# Submission ffdf0381...

Challenge Integer sorting zac.creditmint.eth 2018-27-28 175895
/**
* This file is part of the 1st Solidity Gas Golfing Contest.
*
*/

pragma solidity ^0.4.23;

contract Sort {
/**
* @dev Sorts a list of integers in ascending order.
*
* The input list may be of any length.
*
* @param input The list of integers to sort.
* @return The sorted list.
*/

// It's a sorting algorithm! I've gone for quicksort because mergesort consumes
// 2x memory and memory is expensive! I tried thinking of ways to implement an
// efficient counting/radix sort, but considering the numbers being sorted can
// be up to 256 bits none of the ideas I came up with were remotely competative with
// quicksort.

// This thing uses the Hoare partition scheme. I also test for worst-case
// 'perfect' runs of sorted or reverse-sorted data. A bit cheeky as in the
// general-case the overheads would probably not be worth the cost, but hey,
// this is code golf!

// When the partition sizes get down to 8 items or less I switch to an insertion
// sort algorithm. I believe optimized quicksorts usually switch to insertion sort
// at around 32/64 values, but I went with 8 because that's the maximum number of
// values that can be sorted with a pure stack-based implementation, which is super fast.
// I also use a lookup table to convert partition size to a jump destination for the
// relevant insertion sort, which is probably why Remix cheerfully crashes whenever I try
// to debug a transaction :/

// For the pivot, we can get a pseudorandom index by multiplying the amount of available gas
// by a large prime, taking the modulus mod (difference between first and last partition index),
// then masking off the 5 least significant bits and adding to the first partition index to get
// a memory index to load the pivot from
function sort(uint[] input) external view returns(uint[]) {
assembly {
calldatacopy(0x100, 0x04, calldatasize)
if eq(calldatasize, 0x44) {
return(0x00, 0x40)
}
mstore(0x00, finished_insertion_sort)
mstore(0x20, sort_two)
mstore(0x40, sort_three)
mstore(0x60, sort_four)
mstore(0x80, sort_five)
mstore(0xa0, sort_six)
mstore(0xc0, sort_seven)
mstore(0xe0, sort_eight)
let it := 0x160
let size := add(0x100, sub(calldatasize, 0x24))
check_if_perfect_start:
jumpi(check_if_perfect_start, lt(it, end))
return(0x100, add(end, 0x40)) // hey it's perfect!
check_if_perfect_skip:
it := 0x160
check_if_reverse_start:
jumpi(check_if_reverse_start, lt(it, end))
it := size
end := msize
for {} gt(it, 0x120) {} {
it := sub(it, 0x20)
}
mstore(sub(end, 0x40), 0x20)
return(sub(end, 0x40), add(size, 0x60)) // hey it's reversed!
check_if_reverse_skip:

// one run of recursion will add the indices of the next set of partition start/end points on the stack
// we start by adding 0 onto the stack, at the start of our routine we check whether the next stack item is 0 to
// evaluate whether to proceed.
0
0x140 size           // p_high p_low 0

asm_evaluate_stack:
0xe0 dup3 dup3 sub gt asm_partition jumpi

dup2 swap1 sub mload jump // p_low
finished_insertion_sort:
// dup1 dup3 lt asm_partition jumpi
pop
dup1 asm_evaluate_stack jumpi
asm_finish_sort jump
asm_partition:
// partition
dup2 dup2 sub 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47 gas mulmod 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0 and dup3 add
// 0x20 0x20 dup4 dup4 sub div 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47 gas mulmod mul dup3 add
// dup2

