[Question]
  [
## Challenge
Given a string as input, golf down the [Fourier program](http://esolangs.org/wiki/Fourier) which outputs that string.
In Fourier there is no easy way to output a string: you have to go through each character code and output that as a character.
## Fourier
The language is based upon an accumulator, a global variable which is initialised to 0 at the start of the program. This is used by almost every operator in the language. Only some do not change the value of the accumulator.
### Character out
```
a
```
Takes the value of the accumulator as the ASCII code and outputs the character. Does not change the value of the accumulator.
If the accumulator is greater than 255, the program will return an error. Likewise if the accumulator is less than 0.
### Number out
```
o
```
Outputs the value of the accumulator. Does not change the value of the accumulator.
### Increase
```
^
```
Increase the accumulator by one.
### Decrease
```
v
```
Decrease the accumulator by one.
### Add
```
+x
```
Sets the accumulator to the value of the accumulator plus the value of x.
### Subtract
```
-x
```
Sets the accumulator to the value of the accumulator minus the value of x.
### Multiply
```
*x
```
Sets the accumulator to the value of the accumulator multiplied by the value of x.
### Divide
```
/x
```
Sets the accumulator to the value of the accumulator divided by the value of x. (Note that this is integer division, so `1/6` results in `0`)
### Number
```
n
```
Set the accumulator to the integer n.
### Note
Here, `x` and `n` can be any integer from `0` to `2^32-1` inclusive.
## More information
You must only use the operators described above. Therefore your outputted Fourier program is invalid if it uses any of the following (note that the following operators are allowed for the bounty):
* Repeat loops
* If statements
* Variables
* Random
* Modulo
* User Input
* Greater/Less than operators
* Equality operators
* Clear screen
* Time delay
* Date functions
Your program can either be a full program or a function, taking in input via STDIN, a file or function arguments. You may also take input straight from the Internet.
Note that if there is a `vv` in your code, you should replace it with `-2`. The same goes for `^^`, replacing it with `+2`.
## Examples
If the input is `7n`, then the expected program is:
```
55a110a
```
But you can save one byte with
```
55a*2a
```
Another way is
```
7o110a
```
Using number out.
---
Similarly if the input is `Hello`, then the expected program is:
```
72a101a108a108a111a
```
You can golf it down by 3 bytes (because outputting doesn't change the accumulator):
```
72a101a108aa111a
```
But wait, we can use the addition operator, saving 2 bytes:
```
72a101a+7aa+3a
```
## Formatting
Because I'll be using Martin Büttner's Stack Snippet leaderboard, please could you format the title like so:
```
# <Language name>, <length of total output> bytes
```
Then, you can put anything you wish below the title.
## Winning
You should post the length of Fourier programs (produced by your code) to output [this text file](https://ia802707.us.archive.org/16/items/hamlet01524gut/2ws2610.txt) and [this text file](http://janelwashere.com/files/bible_daily.txt). Your score is the combined length of both Fourier programs in bytes (non-ASCII characters aren't used in Fourier so it doesn't really make a difference).
The person with the lowest scores wins. If there is a tie, the shortest program in bytes wins.
## Bounty
This 500 rep bounty is for a *new* answer which golfs the strings using any of Fourier's functions. That includes variables, loops and if statements etc. This new answer will not be accepted.
