lib/main/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix2_q15.c

   1 /* ----------------------------------------------------------------------
   2  * Project:      CMSIS DSP Library
   3  * Title:        arm_cfft_radix2_q15.c
   4  * Description:  Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function
   5  *
   6  * $Date:        27. January 2017
   7  * $Revision:    V.1.5.1
   8  *
   9  * Target Processor: Cortex-M cores
  10  * -------------------------------------------------------------------- */
  11 /*
  12  * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
  13  *
  14  * SPDX-License-Identifier: Apache-2.0
  15  *
  16  * Licensed under the Apache License, Version 2.0 (the License); you may
  17  * not use this file except in compliance with the License.
  18  * You may obtain a copy of the License at
  19  *
  20  * www.apache.org/licenses/LICENSE-2.0
  21  *
  22  * Unless required by applicable law or agreed to in writing, software
  23  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
  24  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  25  * See the License for the specific language governing permissions and
  26  * limitations under the License.
  27  */
  28
  29 #include "arm_math.h"
  30
  31 void arm_radix2_butterfly_q15(
  32   q15_t * pSrc,
  33   uint32_t fftLen,
  34   q15_t * pCoef,
  35   uint16_t twidCoefModifier);
  36
  37 void arm_radix2_butterfly_inverse_q15(
  38   q15_t * pSrc,
  39   uint32_t fftLen,
  40   q15_t * pCoef,
  41   uint16_t twidCoefModifier);
  42
  43 void arm_bitreversal_q15(
  44   q15_t * pSrc,
  45   uint32_t fftLen,
  46   uint16_t bitRevFactor,
  47   uint16_t * pBitRevTab);
  48
  49 /**
  50  * @ingroup groupTransforms
  51  */
  52
  53 /**
  54  * @addtogroup ComplexFFT
  55  * @{
  56  */
  57
  58 /**
  59  * @details
  60  * @brief Processing function for the fixed-point CFFT/CIFFT.
  61  * @deprecated Do not use this function.  It has been superseded by \ref arm_cfft_q15 and will be removed
  62  * @param[in]      *S    points to an instance of the fixed-point CFFT/CIFFT structure.
  63  * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
  64  * @return none.
  65  */
  66
  67 void arm_cfft_radix2_q15(
  68   const arm_cfft_radix2_instance_q15 * S,
  69   q15_t * pSrc)
  70 {
  71
  72   if (S->ifftFlag == 1U)
  73   {
  74     arm_radix2_butterfly_inverse_q15(pSrc, S->fftLen,
  75                                      S->pTwiddle, S->twidCoefModifier);
  76   }
  77   else
  78   {
  79     arm_radix2_butterfly_q15(pSrc, S->fftLen,
  80                              S->pTwiddle, S->twidCoefModifier);
  81   }
  82
  83   arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
  84 }
  85
  86 /**
  87  * @} end of ComplexFFT group
  88  */
  89
  90 void arm_radix2_butterfly_q15(
  91   q15_t * pSrc,
  92   uint32_t fftLen,
  93   q15_t * pCoef,
  94   uint16_t twidCoefModifier)
  95 {
  96 #if defined (ARM_MATH_DSP)
  97
  98   unsigned i, j, k, l;
  99   unsigned n1, n2, ia;
 100   q15_t in;
 101   q31_t T, S, R;
 102   q31_t coeff, out1, out2;
 103
 104   //N = fftLen;
 105   n2 = fftLen;
 106
 107   n1 = n2;
 108   n2 = n2 >> 1;
 109   ia = 0;
 110
 111   // loop for groups
 112   for (i = 0; i < n2; i++)
 113   {
 114     coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 115
 116     ia = ia + twidCoefModifier;
 117
 118     l = i + n2;
 119
 120     T = _SIMD32_OFFSET(pSrc + (2 * i));
 121     in = ((int16_t) (T & 0xFFFF)) >> 1;
 122     T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 123
 124     S = _SIMD32_OFFSET(pSrc + (2 * l));
 125     in = ((int16_t) (S & 0xFFFF)) >> 1;
 126     S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 127
 128     R = __QSUB16(T, S);
 129
 130     _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 131
 132 #ifndef ARM_MATH_BIG_ENDIAN
 133
 134     out1 = __SMUAD(coeff, R) >> 16;
 135     out2 = __SMUSDX(coeff, R);
 136
 137 #else
 138
 139     out1 = __SMUSDX(R, coeff) >> 16U;
 140     out2 = __SMUAD(coeff, R);
 141
