arm_cos_f32.c
254 lines
| 10.6 KiB
| text/x-c
|
CLexer
r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_cos_f32.c | ||||
* | ||||
* Description: Fast cosine calculation for floating-point values. | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | ||||
* | ||||
* Version 1.0.10 2011/7/15 | ||||
* Big Endian support added and Merged M0 and M3/M4 Source code. | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated. | ||||
* -------------------------------------------------------------------- */ | ||||
#include "arm_math.h" | ||||
/** | ||||
* @ingroup groupFastMath | ||||
*/ | ||||
/** | ||||
* @defgroup cos Cosine | ||||
* | ||||
* 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 1) mapping to [0 2*pi). | ||||
* | ||||
* The implementation is based on table lookup using 256 values together with cubic interpolation. | ||||
* The steps used are: | ||||
* -# Calculation of the nearest integer table index | ||||
* -# Fetch the four table values a, b, c, and d | ||||
* -# Compute the fractional portion (fract) of the table index. | ||||
* -# Calculation of wa, wb, wc, wd | ||||
* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> | ||||
* | ||||
* where | ||||
* <pre> | ||||
* a=Table[index-1]; | ||||
* b=Table[index+0]; | ||||
* c=Table[index+1]; | ||||
* d=Table[index+2]; | ||||
* </pre> | ||||
* and | ||||
* <pre> | ||||
* 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; | ||||
* </pre> | ||||
*/ | ||||
/** | ||||
* @addtogroup cos | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* \par | ||||
* <b>Example code for Generation of Cos Table:</b> | ||||
* tableSize = 256; | ||||
* <pre>for(n = -1; n < (tableSize + 1); n++) | ||||
* { | ||||
* cosTable[n+1]= cos(2*pi*n/tableSize); | ||||
* } </pre> | ||||
* where pi value is 3.14159265358979 | ||||
*/ | ||||
static const float32_t cosTable[259] = { | ||||
0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f, | ||||
0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f, | ||||
0.992479562759399410f, 0.989176511764526370f, | ||||
0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f, | ||||
0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f, | ||||
0.949528157711029050f, 0.941544055938720700f, | ||||
0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f, | ||||
0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f, | ||||
0.870086967945098880f, 0.857728600502014160f, | ||||
0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f, | ||||
0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f, | ||||
0.757208824157714840f, 0.740951120853424070f, | ||||
0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f, | ||||
0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f, | ||||
0.615231573581695560f, 0.595699310302734380f, | ||||
0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f, | ||||
0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f, | ||||
0.449611335992813110f, 0.427555084228515630f, | ||||
0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f, | ||||
0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f, | ||||
0.266712754964828490f, 0.242980182170867920f, | ||||
0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f, | ||||
0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f, | ||||
0.073564566671848297f, 0.049067676067352295f, | ||||
0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f, | ||||
-0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f, | ||||
-0.122410677373409270f, -0.146730467677116390f, | ||||
-0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f, | ||||
-0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f, | ||||
-0.313681751489639280f, -0.336889863014221190f, | ||||
-0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f, | ||||
-0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f, | ||||
-0.492898195981979370f, -0.514102756977081300f, | ||||
-0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f, | ||||
-0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f, | ||||
-0.653172850608825680f, -0.671558976173400880f, | ||||
-0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f, | ||||
-0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f, | ||||
-0.788346409797668460f, -0.803207516670227050f, | ||||
-0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f, | ||||
-0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f, | ||||
-0.893224298954010010f, -0.903989315032958980f, | ||||
-0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f, | ||||
-0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f, | ||||
-0.963776051998138430f, -0.970031261444091800f, | ||||
-0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f, | ||||
-0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f, | ||||
-0.997290432453155520f, -0.998795449733734130f, | ||||
-0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f, | ||||
-0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f, | ||||
