00001 /* ---------------------------------------------------------------------- 00002 * Copyright (C) 2010 ARM Limited. All rights reserved. 00003 * 00004 * $Date: 15. July 2011 00005 * $Revision: V1.0.10 00006 * 00007 * Project: CMSIS DSP Library 00008 * Title: arm_dct4_q15.c 00009 * 00010 * Description: Processing function of DCT4 & IDCT4 Q15. 00011 * 00012 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 00013 * 00014 * Version 1.0.10 2011/7/15 00015 * Big Endian support added and Merged M0 and M3/M4 Source code. 00016 * 00017 * Version 1.0.3 2010/11/29 00018 * Re-organized the CMSIS folders and updated documentation. 00019 * 00020 * Version 1.0.2 2010/11/11 00021 * Documentation updated. 00022 * 00023 * Version 1.0.1 2010/10/05 00024 * Production release and review comments incorporated. 00025 * 00026 * Version 1.0.0 2010/09/20 00027 * Production release and review comments incorporated. 00028 * -------------------------------------------------------------------- */ 00029 00030 #include "arm_math.h" 00031 00052 void arm_dct4_q15( 00053 const arm_dct4_instance_q15 * S, 00054 q15_t * pState, 00055 q15_t * pInlineBuffer) 00056 { 00057 uint32_t i; /* Loop counter */ 00058 q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */ 00059 q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ 00060 q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ 00061 q15_t in; /* Temporary variable */ 00062 00063 00064 /* DCT4 computation involves DCT2 (which is calculated using RFFT) 00065 * along with some pre-processing and post-processing. 00066 * Computational procedure is explained as follows: 00067 * (a) Pre-processing involves multiplying input with cos factor, 00068 * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) 00069 * where, 00070 * r(n) -- output of preprocessing 00071 * u(n) -- input to preprocessing(actual Source buffer) 00072 * (b) Calculation of DCT2 using FFT is divided into three steps: 00073 * Step1: Re-ordering of even and odd elements of input. 00074 * Step2: Calculating FFT of the re-ordered input. 00075 * Step3: Taking the real part of the product of FFT output and weights. 00076 * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: 00077 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00078 * where, 00079 * Y4 -- DCT4 output, Y2 -- DCT2 output 00080 * (d) Multiplying the output with the normalizing factor sqrt(2/N). 00081 */ 00082 00083 /*-------- Pre-processing ------------*/ 00084 /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ 00085 arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N); 00086 arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N); 00087 00088 /* ---------------------------------------------------------------- 00089 * Step1: Re-ordering of even and odd elements as 00090 * pState[i] = pInlineBuffer[2*i] and 00091 * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 00092 ---------------------------------------------------------------------*/ 00093 00094 /* pS1 initialized to pState */ 00095 pS1 = pState; 00096 00097 /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ 00098 pS2 = pState + (S->N - 1u); 00099 00100 /* pbuff initialized to input buffer */ 00101 pbuff = pInlineBuffer; 00102 00103 00104 #ifndef ARM_MATH_CM0 00105 00106 /* Run the below code for Cortex-M4 and Cortex-M3 */ 00107 00108 /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ 00109 i = (uint32_t) S->Nby2 >> 2u; 00110 00111 /* First part of the processing with loop unrolling. Compute 4 outputs at a time. 00112 ** a second loop below computes the remaining 1 to 3 samples. */ 00113 do 00114 { 00115 /* Re-ordering of even and odd elements */ 00116 /* pState[i] = pInlineBuffer[2*i] */ 00117 *pS1++ = *pbuff++; 00118 /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 00119 *pS2-- = *pbuff++; 00120 00121 *pS1++ = *pbuff++; 00122 *pS2-- = *pbuff++; 00123 00124 *pS1++ = *pbuff++; 00125 *pS2-- = *pbuff++; 00126 00127 *pS1++ = *pbuff++; 00128 *pS2-- = *pbuff++; 00129 00130 /* Decrement the loop counter */ 00131 i--; 00132 } while(i > 0u); 00133 00134 /* pbuff initialized to input buffer */ 00135 pbuff = pInlineBuffer; 00136 00137 /* pS1 initialized to pState */ 00138 pS1 = pState; 00139 00140 /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 00141 i = (uint32_t) S->N >> 2u; 00142 00143 /* Processing with loop unrolling 4 times as N is always multiple of 4. 00144 * Compute 4 outputs at a time */ 00145 do 00146 { 00147 /* Writing the re-ordered output back to inplace input buffer */ 00148 *pbuff++ = *pS1++; 00149 *pbuff++ = *pS1++; 00150 *pbuff++ = *pS1++; 00151 *pbuff++ = *pS1++; 00152 00153 /* Decrement the loop counter */ 00154 i--; 00155 } while(i > 0u); 00156 00157 00158 /* --------------------------------------------------------- 00159 * Step2: Calculate RFFT for N-point input 00160 * ---------------------------------------------------------- */ 00161 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 00162 arm_rfft_q15(S->pRfft, pInlineBuffer, pState); 00163 00164 /*---------------------------------------------------------------------- 00165 * Step3: Multiply the FFT output with the weights. 00166 *----------------------------------------------------------------------*/ 00167 arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N); 00168 00169 /* The output of complex multiplication is in 3.13 format. 