lib/main/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c

   1 /* ----------------------------------------------------------------------
   2  * Project:      CMSIS DSP Library
   3  * Title:        arm_dct4_f32.c
   4  * Description:  Processing function of DCT4 & IDCT4 F32
   5  *
   6  * $Date:        27. January 2017
   7  * $Revision:    V.1.5.1
   8  *
   9  * Target Processor: Cortex-M cores
  10  * -------------------------------------------------------------------- */
  11 /*
  12  * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
  13  *
  14  * SPDX-License-Identifier: Apache-2.0
  15  *
  16  * Licensed under the Apache License, Version 2.0 (the License); you may
  17  * not use this file except in compliance with the License.
  18  * You may obtain a copy of the License at
  19  *
  20  * www.apache.org/licenses/LICENSE-2.0
  21  *
  22  * Unless required by applicable law or agreed to in writing, software
  23  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
  24  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  25  * See the License for the specific language governing permissions and
  26  * limitations under the License.
  27  */
  28
  29 #include "arm_math.h"
  30
  31 /**
  32  * @ingroup groupTransforms
  33  */
  34
  35 /**
  36  * @defgroup DCT4_IDCT4 DCT Type IV Functions
  37  * Representation of signals by minimum number of values is important for storage and transmission.
  38  * The possibility of large discontinuity between the beginning and end of a period of a signal
  39  * in DFT can be avoided by extending the signal so that it is even-symmetric.
  40  * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
  41  * spectrum and is very widely used in signal and image coding applications.
  42  * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
  43  * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
  44  *
  45  * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
  46  * Reordering of the input data makes the computation of DCT just a problem of
  47  * computing the DFT of a real signal with a few additional operations.
  48  * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
  49  *
  50  * 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.
  51  * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
  52  * DCT2 implementation can be described in the following steps:
  53  * - Re-ordering input
  54  * - Calculating Real FFT
  55  * - Multiplication of weights and Real FFT output and getting real part from the product.
  56  *
  57  * This process is explained by the block diagram below:
  58  * \image html DCT4.gif "Discrete Cosine Transform - type-IV"
  59  *
  60  * \par Algorithm:
  61  * The N-point type-IV DCT is defined as a real, linear transformation by the formula:
  62  * \image html DCT4Equation.gif
  63  * where <code>k = 0,1,2,.....N-1</code>
  64  *\par
  65  * Its inverse is defined as follows:
  66  * \image html IDCT4Equation.gif
  67  * where <code>n = 0,1,2,.....N-1</code>
  68  *\par
  69  * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
  70  * The symmetry of the transform matrix indicates that the fast algorithms for the forward
  71  * and inverse transform computation are identical.
  72  * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
  73  *
  74  * \par Lengths supported by the transform:
  75  *  As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192.
  76  * The library provides separate functions for Q15, Q31, and floating-point data types.
  77  * \par Instance Structure
  78  * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
  79  * A separate instance structure must be defined for each transform.
  80  * There are separate instance structure declarations for each of the 3 supported data types.
  81  *
  82  * \par Initialization Functions
  83  * There is also an associated initialization function for each data type.
  84  * The initialization function performs the following operations:
  85  * - Sets the values of the internal structure fields.
  86  * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
  87  * \par
  88  * Use of the initialization function is optional.
  89  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
  90  * To place an instance structure into a const data section, the instance structure must be manually initialized.
  91  * Manually initialize the instance structure as follows:
  92  * <pre>
  93  *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
  94  *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
  95  *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
  96  * </pre>
  97  * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
  98  * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
  99  * \c pTwiddle points to the twiddle factor table;
 100  * \c pCosFactor points to the cosFactor table;
 101  * \c pRfft points to the real FFT instance;
 102  * \c pCfft points to the complex FFT instance;
 103  * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
 104  * and arm_rfft_f32() respectively for details regarding static initialization.
 105  *
 106  * \par Fixed-Point Behavior
 107  * Care must be taken when using the fixed-point versions of the DCT4 transform functions.
 108  * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
 109  * Refer to the function specific documentation below for usage guidelines.
 110  */
 111
 112  /**
 113  * @addtogroup DCT4_IDCT4
 114  * @{
 115  */
 116
 117 /**
 118  * @brief Processing function for the floating-point DCT4/IDCT4.
 119  * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
 120  * @param[in]       *pState        points to state buffer.
 121  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
 122  * @return none.
 123  */
 124
 125 void arm_dct4_f32(
 126   const arm_dct4_instance_f32 * S,
 127   float32_t * pState,
 128   float32_t * pInlineBuffer)
 129 {
 130   uint32_t i;                                    /* Loop counter */
 131   float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
 132   float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
 133   float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
 134   float32_t in;                                  /* Temporary variable */
 135
 136
 137   /* DCT4 computation involves DCT2 (which is calculated using RFFT)
 138    * along with some pre-processing and post-processing.
