arm_dct4_q31.c

00001 /* ----------------------------------------------------------------------    
00002 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
00003 *    
00004 * $Date:        19. March 2015 
00005 * $Revision:    V.1.4.5  
00006 *    
00007 * Project:      CMSIS DSP Library    
00008 * Title:        arm_dct4_q31.c    
00009 *    
00010 * Description:  Processing function of DCT4 & IDCT4 Q31.    
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  * @addtogroup DCT4_IDCT4    
00045  * @{    
00046  */
00047 
00048 /**    
00049  * @brief Processing function for the Q31 DCT4/IDCT4.   
00050  * @param[in]       *S             points to an instance of the Q31 DCT4 structure.   
00051  * @param[in]       *pState        points to state buffer.   
00052  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
00053  * @return none.   
00054  * \par Input an output formats:    
00055  * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,    
00056  * as the conversion from DCT2 to DCT4 involves one subtraction.    
00057  * Internally inputs are downscaled in the RFFT process function to avoid overflows.    
00058  * Number of bits downscaled, depends on the size of the transform.    
00059  * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:     
00060  *    
00061  * \image html dct4FormatsQ31Table.gif    
00062  */
00063 
00064 void arm_dct4_q31(
00065   const arm_dct4_instance_q31 * S,
00066   q31_t * pState,
00067   q31_t * pInlineBuffer)
00068 {
00069   uint16_t i;                                    /* Loop counter */
00070   q31_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */
00071   q31_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */
00072   q31_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */
00073   q31_t in;                                      /* Temporary variable */
00074 
00075 
00076   /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
00077    * along with some pre-processing and post-processing.    
00078    * Computational procedure is explained as follows:    
00079    * (a) Pre-processing involves multiplying input with cos factor,    
00080    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
00081    *              where,    
00082    *                 r(n) -- output of preprocessing    
00083    *                 u(n) -- input to preprocessing(actual Source buffer)    
00084    * (b) Calculation of DCT2 using FFT is divided into three steps:    
00085    *                  Step1: Re-ordering of even and odd elements of input.    
00086    *                  Step2: Calculating FFT of the re-ordered input.    
00087    *                  Step3: Taking the real part of the product of FFT output and weights.    
00088    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
00089    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00090    *                        where,    
00091    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
00092    * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
00093    */
00094 
00095         /*-------- Pre-processing ------------*/
00096   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
00097   arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N);
00098   arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N);
00099 
00100   /* ----------------------------------------------------------------    
00101    * Step1: Re-ordering of even and odd elements as    
00102    *             pState[i] =  pInlineBuffer[2*i] and    
00103    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
00104    ---------------------------------------------------------------------*/
00105 
00106   /* pS1 initialized to pState */
00107   pS1 = pState;
00108 
00109   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
00110   pS2 = pState + (S->N - 1u);
00111 
00112   /* pbuff initialized to input buffer */
00113   pbuff = pInlineBuffer;
00114 
00115 #ifndef ARM_MATH_CM0_FAMILY
00116 
00117   /* Run the below code for Cortex-M4 and Cortex-M3 */
00118 
00119   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
00120   i = S->Nby2 >> 2u;
00121 
00122   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00123    ** a second loop below computes the remaining 1 to 3 samples. */
00124   do
00125   {
00126     /* Re-ordering of even and odd elements */
00127     /* pState[i] =  pInlineBuffer[2*i] */
00128     *pS1++ = *pbuff++;
00129     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00130     *pS2-- = *pbuff++;
00131 
00132     *pS1++ = *pbuff++;
00133     *pS2-- = *pbuff++;
00134 
00135     *pS1++ = *pbuff++;
00136     *pS2-- = *pbuff++;
00137 
00138     *pS1++ = *pbuff++;
00139     *pS2-- = *pbuff++;
00140 
00141     /* Decrement the loop counter */
00142     i--;
00143   } while(i > 0u);
00144 
00145   /* pbuff initialized to input buffer */
00146   pbuff = pInlineBuffer;
00147 
00148   /* pS1 initialized to pState */
00149   pS1 = pState;
00150 
00151   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00152   i = S->N >> 2u;
00153 
00154   /* Processing with loop unrolling 4 times as N is always multiple of 4.    
00155    * Compute 4 outputs at a time */
00156   do
00157   {
00158     /* Writing the re-ordered output back to inplace input buffer */
00159     *pbuff++ = *pS1++;
00160     *pbuff++ = *pS1++;
00161     *pbuff++ = *pS1++;
00162     *pbuff++ = *pS1++;
00163 
00164     /* Decrement the loop counter */
00165     i--;
00166   } while(i > 0u);
00167 
00168 
00169   /* ---------------------------------------------------------    
00170    *     Step2: Calculate RFFT for N-point input    
00171    * ---------------------------------------------------------- */
00172   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00173   arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
00174 
00175   /*----------------------------------------------------------------------    
00176    *  Step3: Multiply the FFT output with the weights.    
00177    *----------------------------------------------------------------------*/
00178   arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
00179 
00180   /* The output of complex multiplication is in 3.29 format.    
