Features of the mql5 language, subtleties and tricks - page 313

[fxsaber]

Calculator for approximate integer division by a constant.

uint Div1000( const uint Value ) { return((Value >> 10) + (Value >> 16) + (Value >> 17)); }

[amrali]

I just looked-up this and it is already called  "shift and add".

For certain multipliers like multiply by 10, the result is exact.

 (x << 3) + (x << 1) # Here 10*x is computed as x*2^3 + x*2

https://www.wikiwand.com/en/articles/Multiplication_algorithm#Usage_in_computers

In base two, long multiplication is sometimes called "shift and add", because the algorithm simplifies and just consists of shifting left (multiplying by powers of two) and adding.

[Dominik Egert]

amrali #:

I just looked-up this and it is already called  "shift and add".

For certain multipliers like multiply by 10, the result is exact.

https://www.wikiwand.com/en/articles/Multiplication_algorithm#Usage_in_computers

In base two, long multiplication is sometimes called "shift and add", because the algorithm simplifies and just consists of shifting left (multiplying by powers of two) and adding.

Aren't CPUs underlying architectures anyways implementing such techniques in hardware already?

Maybe this would require some benchmarking.

[amrali]

This method gives approximate results for multiplication with a compile-time constant (on basic hardware). Nowadays compilers use more advanced optimizations for exact multiplications, see https://www.wikiwand.com/en/articles/Division_algorithm#Division_by_a_constant

Also here:

https://www.mql5.com/en/forum/393227/page280#comment_55325243

There is also a library optimizing integer division with compile-time constants, see https://libdivide.com/

it basically converts the divisor to approximate multiplier: 

fast_d = libdivide_s32_gen(divisor);

[fxsaber]

Speeding up calculation of the sum of all array elements by several times.

[amrali]

fxsaber #: Speeding up the calculation of the sum of all array elements by several times.

is just loop unrolling

[Dominik Egert]

About multiply shift:

https://youtu.be/-HNpim5x-IE?si=fXdDuxFWZUgRx8eX

About at minute 34.

Compilers actually apply this method if they can.

[amrali]

A minimal implementation of the fastdiv algorithm (described here https://www.wikiwand.com/en/articles/Division_algorithm?ai=topQs#Division_by_a_constant)

This demonstrates how a compiler can optimize divsion by a compile-time constant (to multiplication and shift).

Compiler Version: 5283, X64 Regular
13th Gen Intel Core i3-1305U, AVX2 + FMA3
 2.48 ns/call, checksum = 516274437   // div_test
 0.53 ns/call, checksum = 516274437   // fastdiv_test

NB: this fastdiv optimization cannot be applied for divisors that are unkown at compile-time (e.g., division by a runtime variable).

[Andrei Iakovlev]

Is there any way to choose which loop to use depending on the value of the bool variable? Inside the loops everything is the same, so I want to select the loop itself 1 time.

There is a bool variable Up. If its value is true, we need the LOOP_Up loop, if false LOOP_Down.

#define  LOOP_Up   for(i = 21;    i >= start; i--)
#define  LOOP_Down for(i = start; i <  22;    i++)
if(Up)  LOOP_Up   else LOOP_Down {

This option causes an error:

illegal 'else' without matching 'if'

It doesn't work this way either:

if(Up) LOOP_Up if(!Up) LOOP_Down {

[dcstoyanov]

Andrei Iakovlev #:

  int start = 0;
  int end = 21;
  bool up = false;
  
  for (int i = up ? end : start; up ? i >= start : i < end; up ? i-- : i++) {
    Print(i);
  }