diff options
Diffstat (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c')
| -rw-r--r-- | Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c | 1809 |
1 files changed, 1809 insertions, 0 deletions
diff --git a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c new file mode 100644 index 0000000..825a16b --- /dev/null +++ b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c @@ -0,0 +1,1809 @@ +/* ----------------------------------------------------------------------
+ * Project: CMSIS DSP Library
+ * Title: arm_cfft_radix4_q15.c
+ * Description: This file has function definition of Radix-4 FFT & IFFT function and
+ * In-place bit reversal using bit reversal table
+ *
+ * $Date: 18. March 2019
+ * $Revision: V1.6.0
+ *
+ * Target Processor: Cortex-M cores
+ * -------------------------------------------------------------------- */
+/*
+ * Copyright (C) 2010-2019 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"
+
+
+void arm_radix4_butterfly_q15(
+ q15_t * pSrc16,
+ uint32_t fftLen,
+ const q15_t * pCoef16,
+ uint32_t twidCoefModifier);
+
+void arm_radix4_butterfly_inverse_q15(
+ q15_t * pSrc16,
+ uint32_t fftLen,
+ const q15_t * pCoef16,
+ uint32_t twidCoefModifier);
+
+void arm_bitreversal_q15(
+ q15_t * pSrc,
+ uint32_t fftLen,
+ uint16_t bitRevFactor,
+ const uint16_t * pBitRevTab);
+
+/**
+ @ingroup groupTransforms
+ */
+
+/**
+ @addtogroup ComplexFFT
+ @{
+ */
+
+
+/**
+ @brief Processing function for the Q15 CFFT/CIFFT.
+ @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed in the future.
+ @param[in] S points to an instance of the Q15 CFFT/CIFFT structure.
+ @param[in,out] pSrc points to the complex data buffer. Processing occurs in-place.
+ @return none
+
+ @par Input and output formats:
+ Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
+ Hence the output format is different for different FFT sizes.
+ The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
+ @par
+ \image html CFFTQ15.gif "Input and Output Formats for Q15 CFFT"
+ \image html CIFFTQ15.gif "Input and Output Formats for Q15 CIFFT"
+ */
+
+void arm_cfft_radix4_q15(
+ const arm_cfft_radix4_instance_q15 * S,
+ q15_t * pSrc)
+{
+ if (S->ifftFlag == 1U)
+ {
+ /* Complex IFFT radix-4 */
+ arm_radix4_butterfly_inverse_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
+ }
+ else
+ {
+ /* Complex FFT radix-4 */
+ arm_radix4_butterfly_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
+ }
+
+ if (S->bitReverseFlag == 1U)
+ {
+ /* Bit Reversal */
+ arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+ }
+
+}
+
+/**
+ @} end of ComplexFFT group
+ */
+
+/*
+ * Radix-4 FFT algorithm used is :
+ *
+ * Input real and imaginary data:
+ * x(n) = xa + j * ya
+ * x(n+N/4 ) = xb + j * yb
+ * x(n+N/2 ) = xc + j * yc
+ * x(n+3N 4) = xd + j * yd
+ *
+ *
+ * Output real and imaginary data:
+ * x(4r) = xa'+ j * ya'
+ * x(4r+1) = xb'+ j * yb'
+ * x(4r+2) = xc'+ j * yc'
+ * x(4r+3) = xd'+ j * yd'
+ *
+ *
+ * Twiddle factors for radix-4 FFT:
+ * Wn = co1 + j * (- si1)
+ * W2n = co2 + j * (- si2)
+ * W3n = co3 + j * (- si3)
+
+ * The real and imaginary output values for the radix-4 butterfly are
+ * xa' = xa + xb + xc + xd
+ * ya' = ya + yb + yc + yd
+ * xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
+ * yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
+ * xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
+ * yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
+ * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
+ * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
+ *
+ */
+
+/**
+ @brief Core function for the Q15 CFFT butterfly process.
+ @param[in,out] pSrc16 points to the in-place buffer of Q15 data type
+ @param[in] fftLen length of the FFT
+ @param[in] pCoef16 points to twiddle coefficient buffer
+ @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table
+ @return none
+ */
+
+void arm_radix4_butterfly_q15(
+ q15_t * pSrc16,
+ uint32_t fftLen,
+ const q15_t * pCoef16,
+ uint32_t twidCoefModifier)
+{
+
+#if defined (ARM_MATH_DSP)
+
+ q31_t R, S, T, U;
+ q31_t C1, C2, C3, out1, out2;
+ uint32_t n1, n2, ic, i0, j, k;
+
+ q15_t *ptr1;
+ q15_t *pSi0;
+ q15_t *pSi1;
+ q15_t *pSi2;
+ q15_t *pSi3;
+
+ q31_t xaya, xbyb, xcyc, xdyd;
+
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+
+ /* Index for twiddle coefficient */
+ ic = 0U;
+
+ /* Index for input read and output write */
+ j = n2;
+
+ pSi0 = pSrc16;
+ pSi1 = pSi0 + 2 * n2;
+ pSi2 = pSi1 + 2 * n2;
+ pSi3 = pSi2 + 2 * n2;
+
+ /* Input is in 1.15(q15) format */
+
+ /* start of first stage process */
+ do
+ {
+ /* Butterfly implementation */
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T = read_q15x2 (pSi0);
+ T = __SHADD16(T, 0); /* this is just a SIMD arithmetic shift right by 1 */
+ T = __SHADD16(T, 0); /* it turns out doing this twice is 2 cycles, the alternative takes 3 cycles */
+/*
+ in = ((int16_t) (T & 0xFFFF)) >> 2; // alternative code that takes 3 cycles
+ T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
+*/
+
+ /* Read yc (real), xc(imag) input */
+ S = read_q15x2 (pSi2);
+ S = __SHADD16(S, 0);
+ S = __SHADD16(S, 0);
+
+ /* R = packed((ya + yc), (xa + xc) ) */
+ R = __QADD16(T, S);
+
+ /* S = packed((ya - yc), (xa - xc) ) */
+ S = __QSUB16(T, S);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+ T = __SHADD16(T, 0);
+ T = __SHADD16(T, 0);
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+ U = __SHADD16(U, 0);
+ U = __SHADD16(U, 0);
+
+ /* T = packed((yb + yd), (xb + xd) ) */
+ T = __QADD16(T, U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ write_q15x2_ia (&pSi0, __SHADD16(R, T));
+
+ /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
+ R = __QSUB16(R, T);
