tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/TransformFunctions/arm_dct4_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_dct4_f32.c
   9 *
  10 * Description:  Processing function of DCT4 & IDCT4 F32.
  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:
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  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
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  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
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  39 * -------------------------------------------------------------------- */
  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupTransforms
  45  */
  46
  47 /**
  48  * @defgroup DCT4_IDCT4 DCT Type IV Functions
  49  * Representation of signals by minimum number of values is important for storage and transmission.
  50  * The possibility of large discontinuity between the beginning and end of a period of a signal
  51  * in DFT can be avoided by extending the signal so that it is even-symmetric.
  52  * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
  53  * spectrum and is very widely used in signal and image coding applications.
  54  * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
  55  * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
  56  *
  57  * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
  58  * Reordering of the input data makes the computation of DCT just a problem of
  59  * computing the DFT of a real signal with a few additional operations.
  60  * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
  61  *
  62  * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.
  63  * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
  64  * DCT2 implementation can be described in the following steps:
  65  * - Re-ordering input
  66  * - Calculating Real FFT
  67  * - Multiplication of weights and Real FFT output and getting real part from the product.
  68  *
  69  * This process is explained by the block diagram below:
  70  * \image html DCT4.gif "Discrete Cosine Transform - type-IV"
  71  *
  72  * \par Algorithm:
  73  * The N-point type-IV DCT is defined as a real, linear transformation by the formula:
  74  * \image html DCT4Equation.gif
  75  * where <code>k = 0,1,2,.....N-1</code>
  76  *\par
  77  * Its inverse is defined as follows:
  78  * \image html IDCT4Equation.gif
  79  * where <code>n = 0,1,2,.....N-1</code>
  80  *\par
  81  * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
  82  * The symmetry of the transform matrix indicates that the fast algorithms for the forward
  83  * and inverse transform computation are identical.
  84  * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
  85  *
  86  * \par Lengths supported by the transform:
  87  *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().
  88  * The library provides separate functions for Q15, Q31, and floating-point data types.
  89  * \par Instance Structure
  90  * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
  91  * A separate instance structure must be defined for each transform.
  92  * There are separate instance structure declarations for each of the 3 supported data types.
  93  *
  94  * \par Initialization Functions
  95  * There is also an associated initialization function for each data type.
  96  * The initialization function performs the following operations:
  97  * - Sets the values of the internal structure fields.
  98  * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
  99  * \par
 100  * Use of the initialization function is optional.
 101  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 102  * To place an instance structure into a const data section, the instance structure must be manually initialized.
 103  * Manually initialize the instance structure as follows:
 104  * <pre>
 105  *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 106  *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 107  *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 108  * </pre>
 109  * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
 110  * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
 111  * \c pTwiddle points to the twiddle factor table;
 112  * \c pCosFactor points to the cosFactor table;
 113  * \c pRfft points to the real FFT instance;
 114  * \c pCfft points to the complex FFT instance;
 115  * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
 116  * and arm_rfft_f32() respectively for details regarding static initialization.
 117  *
 118  * \par Fixed-Point Behavior
 119  * Care must be taken when using the fixed-point versions of the DCT4 transform functions.
 120  * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
 121  * Refer to the function specific documentation below for usage guidelines.
 122  */
 123
 124  /**
 125  * @addtogroup DCT4_IDCT4
 126  * @{
 127  */
 128
 129 /**
 130  * @brief Processing function for the floating-point DCT4/IDCT4.
 131  * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
 132  * @param[in]       *pState        points to state buffer.
 133  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
 134  * @return none.
 135  */
 136
 137 void arm_dct4_f32(
 138   const arm_dct4_instance_f32 * S,
 139   float32_t * pState,
 140   float32_t * pInlineBuffer)
 141 {
 142   uint32_t i;                                    /* Loop counter */
 143   float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
 144   float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
 145   float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
 146   float32_t in;                                  /* Temporary variable */
 147
 148
 149   /* DCT4 computation involves DCT2 (which is calculated using RFFT)
 150    * along with some pre-processing and post-processing.
 151    * Computational procedure is explained as follows:
 152    * (a) Pre-processing involves multiplying input with cos factor,
 153    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
 154    *              where,
 155    *                 r(n) -- output of preprocessing
 156    *                 u(n) -- input to preprocessing(actual Source buffer)
 157    * (b) Calculation of DCT2 using FFT is divided into three steps:
 158    *                  Step1: Re-ordering of even and odd elements of input.
