arm_dct4_f32.c

00001 /* ----------------------------------------------------------------------  
00002 * Copyright (C) 2010 ARM Limited. All rights reserved.  
00003 *  
00004 * $Date:        29. November 2010  
00005 * $Revision:    V1.0.3  
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
00013 *  
00014 * Version 1.0.3 2010/11/29 
00015 *    Re-organized the CMSIS folders and updated documentation.  
00016 *   
00017 * Version 1.0.2 2010/11/11  
00018 *    Documentation updated.   
00019 *  
00020 * Version 1.0.1 2010/10/05   
00021 *    Production release and review comments incorporated.  
00022 *  
00023 * Version 1.0.0 2010/09/20   
00024 *    Production release and review comments incorporated.  
00025 * -------------------------------------------------------------------- */ 
00026  
00027 #include "arm_math.h" 
00028  
00029 /**  
00030  * @ingroup groupTransforms  
00031  */ 
00032  
00033 /**  
00034  * @defgroup DCT4_IDCT4 DCT Type IV Functions  
00035  * Representation of signals by minimum number of values is important for storage and transmission.  
00036  * The possibility of large discontinuity between the beginning and end of a period of a signal  
00037  * in DFT can be avoided by extending the signal so that it is even-symmetric.  
00038  * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the  
00039  * spectrum and is very widely used in signal and image coding applications.  
00040  * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.  
00041  * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.  
00042  *  
00043  * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.  
00044  * Reordering of the input data makes the computation of DCT just a problem of  
00045  * computing the DFT of a real signal with a few additional operations.  
00046  * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.  
00047  *   
00048  * 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.  
00049  * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.  
00050  * DCT2 implementation can be described in the following steps:  
00051  * - Re-ordering input  
00052  * - Calculating Real FFT  
00053  * - Multiplication of weights and Real FFT output and getting real part from the product.  
00054  *  
00055  * This process is explained by the block diagram below:  
00056  * \image html DCT4.gif "Discrete Cosine Transform - type-IV"  
00057  *  
00058  * \par Algorithm:  
00059  * The N-point type-IV DCT is defined as a real, linear transformation by the formula:  
00060  * \image html DCT4Equation.gif  
00061  * where <code>k = 0,1,2,.....N-1</code>  
00062  *\par  
00063  * Its inverse is defined as follows:  
00064  * \image html IDCT4Equation.gif  
00065  * where <code>n = 0,1,2,.....N-1</code>  
00066  *\par  
00067  * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).  
00068  * The symmetry of the transform matrix indicates that the fast algorithms for the forward  
00069  * and inverse transform computation are identical.  
00070  * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.  
00071  *  
00072  * \par Lengths supported by the transform:  
00073  *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().  
00074  * The library provides separate functions for Q15, Q31, and floating-point data types.  
00075  * \par Instance Structure  
00076  * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.  
00077  * A separate instance structure must be defined for each transform.  
00078  * There are separate instance structure declarations for each of the 3 supported data types.  
00079  *  
00080  * \par Initialization Functions  
00081  * There is also an associated initialization function for each data type.  
00082  * The initialization function performs the following operations:  
00083  * - Sets the values of the internal structure fields.  
00084  * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().  
00085  * \par  
00086  * Use of the initialization function is optional.  
00087  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
00088  * To place an instance structure into a const data section, the instance structure must be manually initialized.  
00089  * Manually initialize the instance structure as follows:  
00090  * <pre>  
00091  *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};  
00092  *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; 
00093  *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; 
00094  * </pre> 
00095  * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4; 
00096  * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;  
00097  * \c pTwiddle points to the twiddle factor table; 
00098  * \c pCosFactor points to the cosFactor table; 
00099  * \c pRfft points to the real FFT instance; 
00100  * \c pCfft points to the complex FFT instance; 
00101  * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32() 
00102  * and arm_rfft_f32() respectively for details regarding static initialization. 