+
+ /* co2 & si2 are read from SIMD Coefficient pointer */
+ C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ out1 = __SMUAD(C2, R) >> 16U;
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = __SMUSDX(C2, R);
+#else
+ /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out1 = __SMUSDX(R, C2) >> 16U;
+ /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ out2 = __SMUAD(C2, R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* Reading i0+fftLen/4 */
+ /* T = packed(yb, xb) */
+ T = read_q15x2 (pSi1);
+ T = __SHADD16(T, 0);
+ T = __SHADD16(T, 0);
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* writing output(xc', yc') in little endian format */
+ write_q15x2_ia (&pSi1, (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+
+ /* Butterfly calculations */
+ /* U = packed(yd, xd) */
+ U = read_q15x2 (pSi3);
+ U = __SHADD16(U, 0);
+ U = __SHADD16(U, 0);
+
+ /* T = packed(yb-yd, xb-xd) */
+ T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __QASX(S, T);
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __QSAX(S, T);
+#else
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __QSAX(S, T);
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __QASX(S, T);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* co1 & si1 are read from SIMD Coefficient pointer */
+ C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
+ /* Butterfly process for the i0+fftLen/2 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ out1 = __SMUAD(C1, S) >> 16U;
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ out2 = __SMUSDX(C1, S);
+#else
+ /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ out1 = __SMUSDX(S, C1) >> 16U;
+ /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ out2 = __SMUAD(C1, S);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* writing output(xb', yb') in little endian format */
+ write_q15x2_ia (&pSi2, ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF));
+
+ /* co3 & si3 are read from SIMD Coefficient pointer */
+ C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
+ /* Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ out1 = __SMUAD(C3, R) >> 16U;
+ /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ out2 = __SMUSDX(C3, R);
+#else
+ /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ out1 = __SMUSDX(R, C3) >> 16U;
+ /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ out2 = __SMUAD(C3, R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* writing output(xd', yd') in little endian format */
+ write_q15x2_ia (&pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ } while (--j);
+ /* data is in 4.11(q11) format */
+
+ /* end of first stage process */
+
+
+ /* start of middle stage process */
+
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+
+ /* Calculation of Middle stage */
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the middle stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ic = 0U;
+
+ for (j = 0U; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
+ C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
+ C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ pSi0 = pSrc16 + 2 * j;
+ pSi1 = pSi0 + 2 * n2;
+ pSi2 = pSi1 + 2 * n2;
+ pSi3 = pSi2 + 2 * n2;
+
+ /* Butterfly implementation */
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T = read_q15x2 (pSi0);
+
+ /* Read yc (real), xc(imag) input */
+ S = read_q15x2 (pSi2);
+
+ /* R = packed( (ya + yc), (xa + xc)) */
+ R = __QADD16(T, S);
+
+ /* S = packed((ya - yc), (xa - xc)) */
+ S = __QSUB16(T, S);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+
+ /* T = packed( (yb + yd), (xb + xd)) */
+ T = __QADD16(T, U);
+
+ /* writing the butterfly processed i0 sample */
+
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ out1 = __SHADD16(R, T);
+ out1 = __SHADD16(out1, 0);
+ write_q15x2 (pSi0, out1);
+ pSi0 += 2 * n1;
+
+ /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
+ R = __SHSUB16(R, T);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+ out1 = __SMUAD(C2, R) >> 16U;
+
+ /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = __SMUSDX(C2, R);
+#else
+ /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out1 = __SMUSDX(R, C2) >> 16U;
+
+ /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+ out2 = __SMUAD(C2, R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* Reading i0+3fftLen/4 */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ write_q15x2 (pSi1, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi1 += 2 * n1;
+
+ /* Butterfly calculations */
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+
+ /* T = packed(yb-yd, xb-xd) */
+ T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __SHASX(S, T);
+
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __SHSAX(S, T);
+
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = __SMUAD(C1, S) >> 16U;
+ out2 = __SMUSDX(C1, S);
+#else
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __SHSAX(S, T);
+
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __SHASX(S, T);
+
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = __SMUSDX(S, C1) >> 16U;
+ out2 = __SMUAD(C1, S);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ write_q15x2 (pSi2, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi2 += 2 * n1;
+
+ /* Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ out1 = __SMUAD(C3, R) >> 16U;
+ out2 = __SMUSDX(C3, R);
+#else
+ out1 = __SMUSDX(R, C3) >> 16U;
+ out2 = __SMUAD(C3, R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ write_q15x2 (pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi3 += 2 * n1;
+ }
+ }
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+ }
+ /* end of middle stage process */
+
+
