How to replace multiplication by a constant with shift and add operations.

mult_replace.rs

// Multiplication by a constant can be replaced by multiple shift and addition operations:
// The following table shows that for constants from 1 to 36.
// 
// ============================================================================
//  N | Factorized         | # Ops | Ops with x as input
// ----------------------------------------------------------------------------
//  1 | 1                  | 0     | x
//  2 | 2                  | 1     | x << 1
//  3 | 2 + 1              | 2     | x << 1 + x
//  4 | 4                  | 1     | x << 2
//  5 | 4 + 1              | 2     | x << 2 + x
//  6 | 4 + 2              | 3     | x << 2 + x << 1
//  7 | 4 + 2 + 1          | 4     | x << 2 + x << 1 + x
//  8 | 8                  | 1     | x << 3
//  9 | 8 + 1              | 2     | x << 3 + x
// 10 | 8 + 2              | 3     | x << 3 + x << 1
// 11 | 8 + 2 + 1          | 4     | x << 3 + x << 1 + x
// 12 | 8 + 4              | 3     | x << 3 + x << 2
// 13 | 8 + 4 + 1          | 4     | x << 3 + x << 2 + x
// 14 | 8 + 4 + 2          | 5     | x << 3 + x << 2 + x << 1
// 15 | 8 + 4 + 2 + 1      | 6     | x << 3 + x << 2 + x << 1 + x
// 16 | 16                 | 1     | x << 4
// 17 | 16 + 1             | 2     | x << 4 + x
// 18 | 16 + 2             | 3     | x << 4 + x << 1
// 19 | 16 + 2 + 1         | 4     | x << 4 + x << 1 + x
// 20 | 16 + 4             | 3     | x << 4 + x << 2
// 21 | 16 + 4 + 1         | 4     | x << 4 + x << 2 + x
// 22 | 16 + 4 + 2         | 5     | x << 4 + x << 2 + x << 1
// 23 | 16 + 4 + 2 + 1     | 6     | x << 4 + x << 2 + x << 1 + x
// 24 | 16 + 8             | 3     | x << 4 + x << 3
// 25 | 16 + 8 + 1         | 4     | x << 4 + x << 3 + x
// 26 | 16 + 8 + 2         | 5     | x << 4 + x << 3 + x << 1
// 27 | 16 + 8 + 2 + 1     | 6     | x << 4 + x << 3 + x << 1 + x
// 28 | 16 + 8 + 4         | 5     | x << 4 + x << 3 + x << 2
// 29 | 16 + 8 + 4 + 1     | 6     | x << 4 + x << 3 + x << 2 + x
// 30 | 16 + 8 + 4 + 2     | 7     | x << 4 + x << 3 + x << 2 + x << 1
// 31 | 16 + 8 + 4 + 2 + 1 | 8     | x << 4 + x << 3 + x << 2 + x << 1 + x
// 32 | 32                 | 1     | x << 5
// 33 | 32 + 1             | 2     | x << 5 + x
// 34 | 32 + 2             | 3     | x << 5 + x << 1
// 35 | 32 + 2 + 1         | 4     | x << 5 + x << 1 + x
// 36 | 32 + 4             | 3     | x << 5 + x << 2