arm_dct4_f32.c

00001 /* ----------------------------------------------------------------------
00002  * Project:      CMSIS DSP Library
00003  * Title:        arm_dct4_f32.c
00004  * Description:  Processing function of DCT4 & IDCT4 F32
00005  *
00006  * $Date:        27. January 2017
00007  * $Revision:    V.1.5.1
00008  *
00009  * Target Processor: Cortex-M cores
00010  * -------------------------------------------------------------------- */
00011 /*
00012  * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
00013  *
00014  * SPDX-License-Identifier: Apache-2.0
00015  *
00016  * Licensed under the Apache License, Version 2.0 (the License); you may
00017  * not use this file except in compliance with the License.
00018  * You may obtain a copy of the License at
00019  *
00020  * www.apache.org/licenses/LICENSE-2.0
00021  *
00022  * Unless required by applicable law or agreed to in writing, software
00023  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
00024  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
00025  * See the License for the specific language governing permissions and
00026  * limitations under the License.
00027  */
00028 
00029 #include "arm_math.h"
00030 
00031 /**
00032  * @ingroup groupTransforms
00033  */
00034 
00035 /**
00036  * @defgroup DCT4_IDCT4 DCT Type IV Functions
00037  * Representation of signals by minimum number of values is important for storage and transmission.
00038  * The possibility of large discontinuity between the beginning and end of a period of a signal
00039  * in DFT can be avoided by extending the signal so that it is even-symmetric.
00040  * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
00041  * spectrum and is very widely used in signal and image coding applications.
00042  * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
00043  * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
00044  *
00045  * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
00046  * Reordering of the input data makes the computation of DCT just a problem of
00047  * computing the DFT of a real signal with a few additional operations.
00048  * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
00049  *
00050  * 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.
00051  * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
00052  * DCT2 implementation can be described in the following steps:
00053  * - Re-ordering input
00054  * - Calculating Real FFT
00055  * - Multiplication of weights and Real FFT output and getting real part from the product.
00056  *
00057  * This process is explained by the block diagram below:
00058  * \image html DCT4.gif "Discrete Cosine Transform - type-IV"
00059  *
00060  * \par Algorithm:
00061  * The N-point type-IV DCT is defined as a real, linear transformation by the formula:
00062  * \image html DCT4Equation.gif
00063  * where <code>k = 0,1,2,.....N-1</code>
00064  *\par
00065  * Its inverse is defined as follows:
00066  * \image html IDCT4Equation.gif
00067  * where <code>n = 0,1,2,.....N-1</code>
00068  *\par
00069  * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
00070  * The symmetry of the transform matrix indicates that the fast algorithms for the forward
00071  * and inverse transform computation are identical.
00072  * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
00073  *
00074  * \par Lengths supported by the transform:
00075  *  As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192.
00076  * The library provides separate functions for Q15, Q31, and floating-point data types.
00077  * \par Instance Structure
00078  * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
00079  * A separate instance structure must be defined for each transform.
00080  * There are separate instance structure declarations for each of the 3 supported data types.
00081  *
00082  * \par Initialization Functions
00083  * There is also an associated initialization function for each data type.
00084  * The initialization function performs the following operations:
00085  * - Sets the values of the internal structure fields.
00086  * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
00087  * \par
00088  * Use of the initialization function is optional.
00089  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
00090  * To place an instance structure into a const data section, the instance structure must be manually initialized.
00091  * Manually initialize the instance structure as follows:
00092  * <pre>
00093  *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
00094  *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
00095  *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
00096  * </pre>
00097  * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
00098  * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
00099  * \c pTwiddle points to the twiddle factor table;
00100  * \c pCosFactor points to the cosFactor table;
00101  * \c pRfft points to the real FFT instance;
00102  * \c pCfft points to the complex FFT instance;
00103  * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
00104  * and arm_rfft_f32() respectively for details regarding static initialization.
00105  *
00106  * \par Fixed-Point Behavior
00107  * Care must be taken when using the fixed-point versions of the DCT4 transform functions.
00108  * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
00109  * Refer to the function specific documentation below for usage guidelines.
00110  */
00111 
00112  /**
00113  * @addtogroup DCT4_IDCT4
00114  * @{
00115  */
00116 
00117 /**
00118  * @brief Processing function for the floating-point DCT4/IDCT4.
00119  * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
00120  * @param[in]       *pState        points to state buffer.
00121  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
00122  * @return none.
00123  */
00124 
00125 void arm_dct4_f32(
00126   const arm_dct4_instance_f32 * S,
00127   float32_t * pState,
00128   float32_t * pInlineBuffer)
00129 {
00130   uint32_t i;                                    /* Loop counter */
00131   float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
00132   float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
00133   float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
00134   float32_t in;                                  /* Temporary variable */
00135 
00136 
00137   /* DCT4 computation involves DCT2 (which is calculated using RFFT)
00138    * along with some pre-processing and post-processing.