+ /* data is in 10.6(q6) format for the 1024 point */
+ /* data is in 8.8(q8) format for the 256 point */
+ /* data is in 6.10(q10) format for the 64 point */
+ /* data is in 4.12(q12) format for the 16 point */
+
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+
+ ptr1 = &pSrc16[0];
+
+ /* start of last stage process */
+
+ /* Butterfly implementation */
+ do
+ {
+ /* Read xa (real), ya(imag) input */
+ xaya = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xd (real), yd(imag) input */
+ xdyd = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* R = packed((ya + yc), (xa + xc)) */
+ R = __QADD16(xaya, xcyc);
+
+ /* T = packed((yb + yd), (xb + xd)) */
+ T = __QADD16(xbyb, xdyd);
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8U;
+
+
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ write_q15x2_ia (&ptr1, __SHADD16(R, T));
+
+ /* T = packed((yb + yd), (xb + xd)) */
+ T = __QADD16(xbyb, xdyd);
+
+ /* xc' = (xa-xb+xc-xd) */
+ /* yc' = (ya-yb+yc-yd) */
+ write_q15x2_ia (&ptr1, __SHSUB16(R, T));
+
+ /* S = packed((ya - yc), (xa - xc)) */
+ S = __QSUB16(xaya, xcyc);
+
+ /* Read yd (real), xd(imag) input */
+ /* T = packed( (yb - yd), (xb - xd)) */
+ U = __QSUB16(xbyb, xdyd);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xb' = (xa+yb-xc-yd) */
+ /* yb' = (ya-xb-yc+xd) */
+ write_q15x2_ia (&ptr1, __SHSAX(S, U));
+
+ /* xd' = (xa-yb-xc+yd) */
+ /* yd' = (ya+xb-yc-xd) */
+ write_q15x2_ia (&ptr1, __SHASX(S, U));
+#else
+ /* xb' = (xa+yb-xc-yd) */
+ /* yb' = (ya-xb-yc+xd) */
+ write_q15x2_ia (&ptr1, __SHASX(S, U));
+
+ /* xd' = (xa-yb-xc+yd) */
+ /* yd' = (ya+xb-yc-xd) */
+ write_q15x2_ia (&ptr1, __SHSAX(S, U));
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ } while (--j);
+
+ /* end of last stage process */
+
+ /* output is in 11.5(q5) format for the 1024 point */
+ /* output is in 9.7(q7) format for the 256 point */
+ /* output is in 7.9(q9) format for the 64 point */
+ /* output is in 5.11(q11) format for the 16 point */
+
+
+#else /* #if defined (ARM_MATH_DSP) */
+
+ q15_t R0, R1, S0, S1, T0, T1, U0, U1;
+ q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
+ uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+
+ /* Index for twiddle coefficient */
+ ic = 0U;
+
+ /* Index for input read and output write */
+ i0 = 0U;
+ j = n2;
+
+ /* Input is in 1.15(q15) format */
+
+ /* start of first stage process */
+ do
+ {
+ /* Butterfly implementation */
+
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+
+ /* input is down scale by 4 to avoid overflow */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U] >> 2U;
+ T1 = pSrc16[(i0 * 2U) + 1U] >> 2U;
+
+ /* input is down scale by 4 to avoid overflow */
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U] >> 2U;
+ S1 = pSrc16[(i2 * 2U) + 1U] >> 2U;
+
+ /* R0 = (ya + yc) */
+ R0 = __SSAT(T0 + S0, 16U);
+ /* R1 = (xa + xc) */
+ R1 = __SSAT(T1 + S1, 16U);
+
+ /* S0 = (ya - yc) */
+ S0 = __SSAT(T0 - S0, 16);
+ /* S1 = (xa - xc) */
+ S1 = __SSAT(T1 - S1, 16);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* input is down scale by 4 to avoid overflow */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U] >> 2U;
+ T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
+
+ /* input is down scale by 4 to avoid overflow */
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U] >> 2U;
+ U1 = pSrc16[(i3 * 2U) + 1] >> 2U;
+
+ /* T0 = (yb + yd) */
+ T0 = __SSAT(T0 + U0, 16U);
+ /* T1 = (xb + xd) */
+ T1 = __SSAT(T1 + U1, 16U);
+
+ /* writing the butterfly processed i0 sample */
+ /* ya' = ya + yb + yc + yd */
+ /* xa' = xa + xb + xc + xd */
+ pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
+ pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
+
+ /* R0 = (ya + yc) - (yb + yd) */
+ /* R1 = (xa + xc) - (xb + xd) */
+ R0 = __SSAT(R0 - T0, 16U);
+ R1 = __SSAT(R1 - T1, 16U);
+
+ /* co2 & si2 are read from Coefficient pointer */
+ Co2 = pCoef16[2U * ic * 2U];
+ Si2 = pCoef16[(2U * ic * 2U) + 1];
+
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U);
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U);
+
+ /* Reading i0+fftLen/4 */
+ /* input is down scale by 4 to avoid overflow */
+ /* T0 = yb, T1 = xb */
+ T0 = pSrc16[i1 * 2U] >> 2;
+ T1 = pSrc16[(i1 * 2U) + 1] >> 2;
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* writing output(xc', yc') in little endian format */
+ pSrc16[i1 * 2U] = out1;
+ pSrc16[(i1 * 2U) + 1] = out2;
+
+ /* Butterfly calculations */
+ /* input is down scale by 4 to avoid overflow */
+ /* U0 = yd, U1 = xd */
+ U0 = pSrc16[i3 * 2U] >> 2;
+ U1 = pSrc16[(i3 * 2U) + 1] >> 2;
+ /* T0 = yb-yd */
+ T0 = __SSAT(T0 - U0, 16);
+ /* T1 = xb-xd */
+ T1 = __SSAT(T1 - U1, 16);
+
+ /* R1 = (ya-yc) + (xb- xd), R0 = (xa-xc) - (yb-yd)) */
+ R0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16);
+ R1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16);
+
+ /* S1 = (ya-yc) - (xb- xd), S0 = (xa-xc) + (yb-yd)) */
+ S0 = (q15_t) __SSAT(((q31_t) S0 + T1), 16U);
+ S1 = (q15_t) __SSAT(((q31_t) S1 - T0), 16U);
+
+ /* co1 & si1 are read from Coefficient pointer */
+ Co1 = pCoef16[ic * 2U];
+ Si1 = pCoef16[(ic * 2U) + 1];
+ /* Butterfly process for the i0+fftLen/2 sample */
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ out1 = (q15_t) ((Si1 * S1 + Co1 * S0) >> 16);
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16);
+
+ /* writing output(xb', yb') in little endian format */
+ pSrc16[i2 * 2U] = out1;
+ pSrc16[(i2 * 2U) + 1] = out2;
+
+ /* Co3 & si3 are read from Coefficient pointer */
+ Co3 = pCoef16[3U * (ic * 2U)];
+ Si3 = pCoef16[(3U * (ic * 2U)) + 1];
+ /* Butterfly process for the i0+3fftLen/4 sample */
+ /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
