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Cosine
Functions | Variables

Cosine
[Fast Math Functions]

Computes the trigonometric cosine function using a combination of table lookup and cubic interpolation. More...

Functions

float32_t arm_cos_f32 (float32_t x)
 Fast approximation to the trigonometric cosine function for floating-point data.
q15_t arm_cos_q15 (q15_t x)
 Fast approximation to the trigonometric cosine function for Q15 data.
q31_t arm_cos_q31 (q31_t x)
 Fast approximation to the trigonometric cosine function for Q31 data.

Variables

static const float32_t cosTable [260]
static const q15_t cosTableQ15 [259]
static const q31_t cosTableQ31 [259]

Detailed Description

Computes the trigonometric cosine function using a combination of table lookup and cubic interpolation.

There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a value of 2*pi wraps around to 0.

The implementation is based on table lookup using 256 values together with cubic interpolation. The steps used are:

  1. Calculation of the nearest integer table index
  2. Fetch the four table values a, b, c, and d
  3. Compute the fractional portion (fract) of the table index.
  4. Calculation of wa, wb, wc, wd
  5. The final result equals a*wa + b*wb + c*wc + d*wd

where 

    
    a=Table[index-1];    
    b=Table[index+0];    
    c=Table[index+1];    
    d=Table[index+2];

and 

    
    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;    
    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;    
    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;    
    wd=(1/6)*fract.^3 - (1/6)*fract;

Function Documentation

float32_t arm_cos_f32 ( float32_t  x )

Fast approximation to the trigonometric cosine function for floating-point data.

Parameters:
[in]xinput value in radians.
Returns:
cos(x).

Definition at line 207 of file arm_cos_f32.c.

q15_t arm_cos_q15 ( q15_t  x )

Fast approximation to the trigonometric cosine function for Q15 data.

Parameters:
[in]xScaled input value in radians.
Returns:
cos(x).

The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).

Definition at line 117 of file arm_cos_q15.c.

q31_t arm_cos_q31 ( q31_t  x )

Fast approximation to the trigonometric cosine function for Q31 data.

Parameters:
[in]xScaled input value in radians.
Returns:
cos(x).

The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).

Definition at line 149 of file arm_cos_q31.c.

Variable Documentation

const float32_t cosTable[260] [static]
Example code for Generation of Cos Table: 
 tableSize = 256;    
 for(n = -1; n < (tableSize + 2); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 }
where pi value is 3.14159265358979

Definition at line 99 of file arm_cos_f32.c.

const q15_t cosTableQ15[259] [static]
Table values are in Q15 (1.15 fixed-point format) and generation is done in three steps. First, generate cos values in floating point: 
 tableSize = 256;
 for(n = -1; n < (tableSize + 1); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 }
where pi value is 3.14159265358979
Second, convert floating-point to Q15 (fixed-point): (cosTable[i] * pow(2, 15))
Finally, round to the nearest integer value: cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);

Definition at line 71 of file arm_cos_q15.c.

const q31_t cosTableQ31[259] [static]
Table values are in Q31 (1.31 fixed-point format) and generation is done in three steps. First, generate cos values in floating point: 
 tableSize = 256;      
 for(n = -1; n < (tableSize + 1); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 }
where pi value is 3.14159265358979
Second, convert floating-point to Q31 (Fixed point): (cosTable[i] * pow(2, 31))
Finally, round to the nearest integer value: cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);

Definition at line 72 of file arm_cos_q31.c.

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