 159    *                  Step2: Calculating FFT of the re-ordered input.
 160    *                  Step3: Taking the real part of the product of FFT output and weights.
 161    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
 162    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 163    *                        where,
 164    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output
 165    * (d) Multiplying the output with the normalizing factor sqrt(2/N).
 166    */
 167
 168         /*-------- Pre-processing ------------*/
 169   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
 170   arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
 171   arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
 172
 173   /* ----------------------------------------------------------------
 174    * Step1: Re-ordering of even and odd elements as,
 175    *             pState[i] =  pInlineBuffer[2*i] and
 176    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
 177    ---------------------------------------------------------------------*/
 178
 179   /* pS1 initialized to pState */
 180   pS1 = pState;
 181
 182   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
 183   pS2 = pState + (S->N - 1u);
 184
 185   /* pbuff initialized to input buffer */
 186   pbuff = pInlineBuffer;
 187
 188 #ifndef ARM_MATH_CM0_FAMILY
 189
 190   /* Run the below code for Cortex-M4 and Cortex-M3 */
 191
 192   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
 193   i = (uint32_t) S->Nby2 >> 2u;
 194
 195   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
 196    ** a second loop below computes the remaining 1 to 3 samples. */
 197   do
 198   {
 199     /* Re-ordering of even and odd elements */
 200     /* pState[i] =  pInlineBuffer[2*i] */
 201     *pS1++ = *pbuff++;
 202     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
 203     *pS2-- = *pbuff++;
 204
 205     *pS1++ = *pbuff++;
 206     *pS2-- = *pbuff++;
 207
 208     *pS1++ = *pbuff++;
 209     *pS2-- = *pbuff++;
 210
 211     *pS1++ = *pbuff++;
 212     *pS2-- = *pbuff++;
 213
 214     /* Decrement the loop counter */
 215     i--;
 216   } while(i > 0u);
 217
 218   /* pbuff initialized to input buffer */
 219   pbuff = pInlineBuffer;
 220
 221   /* pS1 initialized to pState */
 222   pS1 = pState;
 223
 224   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
 225   i = (uint32_t) S->N >> 2u;
 226
 227   /* Processing with loop unrolling 4 times as N is always multiple of 4.
 228    * Compute 4 outputs at a time */
 229   do
 230   {
 231     /* Writing the re-ordered output back to inplace input buffer */
 232     *pbuff++ = *pS1++;
 233     *pbuff++ = *pS1++;
 234     *pbuff++ = *pS1++;
 235     *pbuff++ = *pS1++;
 236
 237     /* Decrement the loop counter */
 238     i--;
 239   } while(i > 0u);
 240
 241
 242   /* ---------------------------------------------------------
 243    *     Step2: Calculate RFFT for N-point input
 244    * ---------------------------------------------------------- */
 245   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
 246   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
 247
 248         /*----------------------------------------------------------------------
 249          *  Step3: Multiply the FFT output with the weights.
 250          *----------------------------------------------------------------------*/
 251   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
 252
 253   /* ----------- Post-processing ---------- */
 254   /* DCT-IV can be obtained from DCT-II by the equation,
 255    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 256    *       Hence, Y4(0) = Y2(0)/2  */
 257   /* Getting only real part from the output and Converting to DCT-IV */
 258
 259   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
 260   i = ((uint32_t) S->N - 1u) >> 2u;
 261
 262   /* pbuff initialized to input buffer. */
 263   pbuff = pInlineBuffer;
 264
 265   /* pS1 initialized to pState */
 266   pS1 = pState;
 267
 268   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
 269   in = *pS1++ * (float32_t) 0.5;
 270   /* input buffer acts as inplace, so output values are stored in the input itself. */
 271   *pbuff++ = in;
 272
 273   /* pState pointer is incremented twice as the real values are located alternatively in the array */
 274   pS1++;
 275
 276   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
 277    ** a second loop below computes the remaining 1 to 3 samples. */
 278   do
 279   {
 280     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 281     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 282     in = *pS1++ - in;
 283     *pbuff++ = in;
 284     /* points to the next real value */
 285     pS1++;
 286
 287     in = *pS1++ - in;
 288     *pbuff++ = in;
 289     pS1++;
 290
 291     in = *pS1++ - in;