+ out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U);
+ /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
+ out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U);
+ /* writing output(xd', yd') in little endian format */
+ pSrc16[i3 * 2U] = out1;
+ pSrc16[(i3 * 2U) + 1] = out2;
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1U;
+
+ } while (--j);
+ /* data is in 4.11(q11) format */
+
+ /* end of first stage process */
+
+
+ /* start of middle stage process */
+
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+
+ /* Calculation of Middle stage */
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the middle stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ic = 0U;
+
+ for (j = 0U; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ Co1 = pCoef16[ic * 2U];
+ Si1 = pCoef16[(ic * 2U) + 1U];
+ Co2 = pCoef16[2U * (ic * 2U)];
+ Si2 = pCoef16[(2U * (ic * 2U)) + 1U];
+ Co3 = pCoef16[3U * (ic * 2U)];
+ Si3 = pCoef16[(3U * (ic * 2U)) + 1U];
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ /* Butterfly implementation */
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U];
+ T1 = pSrc16[(i0 * 2U) + 1U];
+
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U];
+ S1 = pSrc16[(i2 * 2U) + 1U];
+
+ /* R0 = (ya + yc), R1 = (xa + xc) */
+ R0 = __SSAT(T0 + S0, 16);
+ R1 = __SSAT(T1 + S1, 16);
+
+ /* S0 = (ya - yc), S1 =(xa - xc) */
+ S0 = __SSAT(T0 - S0, 16);
+ S1 = __SSAT(T1 - S1, 16);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+
+ /* T0 = (yb + yd), T1 = (xb + xd) */
+ T0 = __SSAT(T0 + U0, 16);
+ T1 = __SSAT(T1 + U1, 16);
+
+ /* writing the butterfly processed i0 sample */
+
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ out1 = ((R0 >> 1U) + (T0 >> 1U)) >> 1U;
+ out2 = ((R1 >> 1U) + (T1 >> 1U)) >> 1U;
+
+ pSrc16[i0 * 2U] = out1;
+ pSrc16[(2U * i0) + 1U] = out2;
+
+ /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+ R0 = (R0 >> 1U) - (T0 >> 1U);
+ R1 = (R1 >> 1U) - (T1 >> 1U);
+
+ /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+ out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U);
+
+ /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U);
+
+ /* Reading i0+3fftLen/4 */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ pSrc16[i1 * 2U] = out1;
+ pSrc16[(i1 * 2U) + 1U] = out2;
+
+ /* Butterfly calculations */
+
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+ /* T0 = yb-yd, T1 = xb-xd */
+ T0 = __SSAT(T0 - U0, 16);
+ T1 = __SSAT(T1 - U1, 16);
+
+ /* R0 = (ya-yc) + (xb- xd), R1 = (xa-xc) - (yb-yd)) */
+ R0 = (S0 >> 1U) - (T1 >> 1U);
+ R1 = (S1 >> 1U) + (T0 >> 1U);
+
+ /* S0 = (ya-yc) - (xb- xd), S1 = (xa-xc) + (yb-yd)) */
+ S0 = (S0 >> 1U) + (T1 >> 1U);
+ S1 = (S1 >> 1U) - (T0 >> 1U);
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = (q15_t) ((Co1 * S0 + Si1 * S1) >> 16U);
+
+ out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16U);
+
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ pSrc16[i2 * 2U] = out1;
+ pSrc16[(i2 * 2U) + 1U] = out2;
+
+ /* Butterfly process for the i0+3fftLen/4 sample */
+ out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U);
+
+ out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U);
+ /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
+ /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
+ pSrc16[i3 * 2U] = out1;
+ pSrc16[(i3 * 2U) + 1U] = out2;
+ }
+ }
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+ }
+ /* end of middle stage process */
+
+
+ /* data is in 10.6(q6) format for the 1024 point */
+ /* data is in 8.8(q8) format for the 256 point */
+ /* data is in 6.10(q10) format for the 64 point */
+ /* data is in 4.12(q12) format for the 16 point */
+
+ /* Initializations for the last stage */
+ n1 = n2;
+ n2 >>= 2U;
+
+ /* start of last stage process */
+
+ /* Butterfly implementation */
+ for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U];
+ T1 = pSrc16[(i0 * 2U) + 1U];
+
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U];
+ S1 = pSrc16[(i2 * 2U) + 1U];
+
+ /* R0 = (ya + yc), R1 = (xa + xc) */
+ R0 = __SSAT(T0 + S0, 16U);
+ R1 = __SSAT(T1 + S1, 16U);
+
+ /* S0 = (ya - yc), S1 = (xa - xc) */
+ S0 = __SSAT(T0 - S0, 16U);
+ S1 = __SSAT(T1 - S1, 16U);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+ /* T0 = (yb + yd), T1 = (xb + xd)) */
+ T0 = __SSAT(T0 + U0, 16U);
+ T1 = __SSAT(T1 + U1, 16U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
+ pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
+
+ /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+ R0 = (R0 >> 1U) - (T0 >> 1U);
+ R1 = (R1 >> 1U) - (T1 >> 1U);
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd) */
+ /* yc' = (ya-yb+yc-yd) */
+ pSrc16[i1 * 2U] = R0;
+ pSrc16[(i1 * 2U) + 1U] = R1;
+
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+ /* T0 = (yb - yd), T1 = (xb - xd) */
+ T0 = __SSAT(T0 - U0, 16U);
+ T1 = __SSAT(T1 - U1, 16U);
+
+ /* writing the butterfly processed i0 + fftLen/2 sample */
+ /* xb' = (xa+yb-xc-yd) */
+ /* yb' = (ya-xb-yc+xd) */
+ pSrc16[i2 * 2U] = (S0 >> 1U) + (T1 >> 1U);
+ pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U);
+
+ /* writing the butterfly processed i0 + 3fftLen/4 sample */
+ /* xd' = (xa-yb-xc+yd) */
+ /* yd' = (ya+xb-yc-xd) */
+ pSrc16[i3 * 2U] = (S0 >> 1U) - (T1 >> 1U);
+ pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U);
+
+ }
+
+ /* end of last stage process */
+
+ /* output is in 11.5(q5) format for the 1024 point */
+ /* output is in 9.7(q7) format for the 256 point */
+ /* output is in 7.9(q9) format for the 64 point */
+ /* output is in 5.11(q11) format for the 16 point */
+
+#endif /* #if defined (ARM_MATH_DSP) */
+
+}
+
+
+/**
+ @brief Core function for the Q15 CIFFT butterfly process.