 142 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 143
 144     _SIMD32_OFFSET(pSrc + (2U * l)) =
 145       (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 146
 147     coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 148
 149     ia = ia + twidCoefModifier;
 150
 151     // loop for butterfly
 152     i++;
 153     l++;
 154
 155     T = _SIMD32_OFFSET(pSrc + (2 * i));
 156     in = ((int16_t) (T & 0xFFFF)) >> 1;
 157     T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 158
 159     S = _SIMD32_OFFSET(pSrc + (2 * l));
 160     in = ((int16_t) (S & 0xFFFF)) >> 1;
 161     S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 162
 163     R = __QSUB16(T, S);
 164
 165     _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 166
 167 #ifndef ARM_MATH_BIG_ENDIAN
 168
 169     out1 = __SMUAD(coeff, R) >> 16;
 170     out2 = __SMUSDX(coeff, R);
 171
 172 #else
 173
 174     out1 = __SMUSDX(R, coeff) >> 16U;
 175     out2 = __SMUAD(coeff, R);
 176
 177 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 178
 179     _SIMD32_OFFSET(pSrc + (2U * l)) =
 180       (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 181
 182   }                             // groups loop end
 183
 184   twidCoefModifier = twidCoefModifier << 1U;
 185
 186   // loop for stage
 187   for (k = fftLen / 2; k > 2; k = k >> 1)
 188   {
 189     n1 = n2;
 190     n2 = n2 >> 1;
 191     ia = 0;
 192
 193     // loop for groups
 194     for (j = 0; j < n2; j++)
 195     {
 196       coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 197
 198       ia = ia + twidCoefModifier;
 199
 200       // loop for butterfly
 201       for (i = j; i < fftLen; i += n1)
 202       {
 203         l = i + n2;
 204
 205         T = _SIMD32_OFFSET(pSrc + (2 * i));
 206
 207         S = _SIMD32_OFFSET(pSrc + (2 * l));
 208
 209         R = __QSUB16(T, S);
 210
 211         _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 212
 213 #ifndef ARM_MATH_BIG_ENDIAN
 214
 215         out1 = __SMUAD(coeff, R) >> 16;
 216         out2 = __SMUSDX(coeff, R);
 217
 218 #else
 219
 220         out1 = __SMUSDX(R, coeff) >> 16U;
 221         out2 = __SMUAD(coeff, R);
 222
 223 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 224
 225         _SIMD32_OFFSET(pSrc + (2U * l)) =
 226           (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 227
 228         i += n1;
 229
 230         l = i + n2;
 231
 232         T = _SIMD32_OFFSET(pSrc + (2 * i));
 233
 234         S = _SIMD32_OFFSET(pSrc + (2 * l));
 235
 236         R = __QSUB16(T, S);
 237
 238         _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 239
 240 #ifndef ARM_MATH_BIG_ENDIAN
 241
 242         out1 = __SMUAD(coeff, R) >> 16;
 243         out2 = __SMUSDX(coeff, R);
 244
 245 #else
 246
 247         out1 = __SMUSDX(R, coeff) >> 16U;
 248         out2 = __SMUAD(coeff, R);
 249
 250 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 251
 252         _SIMD32_OFFSET(pSrc + (2U * l)) =
 253           (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 254
 255       }                         // butterfly loop end
 256
 257     }                           // groups loop end
 258
 259     twidCoefModifier = twidCoefModifier << 1U;
 260   }                             // stages loop end
 261
 262   n1 = n2;
 263   n2 = n2 >> 1;
 264   ia = 0;
 265
 266   coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 267
 268   ia = ia + twidCoefModifier;
 269
 270   // loop for butterfly
 271   for (i = 0; i < fftLen; i += n1)
 272   {
 273     l = i + n2;
 274
 275     T = _SIMD32_OFFSET(pSrc + (2 * i));
 276
 277     S = _SIMD32_OFFSET(pSrc + (2 * l));
 278
 279     R = __QSUB16(T, S);
 280
 281     _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
 282
 283     _SIMD32_OFFSET(pSrc + (2U * l)) = R;
 284
 285     i += n1;
 286     l = i + n2;
 287
 288     T = _SIMD32_OFFSET(pSrc + (2 * i));
 289
 290     S = _SIMD32_OFFSET(pSrc + (2 * l));
 291
 292     R = __QSUB16(T, S);
 293
 294     _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
 295
 296     _SIMD32_OFFSET(pSrc + (2U * l)) = R;