0x20 dup4 sub       // i p p_high p_low
dup3 0x20 add       // j i p p_high p_low
asm_decrease_j jump

asm_partition_swap:
// j i p p_high p_low
dup1 mload      // vj j i p p_high p_low
dup3 mload      // vi vj j i p p_high p_low
dup3 mstore     // vj j i p p_high p_low
dup3 mstore     // j i p p_high p_low

asm_decrease_j:
0x20 swap1 sub  // j i p p_high p_low
dup3 dup2 mload gt asm_decrease_j jumpi
swap1               // i j p p_high p_low
asm_increase_i:
dup3 dup2 mload lt asm_increase_i jumpi
swap1
dup1 dup3 lt asm_partition_swap jumpi

swap2 pop pop       // p' p_high p_low
dup1 0x20 add       // p'' p' p_high p_low
swap3 swap1         // p' p_low p_high p''

asm_evaluate_stack jump

asm_finish_sort:
0x04 calldatasize sub 0x100 return
pop pop pop
// hoareQuickSort(0x40, size)

sort_two:
dup2 dup2 lt        // 0 1 p
two_0_1_skip jumpi
swap1
two_0_1_skip:               // (max) (min) p
dup3 mstore
jump(finished_insertion_sort)

sort_three:
dup2 0x20 add       // p1 p2 p
dup2 mload          // 2 p1 p2 p
dup2 mload          // 1 2 p1 p2 p
dup5 mload          // 0 1 2 p1 p2 p

dup3 dup3 lt three_1_2_skip jumpi
swap2               // 2 1 0
swap1               // 1 2 0
swap2               // 0 2 1
three_1_2_skip:         // 0 1 2
dup3 dup2 lt three_0_2_skip jumpi
swap2
three_0_2_skip:         // 0 1 2
dup2 dup2 lt three_0_1_skip jumpi
swap1
three_0_1_skip:         // 0 1 2 p1 p2 p
dup6 mstore             // 1 2 p1 p2 p
swap3 mstore            // p1 1 p
mstore                  // p

jump(finished_insertion_sort)

sort_four:
dup3 mload          // 3 p1 p2 p3 p
dup3 mload          // 1 2 3 p1 p2 p3 p
dup7 mload          // 0 1 2 3 p1 p2 p3

dup2 dup2 lt four_0_1_skip jumpi
swap1
four_0_1_skip:          // 0 1 2 3 p
dup4 dup4 lt four_2_3_skip jumpi
swap3                   // 3 1 2 0
swap2                   // 2 1 3 0
swap3                   // 0 1 3 2
four_2_3_skip:          // 0 1 2 3 p
dup3 dup2 lt four_0_2_skip jumpi
swap2
four_0_2_skip:          // 0 1 2 3 p
dup4 dup3 lt four_1_3_skip jumpi
swap3 swap1 swap3
four_1_3_skip:          // 0 1 2 3 p
dup3 dup3 lt four_1_2_skip jumpi
swap1 swap2 swap1
four_1_2_skip:          // 0 1 2 3 p1 p2 p3 p
dup8 mstore             // 1 2 3 p1 p2 p3 p
swap4 mstore            // 3 p1 1 p3 p
swap2 swap1 mstore
swap1 mstore

jump(finished_insertion_sort)

sort_five:
dup4 0x20 add       // p1 p2 p3 p4 p
dup4 mload          // 4 p1 p2 p3 p4 p
dup9 mload          // 0 1 2 3 4 p1 p2 p3 p4 p
dup2 dup2 lt five_0_1_skip jumpi
swap1
five_0_1_skip:          // 0 1 2 3 4
dup5 dup5 lt five_3_4_skip jumpi
swap3 swap4 swap3
five_3_4_skip:          // 0 1 2 3 4
dup5 dup4 lt five_2_4_skip jumpi
swap2 swap4 swap2
five_2_4_skip:          // 0 1 2 3 4
dup4 dup4 lt five_2_3_skip jumpi
swap2 swap3 swap2
five_2_3_skip:          // 0 1 2 3 4
dup5 dup3 lt five_1_4_skip jumpi
swap1 swap4 swap1
five_1_4_skip:          // 0 1 2 3 4
dup4 dup2 lt five_0_3_skip jumpi
swap3
five_0_3_skip:          // 0 1 2 3 4
dup3 dup2 lt five_0_2_skip jumpi
swap2
five_0_2_skip:
dup4 dup3 lt five_1_3_skip jumpi
swap1 swap3 swap1
five_1_3_skip:          // 0 1 2 3 4
dup3 dup3 lt five_1_2_skip jumpi
swap1 swap2 swap1
five_1_2_skip:          // 0 1 2 3 4 p1 p2 p3 p4 p
dup10 mstore            // 1 2 3 4 p1 p2 p3 p4 p
swap5 mstore            // 3 4 p1 1 p3 p4 p
swap5 mstore            // p1 1 p3 3 p
mstore                  // p3 3 p
mstore                  // p
jump(finished_insertion_sort)