+ @param[in,out] pSrc16 points to the in-place buffer of Q15 data type
+ @param[in] fftLen length of the FFT
+ @param[in] pCoef16 points to twiddle coefficient buffer
+ @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+ @return none
+ */
+
+/*
+ * Radix-4 IFFT algorithm used is :
+ *
+ * CIFFT uses same twiddle coefficients as CFFT function
+ * x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
+ *
+ *
+ * IFFT is implemented with following changes in equations from FFT
+ *
+ * Input real and imaginary data:
+ * x(n) = xa + j * ya
+ * x(n+N/4 ) = xb + j * yb
+ * x(n+N/2 ) = xc + j * yc
+ * x(n+3N 4) = xd + j * yd
+ *
+ *
+ * Output real and imaginary data:
+ * x(4r) = xa'+ j * ya'
+ * x(4r+1) = xb'+ j * yb'
+ * x(4r+2) = xc'+ j * yc'
+ * x(4r+3) = xd'+ j * yd'
+ *
+ *
+ * Twiddle factors for radix-4 IFFT:
+ * Wn = co1 + j * (si1)
+ * W2n = co2 + j * (si2)
+ * W3n = co3 + j * (si3)
+
+ * The real and imaginary output values for the radix-4 butterfly are
+ * xa' = xa + xb + xc + xd
+ * ya' = ya + yb + yc + yd
+ * xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
+ * yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
+ * xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
+ * yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
+ * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
+ * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
+ *
+ */
+
+void arm_radix4_butterfly_inverse_q15(
+ q15_t * pSrc16,
+ uint32_t fftLen,
+ const q15_t * pCoef16,
+ uint32_t twidCoefModifier)
+{
+
+#if defined (ARM_MATH_DSP)
+
+ q31_t R, S, T, U;
+ q31_t C1, C2, C3, out1, out2;
+ uint32_t n1, n2, ic, i0, j, k;
+
+ q15_t *ptr1;
+ q15_t *pSi0;
+ q15_t *pSi1;
+ q15_t *pSi2;
+ q15_t *pSi3;
+
+ q31_t xaya, xbyb, xcyc, xdyd;
+
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+
+ /* Index for twiddle coefficient */
+ ic = 0U;
+
+ /* Index for input read and output write */
+ j = n2;
+
+ pSi0 = pSrc16;
+ pSi1 = pSi0 + 2 * n2;
+ pSi2 = pSi1 + 2 * n2;
+ pSi3 = pSi2 + 2 * n2;
+
+ /* Input is in 1.15(q15) format */
+
+ /* start of first stage process */
+ do
+ {
+ /* Butterfly implementation */
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T = read_q15x2 (pSi0);
+ T = __SHADD16(T, 0);
+ T = __SHADD16(T, 0);
+
+ /* Read yc (real), xc(imag) input */
+ S = read_q15x2 (pSi2);
+ S = __SHADD16(S, 0);
+ S = __SHADD16(S, 0);
+
+ /* R = packed((ya + yc), (xa + xc) ) */
+ R = __QADD16(T, S);
+
+ /* S = packed((ya - yc), (xa - xc) ) */
+ S = __QSUB16(T, S);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+ T = __SHADD16(T, 0);
+ T = __SHADD16(T, 0);
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+ U = __SHADD16(U, 0);
+ U = __SHADD16(U, 0);
+
+ /* T = packed((yb + yd), (xb + xd) ) */
+ T = __QADD16(T, U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ write_q15x2_ia (&pSi0, __SHADD16(R, T));
+
+ /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
+ R = __QSUB16(R, T);
+
+ /* co2 & si2 are read from SIMD Coefficient pointer */
+ C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ out1 = __SMUSD(C2, R) >> 16U;
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = __SMUADX(C2, R);
+#else
+ /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out1 = __SMUADX(C2, R) >> 16U;
+ /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ out2 = __SMUSD(__QSUB16(0, C2), R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* Reading i0+fftLen/4 */
+ /* T = packed(yb, xb) */
+ T = read_q15x2 (pSi1);
+ T = __SHADD16(T, 0);
+ T = __SHADD16(T, 0);
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* writing output(xc', yc') in little endian format */
+ write_q15x2_ia (&pSi1, (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+
+ /* Butterfly calculations */
+ /* U = packed(yd, xd) */
+ U = read_q15x2 (pSi3);
+ U = __SHADD16(U, 0);
+ U = __SHADD16(U, 0);
+
+ /* T = packed(yb-yd, xb-xd) */
+ T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __QSAX(S, T);
+ /* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
+ S = __QASX(S, T);
+#else
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __QASX(S, T);
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __QSAX(S, T);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* co1 & si1 are read from SIMD Coefficient pointer */
+ C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
+ /* Butterfly process for the i0+fftLen/2 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ out1 = __SMUSD(C1, S) >> 16U;
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ out2 = __SMUADX(C1, S);
+#else
+ /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ out1 = __SMUADX(C1, S) >> 16U;
+ /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ out2 = __SMUSD(__QSUB16(0, C1), S);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* writing output(xb', yb') in little endian format */
+ write_q15x2_ia (&pSi2, ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF));
+
+ /* co3 & si3 are read from SIMD Coefficient pointer */
+ C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
+ /* Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ out1 = __SMUSD(C3, R) >> 16U;
+ /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ out2 = __SMUADX(C3, R);
+#else
+ /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ out1 = __SMUADX(C3, R) >> 16U;
