Q15 Library
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Q15 Library

mikroC PRO for PIC32 includes a library for operating and working with Q15 fractional number format.

Library Routines

Q15_Abs

Prototype

unsigned int Q15_Abs (int in, int *out);
Description

Function calculates absolute value of the Q15 fractional format number.
Parameters
  • in: Q15 input number, ranging from -32768 to 32767.
  • out: pointer to Q15 output number.
Returns

Function always returns zero.

Q15_Add

Prototype

unsigned int Q15_Add(int in1, int in2, int *out);
Description

Function sums two Q15 format numbers.

If the result exceeds [-32768, 32767] limits, result will be maximal(minimal) number in Q15 format.
Parameters
  • in1: First Q15 number, ranging from -32768 to 32767.
  • in2: Second Q15 number, ranging from -32768 to 32767.
  • out: pointer to Q15 output number.
Returns
  • 1 - if the result exceeds [-32768, 32767] limits.
  • 0 - otherwise.

Q15_Sub

Prototype

unsigned int Q15_Sub(int in1, int in2, int *out);
Description

Function subtracts two Q15 format numbers.

If the result exceeds [-32768, 32767] limits, result will be maximal(minimal) number in Q15 format.
Parameters
  • in1: First Q15 number, ranging from -32768 to 32767.
  • in2: Second Q15 number, ranging from -32768 to 32767.
  • out: pointer to Q15 output number.
Returns
  • 1 - if the result exceeds [-2147483648, 2147483647] limits.
  • 0 - otherwise.

Q15_Itof

Prototype

unsigned int Q15_Itof(int x, float *f);
Description

Function converts number from the Q15 fractional number format to floating point number format.
Parameters
  • x: input Q15 number, ranging from -32768 to 32767.
  • f: pointer to the resulting floating point number.
Returns

Function always returns zero.

Q15_Ftoi

Prototype

unsigned int Q15_Ftoi(float f, int *x);
Description

Function converts number from the floating point number format to Q15 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 0x7FFF (0x8000).
Parameters
  • f: floating format number to be converted.
  • x: pointer to the resulting Q15 fractional format number.
Returns
  • 1 - If overflow has been detected.
  • 0 - If no errors occured.

Q15_Itoa

Prototype

void Q15_Itoa(int x, char *s);
Description

Function converts number from the Q15 fractional format to ASCII string.

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

  • s - sign; '-' negative, space - positive.
  • n - integer part; 0 or 1.
  • d - decimal part; 0..9 (ending zeros are not displayed).
Parameters
  • x: Q15 format number to be converted.
  • s: pointer to the resulting ASCII string.
Returns

Nothing.

Q15_Atoi

Prototype

unsigned int Q15_Atoi(char *s, int* out);
Description

Function converts the input ASCII string s into a number in Q15 fractional point format.

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

  • 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 Q15 format.
Returns
  • 2 - If input string is in not in the appropriate format.
  • 1 - If overflow has been detected.
  • 0 - If no errors occured.

Q15_Cos

Prototype

int Q15_Cos(int x);
Description

Function returns the cosine of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from 17748 to 32767.
Parameters
  • x: input number in the Q15 format number, ranging from -32768 to 32767
Returns

Function returns value in the Q15 format, ranging from 17748 to 32767.

Q15_Sin

Prototype

int Q15_Sin(int x);
Description

Function returns the sine of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from -27580 to 27578.
Parameters
  • x: input number in the Q15 format number, ranging from -32768 to 32767.
Returns

Function returns value in the Q15 format, ranging from -27580 to 27578.

Q15_Tan

Prototype

int Q15_Tan(int x);
Description

Function returns the tangent of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from -32768 to 32767.
Parameters
  • x: input number in the Q15 format number, ranging from -25733 to 25738.
Returns

Function returns value in the Q15 format, ranging from -32768 to 32767.

Q15_Asin

Prototype

int Q15_Asin(int x);
Description

Function returns the arc sine of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from -32768 to 32767.
Parameters
  • x: input number in the Q15 format number, ranging from -27568 to 27578.
Returns

Function returns value in the Q15 format, ranging from -32768 to 32767.

Q15_Atan

Prototype

int Q15_Atan(int x);
Description

Function returns the arc tangent of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from -25532 to 25509.
Parameters
  • x: input number in the Q15 format number, ranging from -32768 to 32767.
Returns

Function returns value in the Q15 format, ranging from -25532 to 25509.

