1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
|
/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_dct4_q15.c
* Description: Processing function of DCT4 & IDCT4 Q15
*
* $Date: 27. January 2017
* $Revision: V.1.5.1
*
* Target Processor: Cortex-M cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "arm_math.h"
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/**
* @brief Processing function for the Q15 DCT4/IDCT4.
* @param[in] *S points to an instance of the Q15 DCT4 structure.
* @param[in] *pState points to state buffer.
* @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
* @return none.
*
* \par Input an output formats:
* Internally inputs are downscaled in the RFFT process function to avoid overflows.
* Number of bits downscaled, depends on the size of the transform.
* The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:
*
* \image html dct4FormatsQ15Table.gif
*/
void arm_dct4_q15(
const arm_dct4_instance_q15 * S,
q15_t * pState,
q15_t * pInlineBuffer)
{
uint32_t i; /* Loop counter */
q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */
q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
q15_t in; /* Temporary variable */
/* DCT4 computation involves DCT2 (which is calculated using RFFT)
* along with some pre-processing and post-processing.
* Computational procedure is explained as follows:
* (a) Pre-processing involves multiplying input with cos factor,
* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
* where,
* r(n) -- output of preprocessing
* u(n) -- input to preprocessing(actual Source buffer)
* (b) Calculation of DCT2 using FFT is divided into three steps:
* Step1: Re-ordering of even and odd elements of input.
* Step2: Calculating FFT of the re-ordered input.
* Step3: Taking the real part of the product of FFT output and weights.
* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* where,
* Y4 -- DCT4 output, Y2 -- DCT2 output
* (d) Multiplying the output with the normalizing factor sqrt(2/N).
*/
/*-------- Pre-processing ------------*/
/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N);
arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N);
/* ----------------------------------------------------------------
* Step1: Re-ordering of even and odd elements as
* pState[i] = pInlineBuffer[2*i] and
* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
---------------------------------------------------------------------*/
/* pS1 initialized to pState */
pS1 = pState;
/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
pS2 = pState + (S->N - 1U);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
#if defined (ARM_MATH_DSP)
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
i = (uint32_t) S->Nby2 >> 2U;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2U;
/* Processing with loop unrolling 4 times as N is always multiple of 4.
* Compute 4 outputs at a time */
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.13 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
arm_shift_q15(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
i = ((uint32_t) S->N - 1U) >> 2U;
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1U;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
i = ((uint32_t) S->N - 1U) % 0x4U;
while (i > 0U)
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2U;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
/* Decrement the loop counter */
i--;
} while (i > 0U);
#else
/* Run the below code for Cortex-M0 */
/* Initializing the loop counter to N/2 */
i = (uint32_t) S->Nby2;
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter */
i = (uint32_t) S->N;
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.13 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
arm_shift_q15(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter */
i = ((uint32_t) S->N - 1U);
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1U;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
} while (i > 0U);
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter */
i = (uint32_t) S->N;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
/* Decrement the loop counter */
i--;
} while (i > 0U);
#endif /* #if defined (ARM_MATH_DSP) */
}
/**
* @} end of DCT4_IDCT4 group
*/
|