00170 * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ 00171 arm_shift_q15(pState, 2, pState, S->N * 2); 00172 00173 /* ----------- Post-processing ---------- */ 00174 /* DCT-IV can be obtained from DCT-II by the equation, 00175 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00176 * Hence, Y4(0) = Y2(0)/2 */ 00177 /* Getting only real part from the output and Converting to DCT-IV */ 00178 00179 /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ 00180 i = ((uint32_t) S->N - 1u) >> 2u; 00181 00182 /* pbuff initialized to input buffer. */ 00183 pbuff = pInlineBuffer; 00184 00185 /* pS1 initialized to pState */ 00186 pS1 = pState; 00187 00188 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 00189 in = *pS1++ >> 1u; 00190 /* input buffer acts as inplace, so output values are stored in the input itself. */ 00191 *pbuff++ = in; 00192 00193 /* pState pointer is incremented twice as the real values are located alternatively in the array */ 00194 pS1++; 00195 00196 /* First part of the processing with loop unrolling. Compute 4 outputs at a time. 00197 ** a second loop below computes the remaining 1 to 3 samples. */ 00198 do 00199 { 00200 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00201 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00202 in = *pS1++ - in; 00203 *pbuff++ = in; 00204 /* points to the next real value */ 00205 pS1++; 00206 00207 in = *pS1++ - in; 00208 *pbuff++ = in; 00209 pS1++; 00210 00211 in = *pS1++ - in; 00212 *pbuff++ = in; 00213 pS1++; 00214 00215 in = *pS1++ - in; 00216 *pbuff++ = in; 00217 pS1++; 00218 00219 /* Decrement the loop counter */ 00220 i--; 00221 } while(i > 0u); 00222 00223 /* If the blockSize is not a multiple of 4, compute any remaining output samples here. 00224 ** No loop unrolling is used. */ 00225 i = ((uint32_t) S->N - 1u) % 0x4u; 00226 00227 while(i > 0u) 00228 { 00229 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00230 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00231 in = *pS1++ - in; 00232 *pbuff++ = in; 00233 /* points to the next real value */ 00234 pS1++; 00235 00236 /* Decrement the loop counter */ 00237 i--; 00238 } 00239 00240 00241 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 00242 00243 /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 00244 i = (uint32_t) S->N >> 2u; 00245 00246 /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 00247 pbuff = pInlineBuffer; 00248 00249 /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ 00250 do 00251 { 00252 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 00253 in = *pbuff; 00254 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); 00255 00256 in = *pbuff; 00257 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); 00258 00259 in = *pbuff; 00260 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); 00261 00262 in = *pbuff; 00263 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); 00264 00265 /* Decrement the loop counter */ 00266 i--; 00267 } while(i > 0u); 00268 00269 00270 #else 00271 00272 /* Run the below code for Cortex-M0 */ 00273 00274 /* Initializing the loop counter to N/2 */ 00275 i = (uint32_t) S->Nby2; 00276 00277 do 00278 { 00279 /* Re-ordering of even and odd elements */ 00280 /* pState[i] = pInlineBuffer[2*i] */ 00281 *pS1++ = *pbuff++; 00282 /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 00283 *pS2-- = *pbuff++; 00284 00285 /* Decrement the loop counter */ 00286 i--; 00287 } while(i > 0u); 00288 00289 /* pbuff initialized to input buffer */ 00290 pbuff = pInlineBuffer; 00291 00292 /* pS1 initialized to pState */ 00293 pS1 = pState; 00294 00295 /* Initializing the loop counter */ 00296 i = (uint32_t) S->N; 00297 00298 do 00299 { 00300 /* Writing the re-ordered output back to inplace input buffer */ 00301 *pbuff++ = *pS1++; 00302 00303 /* Decrement the loop counter */ 00304 i--; 00305 } while(i > 0u); 00306 00307 00308 /* --------------------------------------------------------- 00309 * Step2: Calculate RFFT for N-point input 00310 * ---------------------------------------------------------- */ 00311 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 00312 arm_rfft_q15(S->pRfft, pInlineBuffer, pState); 00313 00314 /*---------------------------------------------------------------------- 00315 * Step3: Multiply the FFT output with the weights. 00316 *----------------------------------------------------------------------*/ 00317 arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N); 00318 00319 /* The output of complex multiplication is in 3.13 format. 00320 * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ 00321 arm_shift_q15(pState, 2, pState, S->N * 2); 00322 00323 /* ----------- Post-processing ---------- */ 00324 /* DCT-IV can be obtained from DCT-II by the equation, 00325 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00326 * Hence, Y4(0) = Y2(0)/2 */ 00327 /* Getting only real part from the output and Converting to DCT-IV */ 00328 00329 /* Initializing the loop counter */ 00330 i = ((uint32_t) S->N - 1u); 00331 00332 /* pbuff initialized to input buffer. */ 00333 pbuff = pInlineBuffer; 00334 00335 /* pS1 initialized to pState */ 00336 pS1 = pState; 00337 00338 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 00339 in = *pS1++ >> 1u; 00340 /* input buffer acts as inplace, so output values are stored in the input itself. */ 00341 *pbuff++ = in; 00342 00343 /* pState pointer is incremented twice as the real values are located alternatively in the array */ 00344 pS1++; 00345 00346 do 00347 { 00348 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00349 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00350 in = *pS1++ - in; 00351 *pbuff++ = in; 00352 /* points to the next real value */ 00353 pS1++; 00354 00355 /* Decrement the loop counter */ 00356 i--; 00357 } while(i > 0u); 00358 00359 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 00360 00361 /* Initializing the loop counter */ 00362 i = (uint32_t) S->N; 00363 00364 /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 00365 pbuff = pInlineBuffer; 00366 00367 do 00368 { 00369 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 00370 in = *pbuff; 00371 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); 00372 00373 /* Decrement the loop counter */ 00374 i--; 00375 } while(i > 0u); 00376 00377 #endif /* #ifndef ARM_MATH_CM0 */ 00378 00379 } 00380