m n p r s t w y z > X~ < a e i o u >;
my %htnys = @synth.antipairs;
my $exp = @synth.elems;
 
sub synth (Int $v) { @synth[($v + (^18).pick * 28126).polymod($exp xx *).reverse || 0].join }
 
sub thnys (Str $v) { (sum %htnys{$v.comb(2).reverse} Z* 1, $exp, $exp**2) % 28126 }
 
 
# ENCODE / DECODE
sub w-encode ( Rat(Real) $lat, Rat(Real) $lon, :&f = &synth ) {
$_ = (($lat + 90) * 10000).round.fmt('%021b') ~ (($lon + 180) * 10000).round.fmt('%022b');
(:2(.substr(0,15)), :2(.substr(15,14)),:2(.substr(29)))».&f
}
 
sub w-decode ( *@words, :&f = &thnys ) {
my $bin = (@words».&f Z, <0 1 1>).map({.[0].fmt('%015b').substr(.[1])}).join;
(:2($bin.substr(0,21))/10000) - 90, (:2($bin.substr(21))/10000) - 180
}
 
 
# TESTING
for 51.4337, -0.2141, # Wimbledon
21.2596,-157.8117, # Diamond Head crater
-55.9652, -67.2256, # Monumento Cabo De Hornos
59.3586, 24.7447, # Lake Raku
29.2021, 81.5324, # Village Raku
-7.1662, 53.9470, # The Indian ocean, south west of Seychelles
28.3852, -81.5638 # Walt Disney World
-> $lat, $lon {
my @words = w-encode $lat, $lon;
my @index = w-encode $lat, $lon, :f( { $_ } );
printf "Coordinates: %s, %s\n To Index: %s\n To 3-word: %s\nFrom 3-word: %s, %s\n From Index: %s, %s\n\n",
$lat, $lon, @index.Str, @words.Str, w-decode(@words), w-decode @index, :f( { $_ } );
}
Output:
Coordinates: 51.4337, -0.2141
   To Index: 22099 365 12003
  To 3-word: zofobe fohujo habute
From 3-word: 51.4337, -0.2141
 From Index: 51.4337, -0.2141

Coordinates: 21.2596, -157.8117
   To Index: 17384 5133 8891
  To 3-word: nijemo zanaza fupawu
From 3-word: 21.2596, -157.8117
 From Index: 21.2596, -157.8117

Coordinates: -55.9652, -67.2256
   To Index: 5317 15428 13632
  To 3-word: zanohu julaso husese
From 3-word: -55.9652, -67.2256
 From Index: -55.9652, -67.2256

Coordinates: 59.3586, 24.7447
   To Index: 23337 4732 15831
  To 3-word: kapupi hokame supoku
From 3-word: 59.3586, 24.7447
 From Index: 59.3586, 24.7447

Coordinates: 29.2021, 81.5324
   To Index: 18625 5535 10268
  To 3-word: dijule nutuza nefini
From 3-word: 29.2021, 81.5324
 From Index: 29.2021, 81.5324

Coordinates: -7.1662, 53.947
   To Index: 12942 12942 12942
  To 3-word: rakudo rakudo rakudo
From 3-word: -7.1662, 53.947
 From Index: -7.1662, 53.947

Coordinates: 28.3852, -81.5638
   To Index: 18497 11324 1322
  To 3-word: tabesa nekaso bupodo
From 3-word: 28.3852, -81.5638
 From Index: 28.3852, -81.5638

(Ok, I admit I manipulated that second to last one, but it is a correct and valid 3-word location in this implementation. There is less than 1 chance in 5000 that it will produce that specific word group though.)

A thought experiment[edit]

A little thought experiment... Latitude, longitude to four decimal places is accurate to about 11.1 meters at the equator, smaller the further from the equator you get. What would it take to support five decimal places? (Accurate to 1.11 meters.)

360 * 100000 == 36000000; ceiling 36000000.log(2) == 26;

So we need 26 bits to cover 360.00000; half of that for 180.00000, or 26 bits + 25 bits == 51 bits. 51 / 3 == 17. 2**17 == 131072 indices. The previous synthetics routine provides much more than enough.

How many sylabics will we need to minimally cover it?

∛131072 == 50.7968...

So at least 51. The synthetics routine provide sylabics in blocks of 5, so we would need at least 11 consonants.

Capriciously and somewhat randomly cutting down the list we arrive at this.

10 times better accuracy in the same three, 6-letter word space.

