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| bfc108 | 1 | /* ---------------------------------------------------------------------- |
| Q | 2 | * Copyright (C) 2010-2014 ARM Limited. All rights reserved. |
| 3 | * | |
| 4 | * $Date: 19. March 2015 | |
| 5 | * $Revision: V.1.4.5 | |
| 6 | * | |
| 7 | * Project: CMSIS DSP Library | |
| 8 | * Title: arm_dct4_q31.c | |
| 9 | * | |
| 10 | * Description: Processing function of DCT4 & IDCT4 Q31. | |
| 11 | * | |
| 12 | * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | |
| 13 | * | |
| 14 | * Redistribution and use in source and binary forms, with or without | |
| 15 | * modification, are permitted provided that the following conditions | |
| 16 | * are met: | |
| 17 | * - Redistributions of source code must retain the above copyright | |
| 18 | * notice, this list of conditions and the following disclaimer. | |
| 19 | * - Redistributions in binary form must reproduce the above copyright | |
| 20 | * notice, this list of conditions and the following disclaimer in | |
| 21 | * the documentation and/or other materials provided with the | |
| 22 | * distribution. | |
| 23 | * - Neither the name of ARM LIMITED nor the names of its contributors | |
| 24 | * may be used to endorse or promote products derived from this | |
| 25 | * software without specific prior written permission. | |
| 26 | * | |
| 27 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
| 28 | * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| 29 | * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS | |
| 30 | * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE | |
| 31 | * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, | |
| 32 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, | |
| 33 | * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
| 34 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER | |
| 35 | * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
| 36 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN | |
| 37 | * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | |
| 38 | * POSSIBILITY OF SUCH DAMAGE. | |
| 39 | * -------------------------------------------------------------------- */ | |
| 40 | ||
| 41 | #include "arm_math.h" | |
| 42 | ||
| 43 | /** | |
| 44 | * @addtogroup DCT4_IDCT4 | |
| 45 | * @{ | |
| 46 | */ | |
| 47 | ||
| 48 | /** | |
| 49 | * @brief Processing function for the Q31 DCT4/IDCT4. | |
| 50 | * @param[in] *S points to an instance of the Q31 DCT4 structure. | |
| 51 | * @param[in] *pState points to state buffer. | |
| 52 | * @param[in,out] *pInlineBuffer points to the in-place input and output buffer. | |
| 53 | * @return none. | |
| 54 | * \par Input an output formats: | |
| 55 | * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process, | |
| 56 | * as the conversion from DCT2 to DCT4 involves one subtraction. | |
| 57 | * Internally inputs are downscaled in the RFFT process function to avoid overflows. | |
| 58 | * Number of bits downscaled, depends on the size of the transform. | |
| 59 | * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below: | |
| 60 | * | |
| 61 | * \image html dct4FormatsQ31Table.gif | |
| 62 | */ | |
| 63 | ||
| 64 | void arm_dct4_q31( | |
| 65 | const arm_dct4_instance_q31 * S, | |
| 66 | q31_t * pState, | |
| 67 | q31_t * pInlineBuffer) | |
| 68 | { | |
| 69 | uint16_t i; /* Loop counter */ | |
| 70 | q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */ | |
| 71 | q31_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ | |
| 72 | q31_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ | |
| 73 | q31_t in; /* Temporary variable */ | |
| 74 | ||
| 75 | ||
| 76 | /* DCT4 computation involves DCT2 (which is calculated using RFFT) | |
| 77 | * along with some pre-processing and post-processing. | |
| 78 | * Computational procedure is explained as follows: | |
| 79 | * (a) Pre-processing involves multiplying input with cos factor, | |