00181    * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
00182   arm_shift_q31(pState, 2, pState, S->N * 2);
00183 
00184   /* ----------- Post-processing ---------- */
00185   /* DCT-IV can be obtained from DCT-II by the equation,    
00186    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00187    *       Hence, Y4(0) = Y2(0)/2  */
00188   /* Getting only real part from the output and Converting to DCT-IV */
00189 
00190   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
00191   i = (S->N - 1u) >> 2u;
00192 
00193   /* pbuff initialized to input buffer. */
00194   pbuff = pInlineBuffer;
00195 
00196   /* pS1 initialized to pState */
00197   pS1 = pState;
00198 
00199   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00200   in = *pS1++ >> 1u;
00201   /* input buffer acts as inplace, so output values are stored in the input itself. */
00202   *pbuff++ = in;
00203 
00204   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00205   pS1++;
00206 
00207   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00208    ** a second loop below computes the remaining 1 to 3 samples. */
00209   do
00210   {
00211     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00212     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00213     in = *pS1++ - in;
00214     *pbuff++ = in;
00215     /* points to the next real value */
00216     pS1++;
00217 
00218     in = *pS1++ - in;
00219     *pbuff++ = in;
00220     pS1++;
00221 
00222     in = *pS1++ - in;
00223     *pbuff++ = in;
00224     pS1++;
00225 
00226     in = *pS1++ - in;
00227     *pbuff++ = in;
00228     pS1++;
00229 
00230     /* Decrement the loop counter */
00231     i--;
00232   } while(i > 0u);
00233 
00234   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
00235    ** No loop unrolling is used. */
00236   i = (S->N - 1u) % 0x4u;
00237 
00238   while(i > 0u)
00239   {
00240     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00241     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00242     in = *pS1++ - in;
00243     *pbuff++ = in;
00244     /* points to the next real value */
00245     pS1++;
00246 
00247     /* Decrement the loop counter */
00248     i--;
00249   }
00250 
00251 
00252         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00253 
00254   /* Initializing the loop counter to N/4 instead of N for loop unrolling */
00255   i = S->N >> 2u;
00256 
00257   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00258   pbuff = pInlineBuffer;
00259 
00260   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
00261   do
00262   {
00263     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00264     in = *pbuff;
00265     *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
00266 
00267     in = *pbuff;
00268     *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
00269 
00270     in = *pbuff;
00271     *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
00272 
00273     in = *pbuff;
00274     *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
00275 
00276     /* Decrement the loop counter */
00277     i--;
00278   } while(i > 0u);
00279 
00280 
00281 #else
00282 
00283   /* Run the below code for Cortex-M0 */
00284 
00285   /* Initializing the loop counter to N/2 */
00286   i = S->Nby2;
00287 
00288   do
00289   {
00290     /* Re-ordering of even and odd elements */
00291     /* pState[i] =  pInlineBuffer[2*i] */
00292     *pS1++ = *pbuff++;
00293     /* pState[N-i-1] = pInlineBuffer[2*i+1] */
00294     *pS2-- = *pbuff++;
00295 
00296     /* Decrement the loop counter */
00297     i--;
00298   } while(i > 0u);
00299 
00300   /* pbuff initialized to input buffer */
00301   pbuff = pInlineBuffer;
00302 
00303   /* pS1 initialized to pState */
00304   pS1 = pState;
00305 
00306   /* Initializing the loop counter */
00307   i = S->N;
00308 
00309   do
00310   {
00311     /* Writing the re-ordered output back to inplace input buffer */
00312     *pbuff++ = *pS1++;
00313 
00314     /* Decrement the loop counter */
00315     i--;
00316   } while(i > 0u);
00317 
00318 
00319   /* ---------------------------------------------------------    
00320    *     Step2: Calculate RFFT for N-point input    
00321    * ---------------------------------------------------------- */
00322   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
00323   arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
00324 
00325   /*----------------------------------------------------------------------    
00326    *  Step3: Multiply the FFT output with the weights.    
00327    *----------------------------------------------------------------------*/
00328   arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
00329 
00330   /* The output of complex multiplication is in 3.29 format.    
00331    * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
00332   arm_shift_q31(pState, 2, pState, S->N * 2);
00333 
00334   /* ----------- Post-processing ---------- */
00335   /* DCT-IV can be obtained from DCT-II by the equation,    
00336    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
00337    *       Hence, Y4(0) = Y2(0)/2  */
00338   /* Getting only real part from the output and Converting to DCT-IV */
00339 
00340   /* pbuff initialized to input buffer. */
00341   pbuff = pInlineBuffer;
00342 
00343   /* pS1 initialized to pState */
00344   pS1 = pState;
00345 
00346   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
00347   in = *pS1++ >> 1u;
00348   /* input buffer acts as inplace, so output values are stored in the input itself. */
00349   *pbuff++ = in;
00350 
00351   /* pState pointer is incremented twice as the real values are located alternatively in the array */
00352   pS1++;
00353 
00354   /* Initializing the loop counter */
00355   i = (S->N - 1u);
00356 
00357   while(i > 0u)
00358   {
00359     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
00360     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
00361     in = *pS1++ - in;
00362     *pbuff++ = in;
00363     /* points to the next real value */
00364     pS1++;
00365 
00366     /* Decrement the loop counter */
00367     i--;
00368   }
00369 
00370 
00371         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
00372 
00373   /* Initializing the loop counter */
00374   i = S->N;
00375 
00376   /* pbuff initialized to the pInlineBuffer(now contains the output values) */
00377   pbuff = pInlineBuffer;
00378 
00379   do
00380   {
00381     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
00382     in = *pbuff;
00383     *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
00384 
00385     /* Decrement the loop counter */
00386     i--;
00387   } while(i > 0u);
00388 
00389 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
00390 
00391 }
00392 
00393 /**    
00394    * @} end of DCT4_IDCT4 group    
00395    */