Q31 Library
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Q31 Library

mikroPascal PRO for PIC32 includes a library for operating and working with Q31 fractional number format.

Library Routines

Q31_Abs

Prototype

function Q31_Abs(input : longint; output : ^longint) : word;
Description

Function calculates absolute value of the Q31 fractional format number.
Parameters
  • input: Q31 input number.
  • output: number pointer to Q31 output number.
Returns

Function always returns zero.

Q31_Add

Prototype

function Q31_Add(input1 : longint; input2 : longint; output : ^longint) : word;
Description

Function sums two Q31 format numbers.

If the result exceeds [-2147483648, 2147483647] limits, result will be maximal(minimal) number in Q31 format.
Parameters
  • input1: First Q31 number.
  • input2: Second Q31 number.
  • output: number pointer to Q31 output number.
Returns
  • 1 - if the result exceeds [-2147483648, 2147483647] limits.
  • 0 - otherwise.

Q31_Sub

Prototype

function Q31_Sub(input1 : longint; input2 : longint; output : ^longint) : word;
Description

Function subtracts two Q31 format numbers.

If the result exceeds [-2147483648, 2147483647] limits, result will be maximal(minimal) number in Q31 format.
Parameters
  • input1: First Q31 number.
  • input2: Second Q31 number.
  • output: number pointer to Q31 output number.
Returns
  • 1 - if the result exceeds [-2147483648, 2147483647] limits.
  • 0 - otherwise.

Q31_Itof

Prototype

function Q31_Itof(x : longint; f : ^real) : word;
Description

Function converts number from the Q31 fractional number format to floating point number format.
Parameters
  • x: input Q31 number, ranging from -2147483648 to 2147483647.
  • f: pointer to the resulting floating point number.
Returns

Function always returns zero.

Q31_Ftoi

Prototype

function Q31_Ftoi(f : real; x : ^longint) : word;
Description

Function converts number from the floating point number format to Q31 fractional number format.

Input number scope should be in the range of [-1.00000, 0.99996].

If the floating point number is not in this range, the resulting number will be 0x7FFFFFFF (0x80000000).
Parameters
  • f: floating format number to be converted.
  • x: pointer to the resulting Q31 fractional format number.
Returns
  • 1 - If overflow has been detected.
  • 0 - If no errors occured.

Q31_Itoa

Prototype

procedure Q31_Itoa(x : longint; s : ^char);
Description

Function converts number from the Q31 fractional format to ASCII string.

Output ASCII string is in the following format : sn.ddddddddddddddddddddddddddddddd

  • s - sign; '-' negative, space - positive.
  • n - integer part; 0 or 1.
  • d - decimal part; 0..9 (ending zeros are not displayed).
Parameters
  • x: Q31 format number to be converted.
  • src: pointer to the resulting ASCII string.
Returns

Nothing.

Q31_Atoi

Prototype

function Q31_Atoi(s : ^char; x : ^longint) : word;
Description

Function converts the input ASCII string s into a number in Q31 fractional point format.

Input ASCII string should be in the following format: sn.ddddddddddddddddddddddddddddddd

  • s - sign; '-' negative, space - positive.
  • n - integer part; 0 or 1.
  • d - decimal part; 0..9 (ending zeros are not displayed).
Parameters
  • s: pointer to the input ASCII string.
  • out: pointer to the resulting number in Q31 format.
Returns
  • 2 - If input string is in not in the appropriate format.
  • 1 - If overflow has been detected.
  • 0 - If no errors occured.

Q31_Cos

Prototype

function Q31_Cos(x : longint) : longint;
Description

Function returns the cosine of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from 1160290361 to 2147483647.
Parameters
  • x: input number in the Q31 format number, ranging from -2147483648 to 2147483647
Returns

Function returns value in the Q31 format, ranging from 1160290361 to 2147483647.

Q31_Sin

Prototype

function Q31_Sin(x : longint) : longint;
Description

Function returns the sine of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from -1807039907 to 1807039904.
Parameters
  • x: input number in the Q31 format number, ranging from -2147483648 to 2147483647.
Returns

Function returns value in the Q31 format, ranging from -1807039907 to 1807039904.

Q31_Tan

Prototype

function Q31_Tan(x : longint) : longint;
Description

Function returns the tangent of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from -2147483648 to 2147483648.
Parameters
  • x: input number in the Q31 format number, ranging from -1686629760 to 1686629760.
Returns

Function returns value in the Q31 format, ranging from -2147483648 to 2147483647.

Q31_Asin

Prototype

function Q31_Asin(x : longint) : longint;
Description

Function returns the arc sine of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from -2147483648 to 2147483648.
Parameters
  • x: input number in the Q31 format number, ranging from -1807076313 to 1807076320.
Returns

Function returns value in the Q31 format, ranging from -2147483648 to 2147483647.

Q31_Atan

Prototype

function Q31_Atan(x : longint) : longint;
Description

Function returns the arc tangent of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from -1673210000 do 1673209982.
Parameters
  • x: input number in the Q31 format number, ranging from -2147483648 to 2147483647.
Returns

Function returns value in the Q31 format, ranging from -1673210000 do 1673209982.