| 80 | * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) | |
| 81 | * where, | |
| 82 | * r(n) -- output of preprocessing | |
| 83 | * u(n) -- input to preprocessing(actual Source buffer) | |
| 84 | * (b) Calculation of DCT2 using FFT is divided into three steps: | |
| 85 | * Step1: Re-ordering of even and odd elements of input. | |
| 86 | * Step2: Calculating FFT of the re-ordered input. | |
| 87 | * Step3: Taking the real part of the product of FFT output and weights. | |
| 88 | * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: | |
| 89 | * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) | |
| 90 | * where, | |
| 91 | * Y4 -- DCT4 output, Y2 -- DCT2 output | |
| 92 | * (d) Multiplying the output with the normalizing factor sqrt(2/N). | |
| 93 | */ | |
| 94 | ||
| 95 | /*-------- Pre-processing ------------*/ | |
| 96 | /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ | |
| 97 | arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N); | |
| 98 | arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N); | |
| 99 | ||
| 100 | /* ---------------------------------------------------------------- | |
| 101 | * Step1: Re-ordering of even and odd elements as | |
| 102 | * pState[i] = pInlineBuffer[2*i] and | |
| 103 | * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 | |
| 104 | ---------------------------------------------------------------------*/ | |
| 105 | ||
| 106 | /* pS1 initialized to pState */ | |
| 107 | pS1 = pState; | |
| 108 | ||
| 109 | /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ | |
| 110 | pS2 = pState + (S->N - 1u); | |
| 111 | ||
| 112 | /* pbuff initialized to input buffer */ | |
| 113 | pbuff = pInlineBuffer; | |
| 114 | ||
| 115 | #ifndef ARM_MATH_CM0_FAMILY | |
| 116 | ||
| 117 | /* Run the below code for Cortex-M4 and Cortex-M3 */ | |
| 118 | ||
| 119 | /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ | |
| 120 | i = S->Nby2 >> 2u; | |
| 121 | ||
| 122 | /* First part of the processing with loop unrolling. Compute 4 outputs at a time. | |
| 123 | ** a second loop below computes the remaining 1 to 3 samples. */ | |
| 124 | do | |
| 125 | { | |
| 126 | /* Re-ordering of even and odd elements */ | |
| 127 | /* pState[i] = pInlineBuffer[2*i] */ | |
| 128 | *pS1++ = *pbuff++; | |
| 129 | /* pState[N-i-1] = pInlineBuffer[2*i+1] */ | |
| 130 | *pS2-- = *pbuff++; | |
| 131 | ||
| 132 | *pS1++ = *pbuff++; | |
| 133 | *pS2-- = *pbuff++; | |
| 134 | ||
| 135 | *pS1++ = *pbuff++; | |
| 136 | *pS2-- = *pbuff++; | |
| 137 | ||
| 138 | *pS1++ = *pbuff++; | |
| 139 | *pS2-- = *pbuff++; | |
| 140 | ||
| 141 | /* Decrement the loop counter */ | |
| 142 | i--; | |
| 143 | } while(i > 0u); | |
| 144 | ||
| 145 | /* pbuff initialized to input buffer */ | |
| 146 | pbuff = pInlineBuffer; | |
| 147 | ||
| 148 | /* pS1 initialized to pState */ | |
| 149 | pS1 = pState; | |
| 150 | ||
| 151 | /* Initializing the loop counter to N/4 instead of N for loop unrolling */ | |
| 152 | i = S->N >> 2u; | |
| 153 | ||
| 154 | /* Processing with loop unrolling 4 times as N is always multiple of 4. | |
| 155 | * Compute 4 outputs at a time */ | |
| 156 | do | |
| 157 | { | |
| 158 | /* Writing the re-ordered output back to inplace input buffer */ | |
| 159 | *pbuff++ = *pS1++; | |
| 160 | *pbuff++ = *pS1++; | |
| 161 | *pbuff++ = *pS1++; | |
| 162 | *pbuff++ = *pS1++; | |
| 163 | ||
| 164 | /* Decrement the loop counter */ | |
| 165 | i--; | |
| 166 | } while(i > 0u); | |
| 167 | ||
| 168 | ||
| 169 | /* --------------------------------------------------------- | |
| 170 | * Step2: Calculate RFFT for N-point input | |
| 171 | * ---------------------------------------------------------- */ | |
| 172 | /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ | |
| 173 | arm_rfft_q31(S->pRfft, pInlineBuffer, pState); | |
| 174 | ||
| 175 | /*---------------------------------------------------------------------- | |
| 176 | * Step3: Multiply the FFT output with the weights. | |
