Cosine

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

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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), Where range excludes 2*pi.

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;    
 

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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

Referenced by arm_cos_f32().

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

Secondly Convert Floating point to Q15(Fixed point): (cosTable[i] * pow(2, 15))

Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);

Referenced by arm_cos_q15().

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

Secondly Convert Floating point to Q31(Fixed point): (cosTable[i] * pow(2, 31))

Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);

Referenced by arm_cos_q31().

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Function Documentation

float32_t arm_cos_f32

(

float32_t

x

)

Parameters:

[in]

x

input value in radians.

Returns:

cos(x).

Examples:

arm_sin_cos_example_f32.c.

References cosTable, and TABLE_SIZE.

Referenced by main().

q15_t arm_cos_q15

(

q15_t

x

)

Parameters:

[in]

x

Scaled 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), Here range excludes 2*pi.

References cosTableQ15, and TABLE_SPACING_Q15.

q31_t arm_cos_q31

(

q31_t

x

)

Parameters:

[in]

x

Scaled 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), Here range excludes 2*pi.

References cosTableQ31, and TABLE_SPACING_Q31.