+ /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ out2 = __SMUSD(__QSUB16(0, C3), R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* writing output(xd', yd') in little endian format */
+ write_q15x2_ia (&pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ } while (--j);
+ /* data is in 4.11(q11) format */
+
+ /* end of first stage process */
+
+
+ /* start of middle stage process */
+
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+
+ /* Calculation of Middle stage */
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the middle stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ic = 0U;
+
+ for (j = 0U; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
+ C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
+ C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ pSi0 = pSrc16 + 2 * j;
+ pSi1 = pSi0 + 2 * n2;
+ pSi2 = pSi1 + 2 * n2;
+ pSi3 = pSi2 + 2 * n2;
+
+ /* Butterfly implementation */
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T = read_q15x2 (pSi0);
+
+ /* Read yc (real), xc(imag) input */
+ S = read_q15x2 (pSi2);
+
+ /* R = packed( (ya + yc), (xa + xc)) */
+ R = __QADD16(T, S);
+
+ /* S = packed((ya - yc), (xa - xc)) */
+ S = __QSUB16(T, S);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+
+ /* T = packed( (yb + yd), (xb + xd)) */
+ T = __QADD16(T, U);
+
+ /* writing the butterfly processed i0 sample */
+
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ out1 = __SHADD16(R, T);
+ out1 = __SHADD16(out1, 0);
+ write_q15x2 (pSi0, out1);
+ pSi0 += 2 * n1;
+
+ /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
+ R = __SHSUB16(R, T);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+ out1 = __SMUSD(C2, R) >> 16U;
+
+ /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out2 = __SMUADX(C2, R);
+#else
+ /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ out1 = __SMUADX(R, C2) >> 16U;
+
+ /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
+ out2 = __SMUSD(__QSUB16(0, C2), R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* Reading i0+3fftLen/4 */
+ /* Read yb (real), xb(imag) input */
+ T = read_q15x2 (pSi1);
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
+ /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
+ write_q15x2 (pSi1, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi1 += 2 * n1;
+
+ /* Butterfly calculations */
+
+ /* Read yd (real), xd(imag) input */
+ U = read_q15x2 (pSi3);
+
+ /* T = packed(yb-yd, xb-xd) */
+ T = __QSUB16(T, U);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __SHSAX(S, T);
+
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __SHASX(S, T);
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = __SMUSD(C1, S) >> 16U;
+ out2 = __SMUADX(C1, S);
+#else
+ /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
+ R = __SHASX(S, T);
+
+ /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
+ S = __SHSAX(S, T);
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = __SMUADX(S, C1) >> 16U;
+ out2 = __SMUSD(__QSUB16(0, C1), S);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
+ /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
+ write_q15x2 (pSi2, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi2 += 2 * n1;
+
+ /* Butterfly process for the i0+3fftLen/4 sample */
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ out1 = __SMUSD(C3, R) >> 16U;
+ out2 = __SMUADX(C3, R);
+#else
+ out1 = __SMUADX(C3, R) >> 16U;
+ out2 = __SMUSD(__QSUB16(0, C3), R);
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
+ /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
+ write_q15x2 (pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
+ pSi3 += 2 * n1;
+ }
+ }
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+ }
+ /* end of middle stage process */
+
+ /* data is in 10.6(q6) format for the 1024 point */
+ /* data is in 8.8(q8) format for the 256 point */
+ /* data is in 6.10(q10) format for the 64 point */
+ /* data is in 4.12(q12) format for the 16 point */
+
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+
+ ptr1 = &pSrc16[0];
+
+ /* start of last stage process */
+
+ /* Butterfly implementation */
+ do
+ {
+ /* Read xa (real), ya(imag) input */
+ xaya = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* Read xd (real), yd(imag) input */
+ xdyd = read_q15x2_ia ((q15_t **) &ptr1);
+
+ /* R = packed((ya + yc), (xa + xc)) */
+ R = __QADD16(xaya, xcyc);
+
+ /* T = packed((yb + yd), (xb + xd)) */
+ T = __QADD16(xbyb, xdyd);
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8U;
+
+
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ write_q15x2_ia (&ptr1, __SHADD16(R, T));
+
+ /* T = packed((yb + yd), (xb + xd)) */
+ T = __QADD16(xbyb, xdyd);
+
+ /* xc' = (xa-xb+xc-xd) */
+ /* yc' = (ya-yb+yc-yd) */
+ write_q15x2_ia (&ptr1, __SHSUB16(R, T));
+
+ /* S = packed((ya - yc), (xa - xc)) */
+ S = __QSUB16(xaya, xcyc);
+
+ /* Read yd (real), xd(imag) input */
+ /* T = packed( (yb - yd), (xb - xd)) */
+ U = __QSUB16(xbyb, xdyd);
+
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* xb' = (xa+yb-xc-yd) */
+ /* yb' = (ya-xb-yc+xd) */
+ write_q15x2_ia (&ptr1, __SHASX(S, U));
+
+ /* xd' = (xa-yb-xc+yd) */
+ /* yd' = (ya+xb-yc-xd) */
+ write_q15x2_ia (&ptr1, __SHSAX(S, U));
+#else
+ /* xb' = (xa+yb-xc-yd) */