 297
 298   }                             // groups loop end
 299
 300
 301 #else
 302
 303   unsigned i, j, k, l;
 304   unsigned n1, n2, ia;
 305   q15_t xt, yt, cosVal, sinVal;
 306
 307
 308   //N = fftLen;
 309   n2 = fftLen;
 310
 311   n1 = n2;
 312   n2 = n2 >> 1;
 313   ia = 0;
 314
 315   // loop for groups
 316   for (j = 0; j < n2; j++)
 317   {
 318     cosVal = pCoef[ia * 2];
 319     sinVal = pCoef[(ia * 2) + 1];
 320     ia = ia + twidCoefModifier;
 321
 322     // loop for butterfly
 323     for (i = j; i < fftLen; i += n1)
 324     {
 325       l = i + n2;
 326       xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U);
 327       pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U;
 328
 329       yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U);
 330       pSrc[2 * i + 1] =
 331         ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U;
 332
 333       pSrc[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) +
 334                       ((int16_t) (((q31_t) yt * sinVal) >> 16)));
 335
 336       pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) -
 337                            ((int16_t) (((q31_t) xt * sinVal) >> 16)));
 338
 339     }                           // butterfly loop end
 340
 341   }                             // groups loop end
 342
 343   twidCoefModifier = twidCoefModifier << 1U;
 344
 345   // loop for stage
 346   for (k = fftLen / 2; k > 2; k = k >> 1)
 347   {
 348     n1 = n2;
 349     n2 = n2 >> 1;
 350     ia = 0;
 351
 352     // loop for groups
 353     for (j = 0; j < n2; j++)
 354     {
 355       cosVal = pCoef[ia * 2];
 356       sinVal = pCoef[(ia * 2) + 1];
 357       ia = ia + twidCoefModifier;
 358
 359       // loop for butterfly
 360       for (i = j; i < fftLen; i += n1)
 361       {
 362         l = i + n2;
 363         xt = pSrc[2 * i] - pSrc[2 * l];
 364         pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U;
 365
 366         yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
 367         pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U;
 368
 369         pSrc[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) +
 370                         ((int16_t) (((q31_t) yt * sinVal) >> 16)));
 371
 372         pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) -
 373                              ((int16_t) (((q31_t) xt * sinVal) >> 16)));
 374
 375       }                         // butterfly loop end
 376
 377     }                           // groups loop end
 378
 379     twidCoefModifier = twidCoefModifier << 1U;
 380   }                             // stages loop end
 381
 382   n1 = n2;
 383   n2 = n2 >> 1;
 384   ia = 0;
 385
 386   // loop for groups
 387   for (j = 0; j < n2; j++)
 388   {
 389     cosVal = pCoef[ia * 2];
 390     sinVal = pCoef[(ia * 2) + 1];
 391
 392     ia = ia + twidCoefModifier;
 393
 394     // loop for butterfly
 395     for (i = j; i < fftLen; i += n1)
 396     {
 397       l = i + n2;
 398       xt = pSrc[2 * i] - pSrc[2 * l];
 399       pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
 400
 401       yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
 402       pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
 403
 404       pSrc[2U * l] = xt;
 405
 406       pSrc[2U * l + 1U] = yt;
 407
 408     }                           // butterfly loop end
 409
 410   }                             // groups loop end
 411
 412   twidCoefModifier = twidCoefModifier << 1U;
 413
 414 #endif //             #if defined (ARM_MATH_DSP)
 415
 416 }
 417
 418
 419 void arm_radix2_butterfly_inverse_q15(
 420   q15_t * pSrc,
 421   uint32_t fftLen,
 422   q15_t * pCoef,
 423   uint16_t twidCoefModifier)
 424 {
 425 #if defined (ARM_MATH_DSP)
 426
 427   unsigned i, j, k, l;
 428   unsigned n1, n2, ia;
 429   q15_t in;
 430   q31_t T, S, R;
 431   q31_t coeff, out1, out2;
 432
 433   //N = fftLen;
 434   n2 = fftLen;
 435
 436   n1 = n2;
 437   n2 = n2 >> 1;
 438   ia = 0;
 439
 440   // loop for groups
 441   for (i = 0; i < n2; i++)
 442   {