| 177 | *----------------------------------------------------------------------*/ | |
| 178 | arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); | |
| 179 | ||
| 180 | /* The output of complex multiplication is in 3.29 format. | |
| 181 | * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ | |
| 182 | arm_shift_q31(pState, 2, pState, S->N * 2); | |
| 183 | ||
| 184 | /* ----------- Post-processing ---------- */ | |
| 185 | /* DCT-IV can be obtained from DCT-II by the equation, | |
| 186 | * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) | |
| 187 | * Hence, Y4(0) = Y2(0)/2 */ | |
| 188 | /* Getting only real part from the output and Converting to DCT-IV */ | |
| 189 | ||
| 190 | /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ | |
| 191 | i = (S->N - 1u) >> 2u; | |
| 192 | ||
| 193 | /* pbuff initialized to input buffer. */ | |
| 194 | pbuff = pInlineBuffer; | |
| 195 | ||
| 196 | /* pS1 initialized to pState */ | |
| 197 | pS1 = pState; | |
| 198 | ||
| 199 | /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ | |
| 200 | in = *pS1++ >> 1u; | |
| 201 | /* input buffer acts as inplace, so output values are stored in the input itself. */ | |
| 202 | *pbuff++ = in; | |
| 203 | ||
| 204 | /* pState pointer is incremented twice as the real values are located alternatively in the array */ | |
| 205 | pS1++; | |
| 206 | ||
| 207 | /* First part of the processing with loop unrolling. Compute 4 outputs at a time. | |
| 208 | ** a second loop below computes the remaining 1 to 3 samples. */ | |
| 209 | do | |
| 210 | { | |
| 211 | /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ | |
| 212 | /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ | |
| 213 | in = *pS1++ - in; | |
| 214 | *pbuff++ = in; | |
| 215 | /* points to the next real value */ | |
| 216 | pS1++; | |
| 217 | ||
| 218 | in = *pS1++ - in; | |
| 219 | *pbuff++ = in; | |
| 220 | pS1++; | |
| 221 | ||
| 222 | in = *pS1++ - in; | |
| 223 | *pbuff++ = in; | |
| 224 | pS1++; | |
| 225 | ||
| 226 | in = *pS1++ - in; | |
| 227 | *pbuff++ = in; | |
| 228 | pS1++; | |
| 229 | ||
| 230 | /* Decrement the loop counter */ | |
| 231 | i--; | |
| 232 | } while(i > 0u); | |
| 233 | ||
| 234 | /* If the blockSize is not a multiple of 4, compute any remaining output samples here. | |
| 235 | ** No loop unrolling is used. */ | |
| 236 | i = (S->N - 1u) % 0x4u; | |
| 237 | ||
| 238 | while(i > 0u) | |
| 239 | { | |
| 240 | /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ | |
| 241 | /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ | |
| 242 | in = *pS1++ - in; | |
| 243 | *pbuff++ = in; | |
| 244 | /* points to the next real value */ | |
| 245 | pS1++; | |
| 246 | ||
| 247 | /* Decrement the loop counter */ | |
| 248 | i--; | |
| 249 | } | |
| 250 | ||
| 251 | ||
| 252 | /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ | |
| 253 | ||
| 254 | /* Initializing the loop counter to N/4 instead of N for loop unrolling */ | |
| 255 | i = S->N >> 2u; | |
| 256 | ||
| 257 | /* pbuff initialized to the pInlineBuffer(now contains the output values) */ | |
| 258 | pbuff = pInlineBuffer; | |
| 259 | ||
| 260 | /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ | |
| 261 | do | |
| 262 | { | |
| 263 | /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ | |
| 264 | in = *pbuff; | |
| 265 | *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | |
| 266 | ||
| 267 | in = *pbuff; | |
| 268 | *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | |
| 269 | ||
| 270 | in = *pbuff; | |
| 271 | *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | |
| 272 | ||
| 273 | in = *pbuff; | |
| 274 | *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | |
| 275 | ||
| 276 | /* Decrement the loop counter */ | |
| 277 | i--; | |
| 278 | } while(i > 0u); | |
| 279 | ||
| 280 | ||
| 281 | #else | |
| 282 | ||
| 283 | /* Run the below code for Cortex-M0 */ | |
| 284 | ||
