Help me golf my numbers!

Question

When writing code-golf programs, I usually end up using some numeric constants. I always put them in decimal because that's how I think, but I just realized that my language supports other number formats that might let me shorten my code slightly.

Challenge

Given a non-negative integer less than 2^53-1, decide whether that integer has the shortest representation in:

• Decimal
• Hexadecimal
• Scientific Notation

Decimal

Since this is the default format of my language, there is no extra notation needed for this format. Every number is represented as usual for decimal.

Hexadecimal

My languages uses the 0x prefix for hexadecimal constants. This means that if a number has 4 hexadecimal digits, it will take 6 bytes to represent that number.

Scientific notation

My language uses the following format for scientific notation:

[Real base]e[Integer exponent of 10]

For example, 700 would be represented as 7e3, and 699 would be represented as 6.99e3, because the base must be between -10 and 10 (non-inclusive). For the purposes of this challenge, the base will always be at least 0, since the inputted number is non-negative.

Output

You should return a way of identifying which format is shortest (i.e. 0 for decimal, 1 for hex, 2 for scientific). Alternatively, you may output the smallest representation of the number itself.

Test cases

Decimal       | Hexadecimal  | Scientific        | Winner
--------------|--------------|-------------------|-------------
0             | 0x0          | 0e0               | Decimal
15            | 0xF          | 1.5e1             | Decimal
6999          | 0x1B57       | 6.999e3           | Decimal
7000          | 0x1B58       | 7e3               | Scientific
1000000000000 | 0xE8D4A51000 | 1e12              | Scientific
1000000000001 | 0xE8D4A51001 | 1.000000000001e12 | Hexadecimal
1000000001000 | 0xE8D4A513E8 | 1.000000001e12    | Hexadecimal
1000001000000 | 0xE8D4B45240 | 1.000001e12       | Scientific

Scoring

This is code-golf, so the answer in the shortest bytes for each language wins.

Answer 1

05AB1E, 23 bytes

hg̹gD<g>¹ÀðìÁ0ÜðÜg+)Wk

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-1 thanks to Emigna.

0 for hexadecimal, 1 for decimal, 2 for scientific.

Answer 2

05AB1E, 27 bytes

Dg<¹À'.ìÁ0Ü'.Ü…ÿeÿIh…0xÿ)é¬

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Explanation

D                            # duplicate input, one copy will be used as decimal notation
 g<                          # len(input)-1
   ¹À                        # push input and rotate left
     '.ìÁ                    # prepend a dot and rotate right
         0Ü'.Ü               # remove trailing zeroes and then any trailing dot
              …ÿeÿ           # format scientific notation
                  Ih         # input converted to hex
                    …0xÿ     # format hex
                        )    # wrap in a list
                         é   # sort by length
                          ¬  # get the first (shortest) item

Answer 3

Jelly, 28 bytes

TṀµỊ¬+‘
DµL’DL+Ç,L
b⁴L+2;ÇỤḢ

A monadic link returning 1, 2, or 3 for hexadecimal, scientific, or decimal respectively.

Try it online! or see a test suite.

I thought this would be shorter, but I can't see it so am posting.

How this monstrosity works...

TṀµỊ¬+‘    - Link 1, length of mantissa + "e": list of decimal digits  e.g. [7,0,1,0]
T          - truthy indexes                                                 [1,  3  ]
 Ṁ         - maximum                                                             3
  µ        - monadic chain separation, call that m
   Ị       - insignificant? (abs(m)<=1) -- here: 1 for m=1, 0 otherwise          0
    ¬      - logical not                  i.e. 1 if a "." will be used           1
     +     - add m                                                               4
      ‘    - increment                    always uses an 'e'                     5

DµL’DL+Ç,L - Link 2, lengths of scientific and decimal notations: non-negative-integer, n
D          - cast to decimal list
 µ         - monadic chain separation, call that d
  L        - length of d (number of decimal digits of n)
   ’       - decrement (value of exponent)
    D      - cast to decimal list (exponent's digits)
     L     - length (number of characters in the exponent)
       Ç   - call last link (1) as a monad(d) (number of characters in mantissa + "e")
         L - length of d (number of decimal digits of n)
        ,  - pair

b⁴L+2;ÇỤḢ - Main link: non-negative-integer, n
 ⁴        - literal 16
b         - convert n to base 16
  L       - length (number of hexadecimal digits)
   +2     - add two (number of characters including the "0x")
      Ç   - call the last link (2) as a monad (characters in scientific and decimal)
     ;    - concatenate ([charsInHexadecimal, charsInScientific, charsInDecimal])
       Ụ  - sort indexes by value
        Ḣ - head (1-based-index in the above list of (one of) the shortest)

