Find the maximum of 3 numbers without branching

Question

This time around your goal is to find the maximum of 3 integers (from -(2^31) to 2^31 - 1 in binary 2's complement) without using branching or loops.

You are only allowed to use

• Inequality/Equality (==, >, >=, <, <=, !=) These count as 2 tokens.

• Arithmetic (+, -, *, /)

• Logical Operators (! not, && and, || or)

• Bitwise Operators (~ not, & and, | or, ^ xor, <<, >>, >>> arithmetic and logical left and right shifts)

• Constants. 0 tokens

• Variable assignment. 0 tokens

Input 3 variables as a, b and c. Output the maximum number.

Standard atomic code-golf rules apply. If you have any questions please leave them in the comments. One token is any of the above with the special rules.

Answer 1

Javascript

6 tokens

function maxOf3(a, b, c) {
    (b>a) && (a=b);
    (c>a) && (a=c);
    return a;
}

Answer 2

Javascript 10 tokens

Edit Using < and * instead of bit fiddling - as pointed out in comments, bits operations may fail for input near the range limit (over 30 bits)

function Max(x,y,z)
{
  var d=y-x;
  x=y-d*(d<0);
  d=x-z;
  return x-d*(d<0);
}

C 8 tokens

Language agnostic in fact, any C like language will do. To be picky, in standard C it's not portable because right shift may not extend the sign (but in common implementations it does).

In C (and C++, C#, and Java I think) we can easily handle overflow problems using bigger temporary values:

int Max(int x, int y, int z)
{
    long long X = x;
    long long Y = y;
    long long Z = z;
    long long D = Y-X;
    X=Y-((D>>63)&D);
    D=X-Z;
    return (int) (X-((D>>63)&D));
}

Answer 3

C: 10 tokens

int max(int a, int b, int c)
{
    a += (b > a) * (b - a);
    a += (c > a) * (c - a);
    return a;
}

Inspired by @openorclose's answer, but converted to C and made branchless using multiplication rather than short circuit boolean operators.

Answer 4

Javascript

14 tokens

function max (a, b, c)
{
    var ab = (a >= b) * a + (a < b) * b;
    return (ab >= c) * ab + (ab < c) * c;
}

Answer 5

Many languages (Python) (10 tokens)

def max3(x,y,z):
    m = x ^ ((x ^ y) & -(x < y))
    return m ^ ((m ^ z) & -(m < z))

print max3(-1,-2,-3) # -1
print max3(-1,2,10) # 10

https://graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax

Oh, someone already posted it :)

Answer 6

C++11: 15 tokens

Using only arithmetic and bitwise operators (since equality and boolean logic operators make it too easy)...

#include <iostream>

auto max(int32_t a, int32_t b, int32_t c)->int32_t {
  return c - ((c - (a - ((a - b) & (a - b) >> 31))) & (c - (a - ((a - b) & (a - b) >> 31))) >> 31);
}

auto main()->int {
  // test harness
  std::cout << max(9, 38, 7) << std::endl;
  return EXIT_SUCCESS;
}

Answer 7

J (Not competing)

I was just wondering what the a solution in J would look like. This uses a , and a # though, so it won't be competing.

((a<b),(b<c),(c<a))#b,c,a

This would compete, but is way too long, with 9 tokens:

(b*a<:b)+(c*b<c)+(a*c<a)

Answer 8

we have the following assumptions:

• max(a;b)=(a+b + |a-b|)/2

• max(a;b;c)=max(max(a;b);c)

• abs(a)=(a + (a >> 31)) ^ (a >> 31)

we can use the pseudo-code:

function max(a,b,c)

{

out1=( (a+b) + (( (a-b) + ((a-b) >> 31)) ^ ((a-b)>> 31))) div 2

out2=( (out1+c) + (( (out1-c) + ((out1-c) >> 31)) ^ ((out1-c)>> 31))) div 2

return out2

}

Answer 9

C# (2nd try)

I got it... No integrated functions...

But is it allowed to use other integrated datatypes or just plain int? If allowed I would propose:

int foo2(int a, int b, int c)
{
   var x = new SortedList<int,int>();

   x[a] = 1;
   x[b] = 1;
   x[c] = 1;

   return x.Keys[2];
}

Answer 10

javascript 8 tokens

although similar to @openorclose's answer, i do actually use the logical operators for the assignment itself.

function max( a, b, c ) {
    x=( a > b && a) || b;
    return ( x > c && x ) || c;
}

fiddle

Answer 11

R (10 tokens)

function max(a, b, c) {
  max <- a
  max <- max + (b - max) * (b > max)
  max <- max + (c - max) * (c > max)
  return(max)
}

Answer 12

Brainfuck (Not competing)

>,[-<+>>>+<<]>,[-<+>>>+<<]>[>[-<->>]<<]<[-]>[-]>[-]<<<[->>>>+<<<<]>>>>[-<+>>>+<<]>,[-<+>>>+<<]>[>[-<->>]<<]<<

Answer 13

TIS-100, 8 operations

MOV ACC UP #A
SUB UP     #B
SUB 999
ADD 999
ADD UP     #B
SUB UP     #C
SUB 999
ADD 999
ADD UP     #C
MOV ACC DOWN

The provider(UP) only do MOVs so not shown in the code Maybe not work when too near the 999 edge

Answer 14

VBA (6 tokens)

 Function max3(a As Integer, b As Integer, c As Integer)
 i = IIf(a >= b And a >= c, a, IIf(b >= c, b, c))
 max3 = i
 End Function  

not sure if this is not branching.

Answer 15

JavaScript: 4 tokens (** based on broad interpretation of "assignment"!)

Obviously my score of 4 is extremely generous/lenient!

To arrive at that score I've assumed "assignment" (worth 0 tokens in the question) includes such things as additive assignment, subtractive assignment, multiplicative assignment, and XOR-ing (^=) assignment

function f(a, b, c) {
  d = a;
  d -= b;
  d = d >= 0;

  a *= d;  //a = a if (a>=b), else 0
  d ^= true; //invert d
  b *= d;  //b = b if (b<a), else 0

  a += b;  //a is now max(a,b)

  d = a;
  d -= c;
  d = d >= 0;

  a *= d;  //a = a if (a>=c), else 0
  d ^= true; //invert d
  c *= d;  //c = c if (c<a), else 0
  a += c;  //a is now max(max(a,b),c)

  return a;
}

If those assignments actually count the score is 14 :)