| 285 | /* Initializing the loop counter to N/2 */ | |
| 286 | i = S->Nby2; | |
| 287 | ||
| 288 | do | |
| 289 | { | |
| 290 | /* Re-ordering of even and odd elements */ | |
| 291 | /* pState[i] = pInlineBuffer[2*i] */ | |
| 292 | *pS1++ = *pbuff++; | |
| 293 | /* pState[N-i-1] = pInlineBuffer[2*i+1] */ | |
| 294 | *pS2-- = *pbuff++; | |
| 295 | ||
| 296 | /* Decrement the loop counter */ | |
| 297 | i--; | |
| 298 | } while(i > 0u); | |
| 299 | ||
| 300 | /* pbuff initialized to input buffer */ | |
| 301 | pbuff = pInlineBuffer; | |
| 302 | ||
| 303 | /* pS1 initialized to pState */ | |
| 304 | pS1 = pState; | |
| 305 | ||
| 306 | /* Initializing the loop counter */ | |
| 307 | i = S->N; | |
| 308 | ||
| 309 | do | |
| 310 | { | |
| 311 | /* Writing the re-ordered output back to inplace input buffer */ | |
| 312 | *pbuff++ = *pS1++; | |
| 313 | ||
| 314 | /* Decrement the loop counter */ | |
| 315 | i--; | |
| 316 | } while(i > 0u); | |
| 317 | ||
| 318 | ||
| 319 | /* --------------------------------------------------------- | |
| 320 | * Step2: Calculate RFFT for N-point input | |
| 321 | * ---------------------------------------------------------- */ | |
| 322 | /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ | |
| 323 | arm_rfft_q31(S->pRfft, pInlineBuffer, pState); | |
| 324 | ||
| 325 | /*---------------------------------------------------------------------- | |
| 326 | * Step3: Multiply the FFT output with the weights. | |
| 327 | *----------------------------------------------------------------------*/ | |
| 328 | arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); | |
| 329 | ||
| 330 | /* The output of complex multiplication is in 3.29 format. | |
| 331 | * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ | |
| 332 | arm_shift_q31(pState, 2, pState, S->N * 2); | |
| 333 | ||
| 334 | /* ----------- Post-processing ---------- */ | |
| 335 | /* DCT-IV can be obtained from DCT-II by the equation, | |
| 336 | * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) | |
| 337 | * Hence, Y4(0) = Y2(0)/2 */ | |
| 338 | /* Getting only real part from the output and Converting to DCT-IV */ | |
| 339 | ||
| 340 | /* pbuff initialized to input buffer. */ | |
| 341 | pbuff = pInlineBuffer; | |
| 342 | ||
| 343 | /* pS1 initialized to pState */ | |
| 344 | pS1 = pState; | |
| 345 | ||
| 346 | /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ | |
| 347 | in = *pS1++ >> 1u; | |
| 348 | /* input buffer acts as inplace, so output values are stored in the input itself. */ | |
| 349 | *pbuff++ = in; | |
| 350 | ||
| 351 | /* pState pointer is incremented twice as the real values are located alternatively in the array */ | |
| 352 | pS1++; | |
| 353 | ||
| 354 | /* Initializing the loop counter */ | |
| 355 | i = (S->N - 1u); | |
| 356 | ||
| 357 | while(i > 0u) | |
| 358 | { | |
| 359 | /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ | |
| 360 | /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ | |
| 361 | in = *pS1++ - in; | |
| 362 | *pbuff++ = in; | |
| 363 | /* points to the next real value */ | |
| 364 | pS1++; | |
| 365 | ||
| 366 | /* Decrement the loop counter */ | |
| 367 | i--; | |
| 368 | } | |
| 369 | ||
| 370 | ||
| 371 | /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ | |
| 372 | ||
| 373 | /* Initializing the loop counter */ | |
| 374 | i = S->N; | |
| 375 | ||
| 376 | /* pbuff initialized to the pInlineBuffer(now contains the output values) */ | |
| 377 | pbuff = pInlineBuffer; | |
| 378 | ||
| 379 | do | |
| 380 | { | |
| 381 | /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ | |
| 382 | in = *pbuff; | |
| 383 | *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | |
| 384 | ||
| 385 | /* Decrement the loop counter */ | |
| 386 | i--; | |
| 387 | } while(i > 0u); | |
| 388 | ||
| 389 | #endif /* #ifndef ARM_MATH_CM0_FAMILY */ | |
| 390 | ||
| 391 | } | |
| 392 | ||
| 393 | /** | |
| 394 | * @} end of DCT4_IDCT4 group | |
| 395 | */ | |
