tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_f32.c

   1 /* ----------------------------------------------------------------------
   2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
   3 *
   4 * $Date:        17. January 2013
   5 * $Revision:    V1.4.1
   6 *
   7 * Project:          CMSIS DSP Library
   8 * Title:                arm_sin_f32.c
   9 *
  10 * Description:  Fast sine calculation for floating-point values.
  11 *
  12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  13 *
  14 * Redistribution and use in source and binary forms, with or without
  15 * modification, are permitted provided that the following conditions
  16 * are met:
  17 *   - Redistributions of source code must retain the above copyright
  18 *     notice, this list of conditions and the following disclaimer.
  19 *   - Redistributions in binary form must reproduce the above copyright
  20 *     notice, this list of conditions and the following disclaimer in
  21 *     the documentation and/or other materials provided with the
  22 *     distribution.
  23 *   - Neither the name of ARM LIMITED nor the names of its contributors
  24 *     may be used to endorse or promote products derived from this
  25 *     software without specific prior written permission.
  26 *
  27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  38 * POSSIBILITY OF SUCH DAMAGE.
  39 * -------------------------------------------------------------------- */
  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupFastMath
  45  */
  46
  47 /**
  48  * @defgroup sin Sine
  49  *
  50  * Computes the trigonometric sine function using a combination of table lookup
  51  * and cubic interpolation.  There are separate functions for
  52  * Q15, Q31, and floating-point data types.
  53  * The input to the floating-point version is in radians while the
  54  * fixed-point Q15 and Q31 have a scaled input with the range
  55  * [0 +0.9999] mapping to [0 2*pi).  The fixed-point range is chosen so that a
  56  * value of 2*pi wraps around to 0.
  57  *
  58  * The implementation is based on table lookup using 256 values together with cubic interpolation.
  59  * The steps used are:
  60  *  -# Calculation of the nearest integer table index
  61  *  -# Fetch the four table values a, b, c, and d
  62  *  -# Compute the fractional portion (fract) of the table index.
  63  *  -# Calculation of wa, wb, wc, wd
  64  *  -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
  65  *
  66  * where
  67  * <pre>
  68  *    a=Table[index-1];
  69  *    b=Table[index+0];
  70  *    c=Table[index+1];
  71  *    d=Table[index+2];
  72  * </pre>
  73  * and
  74  * <pre>
  75  *    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
  76  *    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
  77  *    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
  78  *    wd=(1/6)*fract.^3 - (1/6)*fract;
  79  * </pre>
  80  */
  81
  82 /**
  83  * @addtogroup sin
  84  * @{
  85  */
  86
  87
  88 /**
  89  * \par
  90  * Example code for the generation of the floating-point sine table:
  91  * <pre>
  92  * tableSize = 256;
  93  * for(n = -1; n < (tableSize + 1); n++)
  94  * {
  95  *      sinTable[n+1]=sin(2*pi*n/tableSize);
  96  * }</pre>
  97  * \par
  98  * where pi value is  3.14159265358979
  99  */
 100
 101 static const float32_t sinTable[259] = {
 102   -0.024541229009628296f, 0.000000000000000000f, 0.024541229009628296f,
 103   0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
 104   0.122410677373409270f, 0.146730467677116390f,
 105   0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
 106   0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
 107   0.313681751489639280f, 0.336889863014221190f,
 108   0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
 109   0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
 110   0.492898195981979370f, 0.514102756977081300f,
 111   0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
 112   0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
 113   0.653172850608825680f, 0.671558976173400880f,
 114   0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
 115   0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
 116   0.788346409797668460f, 0.803207516670227050f,
 117   0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
 118   0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
 119   0.893224298954010010f, 0.903989315032958980f,
 120   0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
 121   0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
 122   0.963776051998138430f, 0.970031261444091800f,
 123   0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
 124   0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
 125   0.997290432453155520f, 0.998795449733734130f,
 126   0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
 127   0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
 128   0.992479562759399410f, 0.989176511764526370f,
 129   0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
 130   0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
 131   0.949528157711029050f, 0.941544055938720700f,
 132   0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
 133   0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
 134   0.870086967945098880f, 0.857728600502014160f,
 135   0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
 136   0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
 137   0.757208824157714840f, 0.740951120853424070f,
 138   0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
 139   0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
 140   0.615231573581695560f, 0.595699310302734380f,
 141   0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
 142   0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
 143   0.449611335992813110f, 0.427555084228515630f,
 144   0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
 145   0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