## Leaderboard
Refer to formatting section above:
```
var QUESTION_ID=55384;function answersUrl(e){return"http://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),e.has_more?getAnswers():process()}})}function shouldHaveHeading(e){var a=!1,r=e.body_markdown.split("\n");try{a|=/^#/.test(e.body_markdown),a|=["-","="].indexOf(r[1][0])>-1,a&=LANGUAGE_REG.test(e.body_markdown)}catch(n){}return a}function shouldHaveScore(e){var a=!1;try{a|=SIZE_REG.test(e.body_markdown.split("\n")[0])}catch(r){}return a}function getAuthorName(e){return e.owner.display_name}function process(){answers=answers.filter(shouldHaveScore).filter(shouldHaveHeading),answers.sort(function(e,a){var r=+(e.body_markdown.split("\n")[0].match(SIZE_REG)||[1/0])[0],n=+(a.body_markdown.split("\n")[0].match(SIZE_REG)||[1/0])[0];return r-n});var e={},a=1,r=null,n=1;answers.forEach(function(s){var t=s.body_markdown.split("\n")[0],o=jQuery("#answer-template").html(),l=(t.match(NUMBER_REG)[0],(t.match(SIZE_REG)||[0])[0]),c=t.match(LANGUAGE_REG)[1],i=getAuthorName(s);l!=r&&(n=a),r=l,++a,o=o.replace("{{PLACE}}",n+".").replace("{{NAME}}",i).replace("{{LANGUAGE}}",c).replace("{{SIZE}}",l).replace("{{LINK}}",s.share_link),o=jQuery(o),jQuery("#answers").append(o),e[c]=e[c]||{lang:c,user:i,size:l,link:s.share_link}});var s=[];for(var t in e)e.hasOwnProperty(t)&&s.push(e[t]);s.sort(function(e,a){return e.lang>a.lang?1:e.lang<a.lang?-1:0});for(var o=0;o<s.length;++o){var l=jQuery("#language-template").html(),t=s[o];l=l.replace("{{LANGUAGE}}",t.lang).replace("{{NAME}}",t.user).replace("{{SIZE}}",t.size).replace("{{LINK}}",t.link),l=jQuery(l),jQuery("#languages").append(l)}}var ANSWER_FILTER="!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe",answers=[],page=1;getAnswers();var SIZE_REG=/\d+(?=[^\d&]*(?:&lt;(?:s&gt;[^&]*&lt;\/s&gt;|[^&]+&gt;)[^\d&]*)*$)/,NUMBER_REG=/\d+/,LANGUAGE_REG=/^#*\s*([^,]+)/;
```
```
body{text-align:left!important}#answer-list,#language-list{padding:10px;width:290px;float:left}table thead{font-weight:700}table td{padding:5px}
```
```
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"><div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr></thead> <tbody id="answers"> </tbody> </table></div> <tbody id="languages"> </tbody> </table></div><table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody></table>
```
  
[Answer]
# ><>, 14310665 bytes
## 601398 for hamlet + 13709267 for genesis
This is still a work in progress and takes a lot of time to complete.
```
v
0
>i:0(?;:r-:?!v:0a-)?v     v
  >~:v       ~      >:a(?v>
 :1+?v~'v'o  v      o'^'~\:0)?v
     >n      vno'+'      ^?=1:<
^        o'a'<
```
[Answer]
# Python, 14307118 bytes
### 601216 for Hamlet + 13705902 for Genesis = 14307118
There are definitely some senarios under which this solution is not optimal, such as for `1111`, where it will output `1111o` as opposed to `11oo`. However, I think it is nearly optimal.
Edit: Saved a few bytes by improving `0o0o` to `0oo`.
The name of the file containing the input is received on STDIN, output to STDOUT.
Results verified with the official interpreter.
```
def opt_str(char, acc):
    opts = []
    char_num = ord(char)
    opts.append(str(char_num))
    if 0 < char_num - acc < 10:
        opts.append('+' + str(char_num - acc))
    if 0 < acc - char_num < 10:
        opts.append('-' + str(acc - char_num))
    if char_num - acc == 1:
        opts.append('^')
    if acc - char_num == 1:
        opts.append('v')
    if acc == char_num:
        opts.append('')
    if acc and char_num % acc == 0:
        opts.append('*' + str(char_num//acc))
    try:
        if acc // (acc // char_num) == char_num:
            opts.append('/' + str(acc // char_num))
    except:
        pass
    return [opt for opt in opts if len(opt) == len(min(opts, key=len))]
acc = 0
result = []
pos = 0
with open(input(), "r") as myfile:
        in_str = myfile.read()
while pos < len(in_str):
    i = in_str[pos]
    pos += 1
    if i in '0123456789':
        if i != '0':
            while pos < len(in_str) and in_str[pos] in '0123456789':
                i += in_str[pos]
                pos += 1
        if i == str(acc):
            result.append('o')
        else:
            result.append(i + 'o')
        acc = int(i)
    else:
        opts = opt_str(i, acc)
        result.append(opts[0] + 'a')
        acc = ord(i)
print(''.join(result))
```
[Answer]
# Java, 14307140 bytes
### Hamlet - 601,218
### Genesis - 13,705,922
The idea here is to do all the work upfront, by making a character->character map. Then you can just loop through and grab the shortest strings.