Q31_Acos

Prototype

function Q31_Acos(x : longint) : longint;
Description

Function returns the arc cosine of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from 189407136 do 2147458881.
Parameters
  • x: input number in the Q31 format number, ranging from 1160311168 do 2147483647.
Returns

Function returns value in the Q31 format, ranging from 189407136 do 2147458881.

Q31_Log

Prototype

function Q31_Log(x : longint) : longint;
Description

Function returns the logarithm of x. The input number is in the Q31 format number and returns value in the Q31 format, ranging from -2144585218 to 0.
Parameters
  • x: input number in the Q31 format number, ranging from 214748368 do 2147483647.
Returns

Function returns value in the Q31 format, ranging from -2144585218 to 0.

Library Example

program Q31_Test;

var Q31_1, Q31_2, l : longint;
    r               : word;
    f               : real;
    stringQ31       : string[35];
    
begin
    // Q31_Ftoi.........................................................
  f := 0.5;
  r := Q31_Ftoi(f, @Q31_1);                      // Q31_1 := 0x40000000; r := 0;
  f := 1.5;
  r := Q31_Ftoi(f, @Q31_1);                      // Q31_1 := 0x7FFFFFF; r := 1;
  f := -2.5;
  r := Q31_Ftoi(f, @Q31_1);                      // Q31_1 := 0x80000000; r := 1;

  // Q31_Itof.........................................................
  Q31_1 := 0x08000000;
  r := Q31_Itof(Q31_1, @f);                      // f := 0.0625; r := 0;

  // Q31_Itoa.........................................................
  Q31_1 := 0x00000001;
  Q31_Itoa(Q31_1, stringQ31);                   // stringQ31 := " 0.0000000004656612873077392578125"

  // Q31_Atoi.........................................................
  r := Q31_Atoi('0.00001525878906', @Q31_1);     // Q31_1 := 0x00007FFF; r := 0;
  r := Q31_Atoi('+1.25', @Q31_1);                // r := 1;

  // Q31_Abs...........................................................
  Q31_Abs(0x12345678, @Q31_1);                           // Q31_1 := 0x12345678;
  Q31_Abs(longint(0xFEDCBA98), @Q31_1);                  // Q31_1 := 0x01234568;

  // Q31_Add...........................................................
  r := Q31_Add(longint(0xE0000000), longint(0xC0000000), @Q31_1);  // Q31_1 := 0xA0000000; r := 0;
  r := Q31_Add(longint(0xA0000000), longint(0xC0000000), @Q31_1);  // Q31_1 := 0x80000000; r := 1;

  // Q31_Sub...........................................................
  r := Q31_Sub(longint(0xE0000000), longint(0xC0000000), @Q31_1);  // Q31_1 := 0x20000000; r := 0;
  r := Q31_Sub(longint(0xA0000000), 0x40000000, @Q31_1);           // Q31_1 := 0x80000000; r := 1;

  // Q31_Cos...........................................................
  Q31_Ftoi(0, @Q31_1);
  Q31_2 := Q31_Cos (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := cos(0) := 1

  Q31_Ftoi(-1, @Q31_1);
  Q31_2 := Q31_Cos (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := cos(-1) := 0.5403023

  // Q31_Sin...........................................................
  Q31_Ftoi(0, @Q31_1);
  Q31_2 := Q31_Sin (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := sin(0) := 0

  Q31_Ftoi(-1, @Q31_1);
  Q31_2 := Q31_Sin (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := sin(-1) := -0.84161138

  // Q31_Tan...........................................................
  Q31_Ftoi(0, @Q31_1);
  Q31_2 := Q31_Tan (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := tan(0) := 0

  Q31_Ftoi(-0.78530, @Q31_1);
  Q31_2 := Q31_Tan (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := tan(-0.78546) := -0.999

  // Q31_Asin.........................................................
  Q31_Ftoi(0, @Q31_1);
  Q31_2 := Q31_Asin (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := asin(0) := 0

  Q31_Ftoi(-0.841308, @Q31_1);
  Q31_2 := Q31_Asin (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := asin(-0.8416137) := -0.99967

  // Q31_Acos.........................................................
  Q31_Ftoi(0.6, @Q31_1);
  Q31_2 := Q31_Acos (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := acos(0.6) := 0.927295

  Q31_Ftoi(0.5403137, @Q31_1);
  Q31_2 := Q31_Acos (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := acos(0.5403137) := 0.9999

  // Q31_Atan.........................................................
  Q31_Ftoi(0, @Q31_1);
  Q31_2 := Q31_Atan (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := atan(0) := 0

  Q31_Ftoi(-1, @Q31_1);
  Q31_2 := Q31_Atan (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := atan(-1) := -0.779149

  // Q31_Log.........................................................
  Q31_Ftoi(0.3, @Q31_1);
  Q31_2 := Q31_Log (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := log(0.3) := -0.5228787

  Q31_Ftoi(0.1, @Q31_1);
  Q31_2 := Q31_Log (Q31_1);
  Q31_Itof(Q31_2, @f);                          // f := log(0.1) := -0.9986508
end.
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