arm_dct4_f32.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_dct4_f32.c    
00009 *    
00010 * Description:  Processing function of DCT4 & IDCT4 F32.    
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 groupTransforms    
00045  */
00046 
00047 /**    
00048  * @defgroup DCT4_IDCT4 DCT Type IV Functions    
00049  * Representation of signals by minimum number of values is important for storage and transmission.    
00050  * The possibility of large discontinuity between the beginning and end of a period of a signal    
00051  * in DFT can be avoided by extending the signal so that it is even-symmetric.    
00052  * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the    
00053  * spectrum and is very widely used in signal and image coding applications.    
00054  * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.    
00055  * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.    
00056  *    
00057  * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.    
00058  * Reordering of the input data makes the computation of DCT just a problem of    
00059  * computing the DFT of a real signal with a few additional operations.    
00060  * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.    
00061  *     
00062  * 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.    
00063  * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.    
00064  * DCT2 implementation can be described in the following steps:    
00065  * - Re-ordering input    
00066  * - Calculating Real FFT    
00067  * - Multiplication of weights and Real FFT output and getting real part from the product.    
00068  *    
00069  * This process is explained by the block diagram below:    
00070  * \image html DCT4.gif "Discrete Cosine Transform - type-IV"    
00071  *    
00072  * \par Algorithm:    
00073  * The N-point type-IV DCT is defined as a real, linear transformation by the formula:    
00074  * \image html DCT4Equation.gif    
00075  * where <code>k = 0,1,2,.....N-1</code>    
00076  *\par    
00077  * Its inverse is defined as follows:    
00078  * \image html IDCT4Equation.gif    
00079  * where <code>n = 0,1,2,.....N-1</code>    
00080  *\par    
00081  * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).    
00082  * The symmetry of the transform matrix indicates that the fast algorithms for the forward    
00083  * and inverse transform computation are identical.    
00084  * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.    
00085  *    
00086  * \par Lengths supported by the transform:    
00087  *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().    
00088  * The library provides separate functions for Q15, Q31, and floating-point data types.    
00089  * \par Instance Structure    
00090  * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.    
00091  * A separate instance structure must be defined for each transform.    
00092  * There are separate instance structure declarations for each of the 3 supported data types.    
00093  *    
00094  * \par Initialization Functions    
00095  * There is also an associated initialization function for each data type.    
00096  * The initialization function performs the following operations:    
00097  * - Sets the values of the internal structure fields.    
00098  * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().    
00099  * \par    
00100  * Use of the initialization function is optional.    
00101  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
00102  * To place an instance structure into a const data section, the instance structure must be manually initialized.    
00103  * Manually initialize the instance structure as follows:    
00104  * <pre>    
00105  *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};    
00106  *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
00107  *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
00108  * </pre>   
00109  * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;   
00110  * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;    
00111  * \c pTwiddle points to the twiddle factor table;   
00112  * \c pCosFactor points to the cosFactor table;   
00113  * \c pRfft points to the real FFT instance;   
00114  * \c pCfft points to the complex FFT instance;   
00115  * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()   
00116  * and arm_rfft_f32() respectively for details regarding static initialization.   
00117  *   
00118  * \par Fixed-Point Behavior    
00119  * Care must be taken when using the fixed-point versions of the DCT4 transform functions.    
00120  * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
00121  * Refer to the function specific documentation below for usage guidelines.    
00122  */
00123 
00124  /**    
00125  * @addtogroup DCT4_IDCT4    
00126  * @{    
00127  */
00128 
00129 /**    
00130  * @brief Processing function for the floating-point DCT4/IDCT4.   
00131  * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.   
00132  * @param[in]       *pState        points to state buffer.   
00133  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
00134  * @return none.   
00135  */
00136 
00137 void arm_dct4_f32(
00138   const arm_dct4_instance_f32 * S,
00139   float32_t * pState,
00140   float32_t * pInlineBuffer)
00141 {
00142   uint32_t i;                                    /* Loop counter */
00143   float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
00144   float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
00145   float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
00146   float32_t in;                                  /* Temporary variable */
00147 
00148 
00149   /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
00150    * along with some pre-processing and post-processing.    
00151    * Computational procedure is explained as follows:    
00152    * (a) Pre-processing involves multiplying input with cos factor,    
00153    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
00154    *              where,    
00155    *                 r(n) -- output of preprocessing    
00156    *                 u(n) -- input to preprocessing(actual Source buffer)    
00157    * (b) Calculation of DCT2 using FFT is divided into three steps:    
00158    *                  Step1: Re-ordering of even and odd elements of input.    
