Clever Geek Handbook

stm32. We look at the root

Instead of introducing



The article contains an example of manual optimization of a critical section of an application program in relation to budget stm32 microcontrollers, which increases performance 5 times or more compared to a library function.



Square root extraction is often used in applications. The sqrt function is included in the standard C library and operates on real numbers:



double sqrt (double num);
long double sqrtl (long double num);


Microcontrollers work primarily with integers; they usually do not have registers for real numbers.



In practice, in addition to the loss of computational speed on multiple transformations "integer <=> real" , accuracy is additionally lost - Example 1.



Example 1: Loss of Precision in Forward and Backward Conversions



//  
uint32_t L1 = 169;
uint32_t L2 = 168;

//  
uint32_t r1 = ( uint32_t )sqrt( ( double ) L1 );
uint32_t r2 = ( uint32_t )sqrt( ( double ) L2 );

//  
L1 = r1*r1; // r1 = 13
L2 = r2*r2; // r2 = 12

//  
// L1 = 169 —  169
// L2 = 144 —  168,    14%


Formulation of the problem



Raise the precision of sqrt calculations by rounding to the nearest integer.

If possible, increase productivity.



The solution of the problem



Create a custom function, for example, sqrt_fpu based on the standard one - Example 2.



Example 2: Calculating an integer root using the sqrt_fpu algorithm



uint16_t sqrt_fpu ( uint32_t L )
{
    if ( L < 2 )
        return ( uint16_t ) L;

    double f_rslt = sqrt( ( double ) L );
    uint32_t rslt = ( uint32_t ) f_rslt;

    if ( !( f_rslt - ( double ) rslt < .5 ) )
        rslt++;

    return ( uint16_t ) rslt;
}


Sqrt_fpu advantages:



  • compact code;
  • the required accuracy is achieved.


Disadvantages of sqrt_fpu:



  • loss of performance due to an extra call and additional floating point operations;
  • lack of obvious potential for optimizing computing speed at the user level.


sqrt_fpu .



— - ().



-: , .



1. :



« , , .»

sqrt_odd — 3.



3: sqrt_odd



uint16_t sqrt_odd ( uint32_t L )
{
    if ( L < 2 )
        return ( uint16_t ) L;

    uint16_t div = 1, rslt = 1;

    while ( 1 )
    {
        div += 2;

        if ( ( uint32_t ) div >= L )
            return rslt;

        L -= div, rslt++;
    }
}


,

.



sqrt_odd:



  • ;


sqrt_odd:



  • ;
  • ; , 10e4+ 150 — 1;
  • .


1: sqrt_odd



2. :



« »:

Rj = ( N / Ri + Ri ) / 2

sqrt_new — 4.



4: sqrt_new



uint16_t sqrt_new ( uint32_t L )
{
    if ( L < 2 )
        return ( uint16_t ) L;

    uint32_t rslt, div;

    rslt = L;
    div = L / 2;

    while ( 1 )
    {
        div = ( L / div + div ) / 2;

        if ( rslt > div )
            rslt = div;
        else
            return ( uint16_t ) rslt;
    }
}


sqrt_new — sqrt_fpu ( 2).



sqrt_new:



  • ;
  • — sqrt_fpu;
  • ;


sqrt_new:



  • .


sqrt_new ( 2):



  • ;
  • .


2: sqtr_new (!)



(!) — 10e5+ 8 .



sqrt_new :



  • , , ( );
  • , -, ;
  • .


2. sqrt_evn ( 5).



sqrt_evn , , [ 0… 0xFFFFFFFF ].



sqrt_evn 2- 5- , sqrt_new ~40%.



[ 1… 10 000 000 ] sqtr_evn 2-3 .



sqrt_evn — 3.

3: sqtr_evn



, sqrt_evn — 5.

5: sqrt_evn



uint16_t sqrt_evn ( uint32_t L )
{
    if ( L < 2 )
        return ( uint16_t ) L;

    uint32_t div;
    uint32_t rslt;
    uint32_t temp;

    if ( L & 0xFFFF0000L )
        if ( L & 0xFF000000L )
            if ( L & 0xF0000000L )
                if ( L & 0xE0000000L )
                    div = 43771;
                else
                    div = 22250;
            else
                if ( L & 0x0C000000L )
                    div = 11310;
                else
                    div = 5749;
        else
            if ( L & 0x00F00000L )
                if ( L & 0x00C00000L )
                    div = 2923;
                else
                    div = 1486;
            else
                if ( L & 0x000C0000L )
                    div = 755;
                else
                    div = 384;
    else
        if ( L & 0xFF00L )
            if ( L & 0xF000L )
                if ( L & 0xC000L )
                    div = 195;
                else
                    div = 99;
            else
                if ( L & 0x0C00L )
                    div = 50;
                else
                    div = 25;
        else
            if ( L & 0xF0L )
                if ( L & 0x80L )
                    div = 13;
                else
                    div = 7;
            else
                div = 3;

    rslt = L;

    while ( 1 )
    {
        temp = L / div;
        temp += div;

        div = temp >> 1;
        div += temp & 1;

        if ( rslt > div )
            rslt = div;
        else
        {
            if ( L / rslt == rslt - 1 && L % rslt == 0 )
                rslt--;

            return ( uint16_t ) rslt;
        }
    }
}


«» — . 1 .



sqrt_evn , .

( 2).



— .



.

[ 3, 7, 13, 25 ] « ». (). .



— .





:



  • : STM32F0308-DISCO, MCU STM32F030R8T6
  • : STM32CubeIDE
  • : USB-UART PL2303HX


:



  • :
  • : CPU — 48 MHz, UART (RS485) — 9600 bit/s
  • : , Release
  • : MCU GCC Linker: Miscellaneous: -u _printf_float


sqrt_fpu, sqrt_new sqrt_evn.



100 000 3- — 4.

4:



.



— sqrt_fpu, . — .



, ( 4), .



( 5) .



5:



( 6) , 1 .

sqrt_fpu 19 531, sqrt_evn 147 059 ; sqrt_evn ~7,5 , sqrt_fpu.



6:





, , , .



At the same time, manual algorithmic code optimization can be effective in mass production of small IoT, due to the use of low-cost microcontroller models, freeing up the space of complex tasks for older models.



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