sort_six:
dup5 0x20 add       // p1 p2 p3 p4 p
dup5 mload          // 4 p1 p2 p3 p4 p
dup11 mload          // 0 1 2 3 4 5 p1 p2 p3 p4 p5 p

dup3 dup3 lt six_1_2_skip jumpi
swap1 swap2 swap1
six_1_2_skip:
dup6 dup6 lt six_4_5_skip jumpi
swap4 swap5 swap4
six_4_5_skip:
dup3 dup2 lt six_0_2_skip jumpi
swap2
six_0_2_skip:
dup6 dup5 lt six_3_5_skip jumpi
swap3 swap5 swap3
six_3_5_skip:
dup2 dup2 lt six_0_1_skip jumpi
swap1
six_0_1_skip:
dup5 dup5 lt six_3_4_skip jumpi
swap3 swap4 swap3
six_3_4_skip:
dup6 dup4 lt six_2_5_skip jumpi
swap2 swap5 swap2
six_2_5_skip:
dup4 dup2 lt six_0_3_skip jumpi
swap3
six_0_3_skip:
dup5 dup3 lt six_1_4_skip jumpi
swap1 swap4 swap1
six_1_4_skip:
dup5 dup4 lt six_2_4_skip jumpi
swap2 swap4 swap2
six_2_4_skip:
dup4 dup3 lt six_1_3_skip jumpi
swap1 swap3 swap1
six_1_3_skip:
dup4 dup4 lt six_2_3_skip jumpi
swap2 swap3 swap2
six_2_3_skip:           // 0 1 2 3 4 5 p1 p2 p3 p4 p5 p
dup12 mstore            // 1 2 3 4 5 p1 p2 p3 p4 p5 p
swap6 mstore            // 3 4 5 p1 1 p3 p4 p5 p
swap6 mstore            // 5 p1 1 p3 3 p5 p
swap2 swap1 mstore      // 5 p3 3 p5 p
swap2 swap1 mstore      // 5 p5 p
swap1 mstore
jump(finished_insertion_sort)

sort_seven:
dup6 0x20 add       // p1 p2 p3 p4 p5 p6 p
dup6 mload          // 4 p1 p2 p3 p4 p
dup13 mload          // 0 1 2 3 4 5 6 p1 p2 p3 p4 p5 p6 p

dup3 dup3 lt seven_1_2_skip jumpi
swap1 swap2 swap1
seven_1_2_skip:
dup5 dup5 lt seven_3_4_skip jumpi
swap3 swap4 swap3
seven_3_4_skip:
dup7 dup7 lt seven_5_6_skip jumpi
swap5 swap6 swap5
seven_5_6_skip:
dup3 dup2 lt seven_0_2_skip jumpi
swap2
seven_0_2_skip:
dup6 dup5 lt seven_3_5_skip jumpi
swap3 swap5 swap3
seven_3_5_skip:
dup7 dup6 lt seven_4_6_skip jumpi
swap4 swap6 swap4
seven_4_6_skip:
dup2 dup2 lt seven_0_1_skip jumpi
swap1
seven_0_1_skip:
dup6 dup6 lt seven_4_5_skip jumpi
swap4 swap5 swap4
seven_4_5_skip:
dup7 dup4 lt seven_2_6_skip jumpi
swap2 swap6 swap2
seven_2_6_skip:
dup5 dup2 lt seven_0_4_skip jumpi
swap4
seven_0_4_skip:
dup6 dup3 lt seven_1_5_skip jumpi
swap1 swap5 swap1
seven_1_5_skip:
dup4 dup2 lt seven_0_3_skip jumpi
swap3
seven_0_3_skip:
dup6 dup4 lt seven_2_5_skip jumpi
swap2 swap5 swap2
seven_2_5_skip:
dup4 dup3 lt seven_1_3_skip jumpi
swap1 swap3 swap1
seven_1_3_skip:
dup5 dup4 lt seven_2_4_skip jumpi
swap2 swap4 swap2
seven_2_4_skip:
dup4 dup4 lt seven_2_3_skip jumpi
swap2 swap3 swap2
seven_2_3_skip:         // 0 1 2 3 4 5 6 p1 p2 p3 p4 p5 p6 p
dup14 mstore            // 1 2 3 4 5 6 p1 p2 p3 p4 p5 p6 p
swap7 mstore            // 3 4 5 6 p1 1 p3 p4 p5 p6 p
swap7 mstore            // 5 6 p1 1 p3 3 p5 p6 p
swap7 mstore            // p1 1 p3 3 p5 5 p
mstore
mstore
mstore
jump(finished_insertion_sort)