-0.992479562759399410f, -0.989176511764526370f, | ||||
-0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f, | ||||
-0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f, | ||||
-0.949528157711029050f, -0.941544055938720700f, | ||||
-0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f, | ||||
-0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f, | ||||
-0.870086967945098880f, -0.857728600502014160f, | ||||
-0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f, | ||||
-0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f, | ||||
-0.757208824157714840f, -0.740951120853424070f, | ||||
-0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f, | ||||
-0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f, | ||||
-0.615231573581695560f, -0.595699310302734380f, | ||||
-0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f, | ||||
-0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f, | ||||
-0.449611335992813110f, -0.427555084228515630f, | ||||
-0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f, | ||||
-0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f, | ||||
-0.266712754964828490f, -0.242980182170867920f, | ||||
-0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f, | ||||
-0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f, | ||||
-0.073564566671848297f, -0.049067676067352295f, | ||||
-0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f, | ||||
0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f, | ||||
0.122410677373409270f, 0.146730467677116390f, | ||||
0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f, | ||||
0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f, | ||||
0.313681751489639280f, 0.336889863014221190f, | ||||
0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f, | ||||
0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f, | ||||
0.492898195981979370f, 0.514102756977081300f, | ||||
0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f, | ||||
0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f, | ||||
0.653172850608825680f, 0.671558976173400880f, | ||||
0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f, | ||||
0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f, | ||||
0.788346409797668460f, 0.803207516670227050f, | ||||
0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f, | ||||
0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f, | ||||
0.893224298954010010f, 0.903989315032958980f, | ||||
0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f, | ||||
0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f, | ||||
0.963776051998138430f, 0.970031261444091800f, | ||||
0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f, | ||||
0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f, | ||||
0.997290432453155520f, 0.998795449733734130f, | ||||
0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f | ||||
}; | ||||
/** | ||||
* @brief Fast approximation to the trigonometric cosine function for floating-point data. | ||||
* @param[in] x input value in radians. | ||||
* @return cos(x). | ||||
*/ | ||||
float32_t arm_cos_f32( | ||||
float32_t x) | ||||
{ | ||||
float32_t cosVal, fract, in; | ||||
uint32_t index; | ||||
uint32_t tableSize = (uint32_t) TABLE_SIZE; | ||||
float32_t wa, wb, wc, wd; | ||||
float32_t a, b, c, d; | ||||
float32_t *tablePtr; | ||||
int32_t n; | ||||
/* input x is in radians */ | ||||
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */ | ||||
in = x * 0.159154943092f; | ||||
/* Calculation of floor value of input */ | ||||
n = (int32_t) in; | ||||
/* Make negative values towards -infinity */ | ||||
if(x < 0.0f) | ||||
{ | ||||
n = n - 1; | ||||
} | ||||
/* Map input value to [0 1] */ | ||||
in = in - (float32_t) n; | ||||
/* Calculation of index of the table */ | ||||
index = (uint32_t) (tableSize * in); | ||||
/* fractional value calculation */ | ||||
fract = ((float32_t) tableSize * in) - (float32_t) index; | ||||
/* Initialise table pointer */ | ||||
tablePtr = (float32_t *) & cosTable[index]; | ||||
/* Read four nearest values of input value from the cos table */ | ||||
a = *tablePtr++; | ||||
b = *tablePtr++; | ||||
c = *tablePtr++; | ||||
d = *tablePtr++; | ||||
/* Cubic interpolation process */ | ||||
wa = -(((0.166666667f) * fract) * (fract * fract)) + | ||||
(((0.5f) * (fract * fract)) - ((0.3333333333333f) * fract)); | ||||
wb = ((((0.5f) * fract) * (fract * fract)) - (fract * fract)) + | ||||
(-((0.5f) * fract) + 1.0f); | ||||
wc = -(((0.5f) * fract) * (fract * fract)) + | ||||
(((0.5f) * (fract * fract)) + fract); | ||||
wd = (((0.166666667f) * fract) * (fract * fract)) - | ||||
((0.166666667f) * fract); | ||||
/* Calculate cos value */ | ||||
cosVal = ((a * wa) + (b * wb)) + ((c * wc) + (d * wd)); | ||||
/* Return the output value */ | ||||
return (cosVal); | ||||
} | ||||
/** | ||||
* @} end of cos group | ||||
*/ | ||||