1 /* ----------------------------------------------------------------------
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_f32.c
9 *
10 * Description: Processing function of DCT4 & IDCT4 F32.
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;
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35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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39 * -------------------------------------------------------------------- */
40
41 #include "arm_math.h"
42
43 /**
44 * @ingroup groupTransforms
45 */
46
47 /**
48 * @defgroup DCT4_IDCT4 DCT Type IV Functions
49 * Representation of signals by minimum number of values is important for storage and transmission.
50 * The possibility of large discontinuity between the beginning and end of a period of a signal
51 * in DFT can be avoided by extending the signal so that it is even-symmetric.
52 * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
53 * spectrum and is very widely used in signal and image coding applications.
54 * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
55 * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
56 *
57 * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
58 * Reordering of the input data makes the computation of DCT just a problem of
59 * computing the DFT of a real signal with a few additional operations.
60 * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
61 *
62 * 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.
63 * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
64 * DCT2 implementation can be described in the following steps:
65 * - Re-ordering input
66 * - Calculating Real FFT
67 * - Multiplication of weights and Real FFT output and getting real part from the product.
68 *
69 * This process is explained by the block diagram below:
70 * \image html DCT4.gif "Discrete Cosine Transform - type-IV"
71 *
72 * \par Algorithm:
73 * The N-point type-IV DCT is defined as a real, linear transformation by the formula:
74 * \image html DCT4Equation.gif
75 * where <code>k = 0,1,2,.....N-1</code>
76 *\par
77 * Its inverse is defined as follows:
78 * \image html IDCT4Equation.gif
79 * where <code>n = 0,1,2,.....N-1</code>
80 *\par
81 * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
82 * The symmetry of the transform matrix indicates that the fast algorithms for the forward
83 * and inverse transform computation are identical.
84 * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
85 *
86 * \par Lengths supported by the transform:
87 * As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().
88 * The library provides separate functions for Q15, Q31, and floating-point data types.
89 * \par Instance Structure
90 * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
91 * A separate instance structure must be defined for each transform.
92 * There are separate instance structure declarations for each of the 3 supported data types.
93 *
94 * \par Initialization Functions
95 * There is also an associated initialization function for each data type.
96 * The initialization function performs the following operations:
97 * - Sets the values of the internal structure fields.
98 * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
99 * \par
100 * Use of the initialization function is optional.
101 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
102 * To place an instance structure into a const data section, the instance structure must be manually initialized.
103 * Manually initialize the instance structure as follows:
104 * <pre>
105 *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
106 *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
107 *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
108 * </pre>
109 * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
110 * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
111 * \c pTwiddle points to the twiddle factor table;
112 * \c pCosFactor points to the cosFactor table;
113 * \c pRfft points to the real FFT instance;
114 * \c pCfft points to the complex FFT instance;
115 * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
116 * and arm_rfft_f32() respectively for details regarding static initialization.
117 *
118 * \par Fixed-Point Behavior
119 * Care must be taken when using the fixed-point versions of the DCT4 transform functions.
120 * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
121 * Refer to the function specific documentation below for usage guidelines.
122 */
123
124 /**
125 * @addtogroup DCT4_IDCT4
126 * @{
127 */
128
129 /**
130 * @brief Processing function for the floating-point DCT4/IDCT4.
131 * @param[in] *S points to an instance of the floating-point DCT4/IDCT4 structure.
132 * @param[in] *pState points to state buffer.
133 * @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
134 * @return none.
135 */
136
arm_dct4_f32(const arm_dct4_instance_f32 * S,float32_t * pState,float32_t * pInlineBuffer)137 void arm_dct4_f32(
138 const arm_dct4_instance_f32 * S,
139 float32_t * pState,
140 float32_t * pInlineBuffer)
141 {
142 uint32_t i; /* Loop counter */
143 float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */
144 float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
145 float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
146 float32_t in; /* Temporary variable */
147
148
149 /* DCT4 computation involves DCT2 (which is calculated using RFFT)
150 * along with some pre-processing and post-processing.
151 * Computational procedure is explained as follows:
152 * (a) Pre-processing involves multiplying input with cos factor,
153 * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
154 * where,
155 * r(n) -- output of preprocessing
156 * u(n) -- input to preprocessing(actual Source buffer)
157 * (b) Calculation of DCT2 using FFT is divided into three steps:
158 * Step1: Re-ordering of even and odd elements of input.
