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_f32.c 00009 * 00010 * Description: Processing function of DCT4 & IDCT4 F32. 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 00126 void arm_dct4_f32( 00127 const arm_dct4_instance_f32 * S, 00128 float32_t * pState, 00129 float32_t * pInlineBuffer) 00130 { 00131 uint32_t i; /* Loop counter */ 00132 float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */ 00133 float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ 00134 float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ 00135 float32_t in; /* Temporary variable */ 00136 00137 00138 /* DCT4 computation involves DCT2 (which is calculated using RFFT) 00139 * along with some pre-processing and post-processing. 00140 * Computational procedure is explained as follows: 00141 * (a) Pre-processing involves multiplying input with cos factor, 00142 * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) 00143 * where, 00144 * r(n) -- output of preprocessing 00145 * u(n) -- input to preprocessing(actual Source buffer) 00146 * (b) Calculation of DCT2 using FFT is divided into three steps: 00147 * Step1: Re-ordering of even and odd elements of input. 00148 * Step2: Calculating FFT of the re-ordered input. 00149 * Step3: Taking the real part of the product of FFT output and weights. 00150 * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: 00151 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00152 * where, 00153 * Y4 -- DCT4 output, Y2 -- DCT2 output 00154 * (d) Multiplying the output with the normalizing factor sqrt(2/N). 00155 */ 00156 00157 /*-------- Pre-processing ------------*/ 00158 /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ 00159 arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N); 00160 arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N); 00161 00162 /* ---------------------------------------------------------------- 00163 * Step1: Re-ordering of even and odd elements as, 00164 * pState[i] = pInlineBuffer[2*i] and 00165 * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 00166 ---------------------------------------------------------------------*/ 00167 00168 /* pS1 initialized to pState */ 00169 pS1 = pState; 00170 00171 /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ 00172 pS2 = pState + (S->N - 1u); 00173 00174 /* pbuff initialized to input buffer */ 00175 pbuff = pInlineBuffer; 00176 00177 #ifndef ARM_MATH_CM0 00178 00179 /* Run the below code for Cortex-M4 and Cortex-M3 */ 00180 00181 /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ 00182 i = (uint32_t) S->Nby2 >> 2u; 00183 00184 /* First part of the processing with loop unrolling. Compute 4 outputs at a time. 00185 ** a second loop below computes the remaining 1 to 3 samples. */ 00186 do 00187 { 00188 /* Re-ordering of even and odd elements */ 00189 /* pState[i] = pInlineBuffer[2*i] */ 00190 *pS1++ = *pbuff++; 00191 /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 00192 *pS2-- = *pbuff++; 00193 00194 *pS1++ = *pbuff++; 00195 *pS2-- = *pbuff++; 00196 00197 *pS1++ = *pbuff++; 00198 *pS2-- = *pbuff++; 00199 00200 *pS1++ = *pbuff++; 00201 *pS2-- = *pbuff++; 00202 00203 /* Decrement the loop counter */ 00204 i--; 00205 } while(i > 0u); 00206 00207 /* pbuff initialized to input buffer */ 00208 pbuff = pInlineBuffer; 00209 00210 /* pS1 initialized to pState */ 00211 pS1 = pState; 00212 00213 /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 00214 i = (uint32_t) S->N >> 2u; 00215 00216 /* Processing with loop unrolling 4 times as N is always multiple of 4. 00217 * Compute 4 outputs at a time */ 00218 do 00219 { 00220 /* Writing the re-ordered output back to inplace input buffer */ 00221 *pbuff++ = *pS1++; 00222 *pbuff++ = *pS1++; 00223 *pbuff++ = *pS1++; 00224 *pbuff++ = *pS1++; 00225 00226 /* Decrement the loop counter */ 00227 i--; 00228 } while(i > 0u); 00229 00230 00231 /* --------------------------------------------------------- 00232 * Step2: Calculate RFFT for N-point input 00233 * ---------------------------------------------------------- */ 00234 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 00235 arm_rfft_f32(S->pRfft, pInlineBuffer, pState); 00236 00237 /*---------------------------------------------------------------------- 00238 * Step3: Multiply the FFT output with the weights. 00239 *----------------------------------------------------------------------*/ 00240 arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); 00241 00242 /* ----------- Post-processing ---------- */ 00243 /* DCT-IV can be obtained from DCT-II by the equation, 00244 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00245 * Hence, Y4(0) = Y2(0)/2 */ 00246 /* Getting only real part from the output and Converting to DCT-IV */ 00247 00248 /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ 00249 i = ((uint32_t) S->N - 1u) >> 2u; 00250 00251 /* pbuff initialized to input buffer. */ 00252 pbuff = pInlineBuffer; 00253 00254 /* pS1 initialized to pState */ 00255 pS1 = pState; 00256 00257 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 00258 in = *pS1++ * (float32_t) 0.5; 00259 /* input buffer acts as inplace, so output values are stored in the input itself. */ 00260 *pbuff++ = in; 