00159    *                  Step2: Calculating FFT of the re-ordered input.    
00160    *                  Step3: Taking the real part of the product of FFT output and weights.    
00161    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
00162    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00163    *                        where,    
00164    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
00165    * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
00166    */
00167 
00168         /*-------- Pre-processing ------------*/
00169   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
00170   arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
00171   arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
00172 
00173   /* ----------------------------------------------------------------    
00174    * Step1: Re-ordering of even and odd elements as,    
00175    *             pState[i] =  pInlineBuffer[2*i] and    
00176    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
00177    ---------------------------------------------------------------------*/
00178 
00179   /* pS1 initialized to pState */
00180   pS1 = pState;
00181 
00182   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
00183   pS2 = pState + (S->N - 1u);
00184 
00185   /* pbuff initialized to input buffer */
00186   pbuff = pInlineBuffer;
00187 
00188 #ifndef ARM_MATH_CM0_FAMILY
00189 
00190   /* Run the below code for Cortex-M4 and Cortex-M3 */
00191 
00192   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
00193   i = (uint32_t) S->Nby2 >> 2u;
00194 
00195   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00196    ** a second loop below computes the remaining 1 to 3 samples. */
00197   do
00198   {
00199     /* Re-ordering of even and odd elements */
00200     /* pState[i] =  pInlineBuffer[2*i] */
00201     *pS1++ = *pbuff++;
00202     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00203     *pS2-- = *pbuff++;
00204 
00205     *pS1++ = *pbuff++;
00206     *pS2-- = *pbuff++;
00207 
00208     *pS1++ = *pbuff++;
00209     *pS2-- = *pbuff++;
00210 
00211     *pS1++ = *pbuff++;
00212     *pS2-- = *pbuff++;
00213 
00214     /* Decrement the loop counter */
00215     i--;
00216   } while(i > 0u);
00217 
00218   /* pbuff initialized to input buffer */
00219   pbuff = pInlineBuffer;
00220 
00221   /* pS1 initialized to pState */
00222   pS1 = pState;
00223 
00224   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00225   i = (uint32_t) S->N >> 2u;
00226 
00227   /* Processing with loop unrolling 4 times as N is always multiple of 4.    
00228    * Compute 4 outputs at a time */
00229   do
00230   {
00231     /* Writing the re-ordered output back to inplace input buffer */
00232     *pbuff++ = *pS1++;
00233     *pbuff++ = *pS1++;
00234     *pbuff++ = *pS1++;
00235     *pbuff++ = *pS1++;
00236 
00237     /* Decrement the loop counter */
00238     i--;
00239   } while(i > 0u);
00240 
00241 
00242   /* ---------------------------------------------------------    
00243    *     Step2: Calculate RFFT for N-point input    
00244    * ---------------------------------------------------------- */
00245   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00246   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
00247 
00248         /*----------------------------------------------------------------------    
00249      *  Step3: Multiply the FFT output with the weights.    
00250      *----------------------------------------------------------------------*/
00251   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
00252 
00253   /* ----------- Post-processing ---------- */
00254   /* DCT-IV can be obtained from DCT-II by the equation,    
00255    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00256    *       Hence, Y4(0) = Y2(0)/2  */
00257   /* Getting only real part from the output and Converting to DCT-IV */
00258 
00259   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
00260   i = ((uint32_t) S->N - 1u) >> 2u;
00261 
00262   /* pbuff initialized to input buffer. */
00263   pbuff = pInlineBuffer;
00264 
00265   /* pS1 initialized to pState */
00266   pS1 = pState;
00267 
00268   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00269   in = *pS1++ * (float32_t) 0.5;
00270   /* input buffer acts as inplace, so output values are stored in the input itself. */
00271   *pbuff++ = in;
00272 
00273   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00274   pS1++;
00275 
00276   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00277    ** a second loop below computes the remaining 1 to 3 samples. */
00278   do
00279   {
00280     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00281     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00282     in = *pS1++ - in;
00283     *pbuff++ = in;
00284     /* points to the next real value */
00285     pS1++;
00286 
00287     in = *pS1++ - in;
00288     *pbuff++ = in;
00289     pS1++;
00290 
00291     in = *pS1++ - in;
00292     *pbuff++ = in;