159 * Step2: Calculating FFT of the re-ordered input.
160 * Step3: Taking the real part of the product of FFT output and weights.
161 * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
162 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
163 * where,
164 * Y4 -- DCT4 output, Y2 -- DCT2 output
165 * (d) Multiplying the output with the normalizing factor sqrt(2/N).
166 */
167
168 /*-------- Pre-processing ------------*/
169 /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
170 arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
171 arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
172
173 /* ----------------------------------------------------------------
174 * Step1: Re-ordering of even and odd elements as,
175 * pState[i] = pInlineBuffer[2*i] and
176 * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
177 ---------------------------------------------------------------------*/
178
179 /* pS1 initialized to pState */
180 pS1 = pState;
181
182 /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
183 pS2 = pState + (S->N - 1u);
184
185 /* pbuff initialized to input buffer */
186 pbuff = pInlineBuffer;
187
188 #ifndef ARM_MATH_CM0_FAMILY
189
190 /* Run the below code for Cortex-M4 and Cortex-M3 */
191
192 /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
193 i = (uint32_t) S->Nby2 >> 2u;
194
195 /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
196 ** a second loop below computes the remaining 1 to 3 samples. */
197 do
198 {
199 /* Re-ordering of even and odd elements */
200 /* pState[i] = pInlineBuffer[2*i] */
201 *pS1++ = *pbuff++;
202 /* pState[N-i-1] = pInlineBuffer[2*i+1] */
203 *pS2-- = *pbuff++;
204
205 *pS1++ = *pbuff++;
206 *pS2-- = *pbuff++;
207
208 *pS1++ = *pbuff++;
209 *pS2-- = *pbuff++;
210
211 *pS1++ = *pbuff++;
212 *pS2-- = *pbuff++;
213
214 /* Decrement the loop counter */
215 i--;
216 } while(i > 0u);
217
218 /* pbuff initialized to input buffer */
219 pbuff = pInlineBuffer;
220
221 /* pS1 initialized to pState */
222 pS1 = pState;
223
224 /* Initializing the loop counter to N/4 instead of N for loop unrolling */
225 i = (uint32_t) S->N >> 2u;
226
227 /* Processing with loop unrolling 4 times as N is always multiple of 4.
228 * Compute 4 outputs at a time */
229 do
230 {
231 /* Writing the re-ordered output back to inplace input buffer */
232 *pbuff++ = *pS1++;
233 *pbuff++ = *pS1++;
234 *pbuff++ = *pS1++;
235 *pbuff++ = *pS1++;
236
237 /* Decrement the loop counter */
238 i--;
239 } while(i > 0u);
240
241
242 /* ---------------------------------------------------------
243 * Step2: Calculate RFFT for N-point input
244 * ---------------------------------------------------------- */
245 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
246 arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
247
248 /*----------------------------------------------------------------------
249 * Step3: Multiply the FFT output with the weights.
