/* ---------------------------------------------------------------------- * Copyright (C) 2010-2013 ARM Limited. All rights reserved. * * $Date: 17. January 2013 * $Revision: V1.4.1 * * Project: CMSIS DSP Library * Title: arm_cos_q15.c * * Description: Fast cosine calculation for Q15 values. * * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * - Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * - Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * - Neither the name of ARM LIMITED nor the names of its contributors * may be used to endorse or promote products derived from this * software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * -------------------------------------------------------------------- */ #include "arm_math.h" /** * @ingroup groupFastMath */ /** * @addtogroup cos * @{ */ /** * \par * 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 * \par * Second, convert floating-point to Q15 (fixed-point): * (cosTable[i] * pow(2, 15)) * \par * Finally, round to the nearest integer value: * cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5); */ static const q15_t cosTableQ15[259] = { 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d, 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885, 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca, 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7, 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40, 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba, 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a, 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648, 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38, 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1, 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32, 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a, 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930, 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a, 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6, 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027, 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163, 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b, 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236, 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129, 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0, 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946, 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6, 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8, 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8, 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f, 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce, 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6, 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0, 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6, 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a, 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9, 0x7ff6, 0x7fff, 0x7ff6 }; /** * @brief Fast approximation to the trigonometric cosine function for Q15 data. * @param[in] x Scaled input value in radians. * @return 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). */ q15_t arm_cos_q15( q15_t x) { q31_t cosVal; /* Temporary variable for output */ q15_t *tablePtr; /* Pointer to table */ q15_t in, in2; /* Temporary variables for input */ q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ q15_t a, b, c, d; /* Four nearest output values */ q15_t fract, fractCube, fractSquare; /* Variables for fractional value */ q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */ q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */ int32_t index; /* Index variable */ in = x; /* Calculate the nearest index */ index = (int32_t) in / tableSpacing; /* Calculate the nearest value of input */ in2 = (q15_t) index *tableSpacing; /* Calculation of fractional value */ fract = (in - in2) << 8; /* fractSquare = fract * fract */ fractSquare = (q15_t) ((fract * fract) >> 15); /* fractCube = fract * fract * fract */ fractCube = (q15_t) ((fractSquare * fract) >> 15); /* Checking min and max index of table */ if(index < 0) { index = 0; } else if(index > 256) { index = 256; } /* Initialise table pointer */ tablePtr = (q15_t *) & cosTableQ15[index]; /* Cubic interpolation process */ /* Calculation of wa */ /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */ wa = (q31_t) oneBy6 *fractCube; wa += (q31_t) 0x2AAA *fract; wa = -(wa >> 15); wa += (fractSquare >> 1u); /* Read first nearest value of output from the cos table */ a = *tablePtr++; /* cosVal = a * wa */ cosVal = a * wa; /* Calculation of wb */ wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF; /* Read second nearest value of output from the cos table */ b = *tablePtr++; /* cosVal += b*wb */ cosVal += b * wb; /* Calculation of wc */ wc = -(q31_t) fractCube + fractSquare; wc = (wc >> 1u) + fract; /* Read third nearest value of output from the cos table */ c = *tablePtr++; /* cosVal += c*wc */ cosVal += c * wc; /* Calculation of wd */ /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ fractCube = fractCube - fract; wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15)); /* Read fourth nearest value of output from the cos table */ d = *tablePtr++; /* cosVal += d*wd; */ cosVal += d * wd; /* Convert output value in 1.15(q15) format and saturate */ cosVal = __SSAT((cosVal >> 15), 16); /* Return the output value in 1.15(q15) format */ return ((q15_t) cosVal); } /** * @} end of cos group */