 292     *pbuff++ = in;
 293     pS1++;
 294
 295     in = *pS1++ - in;
 296     *pbuff++ = in;
 297     pS1++;
 298
 299     /* Decrement the loop counter */
 300     i--;
 301   } while(i > 0u);
 302
 303   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
 304    ** No loop unrolling is used. */
 305   i = ((uint32_t) S->N - 1u) % 0x4u;
 306
 307   while(i > 0u)
 308   {
 309     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 310     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 311     in = *pS1++ - in;
 312     *pbuff++ = in;
 313     /* points to the next real value */
 314     pS1++;
 315
 316     /* Decrement the loop counter */
 317     i--;
 318   }
 319
 320
 321         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
 322
 323   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
 324   i = (uint32_t) S->N >> 2u;
 325
 326   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
 327   pbuff = pInlineBuffer;
 328
 329   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
 330   do
 331   {
 332     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
 333     in = *pbuff;
 334     *pbuff++ = in * S->normalize;
 335
 336     in = *pbuff;
 337     *pbuff++ = in * S->normalize;
 338
 339     in = *pbuff;
 340     *pbuff++ = in * S->normalize;
 341
 342     in = *pbuff;
 343     *pbuff++ = in * S->normalize;
 344
 345     /* Decrement the loop counter */
 346     i--;
 347   } while(i > 0u);
 348
 349
 350 #else
 351
 352   /* Run the below code for Cortex-M0 */
 353
 354   /* Initializing the loop counter to N/2 */
 355   i = (uint32_t) S->Nby2;
 356
 357   do
 358   {
 359     /* Re-ordering of even and odd elements */
 360     /* pState[i] =  pInlineBuffer[2*i] */
 361     *pS1++ = *pbuff++;
 362     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
 363     *pS2-- = *pbuff++;
 364
 365     /* Decrement the loop counter */
 366     i--;
 367   } while(i > 0u);
 368
 369   /* pbuff initialized to input buffer */
 370   pbuff = pInlineBuffer;
 371
 372   /* pS1 initialized to pState */
 373   pS1 = pState;
 374
 375   /* Initializing the loop counter */
 376   i = (uint32_t) S->N;
 377
 378   do
 379   {
 380     /* Writing the re-ordered output back to inplace input buffer */
 381     *pbuff++ = *pS1++;
 382
 383     /* Decrement the loop counter */
 384     i--;
 385   } while(i > 0u);
 386
 387
 388   /* ---------------------------------------------------------
 389    *     Step2: Calculate RFFT for N-point input
 390    * ---------------------------------------------------------- */
 391   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
 392   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
 393
 394         /*----------------------------------------------------------------------
 395          *  Step3: Multiply the FFT output with the weights.
 396          *----------------------------------------------------------------------*/
 397   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
 398
 399   /* ----------- Post-processing ---------- */
 400   /* DCT-IV can be obtained from DCT-II by the equation,
 401    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 402    *       Hence, Y4(0) = Y2(0)/2  */
 403   /* Getting only real part from the output and Converting to DCT-IV */
 404
 405   /* pbuff initialized to input buffer. */
 406   pbuff = pInlineBuffer;
 407
 408   /* pS1 initialized to pState */
 409   pS1 = pState;
 410
 411   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
 412   in = *pS1++ * (float32_t) 0.5;
 413   /* input buffer acts as inplace, so output values are stored in the input itself. */
 414   *pbuff++ = in;
 415
 416   /* pState pointer is incremented twice as the real values are located alternatively in the array */
 417   pS1++;
 418
 419   /* Initializing the loop counter */
 420   i = ((uint32_t) S->N - 1u);
 421
 422   do
 423   {
 424     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 425     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 426     in = *pS1++ - in;
 427     *pbuff++ = in;
 428     /* points to the next real value */
 429     pS1++;
 430
 431
 432     /* Decrement the loop counter */
 433     i--;
 434   } while(i > 0u);
 435
 436
 437         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
 438
 439   /* Initializing the loop counter */
 440   i = (uint32_t) S->N;
 441
 442   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
 443   pbuff = pInlineBuffer;
 444
 445   do
 446   {
 447     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
 448     in = *pbuff;
 449     *pbuff++ = in * S->normalize;
 450
 451     /* Decrement the loop counter */
 452     i--;
 453   } while(i > 0u);
 454
 455 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
 456
 457 }
 458
 459 /**
 460    * @} end of DCT4_IDCT4 group
 461    */