250 *----------------------------------------------------------------------*/
251 arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
252
253 /* ----------- Post-processing ---------- */
254 /* DCT-IV can be obtained from DCT-II by the equation,
255 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
256 * Hence, Y4(0) = Y2(0)/2 */
257 /* Getting only real part from the output and Converting to DCT-IV */
258
259 /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
260 i = ((uint32_t) S->N - 1u) >> 2u;
261
262 /* pbuff initialized to input buffer. */
263 pbuff = pInlineBuffer;
264
265 /* pS1 initialized to pState */
266 pS1 = pState;
267
268 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
269 in = *pS1++ * (float32_t) 0.5;
270 /* input buffer acts as inplace, so output values are stored in the input itself. */
271 *pbuff++ = in;
272
273 /* pState pointer is incremented twice as the real values are located alternatively in the array */
274 pS1++;
275
276 /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
277 ** a second loop below computes the remaining 1 to 3 samples. */
278 do
279 {
280 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
281 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
282 in = *pS1++ - in;
283 *pbuff++ = in;
284 /* points to the next real value */
285 pS1++;
286
287 in = *pS1++ - in;
288 *pbuff++ = in;
289 pS1++;
290
291 in = *pS1++ - in;
292 *pbuff++ = in;
293 pS1++;
294
295 in = *pS1++ - in;
296 *pbuff++ = in;
297 pS1++;
298
299 /* Decrement the loop counter */
300 i--;
301 } while(i > 0u);
302
303 /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
304 ** No loop unrolling is used. */
305 i = ((uint32_t) S->N - 1u) % 0x4u;
306
307 while(i > 0u)
308 {
309 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
310 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
311 in = *pS1++ - in;
312 *pbuff++ = in;
313 /* points to the next real value */
314 pS1++;
315
316 /* Decrement the loop counter */
317 i--;
318 }
319
320
321 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
322
323 /* Initializing the loop counter to N/4 instead of N for loop unrolling */
324 i = (uint32_t) S->N >> 2u;
325
326 /* pbuff initialized to the pInlineBuffer(now contains the output values) */
327 pbuff = pInlineBuffer;
328
329 /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
330 do
331 {
332 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
333 in = *pbuff;
334 *pbuff++ = in * S->normalize;
335
336 in = *pbuff;
337 *pbuff++ = in * S->normalize;
338
339 in = *pbuff;
340 *pbuff++ = in * S->normalize;
341
342 in = *pbuff;
343 *pbuff++ = in * S->normalize;
344
345 /* Decrement the loop counter */
346 i--;
347 } while(i > 0u);
348
349
350 #else
351
352 /* Run the below code for Cortex-M0 */
353
354 /* Initializing the loop counter to N/2 */
355 i = (uint32_t) S->Nby2;
356
357 do
358 {
359 /* Re-ordering of even and odd elements */
360 /* pState[i] = pInlineBuffer[2*i] */
361 *pS1++ = *pbuff++;
362 /* pState[N-i-1] = pInlineBuffer[2*i+1] */
363 *pS2-- = *pbuff++;
364
365 /* Decrement the loop counter */
366 i--;
367 } while(i > 0u);
368
369 /* pbuff initialized to input buffer */
370 pbuff = pInlineBuffer;
371
372 /* pS1 initialized to pState */
373 pS1 = pState;
374
375 /* Initializing the loop counter */
376 i = (uint32_t) S->N;
377
378 do
379 {
380 /* Writing the re-ordered output back to inplace input buffer */
381 *pbuff++ = *pS1++;
382
383 /* Decrement the loop counter */
384 i--;
385 } while(i > 0u);
386
387
388 /* ---------------------------------------------------------
389 * Step2: Calculate RFFT for N-point input
390 * ---------------------------------------------------------- */
391 /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
392 arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
393
394 /*----------------------------------------------------------------------
395 * Step3: Multiply the FFT output with the weights.
396 *----------------------------------------------------------------------*/
397 arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
398
399 /* ----------- Post-processing ---------- */
400 /* DCT-IV can be obtained from DCT-II by the equation,
401 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
402 * Hence, Y4(0) = Y2(0)/2 */
403 /* Getting only real part from the output and Converting to DCT-IV */
404
405 /* pbuff initialized to input buffer. */
406 pbuff = pInlineBuffer;
407
408 /* pS1 initialized to pState */
409 pS1 = pState;
410
411 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
412 in = *pS1++ * (float32_t) 0.5;
413 /* input buffer acts as inplace, so output values are stored in the input itself. */
414 *pbuff++ = in;
415
416 /* pState pointer is incremented twice as the real values are located alternatively in the array */
417 pS1++;
418
419 /* Initializing the loop counter */
420 i = ((uint32_t) S->N - 1u);
421
422 do
423 {
424 /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
425 /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
426 in = *pS1++ - in;
427 *pbuff++ = in;
428 /* points to the next real value */
429 pS1++;
430
431
432 /* Decrement the loop counter */
433 i--;
434 } while(i > 0u);
435
436
437 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
438
439 /* Initializing the loop counter */
440 i = (uint32_t) S->N;
441
442 /* pbuff initialized to the pInlineBuffer(now contains the output values) */
443 pbuff = pInlineBuffer;
444
445 do
446 {
447 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
448 in = *pbuff;
449 *pbuff++ = in * S->normalize;
450
451 /* Decrement the loop counter */
452 i--;
453 } while(i > 0u);
454
455 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
456
457 }
458
459 /**
460 * @} end of DCT4_IDCT4 group
461 */
462