 139    * Computational procedure is explained as follows:
 140    * (a) Pre-processing involves multiplying input with cos factor,
 141    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
 142    *              where,
 143    *                 r(n) -- output of preprocessing
 144    *                 u(n) -- input to preprocessing(actual Source buffer)
 145    * (b) Calculation of DCT2 using FFT is divided into three steps:
 146    *                  Step1: Re-ordering of even and odd elements of input.
 147    *                  Step2: Calculating FFT of the re-ordered input.
 148    *                  Step3: Taking the real part of the product of FFT output and weights.
 149    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
 150    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 151    *                        where,
 152    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output
 153    * (d) Multiplying the output with the normalizing factor sqrt(2/N).
 154    */
 155
 156         /*-------- Pre-processing ------------*/
 157   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
 158   arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
 159   arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
 160
 161   /* ----------------------------------------------------------------
 162    * Step1: Re-ordering of even and odd elements as,
 163    *             pState[i] =  pInlineBuffer[2*i] and
 164    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
 165    ---------------------------------------------------------------------*/
 166
 167   /* pS1 initialized to pState */
 168   pS1 = pState;
 169
 170   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
 171   pS2 = pState + (S->N - 1U);
 172
 173   /* pbuff initialized to input buffer */
 174   pbuff = pInlineBuffer;
 175
 176 #if defined (ARM_MATH_DSP)
 177
 178   /* Run the below code for Cortex-M4 and Cortex-M3 */
 179
 180   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
 181   i = (uint32_t) S->Nby2 >> 2U;
 182
 183   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
 184    ** a second loop below computes the remaining 1 to 3 samples. */
 185   do
 186   {
 187     /* Re-ordering of even and odd elements */
 188     /* pState[i] =  pInlineBuffer[2*i] */
 189     *pS1++ = *pbuff++;
 190     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
 191     *pS2-- = *pbuff++;
 192
 193     *pS1++ = *pbuff++;
 194     *pS2-- = *pbuff++;
 195
 196     *pS1++ = *pbuff++;
 197     *pS2-- = *pbuff++;
 198
 199     *pS1++ = *pbuff++;
 200     *pS2-- = *pbuff++;
 201
 202     /* Decrement the loop counter */
 203     i--;
 204   } while (i > 0U);
 205
 206   /* pbuff initialized to input buffer */
 207   pbuff = pInlineBuffer;
 208
 209   /* pS1 initialized to pState */
 210   pS1 = pState;
 211
 212   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
 213   i = (uint32_t) S->N >> 2U;
 214
 215   /* Processing with loop unrolling 4 times as N is always multiple of 4.
 216    * Compute 4 outputs at a time */
 217   do
 218   {
 219     /* Writing the re-ordered output back to inplace input buffer */
 220     *pbuff++ = *pS1++;
 221     *pbuff++ = *pS1++;
 222     *pbuff++ = *pS1++;
 223     *pbuff++ = *pS1++;
 224
 225     /* Decrement the loop counter */
 226     i--;
 227   } while (i > 0U);
 228
 229
 230   /* ---------------------------------------------------------
 231    *     Step2: Calculate RFFT for N-point input
 232    * ---------------------------------------------------------- */
 233   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
 234   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
 235
 236         /*----------------------------------------------------------------------
 237          *  Step3: Multiply the FFT output with the weights.