Answer 4

JavaScript (ES6), 90 bytes

Returns 0 for decimal, 1 for hexadecimal, -1 for scientific.

n=>(l=Math.log,D=l(n)/l(10),H=l(n)/l(16)+2,S=n.toExponential().length-1,S<H?-(S<D):+(H<D))

f=
n=>(l=Math.log,D=l(n)/l(10),H=l(n)/l(16)+2,S=n.toExponential().length-1,S<H?-(S<D):+(H<D))

console.log(
    f(0),
    f(15),
    f(6999),
    f(7000),
    f(1000000000000),
    f(1000000000001),
    f(1000000001000),
    f(1000001000000)
)

Explanation

• log(n) / log(10): base-10 logarithm of n; roughly the length of n as a decimal.

• log(n) / log(16) + 2: base-16 logarithm of n plus 2; roughly the length of n as a hexadecimal plus the prepended 0x.

• n.toExponential().length - 1: n.toExponential() returns a string with n in scientific format (e.g. 7e+3) but we subtract 1 from its length to account for the extraneous +.

Now that we have the lengths of all 3 representations D, H, andS, we compare:
S<H?-(S<D):+(H<D)

---

JavaScript (ES6), 97 bytes

This one outputs the number in the format with the shortest length. Inspired by @Shaggy's deleted attempt.

n=>[n+'','0x'+n.toString(16),n.toExponential().replace('+','')].sort((x,y)=>x.length-y.length)[0]

f=
n=>[n+'','0x'+n.toString(16),n.toExponential().replace('+','')].sort((x,y)=>x.length-y.length)[0]

console.log(
    f(0),
    f(15),
    f(6999),
    f(7000),
    f(1000000000000),
    f(1000000000001),
    f(1000000001000),
    f(1000001000000)
)

Answer 5

C#, 106 97 96 143 132 bytes

using System.Linq;n=>new[]{n+"",$"0x{n:X}",(n+"").Insert(1,".").TrimEnd('0','.')+"e"+((n+"").Length-1)}.OrderBy(s=>s.Length).First()

Annoyingly in C# the ulong.ToString format specifier e loses precision on the higher numbers so I've had to do it manually. There's probably a shorter way to do it but this works for now. It also formats it incorrectly for this challenge so I would have to manually strip it's output anyway.

If I set a string to the value of n as var s=n+""; it works out longer because of the explicit return and extra curly braces.

It returns the shortest value from the array of each different value where [0] = decimal, [1] = hexadecimal, [2] = scientific.

Full/Formatted version:

using System.Linq;
Func<ulong, string> f = n =>
    new[]
    {
        n + "",
        $"0x{n:X}",
        (n + "").Insert(1, ".").TrimEnd('0', '.') + "e" + ((n + "").Length - 1)
    }.OrderBy(s => s.Length).First();

The correct way to calculate the scientific output is:

(n < 1 ? n + "" : (n + "").Insert(1, ".").TrimEnd('0', '.')) + "e" + ((n + "").Length - 1)

However, seeing as 0 is shorter than 0e0 I can remove that special case.

Answer 6

Python 2, 83 77 bytes

Outputs the smallest representation of the number.

import re
lambda n:min(`n`,hex(n),re.sub('\.?0*e\+0?','e','%.15e'%n),key=len)

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Ungolfed:

import re
n=input()
d=`n`
h=hex(n)
s=re.sub('(.)\.?0*e\+0?',r'\1e','%.15e'%n)
print min(d,h,s,key=len)

The regex removes trailing zeros and the decimal point if necessary, as well as the plus sign and leading zero from the exponent if there is one.

Answer 7

Ohm, 35 bytes

l┼xl2+┼DRîsRl≥al≤Dla°┼îa/ì\?≥;+WD╤k

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Outputs 0 for decimal, 1 for hex and 2 for scientific.