 443     coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 444
 445     ia = ia + twidCoefModifier;
 446
 447     l = i + n2;
 448
 449     T = _SIMD32_OFFSET(pSrc + (2 * i));
 450     in = ((int16_t) (T & 0xFFFF)) >> 1;
 451     T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 452
 453     S = _SIMD32_OFFSET(pSrc + (2 * l));
 454     in = ((int16_t) (S & 0xFFFF)) >> 1;
 455     S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 456
 457     R = __QSUB16(T, S);
 458
 459     _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 460
 461 #ifndef ARM_MATH_BIG_ENDIAN
 462
 463     out1 = __SMUSD(coeff, R) >> 16;
 464     out2 = __SMUADX(coeff, R);
 465 #else
 466
 467     out1 = __SMUADX(R, coeff) >> 16U;
 468     out2 = __SMUSD(__QSUB(0, coeff), R);
 469
 470 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 471
 472     _SIMD32_OFFSET(pSrc + (2U * l)) =
 473       (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 474
 475     coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 476
 477     ia = ia + twidCoefModifier;
 478
 479     // loop for butterfly
 480     i++;
 481     l++;
 482
 483     T = _SIMD32_OFFSET(pSrc + (2 * i));
 484     in = ((int16_t) (T & 0xFFFF)) >> 1;
 485     T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 486
 487     S = _SIMD32_OFFSET(pSrc + (2 * l));
 488     in = ((int16_t) (S & 0xFFFF)) >> 1;
 489     S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF);
 490
 491     R = __QSUB16(T, S);
 492
 493     _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 494
 495 #ifndef ARM_MATH_BIG_ENDIAN
 496
 497     out1 = __SMUSD(coeff, R) >> 16;
 498     out2 = __SMUADX(coeff, R);
 499 #else
 500
 501     out1 = __SMUADX(R, coeff) >> 16U;
 502     out2 = __SMUSD(__QSUB(0, coeff), R);
 503
 504 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 505
 506     _SIMD32_OFFSET(pSrc + (2U * l)) =
 507       (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 508
 509   }                             // groups loop end
 510
 511   twidCoefModifier = twidCoefModifier << 1U;
 512
 513   // loop for stage
 514   for (k = fftLen / 2; k > 2; k = k >> 1)
 515   {
 516     n1 = n2;
 517     n2 = n2 >> 1;
 518     ia = 0;
 519
 520     // loop for groups
 521     for (j = 0; j < n2; j++)
 522     {
 523       coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 524
 525       ia = ia + twidCoefModifier;
 526
 527       // loop for butterfly
 528       for (i = j; i < fftLen; i += n1)
 529       {
 530         l = i + n2;
 531
 532         T = _SIMD32_OFFSET(pSrc + (2 * i));
 533
 534         S = _SIMD32_OFFSET(pSrc + (2 * l));
 535
 536         R = __QSUB16(T, S);
 537
 538         _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 539
 540 #ifndef ARM_MATH_BIG_ENDIAN
 541
 542         out1 = __SMUSD(coeff, R) >> 16;
 543         out2 = __SMUADX(coeff, R);
 544
 545 #else
 546
 547         out1 = __SMUADX(R, coeff) >> 16U;
 548         out2 = __SMUSD(__QSUB(0, coeff), R);
 549
 550 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 551
 552         _SIMD32_OFFSET(pSrc + (2U * l)) =
 553           (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 554
 555         i += n1;
 556
 557         l = i + n2;
 558
 559         T = _SIMD32_OFFSET(pSrc + (2 * i));
 560
 561         S = _SIMD32_OFFSET(pSrc + (2 * l));
 562
 563         R = __QSUB16(T, S);
 564
 565         _SIMD32_OFFSET(pSrc + (2 * i)) = __SHADD16(T, S);
 566
 567 #ifndef ARM_MATH_BIG_ENDIAN
 568
 569         out1 = __SMUSD(coeff, R) >> 16;
 570         out2 = __SMUADX(coeff, R);
 571 #else
 572
 573         out1 = __SMUADX(R, coeff) >> 16U;
 574         out2 = __SMUSD(__QSUB(0, coeff), R);
 575
 576 #endif //     #ifndef ARM_MATH_BIG_ENDIAN
 577
 578         _SIMD32_OFFSET(pSrc + (2U * l)) =
 579           (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
 580
 581       }                         // butterfly loop end
 582
 583     }                           // groups loop end
 584
 585     twidCoefModifier = twidCoefModifier << 1U;
 586   }                             // stages loop end