00139    * Computational procedure is explained as follows:
00140    * (a) Pre-processing involves multiplying input with cos factor,
00141    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
00142    *              where,
00143    *                 r(n) -- output of preprocessing
00144    *                 u(n) -- input to preprocessing(actual Source buffer)
00145    * (b) Calculation of DCT2 using FFT is divided into three steps:
00146    *                  Step1: Re-ordering of even and odd elements of input.
00147    *                  Step2: Calculating FFT of the re-ordered input.
00148    *                  Step3: Taking the real part of the product of FFT output and weights.
00149    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
00150    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
00151    *                        where,
00152    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output
00153    * (d) Multiplying the output with the normalizing factor sqrt(2/N).
00154    */
00155 
00156         /*-------- Pre-processing ------------*/
00157   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
00158   arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
00159   arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
00160 
00161   /* ----------------------------------------------------------------
00162    * Step1: Re-ordering of even and odd elements as,
00163    *             pState[i] =  pInlineBuffer[2*i] and
00164    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
00165    ---------------------------------------------------------------------*/
00166 
00167   /* pS1 initialized to pState */
00168   pS1 = pState;
00169 
00170   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
00171   pS2 = pState + (S->N - 1U);
00172 
00173   /* pbuff initialized to input buffer */
00174   pbuff = pInlineBuffer;
00175 
00176 #if defined (ARM_MATH_DSP)
00177 
00178   /* Run the below code for Cortex-M4 and Cortex-M3 */
00179 
00180   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
00181   i = (uint32_t) S->Nby2 >> 2U;
00182 
00183   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
00184    ** a second loop below computes the remaining 1 to 3 samples. */
00185   do
00186   {
00187     /* Re-ordering of even and odd elements */
00188     /* pState[i] =  pInlineBuffer[2*i] */
00189     *pS1++ = *pbuff++;
00190     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00191     *pS2-- = *pbuff++;
00192 
00193     *pS1++ = *pbuff++;
00194     *pS2-- = *pbuff++;
00195 
00196     *pS1++ = *pbuff++;
00197     *pS2-- = *pbuff++;
00198 
00199     *pS1++ = *pbuff++;
00200     *pS2-- = *pbuff++;
00201 
00202     /* Decrement the loop counter */
00203     i--;
00204   } while (i > 0U);
00205 
00206   /* pbuff initialized to input buffer */
00207   pbuff = pInlineBuffer;
00208 
00209   /* pS1 initialized to pState */
00210   pS1 = pState;
00211 
00212   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00213   i = (uint32_t) S->N >> 2U;
00214 
00215   /* Processing with loop unrolling 4 times as N is always multiple of 4.
00216    * Compute 4 outputs at a time */
00217   do
00218   {
00219     /* Writing the re-ordered output back to inplace input buffer */
00220     *pbuff++ = *pS1++;
00221     *pbuff++ = *pS1++;
00222     *pbuff++ = *pS1++;
00223     *pbuff++ = *pS1++;
00224 
00225     /* Decrement the loop counter */
00226     i--;
00227   } while (i > 0U);
00228 
00229 
00230   /* ---------------------------------------------------------
00231    *     Step2: Calculate RFFT for N-point input
00232    * ---------------------------------------------------------- */
00233   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00234   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
00235 
00236         /*----------------------------------------------------------------------
00237      *  Step3: Multiply the FFT output with the weights.