00103  * 
00104  * \par Fixed-Point Behavior  
00105  * Care must be taken when using the fixed-point versions of the DCT4 transform functions.  
00106  * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.  
00107  * Refer to the function specific documentation below for usage guidelines.  
00108  */ 
00109  
00110  /**  
00111  * @addtogroup DCT4_IDCT4  
00112  * @{  
00113  */ 
00114  
00115 /**  
00116  * @brief Processing function for the floating-point DCT4/IDCT4. 
00117  * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure. 
00118  * @param[in]       *pState        points to state buffer. 
00119  * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer. 
00120  * @return none. 
00121  */ 
00122  
00123 void arm_dct4_f32( 
00124   const arm_dct4_instance_f32 * S, 
00125   float32_t * pState, 
00126   float32_t * pInlineBuffer) 
00127 { 
00128   uint32_t i;                                    /* Loop counter */ 
00129   float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */ 
00130   float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */ 
00131   float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */ 
00132   float32_t in;                                  /* Temporary variable */ 
00133  
00134  
00135   /* DCT4 computation involves DCT2 (which is calculated using RFFT)  
00136    * along with some pre-processing and post-processing.  
00137    * Computational procedure is explained as follows:  
00138    * (a) Pre-processing involves multiplying input with cos factor,  
00139    *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))  
00140    *              where,  
00141    *                 r(n) -- output of preprocessing  
00142    *                 u(n) -- input to preprocessing(actual Source buffer)  
00143    * (b) Calculation of DCT2 using FFT is divided into three steps:  
00144    *                  Step1: Re-ordering of even and odd elements of input.  
00145    *                  Step2: Calculating FFT of the re-ordered input.  
00146    *                  Step3: Taking the real part of the product of FFT output and weights.  
00147    * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:  
00148    *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
00149    *                        where,  
00150    *                           Y4 -- DCT4 output,   Y2 -- DCT2 output  
00151    * (d) Multiplying the output with the normalizing factor sqrt(2/N).  
00152    */ 
00153  
00154         /*-------- Pre-processing ------------*/ 
00155   /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ 
00156   arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N); 
00157   arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N); 
00158  
00159   /* ----------------------------------------------------------------  
00160    * Step1: Re-ordering of even and odd elements as,  
00161    *             pState[i] =  pInlineBuffer[2*i] and  
00162    *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2  
00163    ---------------------------------------------------------------------*/ 
00164  
00165   /* pS1 initialized to pState */ 
00166   pS1 = pState; 
00167  
00168   /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ 
00169   pS2 = pState + (S->N - 1u); 
00170  
00171   /* pbuff initialized to input buffer */ 
00172   pbuff = pInlineBuffer; 
00173  
00174   /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ 
00175   i = (uint32_t) S->Nby2 >> 2u; 
00176  
00177   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00178    ** a second loop below computes the remaining 1 to 3 samples. */ 
00179   do 
00180   { 
00181     /* Re-ordering of even and odd elements */ 
00182     /* pState[i] =  pInlineBuffer[2*i] */ 
00183     *pS1++ = *pbuff++; 
00184     /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 
00185     *pS2-- = *pbuff++; 
00186  
00187     *pS1++ = *pbuff++; 
00188     *pS2-- = *pbuff++; 
00189  
00190     *pS1++ = *pbuff++; 
00191     *pS2-- = *pbuff++; 
00192  
00193     *pS1++ = *pbuff++; 
00194     *pS2-- = *pbuff++; 
00195  
00196     /* Decrement the loop counter */ 
00197     i--; 
00198   } while(i > 0u); 
00199  
00200   /* pbuff initialized to input buffer */ 
00201   pbuff = pInlineBuffer; 
00202  
00203   /* pS1 initialized to pState */ 
00204   pS1 = pState; 
00205  
00206   /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
00207   i = (uint32_t) S->N >> 2u; 
00208  
00209   /* Processing with loop unrolling 4 times as N is always multiple of 4.  