+ /* yb' = (ya-xb-yc+xd) */
+ write_q15x2_ia (&ptr1, __SHSAX(S, U));
+
+ /* xd' = (xa-yb-xc+yd) */
+ /* yd' = (ya+xb-yc-xd) */
+ write_q15x2_ia (&ptr1, __SHASX(S, U));
+#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
+
+ } while (--j);
+
+ /* end of last stage process */
+
+ /* output is in 11.5(q5) format for the 1024 point */
+ /* output is in 9.7(q7) format for the 256 point */
+ /* output is in 7.9(q9) format for the 64 point */
+ /* output is in 5.11(q11) format for the 16 point */
+
+
+#else /* arm_radix4_butterfly_inverse_q15 */
+
+ q15_t R0, R1, S0, S1, T0, T1, U0, U1;
+ q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
+ uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
+
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+
+ /* Index for twiddle coefficient */
+ ic = 0U;
+
+ /* Index for input read and output write */
+ i0 = 0U;
+
+ j = n2;
+
+ /* Input is in 1.15(q15) format */
+
+ /* Start of first stage process */
+ do
+ {
+ /* Butterfly implementation */
+
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* input is down scale by 4 to avoid overflow */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U] >> 2U;
+ T1 = pSrc16[(i0 * 2U) + 1U] >> 2U;
+ /* input is down scale by 4 to avoid overflow */
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U] >> 2U;
+ S1 = pSrc16[(i2 * 2U) + 1U] >> 2U;
+
+ /* R0 = (ya + yc), R1 = (xa + xc) */
+ R0 = __SSAT(T0 + S0, 16U);
+ R1 = __SSAT(T1 + S1, 16U);
+ /* S0 = (ya - yc), S1 = (xa - xc) */
+ S0 = __SSAT(T0 - S0, 16U);
+ S1 = __SSAT(T1 - S1, 16U);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* input is down scale by 4 to avoid overflow */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U] >> 2U;
+ T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
+ /* Read yd (real), xd(imag) input */
+ /* input is down scale by 4 to avoid overflow */
+ U0 = pSrc16[i3 * 2U] >> 2U;
+ U1 = pSrc16[(i3 * 2U) + 1U] >> 2U;
+
+ /* T0 = (yb + yd), T1 = (xb + xd) */
+ T0 = __SSAT(T0 + U0, 16U);
+ T1 = __SSAT(T1 + U1, 16U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
+ pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
+
+ /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc)- (xb + xd) */
+ R0 = __SSAT(R0 - T0, 16U);
+ R1 = __SSAT(R1 - T1, 16U);
+ /* co2 & si2 are read from Coefficient pointer */
+ Co2 = pCoef16[2U * ic * 2U];
+ Si2 = pCoef16[(2U * ic * 2U) + 1U];
+ /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
+ out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16U);
+ /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+ out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16U);
+
+ /* Reading i0+fftLen/4 */
+ /* input is down scale by 4 to avoid overflow */
+ /* T0 = yb, T1 = xb */
+ T0 = pSrc16[i1 * 2U] >> 2U;
+ T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* writing output(xc', yc') in little endian format */
+ pSrc16[i1 * 2U] = out1;
+ pSrc16[(i1 * 2U) + 1U] = out2;
+
+ /* Butterfly calculations */
+ /* input is down scale by 4 to avoid overflow */
+ /* U0 = yd, U1 = xd) */
+ U0 = pSrc16[i3 * 2U] >> 2U;
+ U1 = pSrc16[(i3 * 2U) + 1U] >> 2U;
+
+ /* T0 = yb-yd, T1 = xb-xd) */
+ T0 = __SSAT(T0 - U0, 16U);
+ T1 = __SSAT(T1 - U1, 16U);
+ /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
+ R0 = (q15_t) __SSAT((q31_t) (S0 + T1), 16);
+ R1 = (q15_t) __SSAT((q31_t) (S1 - T0), 16);
+ /* S = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
+ S0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16);
+ S1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16);
+
+ /* co1 & si1 are read from Coefficient pointer */
+ Co1 = pCoef16[ic * 2U];
+ Si1 = pCoef16[(ic * 2U) + 1U];
+ /* Butterfly process for the i0+fftLen/2 sample */
+ /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
+ out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U);
+ /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
+ out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U);
+ /* writing output(xb', yb') in little endian format */
+ pSrc16[i2 * 2U] = out1;
+ pSrc16[(i2 * 2U) + 1U] = out2;
+
+ /* Co3 & si3 are read from Coefficient pointer */
+ Co3 = pCoef16[3U * ic * 2U];
+ Si3 = pCoef16[(3U * ic * 2U) + 1U];
+ /* Butterfly process for the i0+3fftLen/4 sample */
+ /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
+ out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U);
+ /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
+ out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U);
+ /* writing output(xd', yd') in little endian format */
+ pSrc16[i3 * 2U] = out1;
+ pSrc16[(i3 * 2U) + 1U] = out2;
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1U;
+
+ } while (--j);
+
+ /* End of first stage process */
+
+ /* data is in 4.11(q11) format */
+
+
+ /* Start of Middle stage process */
+
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+
+ /* Calculation of Middle stage */
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the middle stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ic = 0U;
+
+ for (j = 0U; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ Co1 = pCoef16[ic * 2U];
+ Si1 = pCoef16[(ic * 2U) + 1U];
+ Co2 = pCoef16[2U * ic * 2U];
+ Si2 = pCoef16[2U * ic * 2U + 1U];
+ Co3 = pCoef16[3U * ic * 2U];
+ Si3 = pCoef16[(3U * ic * 2U) + 1U];