00238      *----------------------------------------------------------------------*/
00239   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
00240 
00241   /* ----------- Post-processing ---------- */
00242   /* DCT-IV can be obtained from DCT-II by the equation,
00243    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
00244    *       Hence, Y4(0) = Y2(0)/2  */
00245   /* Getting only real part from the output and Converting to DCT-IV */
00246 
00247   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
00248   i = ((uint32_t) S->N - 1U) >> 2U;
00249 
00250   /* pbuff initialized to input buffer. */
00251   pbuff = pInlineBuffer;
00252 
00253   /* pS1 initialized to pState */
00254   pS1 = pState;
00255 
00256   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00257   in = *pS1++ * (float32_t) 0.5;
00258   /* input buffer acts as inplace, so output values are stored in the input itself. */
00259   *pbuff++ = in;
00260 
00261   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00262   pS1++;
00263 
00264   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
00265    ** a second loop below computes the remaining 1 to 3 samples. */
00266   do
00267   {
00268     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00269     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00270     in = *pS1++ - in;
00271     *pbuff++ = in;
00272     /* points to the next real value */
00273     pS1++;
00274 
00275     in = *pS1++ - in;
00276     *pbuff++ = in;
00277     pS1++;
00278 
00279     in = *pS1++ - in;
00280     *pbuff++ = in;
00281     pS1++;
00282 
00283     in = *pS1++ - in;
00284     *pbuff++ = in;
00285     pS1++;
00286 
00287     /* Decrement the loop counter */
00288     i--;
00289   } while (i > 0U);
00290 
00291   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
00292    ** No loop unrolling is used. */
00293   i = ((uint32_t) S->N - 1U) % 0x4U;
00294 
00295   while (i > 0U)
00296   {
00297     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00298     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00299     in = *pS1++ - in;
00300     *pbuff++ = in;
00301     /* points to the next real value */
00302     pS1++;
00303 
00304     /* Decrement the loop counter */
00305     i--;
00306   }
00307 
00308 
00309         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00310 
00311   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00312   i = (uint32_t) S->N >> 2U;
00313 
00314   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00315   pbuff = pInlineBuffer;
00316 
00317   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
00318   do
00319   {
00320     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00321     in = *pbuff;
00322     *pbuff++ = in * S->normalize;
00323 
00324     in = *pbuff;
00325     *pbuff++ = in * S->normalize;
00326 
00327     in = *pbuff;
00328     *pbuff++ = in * S->normalize;
00329 
00330     in = *pbuff;
00331     *pbuff++ = in * S->normalize;
00332 
00333     /* Decrement the loop counter */
00334     i--;
00335   } while (i > 0U);
00336 
00337 
00338 #else
00339 
00340   /* Run the below code for Cortex-M0 */
00341 
00342   /* Initializing the loop counter to N/2 */
00343   i = (uint32_t) S->Nby2;
00344 
00345   do
00346   {
00347     /* Re-ordering of even and odd elements */
00348     /* pState[i] =  pInlineBuffer[2*i] */
00349     *pS1++ = *pbuff++;
00350     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00351     *pS2-- = *pbuff++;
00352 
00353     /* Decrement the loop counter */
00354     i--;
00355   } while (i > 0U);
00356 
00357   /* pbuff initialized to input buffer */
00358   pbuff = pInlineBuffer;
00359 
00360   /* pS1 initialized to pState */
00361   pS1 = pState;
00362 
00363   /* Initializing the loop counter */
00364   i = (uint32_t) S->N;
00365 
00366   do
00367   {
00368     /* Writing the re-ordered output back to inplace input buffer */
00369     *pbuff++ = *pS1++;
00370 
00371     /* Decrement the loop counter */
00372     i--;
00373   } while (i > 0U);
00374 
00375 
00376   /* ---------------------------------------------------------
00377    *     Step2: Calculate RFFT for N-point input
00378    * ---------------------------------------------------------- */
00379   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00380   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
00381 
00382         /*----------------------------------------------------------------------
00383      *  Step3: Multiply the FFT output with the weights.
00384      *----------------------------------------------------------------------*/
00385   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
00386 
00387   /* ----------- Post-processing ---------- */
00388   /* DCT-IV can be obtained from DCT-II by the equation,
00389    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
00390    *       Hence, Y4(0) = Y2(0)/2  */
00391   /* Getting only real part from the output and Converting to DCT-IV */
00392 
00393   /* pbuff initialized to input buffer. */
00394   pbuff = pInlineBuffer;
00395 
00396   /* pS1 initialized to pState */
00397   pS1 = pState;
00398 
00399   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00400   in = *pS1++ * (float32_t) 0.5;
00401   /* input buffer acts as inplace, so output values are stored in the input itself. */
00402   *pbuff++ = in;
00403 
00404   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00405   pS1++;
00406 
00407   /* Initializing the loop counter */
00408   i = ((uint32_t) S->N - 1U);
00409 
00410   do
00411   {
00412     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00413     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00414     in = *pS1++ - in;
00415     *pbuff++ = in;
00416     /* points to the next real value */
00417     pS1++;
00418 
00419 
00420     /* Decrement the loop counter */
00421     i--;
00422   } while (i > 0U);
00423 
00424 
00425         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00426 
00427   /* Initializing the loop counter */
00428   i = (uint32_t) S->N;
00429 
00430   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00431   pbuff = pInlineBuffer;
00432 
00433   do
00434   {
00435     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00436     in = *pbuff;
00437     *pbuff++ = in * S->normalize;
00438 
00439     /* Decrement the loop counter */
00440     i--;
00441   } while (i > 0U);
00442 
00443 #endif /* #if defined (ARM_MATH_DSP) */
00444 
00445 }
00446 
00447 /**
00448    * @} end of DCT4_IDCT4 group
00449    */
00450