Q15_Acos

Prototype

int Q15_Acos(int x);
Description

Function returns the arc cosine of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from 2887 to 32767.
Parameters
  • x: input number in the Q15 format number, ranging from 17705 to 32767.
Returns

Function returns value in the Q15 format, ranging from 2887 to 32767.

Q15_Log

Prototype

int Q15_Log(int x);
Description

Function returns the logarithm of x. The input number is in the Q15 format number and returns value in the Q15 format, ranging from -32748 to 0.
Parameters
  • x: input number in the Q15 format number, ranging from 3277 to 32767.
Returns

Function returns value in the Q15 format, ranging from -32748 to 0.

Library Example

int  Q15_1, Q15_2;

int   i;
long  l;
unsigned r;
float f;
char  stringQ15[19];

void main() {

  // Q15_Ftoi
  f = 0.5;
  r = Q15_Ftoi(f, &Q15_1);                      // Q15_1 = 0x4000; r = 0;
  f = 1.5;
  r = Q15_Ftoi(f, &Q15_1);                      // Q15_1 = 0x7FFF; r = 1;
  f = -2.5;
  r = Q15_Ftoi(f, &Q15_1);                      // Q15_1 = 0x8000; r = 1;

  // Q15_Itof
  Q15_1 = 0x1000;
  r = Q15_Itof(Q15_1, &f);                      // f = 0.125; r = 0;

  // Q15_Itoa
  Q15_1 = 0xFFFF;
  Q15_Itoa(Q15_1, stringQ15);                   // stgingQ15 = "-0.000030517578125"

  // Q15_Atoi
  r = Q15_Atoi("+0.25", &Q15_1);                // Q15_1 = 0x2000; r = 0;
  r = Q15_Atoi("        +0.7", &Q15_1);         // Q15_1 = 0x5999; r = 0;
  r = Q15_Atoi("mikroe.25", &Q15_1);            // r = 2;

  // Q15_Abs
  Q15_Abs(0x8000, &Q15_1);                      // Q15_1 = 0x7FFF;
  Q15_Abs(0xE000, &Q15_1);                      // Q15_1 = 0X2000;
  
  // Q15_Add
  r = Q15_Add(0x2000, 0x4000, &Q15_1);          // Q15_1 = 0x6000; r = 0;
  r = Q15_Add(0x7000, 0x4000, &Q15_1);          // Q15_1 = 0x7FFF; r = 1;
  
  // Q15_Sub
  r = Q15_Sub(0x2000, 0x4000, &Q15_1);          // Q15_1 = 0xE000; r = 0;
  r = Q15_Sub(0x7000, 0xC000, &Q15_1);          // Q15_1 = 0x7FFF; r = 1;
  
  // Q15_Cos
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Cos (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = cos(0.5) = 0.8775635
  
  Q15_Ftoi(1, &Q15_1);
  Q15_2 = Q15_Cos (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = cos(1) = 0.5403023
  
  // Q15_Sin
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Sin (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = sin(0.5) = 0.4794006

  Q15_Ftoi(1, &Q15_1);
  Q15_2 = Q15_Sin (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = sin(1) = 0.84161138

  // Q15_Tan
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Tan (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = tan(0.5) = 0.54623

  Q15_Ftoi(0.78546, &Q15_1);
  Q15_2 = Q15_Tan (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = tan(0.78546) = 0.999

  // Q15_Asin
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Asin (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = asin(0.5) = 0.52349

  Q15_Ftoi(0.8416137, &Q15_1);
  Q15_2 = Q15_Asin (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = asin(0.8416137) = 0.999

  Q31_Ftoi(0, &Q31_1);
  Q31_2 = Q31_Asin (Q31_1);
  Q31_Itof(Q31_2, &f);                          // f = asin(0) = 0

  // Q15_Acos
  Q15_Ftoi(0.9, &Q15_1);
  Q15_2 = Q15_Acos (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = acos(0.9) = 0.451026

  Q15_Ftoi(0.8, &Q15_1);
  Q15_2 = Q15_Acos (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = acos(0.8) = 0.6430969

  // Q15_Atan
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Atan (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = atan(0.5) = 0.463531

  Q15_Ftoi(1, &Q15_1);
  Q15_2 = Q15_Atan (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = atan(1) = 0.778472

  // Q15_Log
  Q15_Ftoi(0.5, &Q15_1);
  Q15_2 = Q15_Log (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = log(0.5) = -0.301239

  Q15_Ftoi(1, &Q15_1);
  Q15_2 = Q15_Log (Q15_1);
  Q15_Itof(Q15_2, &f);                          // f = log(1) = 0
}
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