00210    * Compute 4 outputs at a time */ 
00211   do 
00212   { 
00213     /* Writing the re-ordered output back to inplace input buffer */ 
00214     *pbuff++ = *pS1++; 
00215     *pbuff++ = *pS1++; 
00216     *pbuff++ = *pS1++; 
00217     *pbuff++ = *pS1++; 
00218  
00219     /* Decrement the loop counter */ 
00220     i--; 
00221   } while(i > 0u); 
00222  
00223  
00224   /* ---------------------------------------------------------  
00225    *     Step2: Calculate RFFT for N-point input  
00226    * ---------------------------------------------------------- */ 
00227   /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 
00228   arm_rfft_f32(S->pRfft, pInlineBuffer, pState); 
00229  
00230         /*----------------------------------------------------------------------  
00231      *  Step3: Multiply the FFT output with the weights.  
00232      *----------------------------------------------------------------------*/ 
00233   arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); 
00234  
00235   /* ----------- Post-processing ---------- */ 
00236   /* DCT-IV can be obtained from DCT-II by the equation,  
00237    *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
00238    *       Hence, Y4(0) = Y2(0)/2  */ 
00239   /* Getting only real part from the output and Converting to DCT-IV */ 
00240  
00241   /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ 
00242   i = ((uint32_t) S->N - 1u) >> 2u; 
00243  
00244   /* pbuff initialized to input buffer. */ 
00245   pbuff = pInlineBuffer; 
00246  
00247   /* pS1 initialized to pState */ 
00248   pS1 = pState; 
00249  
00250   /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 
00251   in = *pS1++ * (float32_t) 0.5; 
00252   /* input buffer acts as inplace, so output values are stored in the input itself. */ 
00253   *pbuff++ = in; 
00254  
00255   /* pState pointer is incremented twice as the real values are located alternatively in the array */ 
00256   pS1++; 
00257  
00258   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00259    ** a second loop below computes the remaining 1 to 3 samples. */ 
00260   do 
00261   { 
00262     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
00263     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
00264     in = *pS1++ - in; 
00265     *pbuff++ = in; 
00266     /* points to the next real value */ 
00267     pS1++; 
00268  
00269     in = *pS1++ - in; 
00270     *pbuff++ = in; 
00271     pS1++; 
00272  
00273     in = *pS1++ - in; 
00274     *pbuff++ = in; 
00275     pS1++; 
00276  
00277     in = *pS1++ - in; 
00278     *pbuff++ = in; 
00279     pS1++; 
00280  
00281     /* Decrement the loop counter */ 
00282     i--; 
00283   } while(i > 0u); 
00284  
00285   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
00286    ** No loop unrolling is used. */ 
00287   i = ((uint32_t) S->N - 1u) % 0x4u; 
00288  
00289   while(i > 0u) 
00290   { 
00291     /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
00292     /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
00293     in = *pS1++ - in; 
00294     *pbuff++ = in; 
00295     /* points to the next real value */ 
00296     pS1++; 
00297  
00298     /* Decrement the loop counter */ 
00299     i--; 
00300   } 
00301  
00302  
00303         /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 
00304  
00305   /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
00306   i = (uint32_t) S->N >> 2u; 
00307  
00308   /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 
00309   pbuff = pInlineBuffer; 
00310  
00311   /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */ 
00312   do 
00313   { 
00314     /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 
00315     in = *pbuff; 
00316     *pbuff++ = in * S->normalize; 
00317  
00318     in = *pbuff; 
00319     *pbuff++ = in * S->normalize; 
00320  
00321     in = *pbuff; 
00322     *pbuff++ = in * S->normalize; 
00323  
00324     in = *pbuff; 
00325     *pbuff++ = in * S->normalize; 
00326  
00327     /* Decrement the loop counter */ 
00328     i--; 
00329   } while(i > 0u); 
00330  
00331 } 
00332  
00333 /**  
00334    * @} end of DCT4_IDCT4 group  
00335    */