A bit of an exception has to be made for numerals, so I check for them in the main loop. It's still fast, though, and handles the larger test case in a few seconds. I *may* be able to tweak this section for a couple more bytes, but I'm fairly sure it's close to optimum.
Input is a filename as argument. Output is written to a file `inputFilename_out.4`, and the character count is sent to STDOUT.
This is 1737 bytes for the tiebreaker, completely ungolfed. I can golf it a lot if needed, but it's still going to be a bit big.
```
import java.nio.file.Files;
import java.nio.file.OpenOption;
import java.nio.file.Paths;
import java.text.NumberFormat;
public class FourierMapper {
    public static void main(String[] args) throws Exception {
        FourierMapper fm = new FourierMapper();
        fm.createMap();
        String filename = args.length>0? args[0]:"bible.txt";
        String out = fm.fourierize(filename);
        System.out.println(out.length());
        Files.write(Paths.get(filename + "_out.4"), out.getBytes(), new OpenOption[]{});
    }
    
    String[][] map = new String[9999][256];
    void createMap(){
        for(int from=0;from<9999;from++){
            for(int to=0;to<256;to++){
                if(to<10||from<1){
                    map[from][to] = ""+to;
                } else if(to==from){
                    map[from][to] = "";
                } else if(to-from==1){
                    map[from][to] = "^";
                } else if(to-from==-1){
                    map[from][to] = "v";
                } else if(to>99){               
                    if(to%from<1){
                        map[from][to] = "*"+(to/from);
                    } else if(to>from&&to-from<10){
                        map[from][to] = "+"+(to-from);
                    } else if(from>to&&from-to<10){
                        map[from][to] = "-"+(from-to);
                    } else {
                        map[from][to] = ""+to;
                    }
                } else {
                    map[from][to] = ""+to;
                }
            }
        }
    }
    
    String fourierize(String filename) throws Exception{
        StringBuilder out = new StringBuilder();
        byte[] in = Files.readAllBytes(Paths.get(filename));
        String whole = new String(in);
        out.append(in[0] + "a");
        int number = -1;
        for(int i=1;i<in.length;){
            if(in[i]<58&&in[i]>47){
                number = in[i]==48?0:((Number)NumberFormat.getInstance().parse(whole.substring(i,i+4))).intValue();
                out.append(""+number+"o");
                i += (""+number).length();
            } else {
                if(number<0)
                    out.append(map[in[i-1]][in[i]]+"a");
                else
                    out.append(map[number][in[i]]+"a");
                number = -1;
                i++;
            }
        }
        return out.toString();
    }
}
```
[Answer]
# PHP, 14307118 bytes
## 601,216 (Hamlet) + 13,705,902 (Bible)
```
function f($file) {
    $text = file_get_contents($file);
    $a = 0;
    for ($i = 0; $i < strlen($text); $i++) {
        $chr = $text[$i];
        if (ctype_digit($chr)) {
            while ($chr && isset($text[$i + 1]) && ctype_digit($text[$i + 1])) {
                $chr .= $text[$i + 1];
                $i++;
            }
            if ($a == (int)$chr) {
                print "o";
            }
            else {
                $a = (int)$chr;
                print $chr . "o";
            }
            continue;
        }
        $ord = ord($chr);
        $mapping = array(
            '' => $a,
            '^' => $a + 1,
            'v' => $a - 1
        );
        for ($j = 2; $j <= 9; $j++) {
            $mapping["+$j"] = $a + $j;
            $mapping["-$j"] = $a - $j;
            $mapping["*$j"] = $a * $j;
            $mapping["/$j"] = $a / $j;
        }
        foreach ($mapping as $op => $value) {
            if ($value === $ord) {
                $a = $value;
                print $op . "a";
                continue 2;
            }
            else if ($value . '' === $chr) {
                $a = $value;
                print $op . "o";
                continue 2;
            }
        }
        $a = $ord;
        print $ord . "a";
    }
}
```
[Fourier output for Hamlet](https://paste.ee/p/b0H9k)
It works as follows:
1. Iterates over each character in the input;
2. If there is a sequence of non 0 leading digits it will set the accumulator to that number and output it as number. It also checks for similar digits;
3. Otherwise, checks if there is shorter way of outputting the current character (rather than the ASCII code + "a" symbol = 4 characters) by performing a basic operation (+-\*/) on the accumulator with a number between 2 and 9; obviously, it also tries to compare/increment/decrement;
]