+
+ /* Twiddle coefficients index modifier */
+ ic = ic + twidCoefModifier;
+
+ /* Butterfly implementation */
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U];
+ T1 = pSrc16[(i0 * 2U) + 1U];
+
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U];
+ S1 = pSrc16[(i2 * 2U) + 1U];
+
+
+ /* R0 = (ya + yc), R1 = (xa + xc) */
+ R0 = __SSAT(T0 + S0, 16U);
+ R1 = __SSAT(T1 + S1, 16U);
+ /* S0 = (ya - yc), S1 = (xa - xc) */
+ S0 = __SSAT(T0 - S0, 16U);
+ S1 = __SSAT(T1 - S1, 16U);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+ /* T0 = (yb + yd), T1 = (xb + xd) */
+ T0 = __SSAT(T0 + U0, 16U);
+ T1 = __SSAT(T1 + U1, 16U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ pSrc16[i0 * 2U] = ((R0 >> 1U) + (T0 >> 1U)) >> 1U;
+ pSrc16[(i0 * 2U) + 1U] = ((R1 >> 1U) + (T1 >> 1U)) >> 1U;
+
+ /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+ R0 = (R0 >> 1U) - (T0 >> 1U);
+ R1 = (R1 >> 1U) - (T1 >> 1U);
+
+ /* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
+ out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16);
+ /* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+ out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16);
+
+ /* Reading i0+3fftLen/4 */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
+ /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
+ pSrc16[i1 * 2U] = out1;
+ pSrc16[(i1 * 2U) + 1U] = out2;
+
+ /* Butterfly calculations */
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+ /* T0 = yb-yd, T1 = xb-xd) */
+ T0 = __SSAT(T0 - U0, 16U);
+ T1 = __SSAT(T1 - U1, 16U);
+
+ /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
+ R0 = (S0 >> 1U) + (T1 >> 1U);
+ R1 = (S1 >> 1U) - (T0 >> 1U);
+
+ /* S1 = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
+ S0 = (S0 >> 1U) - (T1 >> 1U);
+ S1 = (S1 >> 1U) + (T0 >> 1U);
+
+ /* Butterfly process for the i0+fftLen/2 sample */
+ out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U);
+ out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U);
+ /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
+ /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
+ pSrc16[i2 * 2U] = out1;
+ pSrc16[(i2 * 2U) + 1U] = out2;
+
+ /* Butterfly process for the i0+3fftLen/4 sample */
+ out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U);
+
+ out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U);
+ /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
+ /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
+ pSrc16[i3 * 2U] = out1;
+ pSrc16[(i3 * 2U) + 1U] = out2;
+
+
+ }
+ }
+ /* Twiddle coefficients index modifier */
+ twidCoefModifier <<= 2U;
+ }
+ /* End of Middle stages process */
+
+
+ /* data is in 10.6(q6) format for the 1024 point */
+ /* data is in 8.8(q8) format for the 256 point */
+ /* data is in 6.10(q10) format for the 64 point */
+ /* data is in 4.12(q12) format for the 16 point */
+
+ /* start of last stage process */
+
+
+ /* Initializations for the last stage */
+ n1 = n2;
+ n2 >>= 2U;
+
+ /* Butterfly implementation */
+ for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Reading i0, i0+fftLen/2 inputs */
+ /* Read ya (real), xa(imag) input */
+ T0 = pSrc16[i0 * 2U];
+ T1 = pSrc16[(i0 * 2U) + 1U];
+ /* Read yc (real), xc(imag) input */
+ S0 = pSrc16[i2 * 2U];
+ S1 = pSrc16[(i2 * 2U) + 1U];
+
+ /* R0 = (ya + yc), R1 = (xa + xc) */
+ R0 = __SSAT(T0 + S0, 16U);
+ R1 = __SSAT(T1 + S1, 16U);
+ /* S0 = (ya - yc), S1 = (xa - xc) */
+ S0 = __SSAT(T0 - S0, 16U);
+ S1 = __SSAT(T1 - S1, 16U);
+
+ /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+
+ /* T0 = (yb + yd), T1 = (xb + xd) */
+ T0 = __SSAT(T0 + U0, 16U);
+ T1 = __SSAT(T1 + U1, 16U);
+
+ /* writing the butterfly processed i0 sample */
+ /* xa' = xa + xb + xc + xd */
+ /* ya' = ya + yb + yc + yd */
+ pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
+ pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
+
+ /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
+ R0 = (R0 >> 1U) - (T0 >> 1U);
+ R1 = (R1 >> 1U) - (T1 >> 1U);
+
+ /* Read yb (real), xb(imag) input */
+ T0 = pSrc16[i1 * 2U];
+ T1 = pSrc16[(i1 * 2U) + 1U];
+
+ /* writing the butterfly processed i0 + fftLen/4 sample */
+ /* xc' = (xa-xb+xc-xd) */
+ /* yc' = (ya-yb+yc-yd) */
+ pSrc16[i1 * 2U] = R0;
+ pSrc16[(i1 * 2U) + 1U] = R1;
+
+ /* Read yd (real), xd(imag) input */
+ U0 = pSrc16[i3 * 2U];
+ U1 = pSrc16[(i3 * 2U) + 1U];
+ /* T0 = (yb - yd), T1 = (xb - xd) */
+ T0 = __SSAT(T0 - U0, 16U);
+ T1 = __SSAT(T1 - U1, 16U);
+
+ /* writing the butterfly processed i0 + fftLen/2 sample */
+ /* xb' = (xa-yb-xc+yd) */
+ /* yb' = (ya+xb-yc-xd) */
+ pSrc16[i2 * 2U] = (S0 >> 1U) - (T1 >> 1U);
+ pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U);
+
+
+ /* writing the butterfly processed i0 + 3fftLen/4 sample */
+ /* xd' = (xa+yb-xc-yd) */
+ /* yd' = (ya-xb-yc+xd) */
+ pSrc16[i3 * 2U] = (S0 >> 1U) + (T1 >> 1U);
+ pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U);
+ }
+ /* end of last stage process */
+
+ /* output is in 11.5(q5) format for the 1024 point */
+ /* output is in 9.7(q7) format for the 256 point */
+ /* output is in 7.9(q9) format for the 64 point */
+ /* output is in 5.11(q11) format for the 16 point */
+
+#endif /* #if defined (ARM_MATH_DSP) */
+
+}
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