# SYNTHETICS HANDLING
my @synth = flat < b d f j k n p r s t w > X~ < a e i o u >;
my %htnys = @synth.antipairs;
my $exp = @synth.elems;
my $prec = 100_000;
 
 
sub synth (Int $v) { @synth[$v.polymod($exp xx *).reverse || 0].join }
 
sub thnys (Str $v) { sum %htnys{$v.comb(2).reverse} Z× 1, $exp, $exp² }
 
 
# ENCODE / DECODE
sub w-encode ( Rat(Real) $lat, Rat(Real) $lon, :&f = &synth ) {
$_ = (($lat + 90) × $prec).round.fmt('%025b') ~ (($lon + 180) × $prec).round.fmt('%026b');
(:2(.substr(0,17)), :2(.substr(17,17)), :2(.substr(34)))».&f
}
 
sub w-decode ( *@words, :&f = &thnys ) {
my $bin = @words».&f.map({.fmt('%017b')}).join;
(:2($bin.substr(0,25))/$prec) - 90, (:2($bin.substr(25))/$prec) - 180
}
 
 
# TESTING
for 51.43372, -0.21412, # Wimbledon center court
21.25976,-157.81173, # Diamond Head summit
-55.96525, -67.22557, # Monumento Cabo De Hornos
28.3852, -81.5638, # Walt Disney World
89.99999, 179.99999, # test some
-89.99999,-179.99999 # extremes
-> $lat, $lon {
my @words = w-encode $lat, $lon;
printf "Coordinates: %s, %s\n To Index: %s\n To 3-word: %s\nFrom 3-word: %s, %s\n\n",
$lat, $lon, w-encode($lat, $lon, :f({$_})).Str, @words.Str, w-decode(@words);
}
Output:
Coordinates: 51.43372, -0.21412
   To Index: 55247 71817 21724
  To 3-word: jofuni kosasi diduwu
From 3-word: 51.43372, -0.21412

Coordinates: 21.25976, -157.81173
   To Index: 43460 110608 121675
  To 3-word: fukafa repebo safija
From 3-word: 21.25976, -157.81173

Coordinates: -55.96525, -67.22557
   To Index: 13294 108118 5251
  To 3-word: bukeru rasaso besane
From 3-word: -55.96525, -67.22557

Coordinates: 28.3852, -81.5638
   To Index: 46244 28747 13220
  To 3-word: jajasu duniri bukaka
From 3-word: 28.3852, -81.5638

Coordinates: 89.99999, 179.99999
   To Index: 70312 65298 86271
  To 3-word: kofoki kepifo nonope
From 3-word: 89.99999, 179.99999

Coordinates: -89.99999, -179.99999
   To Index: 0 512 1
  To 3-word: ba duji be
From 3-word: -89.99999, -179.99999

Symsyn[edit]

 
| Three Word Location - convert latitude and longitude to three words
 
lat : 28.3852
lon : -81.5638
 
| build word array W00000 ... W28125
 
i
if i <= 28125
~ i $r
#$r szr
'W00000' $t
(6-szr) szr
szr #$t
+ $r $t
+ $t $wordarray
+ i
goif
endif
 
| make latitude and longitude positive integers
 
{lat * 10000 + 900000} ilat
{lon * 10000 + 1800000} ilon
 
| build 43 bit integer containing latitude (21 bits) and longitude (22 bits)
 
ilat latlon
shl latlon 22
+ ilon latlon
 
| isolate most significant 15 bits for word 1 index
| next 14 bits for word 2 index
| next 14 bits for word 3 index
 
latlon:42:15 w1
latlon:27:14 w2
latlon:13:14 w3
 
| fetch each word from word array
 
(w1*6+1) w1
$wordarray.w1 $w1 6
(w2*6+1) w2
$wordarray.w2 $w2 6
(w3*6+1) w3
$wordarray.w3 $w3 6
 
| display words
 
"$w1 ' ' $w2 ' ' $w3" []
 
 
| reverse the procedure
 
 
| look up each word
 
call bsearch 0 28125 $w1
result w1index
 
call bsearch 0 28125 $w2
result w2index
 
call bsearch 0 28125 $w3
result w3index
 
| build the latlon integer from the word indexes
 
w1index latlon
shl latlon 14
+ w2index latlon
shl latlon 14
+ w3index latlon
 
| isolate the latitude and longitude
 
latlon:21:22 ilon
latlon:42:21 ilat
 
| convert back to floating point values
 
{(ilon - 1800000) / 10000} lon
{(ilat - 900000) / 10000} lat
 
| display values
 
"'latitude = ' lat ' longitude = ' lon" []
 
stop
 
bsearch
param L H $word
if L <= H
((L + H) shr 1) M
(M*6+1) I
$wordarray.I $w 6
if $w > $word
- 1 M H
else
if $w < $word
+ 1 M L
else
return M
endif
endif
goif
endif
return -1
 
 
Output:
W18497 W11324 W01322
latitude =          28.3852 longitude =         -81.5638