Explanation:

l                                      Implicit input, get length                                          
 ┼                                     Input again
  x                                    To hex
   l                                   Get length
    2+                                 Add 2 because of "0x"
      ┼                                Get input again
       D                               Duplicate on the stack
        RîsR                           Remove zeroes at the end (reverse, to int, to string, reverse)
            l                          Get length (= length of base)
             ≥                         Add 1 because to count "e" in the scientific notation
              a                        Swap top two values on the stack
               l≤                      Get length - 1 ( = get the exponent of 10 in scientific notation)
                 D                     Duplicate on the stack
                  l                    Get length ( = length of the exponent)
                   a                   Swap. Now on top of the stack we have the exponent again
                    °                  10^exponent
                     Ō                Get input for the fourth time
                       a/              Divide input by the 10^exp calculated earlier
                         ì\?           If this thing is not an integer...
                            ≥;         ...add one to count the "."
                              +        Sum base length ( + "e") + exponent length ( + ".")
                               W       Wrap stack in array
                                D      Duplicate
                                 ╤k    Get index of min value

Answer 8

PHP, 90 bytes

prints 0 for decimal, 1 for hexadecimal and 2 for scientific

in case of a tie the highest number will be print

<?=array_flip($m=[$l=log10($a=$argn)^0,2+(log($a,16)^0),strlen(($a/10**$l).$l)])[min($m)];

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PHP, 91 bytes

prints 0 for decimal, 1 for hexadecimal and 2 for scientific

in case of a tie the lowest number will be print

<?=array_search(min($m=[$l=log10($a=$argn)^0,2+(log($a,16)^0),strlen(($a/10**$l).$l)]),$m);

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PHP, 103 bytes

prints 0 for decimal, 1 for hexadecimal and 2 for scientific

in case of a tie all numbers will be print

foreach($m=[$l=log10($a=$argn)^0,2+(log($a,16)^0),strlen(($a/10**$l).$l)]as$k=>$v)echo$v-min($m)?"":$k;

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PHP, 109 bytes

Output an array with the shortest solutions

for(;!$p=preg_grep("#^.{".++$i."}$#",[$a=$argn,"0x".dechex($a),$a/10**($l=log10($a)^0)."e$l"]););print_r($p);

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Answer 9

C, 187185 bytes

main(){long long N;scanf("%lli",&N);long long D=log10(N)+1,H=log(N)/log(16)+3,F,S,i=1;while(N>i&&!(N%i))i*=10,F++;S=ceil(log10(D-1))+1+D-F+(D-F>1);printf("%i",N?H>D?2*(D>S):1+(H>S):N);}

Decompressed:

void main(){
    long long N;
    scans("%lli", &N);
    long long D = log10(N) + 1; // Length of number (decimal)
    long long H = log(N)/log(16) + 3; // Length of number (hexadecimal)
    long long F; // Number of 0s at the end of decimal number
    long long S; // Length of number (scientific notation)
    long long i; // Counter (more or less)
    // Get number of zeros at the end of decimal number
    while(N > i && (N % i) == 0){
        i = i * 10;
        F++;
    }
    S = ceil(log10(D - 1)) + 1 + D - F + (D-F>1); // (Power) + (e) + (multiplier + (1 if len(multiplier) > 1))
    printf("%i", N!=0 ?
                (H > D ? 2 * (D > S) : 1 + (H > S)) 
              : 0); // Print the shortest number
}

Prints 0 for decimal, 1 for hex, 2 for scientific notation.

Answer 10

TI-Basic, 130 bytes

Input N:If not(N:Goto 0:1+int(log(N→D:3+int(logBASE(N,16→H:0→F:1→I:While N>I and not(fPart(N/I:10I→I:F+1→F:End:log(D-1→L:1+D-F+(D-F>1):Ans+int(L)+(0≠fPart(L→S:(H>D)2(D>S)+(H≤D)(1+(H>S)→N:Lbl 0:N

Or, alternatively:

�N>θN>�0>1p��ND>3p�������BASEN+16H>0F>1I>�NlI@��N�I>10II>Fp1F>�>�Dq1L>1pDqFpDqFl1>rp�Lp0o�LS>HlD2DlSpHmD1pHlSN>�0>N

Or, in hex:

dc4e3eceb84e3ed7303e3170b1c04e04443e3370b1bbbcbbbfbbb642415345104e2b313604483e3004463e3104493ed14e6c4940b8ba4e83493e31304904493e46703104463ed43ec0447131044c3e317044714670104471466c31113e7270b14c117010306fba4c04533e10486c44113210446c53117010486d441110317010486c5311044e3ed6303e4e

Prints 0 for decimal, 1 for hex, 2 for scientific notation