291 lines
12 KiB
C
291 lines
12 KiB
C
/* ----------------------------------------------------------------------
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* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
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*
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* $Date: 17. January 2013
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* $Revision: V1.4.1
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*
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* Project: CMSIS DSP Library
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* Title: arm_cos_f32.c
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*
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* Description: Fast cosine calculation for floating-point values.
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* - Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* - Neither the name of ARM LIMITED nor the names of its contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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/**
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* @ingroup groupFastMath
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*/
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/**
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* @defgroup cos Cosine
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*
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* Computes the trigonometric cosine function using a combination of table lookup
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* and cubic interpolation. There are separate functions for
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* Q15, Q31, and floating-point data types.
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* The input to the floating-point version is in radians while the
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* fixed-point Q15 and Q31 have a scaled input with the range
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* [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
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* value of 2*pi wraps around to 0.
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*
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* The implementation is based on table lookup using 256 values together with cubic interpolation.
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* The steps used are:
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* -# Calculation of the nearest integer table index
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* -# Fetch the four table values a, b, c, and d
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* -# Compute the fractional portion (fract) of the table index.
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* -# Calculation of wa, wb, wc, wd
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* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
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*
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* where
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* <pre>
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* a=Table[index-1];
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* b=Table[index+0];
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* c=Table[index+1];
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* d=Table[index+2];
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* </pre>
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* and
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* <pre>
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* wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
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* wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
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* wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
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* wd=(1/6)*fract.^3 - (1/6)*fract;
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* </pre>
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*/
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/**
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* @addtogroup cos
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* @{
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*/
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/**
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* \par
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* <b>Example code for Generation of Cos Table:</b>
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* <pre>
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* tableSize = 256;
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* for(n = -1; n < (tableSize + 2); n++)
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* {
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* cosTable[n+1]= cos(2*pi*n/tableSize);
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* } </pre>
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* where pi value is 3.14159265358979
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*/
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static const float32_t cosTable[260] = {
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0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
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0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
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0.992479562759399410f, 0.989176511764526370f,
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0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
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0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
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0.949528157711029050f, 0.941544055938720700f,
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0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
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0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
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0.870086967945098880f, 0.857728600502014160f,
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0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
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0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
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0.757208824157714840f, 0.740951120853424070f,
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0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
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0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
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0.615231573581695560f, 0.595699310302734380f,
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0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
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0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
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0.449611335992813110f, 0.427555084228515630f,
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0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
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0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
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0.266712754964828490f, 0.242980182170867920f,
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0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
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0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
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0.073564566671848297f, 0.049067676067352295f,
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0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f,
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-0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
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-0.122410677373409270f, -0.146730467677116390f,
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-0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
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-0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
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-0.313681751489639280f, -0.336889863014221190f,
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-0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
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-0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
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-0.492898195981979370f, -0.514102756977081300f,
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-0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
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-0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
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-0.653172850608825680f, -0.671558976173400880f,
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-0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
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-0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
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-0.788346409797668460f, -0.803207516670227050f,
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-0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
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-0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
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-0.893224298954010010f, -0.903989315032958980f,
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-0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
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-0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
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-0.963776051998138430f, -0.970031261444091800f,
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-0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
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-0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
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-0.997290432453155520f, -0.998795449733734130f,
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-0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
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-0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
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-0.992479562759399410f, -0.989176511764526370f,
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-0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
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-0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
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-0.949528157711029050f, -0.941544055938720700f,
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-0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
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-0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
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-0.870086967945098880f, -0.857728600502014160f,
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-0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
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-0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
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-0.757208824157714840f, -0.740951120853424070f,
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-0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
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-0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
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-0.615231573581695560f, -0.595699310302734380f,
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-0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
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-0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
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-0.449611335992813110f, -0.427555084228515630f,
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-0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
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-0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
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-0.266712754964828490f, -0.242980182170867920f,
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-0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
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-0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
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-0.073564566671848297f, -0.049067676067352295f,
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-0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f,
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0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
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0.122410677373409270f, 0.146730467677116390f,
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0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
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0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
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0.313681751489639280f, 0.336889863014221190f,
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0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
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0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
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0.492898195981979370f, 0.514102756977081300f,
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0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
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0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
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0.653172850608825680f, 0.671558976173400880f,
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0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
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0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
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0.788346409797668460f, 0.803207516670227050f,
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0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
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0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
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0.893224298954010010f, 0.903989315032958980f,
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0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
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0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
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0.963776051998138430f, 0.970031261444091800f,
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0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
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0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
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0.997290432453155520f, 0.998795449733734130f,
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0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
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0.998795449733734130f
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};
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/**
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* @brief Fast approximation to the trigonometric cosine function for floating-point data.
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* @param[in] x input value in radians.
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* @return cos(x).
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*/
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float32_t arm_cos_f32(
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float32_t x)
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{
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float32_t cosVal, fract, in;
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int32_t index;
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uint32_t tableSize = (uint32_t) TABLE_SIZE;
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float32_t wa, wb, wc, wd;
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float32_t a, b, c, d;
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float32_t *tablePtr;
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int32_t n;
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float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
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float32_t oneminusfractby2;
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float32_t frby2xfrsq, frby6xfrsq;
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/* input x is in radians */
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/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
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in = x * 0.159154943092f;
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/* Calculation of floor value of input */
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n = (int32_t) in;
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/* Make negative values towards -infinity */
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if(x < 0.0f)
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{
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n = n - 1;
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}
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/* Map input value to [0 1] */
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in = in - (float32_t) n;
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/* Calculation of index of the table */
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index = (uint32_t) (tableSize * in);
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/* fractional value calculation */
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fract = ((float32_t) tableSize * in) - (float32_t) index;
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/* Checking min and max index of table */
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if(index < 0)
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{
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index = 0;
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}
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else if(index > 256)
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{
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index = 256;
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}
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/* Initialise table pointer */
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tablePtr = (float32_t *) & cosTable[index];
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/* Read four nearest values of input value from the cos table */
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a = tablePtr[0];
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b = tablePtr[1];
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c = tablePtr[2];
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d = tablePtr[3];
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/* Cubic interpolation process */
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fractsq = fract * fract;
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fractby2 = fract * 0.5f;
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fractby6 = fract * 0.166666667f;
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fractby3 = fract * 0.3333333333333f;
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fractsqby2 = fractsq * 0.5f;
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frby2xfrsq = (fractby2) * fractsq;
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frby6xfrsq = (fractby6) * fractsq;
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oneminusfractby2 = 1.0f - fractby2;
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wb = fractsqby2 - fractby3;
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wc = (fractsqby2 + fract);
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wa = wb - frby6xfrsq;
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wb = frby2xfrsq - fractsq;
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cosVal = wa * a;
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wc = wc - frby2xfrsq;
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wd = (frby6xfrsq) - fractby6;
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wb = wb + oneminusfractby2;
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/* Calculate cos value */
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cosVal = (cosVal + (b * wb)) + ((c * wc) + (d * wd));
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/* Return the output value */
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return (cosVal);
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}
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/**
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* @} end of cos group
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*/
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