00261 00262 /* pState pointer is incremented twice as the real values are located alternatively in the array */ 00263 pS1++; 00264 00265 /* First part of the processing with loop unrolling. Compute 4 outputs at a time. 00266 ** a second loop below computes the remaining 1 to 3 samples. */ 00267 do 00268 { 00269 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00270 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00271 in = *pS1++ - in; 00272 *pbuff++ = in; 00273 /* points to the next real value */ 00274 pS1++; 00275 00276 in = *pS1++ - in; 00277 *pbuff++ = in; 00278 pS1++; 00279 00280 in = *pS1++ - in; 00281 *pbuff++ = in; 00282 pS1++; 00283 00284 in = *pS1++ - in; 00285 *pbuff++ = in; 00286 pS1++; 00287 00288 /* Decrement the loop counter */ 00289 i--; 00290 } while(i > 0u); 00291 00292 /* If the blockSize is not a multiple of 4, compute any remaining output samples here. 00293 ** No loop unrolling is used. */ 00294 i = ((uint32_t) S->N - 1u) % 0x4u; 00295 00296 while(i > 0u) 00297 { 00298 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00299 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00300 in = *pS1++ - in; 00301 *pbuff++ = in; 00302 /* points to the next real value */ 00303 pS1++; 00304 00305 /* Decrement the loop counter */ 00306 i--; 00307 } 00308 00309 00310 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 00311 00312 /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 00313 i = (uint32_t) S->N >> 2u; 00314 00315 /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 00316 pbuff = pInlineBuffer; 00317 00318 /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ 00319 do 00320 { 00321 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 00322 in = *pbuff; 00323 *pbuff++ = in * S->normalize; 00324 00325 in = *pbuff; 00326 *pbuff++ = in * S->normalize; 00327 00328 in = *pbuff; 00329 *pbuff++ = in * S->normalize; 00330 00331 in = *pbuff; 00332 *pbuff++ = in * S->normalize; 00333 00334 /* Decrement the loop counter */ 00335 i--; 00336 } while(i > 0u); 00337 00338 00339 #else 00340 00341 /* Run the below code for Cortex-M0 */ 00342 00343 /* Initializing the loop counter to N/2 */ 00344 i = (uint32_t) S->Nby2; 00345 00346 do 00347 { 00348 /* Re-ordering of even and odd elements */ 00349 /* pState[i] = pInlineBuffer[2*i] */ 00350 *pS1++ = *pbuff++; 00351 /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 00352 *pS2-- = *pbuff++; 00353 00354 /* Decrement the loop counter */ 00355 i--; 00356 } while(i > 0u); 00357 00358 /* pbuff initialized to input buffer */ 00359 pbuff = pInlineBuffer; 00360 00361 /* pS1 initialized to pState */ 00362 pS1 = pState; 00363 00364 /* Initializing the loop counter */ 00365 i = (uint32_t) S->N; 00366 00367 do 00368 { 00369 /* Writing the re-ordered output back to inplace input buffer */ 00370 *pbuff++ = *pS1++; 00371 00372 /* Decrement the loop counter */ 00373 i--; 00374 } while(i > 0u); 00375 00376 00377 /* --------------------------------------------------------- 00378 * Step2: Calculate RFFT for N-point input 00379 * ---------------------------------------------------------- */ 00380 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 00381 arm_rfft_f32(S->pRfft, pInlineBuffer, pState); 00382 00383 /*---------------------------------------------------------------------- 00384 * Step3: Multiply the FFT output with the weights. 00385 *----------------------------------------------------------------------*/ 00386 arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); 00387 00388 /* ----------- Post-processing ---------- */ 00389 /* DCT-IV can be obtained from DCT-II by the equation, 00390 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) 00391 * Hence, Y4(0) = Y2(0)/2 */ 00392 /* Getting only real part from the output and Converting to DCT-IV */ 00393 00394 /* pbuff initialized to input buffer. */ 00395 pbuff = pInlineBuffer; 00396 00397 /* pS1 initialized to pState */ 00398 pS1 = pState; 00399 00400 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 00401 in = *pS1++ * (float32_t) 0.5; 00402 /* input buffer acts as inplace, so output values are stored in the input itself. */ 00403 *pbuff++ = in; 00404 00405 /* pState pointer is incremented twice as the real values are located alternatively in the array */ 00406 pS1++; 00407 00408 /* Initializing the loop counter */ 00409 i = ((uint32_t) S->N - 1u); 00410 00411 do 00412 { 00413 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 00414 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 00415 in = *pS1++ - in; 00416 *pbuff++ = in; 00417 /* points to the next real value */ 00418 pS1++; 00419 00420 00421 /* Decrement the loop counter */ 00422 i--; 00423 } while(i > 0u); 00424 00425 00426 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 00427 00428 /* Initializing the loop counter */ 00429 i = (uint32_t) S->N; 00430 00431 /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 00432 pbuff = pInlineBuffer; 00433 00434 do 00435 { 00436 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 00437 in = *pbuff; 00438 *pbuff++ = in * S->normalize; 00439 00440 /* Decrement the loop counter */ 00441 i--; 00442 } while(i > 0u); 00443 00444 #endif /* #ifndef ARM_MATH_CM0 */ 00445 00446 } 00447