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_q15.c
9 *
10 * Description: Processing function of DCT4 & IDCT4 Q15.
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 Q15 DCT4/IDCT4.
50 * @param[in] *S points to an instance of the Q15 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 *
55 * \par Input an output formats:
56 * Internally inputs are downscaled in the RFFT process function to avoid overflows.
57 * Number of bits downscaled, depends on the size of the transform.
58 * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:
59 *
60 * \image html dct4FormatsQ15Table.gif
61 */
62
arm_dct4_q15(const arm_dct4_instance_q15 * S,q15_t * pState,q15_t * pInlineBuffer)63 void arm_dct4_q15(
64 const arm_dct4_instance_q15 * S,
65 q15_t * pState,
66 q15_t * pInlineBuffer)
67 {
68 uint32_t i; /* Loop counter */
69 q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */
70 q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
71 q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
72 q15_t in; /* Temporary variable */
73
74
75 /* DCT4 computation involves DCT2 (which is calculated using RFFT)
76 * along with some pre-processing and post-processing.
77 * Computational procedure is explained as follows:
78 * (a) Pre-processing involves multiplying input with cos factor,
79 * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
80 * where,
81 * r(n) -- output of preprocessing
82 * u(n) -- input to preprocessing(actual Source buffer)
83 * (b) Calculation of DCT2 using FFT is divided into three steps:
84 * Step1: Re-ordering of even and odd elements of input.
85 * Step2: Calculating FFT of the re-ordered input.
86 * Step3: Taking the real part of the product of FFT output and weights.
87 * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
88 * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
89 * where,
90 * Y4 -- DCT4 output, Y2 -- DCT2 output
91 * (d) Multiplying the output with the normalizing factor sqrt(2/N).
92 */
93
94 /*-------- Pre-processing ------------*/
95 /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
96 arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N);
97 arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N);
98
99 /* ----------------------------------------------------------------
100 * Step1: Re-ordering of even and odd elements as
101 * pState[i] = pInlineBuffer[2*i] and
102 * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
103 ---------------------------------------------------------------------*/
104
105 /* pS1 initialized to pState */
106 pS1 = pState;
107
108 /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
109 pS2 = pState + (S->N - 1u);
110
111 /* pbuff initialized to input buffer */
112 pbuff = pInlineBuffer;
113
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 = (uint32_t) 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 = (uint32_t) 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_q15(S->pRfft, pInlineBuffer, pState);
174
175 /*----------------------------------------------------------------------
176 * Step3: Multiply the FFT output with the weights.
177 *----------------------------------------------------------------------*/
178 arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
179
180 /* The output of complex multiplication is in 3.13 format.
181 * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
182 arm_shift_q15(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 = ((uint32_t) 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 = ((uint32_t) 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 = (uint32_t) 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++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
266
267 in = *pbuff;
268 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
269
270 in = *pbuff;
271 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
272
273 in = *pbuff;
274 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
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 = (uint32_t) 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 = (uint32_t) 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_q15(S->pRfft, pInlineBuffer, pState);
324
325 /*----------------------------------------------------------------------
326 * Step3: Multiply the FFT output with the weights.
327 *----------------------------------------------------------------------*/
328 arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
329
330 /* The output of complex multiplication is in 3.13 format.
331 * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
332 arm_shift_q15(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 /* Initializing the loop counter */
341 i = ((uint32_t) S->N - 1u);
342
343 /* pbuff initialized to input buffer. */
344 pbuff = pInlineBuffer;
345
346 /* pS1 initialized to pState */
347 pS1 = pState;
348
349 /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
350 in = *pS1++ >> 1u;
351 /* input buffer acts as inplace, so output values are stored in the input itself. */
352 *pbuff++ = in;
353
354 /* pState pointer is incremented twice as the real values are located alternatively in the array */
355 pS1++;
356
357 do
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 } while(i > 0u);
369
370 /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
371
372 /* Initializing the loop counter */
373 i = (uint32_t) S->N;
374
375 /* pbuff initialized to the pInlineBuffer(now contains the output values) */
376 pbuff = pInlineBuffer;
377
378 do
379 {
380 /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
381 in = *pbuff;
382 *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
383
384 /* Decrement the loop counter */
385 i--;
386 } while(i > 0u);
387
388 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
389
390 }
391
392 /**
393 * @} end of DCT4_IDCT4 group
394 */
395