00293     pS1++;
00294 
00295     in = *pS1++ - in;
00296     *pbuff++ = in;
00297     pS1++;
00298 
00299     /* Decrement the loop counter */
00300     i--;
00301   } while(i > 0u);
00302 
00303   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
00304    ** No loop unrolling is used. */
00305   i = ((uint32_t) S->N - 1u) % 0x4u;
00306 
00307   while(i > 0u)
00308   {
00309     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00310     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00311     in = *pS1++ - in;
00312     *pbuff++ = in;
00313     /* points to the next real value */
00314     pS1++;
00315 
00316     /* Decrement the loop counter */
00317     i--;
00318   }
00319 
00320 
00321         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00322 
00323   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00324   i = (uint32_t) S->N >> 2u;
00325 
00326   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00327   pbuff = pInlineBuffer;
00328 
00329   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
00330   do
00331   {
00332     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00333     in = *pbuff;
00334     *pbuff++ = in * S->normalize;
00335 
00336     in = *pbuff;
00337     *pbuff++ = in * S->normalize;
00338 
00339     in = *pbuff;
00340     *pbuff++ = in * S->normalize;
00341 
00342     in = *pbuff;
00343     *pbuff++ = in * S->normalize;
00344 
00345     /* Decrement the loop counter */
00346     i--;
00347   } while(i > 0u);
00348 
00349 
00350 #else
00351 
00352   /* Run the below code for Cortex-M0 */
00353 
00354   /* Initializing the loop counter to N/2 */
00355   i = (uint32_t) S->Nby2;
00356 
00357   do
00358   {
00359     /* Re-ordering of even and odd elements */
00360     /* pState[i] =  pInlineBuffer[2*i] */
00361     *pS1++ = *pbuff++;
00362     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00363     *pS2-- = *pbuff++;
00364 
00365     /* Decrement the loop counter */
00366     i--;
00367   } while(i > 0u);
00368 
00369   /* pbuff initialized to input buffer */
00370   pbuff = pInlineBuffer;
00371 
00372   /* pS1 initialized to pState */
00373   pS1 = pState;
00374 
00375   /* Initializing the loop counter */
00376   i = (uint32_t) S->N;
00377 
00378   do
00379   {
00380     /* Writing the re-ordered output back to inplace input buffer */
00381     *pbuff++ = *pS1++;
00382 
00383     /* Decrement the loop counter */
00384     i--;
00385   } while(i > 0u);
00386 
00387 
00388   /* ---------------------------------------------------------    
00389    *     Step2: Calculate RFFT for N-point input    
00390    * ---------------------------------------------------------- */
00391   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00392   arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
00393 
00394         /*----------------------------------------------------------------------    
00395      *  Step3: Multiply the FFT output with the weights.    
00396      *----------------------------------------------------------------------*/
00397   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
00398 
00399   /* ----------- Post-processing ---------- */
00400   /* DCT-IV can be obtained from DCT-II by the equation,    
00401    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00402    *       Hence, Y4(0) = Y2(0)/2  */
00403   /* Getting only real part from the output and Converting to DCT-IV */
00404 
00405   /* pbuff initialized to input buffer. */
00406   pbuff = pInlineBuffer;
00407 
00408   /* pS1 initialized to pState */
00409   pS1 = pState;
00410 
00411   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00412   in = *pS1++ * (float32_t) 0.5;
00413   /* input buffer acts as inplace, so output values are stored in the input itself. */
00414   *pbuff++ = in;
00415 
00416   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00417   pS1++;
00418 
00419   /* Initializing the loop counter */
00420   i = ((uint32_t) S->N - 1u);
00421 
00422   do
00423   {
00424     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00425     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00426     in = *pS1++ - in;
00427     *pbuff++ = in;
00428     /* points to the next real value */
00429     pS1++;
00430 
00431 
00432     /* Decrement the loop counter */
00433     i--;
00434   } while(i > 0u);
00435 
00436 
00437         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00438 
00439   /* Initializing the loop counter */
00440   i = (uint32_t) S->N;
00441 
00442   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00443   pbuff = pInlineBuffer;
00444 
00445   do
00446   {
00447     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00448     in = *pbuff;
00449     *pbuff++ = in * S->normalize;
00450 
00451     /* Decrement the loop counter */
00452     i--;
00453   } while(i > 0u);
00454 
00455 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
00456 
00457 }
00458 
00459 /**    
00460    * @} end of DCT4_IDCT4 group    
00461    */