 587
 588   n1 = n2;
 589   n2 = n2 >> 1;
 590   ia = 0;
 591
 592   // loop for groups
 593   for (j = 0; j < n2; j++)
 594   {
 595     coeff = _SIMD32_OFFSET(pCoef + (ia * 2U));
 596
 597     ia = ia + twidCoefModifier;
 598
 599     // loop for butterfly
 600     for (i = j; i < fftLen; i += n1)
 601     {
 602       l = i + n2;
 603
 604       T = _SIMD32_OFFSET(pSrc + (2 * i));
 605
 606       S = _SIMD32_OFFSET(pSrc + (2 * l));
 607
 608       R = __QSUB16(T, S);
 609
 610       _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S);
 611
 612       _SIMD32_OFFSET(pSrc + (2U * l)) = R;
 613
 614     }                           // butterfly loop end
 615
 616   }                             // groups loop end
 617
 618   twidCoefModifier = twidCoefModifier << 1U;
 619
 620 #else
 621
 622
 623   unsigned i, j, k, l;
 624   unsigned n1, n2, ia;
 625   q15_t xt, yt, cosVal, sinVal;
 626
 627   //N = fftLen;
 628   n2 = fftLen;
 629
 630   n1 = n2;
 631   n2 = n2 >> 1;
 632   ia = 0;
 633
 634   // loop for groups
 635   for (j = 0; j < n2; j++)
 636   {
 637     cosVal = pCoef[ia * 2];
 638     sinVal = pCoef[(ia * 2) + 1];
 639     ia = ia + twidCoefModifier;
 640
 641     // loop for butterfly
 642     for (i = j; i < fftLen; i += n1)
 643     {
 644       l = i + n2;
 645       xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U);
 646       pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U;
 647
 648       yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U);
 649       pSrc[2 * i + 1] =
 650         ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U;
 651
 652       pSrc[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) -
 653                       ((int16_t) (((q31_t) yt * sinVal) >> 16)));
 654
 655       pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) +
 656                            ((int16_t) (((q31_t) xt * sinVal) >> 16)));
 657
 658     }                           // butterfly loop end
 659
 660   }                             // groups loop end
 661
 662   twidCoefModifier = twidCoefModifier << 1U;
 663
 664   // loop for stage
 665   for (k = fftLen / 2; k > 2; k = k >> 1)
 666   {
 667     n1 = n2;
 668     n2 = n2 >> 1;
 669     ia = 0;
 670
 671     // loop for groups
 672     for (j = 0; j < n2; j++)
 673     {
 674       cosVal = pCoef[ia * 2];
 675       sinVal = pCoef[(ia * 2) + 1];
 676       ia = ia + twidCoefModifier;
 677
 678       // loop for butterfly
 679       for (i = j; i < fftLen; i += n1)
 680       {
 681         l = i + n2;
 682         xt = pSrc[2 * i] - pSrc[2 * l];
 683         pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U;
 684
 685         yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
 686         pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U;
 687
 688         pSrc[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) -
 689                         ((int16_t) (((q31_t) yt * sinVal) >> 16)));
 690
 691         pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) +
 692                              ((int16_t) (((q31_t) xt * sinVal) >> 16)));
 693
 694       }                         // butterfly loop end
 695
 696     }                           // groups loop end
 697
 698     twidCoefModifier = twidCoefModifier << 1U;
 699   }                             // stages loop end
 700
 701   n1 = n2;
 702   n2 = n2 >> 1;
 703   ia = 0;
 704
 705   cosVal = pCoef[ia * 2];
 706   sinVal = pCoef[(ia * 2) + 1];
 707
 708   ia = ia + twidCoefModifier;
 709
 710   // loop for butterfly
 711   for (i = 0; i < fftLen; i += n1)
 712   {
 713     l = i + n2;
 714     xt = pSrc[2 * i] - pSrc[2 * l];
 715     pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]);
 716
 717     yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
 718     pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]);
 719
 720     pSrc[2U * l] = xt;
 721
 722     pSrc[2U * l + 1U] = yt;
 723
 724   }                             // groups loop end
 725
 726
 727 #endif //             #if defined (ARM_MATH_DSP)
 728
 729 }