sort_eight:
dup7 0x20 add       // p1 p2 p3 p4 p5 p6 p
dup7 mload          // 4 p1 p2 p3 p4 p
dup15 mload          // 0 1 2 3 4 5 6 7 p1 p2 p3 p4 p5 p6 p7 p

dup2 dup2 lt eight_0_1_skip jumpi
swap1
eight_0_1_skip:
dup4 dup4 lt eight_2_3_skip jumpi
swap2 swap3 swap2
eight_2_3_skip:
dup6 dup6 lt eight_4_5_skip jumpi
swap4 swap5 swap4
eight_4_5_skip:
dup8 dup8 lt eight_6_7_skip jumpi
swap6 swap7 swap6
eight_6_7_skip:
dup3 dup2 lt eight_0_2_skip jumpi
swap2
eight_0_2_skip:
dup4 dup3 lt eight_1_3_skip jumpi
swap1 swap3 swap1
eight_1_3_skip:
dup7 dup6 lt eight_4_6_skip jumpi
swap4 swap6 swap4
eight_4_6_skip:
dup8 dup7 lt eight_5_7_skip jumpi
swap5 swap7 swap5
eight_5_7_skip:
dup3 dup3 lt eight_1_2_skip jumpi
swap1 swap2 swap1
eight_1_2_skip:
dup7 dup7 lt eight_5_6_skip jumpi
swap5 swap6 swap5
eight_5_6_skip:
dup5 dup2 lt eight_0_4_skip jumpi
swap4
eight_0_4_skip:
dup8 dup5 lt eight_3_7_skip jumpi
swap7 swap3 swap7
eight_3_7_skip:
dup6 dup3 lt eight_1_5_skip jumpi
swap1 swap5 swap1
eight_1_5_skip:
dup7 dup4 lt eight_2_6_skip jumpi
swap2 swap6 swap2
eight_2_6_skip:
dup5 dup3 lt eight_1_4_skip jumpi
swap1 swap4 swap1
eight_1_4_skip:
dup7 dup5 lt eight_3_6_skip jumpi
swap3 swap6 swap3
eight_3_6_skip:
dup5 dup4 lt eight_2_4_skip jumpi
swap2 swap4 swap2
eight_2_4_skip:
dup6 dup5 lt eight_3_5_skip jumpi
swap3 swap5 swap3
eight_3_5_skip:
dup5 dup5 lt eight_3_4_skip jumpi
swap3 swap4 swap3
eight_3_4_skip:         // 0 1 2 3 4 5 6 7 p1 p2 p3 p4 p5 p6 p7 p
dup16 mstore            // 1 2 3 4 5 6 7 p1 p2 p3 p4 p5 p6 p7 p
swap8 mstore            // 3 4 5 6 7 p1 1 p3 p4 p5 p6 p7 p
swap8 mstore            // 5 6 7 p1 1 p3 3 p5 p6 p7 p
swap8 mstore            // 7 p1 1 p3 3 p5 5 p7 p
swap2 swap1 mstore      // 7 p3 3 p5 5 p7 p
swap2 swap1 mstore      // 7 p5 5 p7 p
swap2 swap1 mstore      // 7 p7 p
swap1 mstore
jump(finished_insertion_sort)
}
}
}