 238          *----------------------------------------------------------------------*/
 239   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
 240
 241   /* ----------- Post-processing ---------- */
 242   /* DCT-IV can be obtained from DCT-II by the equation,
 243    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 244    *       Hence, Y4(0) = Y2(0)/2  */
 245   /* Getting only real part from the output and Converting to DCT-IV */
 246
 247   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
 248   i = ((uint32_t) S->N - 1U) >> 2U;
 249
 250   /* pbuff initialized to input buffer. */
 251   pbuff = pInlineBuffer;
 252
 253   /* pS1 initialized to pState */
 254   pS1 = pState;
 255
 256   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
 257   in = *pS1++ * (float32_t) 0.5;
 258   /* input buffer acts as inplace, so output values are stored in the input itself. */
 259   *pbuff++ = in;
 260
 261   /* pState pointer is incremented twice as the real values are located alternatively in the array */
 262   pS1++;
 263
 264   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
 265    ** a second loop below computes the remaining 1 to 3 samples. */
 266   do
 267   {
 268     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 269     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 270     in = *pS1++ - in;
 271     *pbuff++ = in;
 272     /* points to the next real value */
 273     pS1++;
 274
 275     in = *pS1++ - in;
 276     *pbuff++ = in;
 277     pS1++;
 278
 279     in = *pS1++ - in;
 280     *pbuff++ = in;
 281     pS1++;
 282
 283     in = *pS1++ - in;
 284     *pbuff++ = in;
 285     pS1++;
 286
 287     /* Decrement the loop counter */
 288     i--;
 289   } while (i > 0U);
 290
 291   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
 292    ** No loop unrolling is used. */
 293   i = ((uint32_t) S->N - 1U) % 0x4U;
 294
 295   while (i > 0U)
 296   {
 297     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 298     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 299     in = *pS1++ - in;
 300     *pbuff++ = in;
 301     /* points to the next real value */
 302     pS1++;
 303
 304     /* Decrement the loop counter */
 305     i--;
 306   }
 307
 308
 309         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
 310
 311   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
 312   i = (uint32_t) S->N >> 2U;
 313
 314   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
 315   pbuff = pInlineBuffer;
 316
 317   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
 318   do
 319   {
 320     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
 321     in = *pbuff;
 322     *pbuff++ = in * S->normalize;
 323
 324     in = *pbuff;
 325     *pbuff++ = in * S->normalize;
 326
 327     in = *pbuff;
 328     *pbuff++ = in * S->normalize;
 329
 330     in = *pbuff;
 331     *pbuff++ = in * S->normalize;
 332
 333     /* Decrement the loop counter */
 334     i--;
 335   } while (i > 0U);
 336
 337
 338 #else
 339
 340   /* Run the below code for Cortex-M0 */
 341
 342   /* Initializing the loop counter to N/2 */
 343   i = (uint32_t) S->Nby2;
 344
 345   do
 346   {
 347     /* Re-ordering of even and odd elements */
 348     /* pState[i] =  pInlineBuffer[2*i] */
 349     *pS1++ = *pbuff++;
 350     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
 351     *pS2-- = *pbuff++;
 352
 353     /* Decrement the loop counter */
 354     i--;
 355   } while (i > 0U);
 356
 357   /* pbuff initialized to input buffer */
 358   pbuff = pInlineBuffer;
 359
 360   /* pS1 initialized to pState */
 361   pS1 = pState;
 362
 363   /* Initializing the loop counter */
 364   i = (uint32_t) S->N;
 365
 366   do
 367   {
 368     /* Writing the re-ordered output back to inplace input buffer */
 369     *pbuff++ = *pS1++;
 370
 371     /* Decrement the loop counter */
 372     i--;
 373   } while (i > 0U);
 374
 375
 376   /* ---------------------------------------------------------
 377    *     Step2: Calculate RFFT for N-point input
 378    * ---------------------------------------------------------- */
 379   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
 380   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
 381
 382         /*----------------------------------------------------------------------
 383          *  Step3: Multiply the FFT output with the weights.
 384          *----------------------------------------------------------------------*/
 385   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
 386
 387   /* ----------- Post-processing ---------- */
 388   /* DCT-IV can be obtained from DCT-II by the equation,
 389    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
 390    *       Hence, Y4(0) = Y2(0)/2  */
 391   /* Getting only real part from the output and Converting to DCT-IV */
 392
 393   /* pbuff initialized to input buffer. */
 394   pbuff = pInlineBuffer;
 395
 396   /* pS1 initialized to pState */
 397   pS1 = pState;
 398
 399   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
 400   in = *pS1++ * (float32_t) 0.5;
 401   /* input buffer acts as inplace, so output values are stored in the input itself. */
 402   *pbuff++ = in;
 403
 404   /* pState pointer is incremented twice as the real values are located alternatively in the array */
 405   pS1++;
 406
 407   /* Initializing the loop counter */
 408   i = ((uint32_t) S->N - 1U);
 409
 410   do
 411   {
 412     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
 413     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
 414     in = *pS1++ - in;
 415     *pbuff++ = in;
 416     /* points to the next real value */
 417     pS1++;
 418
 419
 420     /* Decrement the loop counter */
 421     i--;
 422   } while (i > 0U);
 423
 424
 425         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
 426
 427   /* Initializing the loop counter */
 428   i = (uint32_t) S->N;
 429
 430   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
 431   pbuff = pInlineBuffer;
 432
 433   do
 434   {
 435     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
 436     in = *pbuff;
 437     *pbuff++ = in * S->normalize;
 438
 439     /* Decrement the loop counter */
 440     i--;
 441   } while (i > 0U);
 442
 443 #endif /* #if defined (ARM_MATH_DSP) */
 444
 445 }
 446
 447 /**
 448    * @} end of DCT4_IDCT4 group
 449    */