arm_sin_q15.c

00001 /* ----------------------------------------------------------------------    
00002 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
00003 *    
00004 * $Date:        17. January 2013
00005 * $Revision:    V1.4.1
00006 *    
00007 * Project:      CMSIS DSP Library    
00008 * Title:        arm_sin_q15.c    
00009 *    
00010 * Description:  Fast sine calculation for Q15 values.   
00011 *    
00012 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
00013 *  
00014 * Redistribution and use in source and binary forms, with or without 
00015 * modification, are permitted provided that the following conditions
00016 * are met:
00017 *   - Redistributions of source code must retain the above copyright
00018 *     notice, this list of conditions and the following disclaimer.
00019 *   - Redistributions in binary form must reproduce the above copyright
00020 *     notice, this list of conditions and the following disclaimer in
00021 *     the documentation and/or other materials provided with the 
00022 *     distribution.
00023 *   - Neither the name of ARM LIMITED nor the names of its contributors
00024 *     may be used to endorse or promote products derived from this
00025 *     software without specific prior written permission.
00026 *
00027 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
00028 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
00029 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
00030 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
00031 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
00032 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
00033 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
00034 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
00035 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
00036 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
00037 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
00038 * POSSIBILITY OF SUCH DAMAGE. 
00039 * -------------------------------------------------------------------- */
00040 
00041 #include "arm_math.h"
00042 
00043 /**    
00044  * @ingroup groupFastMath    
00045  */
00046 
00047  /**    
00048  * @addtogroup sin    
00049  * @{    
00050  */
00051 
00052 
00053 /**   
00054 * \par    
00055  * Table values are in Q15 (1.15 fixed-point format) and generation is done in 
00056  * three steps.  First,  generate sin values in floating point:    
00057  * <pre>
00058  * tableSize = 256;
00059  * for(n = -1; n < (tableSize + 1); n++)    
00060  * {    
00061  *  sinTable[n+1]= sin(2*pi*n/tableSize);    
00062  * } </pre>     
00063  * where pi value is  3.14159265358979    
00064  * \par    
00065  * Second, convert floating-point to Q15 (fixed-point):    
00066  *  (sinTable[i] * pow(2, 15))    
00067  * \par    
00068  * Finally, round to the nearest integer value:
00069  *  sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
00070 */
00071 
00072 static const q15_t sinTableQ15 [259] = {
00073   0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
00074   0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
00075   0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
00076   0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
00077   0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
00078   0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
00079   0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
00080   0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
00081   0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
00082   0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
00083   0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
00084   0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
00085   0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
00086   0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
00087   0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
00088   0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
00089   0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
00090   0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
00091   0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
00092   0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
00093   0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
00094   0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
00095   0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
00096   0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
00097   0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
00098   0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
00099   0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
00100   0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
00101   0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
00102   0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
00103   0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
00104   0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
00105   0xfcdc, 0x0, 0x324
00106 };
00107 
00108 
00109 /**   
00110  * @brief Fast approximation to the trigonometric sine function for Q15 data.   
00111  * @param[in] x Scaled input value in radians.   
00112  * @return  sin(x).   
00113  *   
00114  * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).
00115  */
00116 
00117 q15_t arm_sin_q15(
00118   q15_t x)
00119 {
00120   q31_t sinVal;                                  /* Temporary variables output */
00121   q15_t *tablePtr;                               /* Pointer to table */
00122   q15_t fract, in, in2;                          /* Temporary variables for input, output */
00123   q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
00124   q15_t a, b, c, d;                              /* Four nearest output values */
00125   q15_t fractCube, fractSquare;                  /* Temporary values for fractional value */
00126   q15_t oneBy6 = 0x1555;                         /* Fixed point value of 1/6 */
00127   q15_t tableSpacing = TABLE_SPACING_Q15;        /* Table spacing */
00128   int32_t index;                                 /* Index variable */
00129 
00130   in = x;
00131 
00132   /* Calculate the nearest index */
00133   index = (int32_t) in / tableSpacing;
00134 
00135   /* Calculate the nearest value of input */
00136   in2 = (q15_t) ((index) * tableSpacing);
00137 
00138   /* Calculation of fractional value */
00139   fract = (in - in2) << 8;
00140 
00141   /* fractSquare = fract * fract */
00142   fractSquare = (q15_t) ((fract * fract) >> 15);
00143 
00144   /* fractCube = fract * fract * fract */
00145   fractCube = (q15_t) ((fractSquare * fract) >> 15);
00146 
00147   /* Checking min and max index of table */
00148   if(index < 0)
00149   {
00150     index = 0;
00151   }
00152   else if(index > 256)
00153   {
00154     index = 256;
00155   }
00156 
00157   /* Initialise table pointer */
00158   tablePtr = (q15_t *) & sinTableQ15 [index];
00159 
00160   /* Cubic interpolation process */
00161   /* Calculation of wa */
00162   /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
00163   wa = (q31_t) oneBy6 *fractCube;
00164   wa += (q31_t) 0x2AAA *fract;
00165   wa = -(wa >> 15);
00166   wa += ((q31_t) fractSquare >> 1u);
00167 
00168   /* Read first nearest value of output from the sin table */
00169   a = *tablePtr++;
00170 
00171   /* sinVal = a * wa */
00172   sinVal = a * wa;
00173 
00174   /* Calculation of wb */
00175   wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
00176     (((q31_t) fract >> 1u) - 0x7FFF);
00177 
00178   /* Read second nearest value of output from the sin table */
00179   b = *tablePtr++;
00180 
00181   /*      sinVal += b*wb */
00182   sinVal += b * wb;
00183 
00184 
00185   /* Calculation of wc */
00186   wc = -(q31_t) fractCube + fractSquare;
00187   wc = (wc >> 1u) + fract;
00188 
00189   /* Read third nearest value of output from the sin table */
00190   c = *tablePtr++;
00191 
00192   /* sinVal += c*wc */
00193   sinVal += c * wc;
00194 
00195   /* Calculation of wd */
00196   /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
00197   fractCube = fractCube - fract;
00198   wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
00199 
00200   /* Read fourth nearest value of output from the sin table */
00201   d = *tablePtr++;
00202 
00203   /* sinVal += d*wd; */
00204   sinVal += d * wd;
00205 
00206   /* Convert output value in 1.15(q15) format and saturate */
00207   sinVal = __SSAT((sinVal >> 15), 16);
00208 
00209   /* Return the output value in 1.15(q15) format */
00210   return ((q15_t) sinVal);
00211 
00212 }
00213 
00214 /**    
00215  * @} end of sin group    
00216  */