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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
*
* $Date: 17. January 2013
* $Revision: V1.4.1
*
* Project: CMSIS DSP Library
* Title: arm_sin_q15.c
*
* Description: Fast sine 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 sin
* @{
*/
/**
* \par
* Table values are in Q15 (1.15 fixed-point format) and generation is done in
* three steps. First, generate sin values in floating point:
* <pre>
* tableSize = 256;
* for(n = -1; n < (tableSize + 1); n++)
* {
* sinTable[n+1]= sin(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
* \par
* Second, convert floating-point to Q15 (fixed-point):
* (sinTable[i] * pow(2, 15))
* \par
* Finally, round to the nearest integer value:
* sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
*/
static const q15_t sinTableQ15[259] = {
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, 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
};
/**
* @brief Fast approximation to the trigonometric sine function for Q15 data.
* @param[in] x Scaled input value in radians.
* @return sin(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_sin_q15(
q15_t x)
{
q31_t sinVal; /* Temporary variables output */
q15_t *tablePtr; /* Pointer to table */
q15_t fract, in, in2; /* Temporary variables for input, output */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q15_t a, b, c, d; /* Four nearest output values */
q15_t fractCube, fractSquare; /* Temporary values 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 *) & sinTableQ15[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 += ((q31_t) fractSquare >> 1u);
/* Read first nearest value of output from the sin table */
a = *tablePtr++;
/* sinVal = a * wa */
sinVal = a * wa;
/* Calculation of wb */
wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
(((q31_t) fract >> 1u) - 0x7FFF);
/* Read second nearest value of output from the sin table */
b = *tablePtr++;
/* sinVal += b*wb */
sinVal += b * wb;
/* Calculation of wc */
wc = -(q31_t) fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest value of output from the sin table */
c = *tablePtr++;
/* sinVal += c*wc */
sinVal += 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 sin table */
d = *tablePtr++;
/* sinVal += d*wd; */
sinVal += d * wd;
/* Convert output value in 1.15(q15) format and saturate */
sinVal = __SSAT((sinVal >> 15), 16);
/* Return the output value in 1.15(q15) format */
return ((q15_t) sinVal);
}
/**
* @} end of sin group
*/
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