 146   0.266712754964828490f, 0.242980182170867920f,
 147   0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
 148   0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
 149   0.073564566671848297f, 0.049067676067352295f,
 150   0.024541229009628296f, 0.000000000000000122f, -0.024541229009628296f,
 151   -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
 152   -0.122410677373409270f, -0.146730467677116390f,
 153   -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
 154   -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
 155   -0.313681751489639280f, -0.336889863014221190f,
 156   -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
 157   -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
 158   -0.492898195981979370f, -0.514102756977081300f,
 159   -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
 160   -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
 161   -0.653172850608825680f, -0.671558976173400880f,
 162   -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
 163   -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
 164   -0.788346409797668460f, -0.803207516670227050f,
 165   -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
 166   -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
 167   -0.893224298954010010f, -0.903989315032958980f,
 168   -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
 169   -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
 170   -0.963776051998138430f, -0.970031261444091800f,
 171   -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
 172   -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
 173   -0.997290432453155520f, -0.998795449733734130f,
 174   -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
 175   -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
 176   -0.992479562759399410f, -0.989176511764526370f,
 177   -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
 178   -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
 179   -0.949528157711029050f, -0.941544055938720700f,
 180   -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
 181   -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
 182   -0.870086967945098880f, -0.857728600502014160f,
 183   -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
 184   -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
 185   -0.757208824157714840f, -0.740951120853424070f,
 186   -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
 187   -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
 188   -0.615231573581695560f, -0.595699310302734380f,
 189   -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
 190   -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
 191   -0.449611335992813110f, -0.427555084228515630f,
 192   -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
 193   -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
 194   -0.266712754964828490f, -0.242980182170867920f,
 195   -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
 196   -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
 197   -0.073564566671848297f, -0.049067676067352295f,
 198   -0.024541229009628296f, -0.000000000000000245f, 0.024541229009628296f
 199 };
 200
 201
 202 /**
 203  * @brief  Fast approximation to the trigonometric sine function for floating-point data.
 204  * @param[in] x input value in radians.
 205  * @return  sin(x).
 206  */
 207
 208 float32_t arm_sin_f32(
 209   float32_t x)
 210 {
 211   float32_t sinVal, fract, in;                   /* Temporary variables for input, output */
 212   int32_t index;                                 /* Index variable */
 213   uint32_t tableSize = (uint32_t) TABLE_SIZE;    /* Initialise tablesize */
 214   float32_t wa, wb, wc, wd;                      /* Cubic interpolation coefficients */
 215   float32_t a, b, c, d;                          /* Four nearest output values */
 216   float32_t *tablePtr;                           /* Pointer to table */
 217   int32_t n;
 218   float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
 219   float32_t oneminusfractby2;
 220   float32_t frby2xfrsq, frby6xfrsq;
 221
 222   /* input x is in radians */
 223   /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
 224   in = x * 0.159154943092f;
 225
 226   /* Calculation of floor value of input */
 227   n = (int32_t) in;
 228
 229   /* Make negative values towards -infinity */
 230   if(x < 0.0f)
 231   {
 232     n = n - 1;
 233   }
 234
 235   /* Map input value to [0 1] */
 236   in = in - (float32_t) n;
 237
 238   /* Calculation of index of the table */
 239   index = (uint32_t) (tableSize * in);
 240
 241   /* fractional value calculation */
 242   fract = ((float32_t) tableSize * in) - (float32_t) index;
 243
 244   /* Checking min and max index of table */
 245   if(index < 0)
 246   {
 247     index = 0;
 248   }
 249   else if(index > 256)
 250   {
 251     index = 256;
 252   }
 253
 254   /* Initialise table pointer */
 255   tablePtr = (float32_t *) & sinTable[index];
 256
 257   /* Read four nearest values of input value from the sin table */
 258   a = tablePtr[0];
 259   b = tablePtr[1];
 260   c = tablePtr[2];
 261   d = tablePtr[3];
 262
 263   /* Cubic interpolation process */
 264   fractsq = fract * fract;
 265   fractby2 = fract * 0.5f;
 266   fractby6 = fract * 0.166666667f;
 267   fractby3 = fract * 0.3333333333333f;
 268   fractsqby2 = fractsq * 0.5f;
 269   frby2xfrsq = (fractby2) * fractsq;
 270   frby6xfrsq = (fractby6) * fractsq;
 271   oneminusfractby2 = 1.0f - fractby2;
 272   wb = fractsqby2 - fractby3;
 273   wc = (fractsqby2 + fract);
 274   wa = wb - frby6xfrsq;
 275   wb = frby2xfrsq - fractsq;
 276   sinVal = wa * a;
 277   wc = wc - frby2xfrsq;
 278   wd = (frby6xfrsq) - fractby6;
 279   wb = wb + oneminusfractby2;
 280
 281   /* Calculate sin value */
 282   sinVal = (sinVal + (b * wb)) + ((c * wc) + (d * wd));
 283
 284   /* Return the output value */
 285   return (sinVal);
 286
 287 }
 288
 289 /**
 290  * @} end of sin group
 291  */