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/* ----------------------------------------------------------------------
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* Copyright (C) 2010 ARM Limited. All rights reserved.
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*
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* $Date: 15. July 2011
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* $Revision: V1.0.10
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*
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* Project: CMSIS DSP Library
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* Title: arm_cos_q31.c
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*
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* Description: Fast cosine calculation for Q31 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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* Version 1.0.10 2011/7/15
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* Big Endian support added and Merged M0 and M3/M4 Source code.
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*
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* Version 1.0.3 2010/11/29
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* Re-organized the CMSIS folders and updated documentation.
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*
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* Version 1.0.2 2010/11/11
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* Documentation updated.
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*
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* Version 1.0.1 2010/10/05
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* Production release and review comments incorporated.
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*
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* Version 1.0.0 2010/09/20
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* Production release and review comments incorporated.
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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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* @addtogroup cos
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* @{
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*/
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/**
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* \par
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* Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps
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* First Generate cos values in floating point:
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* tableSize = 256;
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* <pre>for(n = -1; n < (tableSize + 1); 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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* \par
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* Secondly Convert Floating point to Q31(Fixed point):
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* (cosTable[i] * pow(2, 31))
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* \par
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* Finally Rounding to nearest integer is done
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* cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
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*/
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static const q31_t cosTableQ31[259] = {
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0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
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0x7f0991c4, 0x7e9d55fc,
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0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
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0x798a23b1, 0x78848414,
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0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
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0x6f5f02b2, 0x6dca0d14,
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0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
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0x60ec3830, 0x5ed77c8a,
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0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
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0x4ebfe8a5, 0x4c3fdff4,
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0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
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0x398cdd32, 0x36ba2014,
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0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
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0x2223a4c5, 0x1f19f97b,
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0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
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0x96a9049, 0x647d97c,
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0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
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0xed37ef91,
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0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
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0xd7d946d8, 0xd4e0cb15,
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0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
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0xc0e8b648, 0xbe31e19b,
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0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
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0xac64d510, 0xaa0a5b2e,
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0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
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0x9b1776da, 0x99307ee0,
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0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
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0x8daad37b, 0x8c4a142f,
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0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
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0x84a2fc62, 0x83d60412,
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0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
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0x8058c94c, 0x80277872,
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0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
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0x80f66e3c, 0x8162aa04,
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0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
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0x8675dc4f, 0x877b7bec,
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0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
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0x90a0fd4e, 0x9235f2ec,
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0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
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0x9f13c7d0, 0xa1288376,
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0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
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0xb140175b, 0xb3c0200c,
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0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
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0xc67322ce, 0xc945dfec,
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0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
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0xdddc5b3b, 0xe0e60685,
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0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
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0xf6956fb7, 0xf9b82684,
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0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
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0x12c8106f,
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0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
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0x2826b928, 0x2b1f34eb,
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0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
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0x3f1749b8, 0x41ce1e65,
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0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
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0x539b2af0, 0x55f5a4d2,
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0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
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0x64e88926, 0x66cf8120,
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0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
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0x72552c85, 0x73b5ebd1,
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0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
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0x7b5d039e, 0x7c29fbee,
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0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
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0x7fa736b4, 0x7fd8878e,
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0x7ff62182, 0x7fffffff, 0x7ff62182
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};
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/**
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* @brief Fast approximation to the trigonometric cosine function for Q31 data.
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* @param[in] x Scaled input value in radians.
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* @return cos(x).
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*
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* The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
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*/
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q31_t arm_cos_q31(
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q31_t x)
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{
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q31_t cosVal, in, in2; /* Temporary variables for input, output */
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q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
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q31_t a, b, c, d; /* Four nearest output values */
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q31_t *tablePtr; /* Pointer to table */
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q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */
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q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
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q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
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q31_t temp; /* Temporary variable for intermediate process */
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uint32_t index; /* Index variable */
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in = x;
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/* Calculate the nearest index */
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index = in / tableSpacing;
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/* Calculate the nearest value of input */
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in2 = ((q31_t) index) * tableSpacing;
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/* Calculation of fractional value */
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fract = (in - in2) << 8;
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/* fractSquare = fract * fract */
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fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
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fractSquare = fractSquare << 1;
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/* fractCube = fract * fract * fract */
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fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
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fractCube = fractCube << 1;
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/* Initialise table pointer */
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tablePtr = (q31_t *) & cosTableQ31[index];
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/* Cubic interpolation process */
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/* Calculation of wa */
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/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
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wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
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temp = 0x2AAAAAAA;
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wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
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wa = -(wa << 1u);
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wa += (fractSquare >> 1u);
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/* Read first nearest value of output from the cos table */
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a = *tablePtr++;
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/* cosVal = a*wa */
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cosVal = ((q31_t) (((q63_t) a * wa) >> 32));
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/* q31(1.31) Fixed point value of 1 */
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temp = 0x7FFFFFFF;
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/* Calculation of wb */
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wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
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/* Read second nearest value of output from the cos table */
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b = *tablePtr++;
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/* cosVal += b*wb */
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cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32);
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/* Calculation of wc */
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wc = -fractCube + fractSquare;
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wc = (wc >> 1u) + fract;
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/* Read third nearest values of output value from the cos table */
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c = *tablePtr++;
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/* cosVal += c*wc */
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cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32);
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/* Calculation of wd */
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/* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
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fractCube = fractCube - fract;
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wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
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wd = (wd << 1u);
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/* Read fourth nearest value of output from the cos table */
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d = *tablePtr++;
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/* cosVal += d*wd; */
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cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32);
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/* convert cosVal in 2.30 format to 1.31 format */
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return (cosVal << 1u);
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}
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/**
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* @} end of cos group
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*/
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