Using Real Words

 
 
| Three Word Location - convert latitude and longitude to three words
 
 
lat : 28.3852
lon : -81.5638
 
| Build real word array of the first 28126 words of 8
| or less characters from list of 69905 words sorted alphabetically
| at http://www-personal.umich.edu/~jlawler/wordlist.
| There are 36282 words of 8 or less characters here.
 
 
opentext 'LargeWordList.txt' wf
if ioresult <> 0
stop
endif
if i <= 28125
[wf] $s
if ioresult <> 0
go closefile
endif
#$s wsz
if wsz <= 8
+ $s $wordarray
(8-wsz) wsz
+ ' ' $wordarray wsz
+ i
endif
goif
endif
closefile close wf
 
| make latitude and longitude positive integers
 
{lat * 10000 + 900000} ilat
{lon * 10000 + 1800000} ilon
 
| build 43 bit integer containing latitude (21 bits) and longitude (22 bits)
 
ilat latlon
shl latlon 22
+ ilon latlon
 
| isolate most significant 15 bits for word 1 index
| next 14 bits for word 2 index
| next 14 bits for word 3 index
 
latlon:42:15 w1
latlon:27:14 w2
latlon:13:14 w3
 
| fetch each word from word array
 
(w1*8+1) w1
$wordarray.w1 $w1 8
(w2*8+1) w2
$wordarray.w2 $w2 8
(w3*8+1) w3
$wordarray.w3 $w3 8
 
| display words
 
"$w1 ' ' $w2 ' ' $w3" []
 
 
| reverse the procedure
 
 
| look up each word
 
call bsearch 0 28125 $w1
result w1index
 
call bsearch 0 28125 $w2
result w2index
 
call bsearch 0 28125 $w3
result w3index
 
| build the latlon integer from the word indexes
 
w1index latlon
shl latlon 14
+ w2index latlon
shl latlon 14
+ w3index latlon
 
| isolate the latitude and longitude
 
latlon:21:22 ilon
latlon:42:21 ilat
 
| convert back to floating point values
 
{(ilon - 1800000) / 10000} lon
{(ilat - 900000) / 10000} lat
 
| display values
 
"'latitude = ' lat ' longitude = ' lon" []
 
stop
 
bsearch
param L H $word
if L <= H
((L + H) shr 1) M
(M*8+1) I
$wordarray.I $w 8
if $w > $word
- 1 M H
else
if $w < $word
+ 1 M L
else
return M
endif
endif
goif
endif
return -1
 
 
Output:
ling     everyone amoral  
latitude =          28.3852 longitude =         -81.5638

Wren[edit]

Library: Wren-fmt
Library: Wren-big

This just follows the steps in the task description though I couldn't see any point in creating a 28,126 element array when two simple functions will do.

Note that bitwise operations are limited to 32-bit unsigned integers in Wren which isn't big enough here so we use BigInts instead.

import "/fmt" for Fmt
import "/big" for BigInt
 
// functions to convert to and from the word format 'W00000'
var toWord = Fn.new { |w| Fmt.swrite("W$05d", w) }
var fromWord = Fn.new { |w| Num.fromString(w[1..-1]) }
 
// set latitude and longitude and print them
System.print("Starting figures:")
var lat = 28.3852
var lon = -81.5638
Fmt.print(" latitude = $0.4f, longitude = $0.4f", lat, lon)
 
// convert lat and lon to positive BigInts
var ilat = BigInt.new(lat * 10000 + 900000)
var ilon = BigInt.new(lon * 10000 + 1800000)
 
// build 43 bit BigInt comprising 21 bits (lat) and 22 bits (lon)
var latlon = (ilat << 22) + ilon
 
// isolate relevant bits and convert back to 'normal' ints
var w1 = ((latlon >> 28) & 0x7fff).toSmall
var w2 = ((latlon >> 14) & 0x3fff).toSmall
var w3 = (latlon & 0x3fff).toSmall
 
// convert to word format
w1 = toWord.call(w1)
w2 = toWord.call(w2)
w3 = toWord.call(w3)
 
// and print the results
System.print("\nThree word location is:")
Fmt.print(" $s $s $s", w1, w2, w3)
 
/* now reverse the procedure */
w1 = BigInt.new(fromWord.call(w1))
w2 = BigInt.new(fromWord.call(w2))
w3 = BigInt.new(fromWord.call(w3))
latlon = (w1 << 28) | (w2 << 14) | w3
ilat = (latlon >> 22).toSmall
ilon = (latlon & 0x3fffff).toSmall
lat = (ilat - 900000) / 10000
lon = (ilon - 1800000) / 10000
 
// and print the results
System.print("\nAfter reversing the procedure:")
Fmt.print(" latitude = $0.4f, longitude = $0.4f", lat, lon)
Output:
Starting figures:
  latitude = 28.3852, longitude = -81.5638

Three word location is:
  W18497 W11324 W01322

After reversing the procedure:
  latitude = 28.3852, longitude = -81.5638