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| author | joshua <joshua@joshuayun.com> | 2023-12-30 23:54:31 -0500 |
|---|---|---|
| committer | joshua <joshua@joshuayun.com> | 2023-12-30 23:54:31 -0500 |
| commit | 86608c6770cf08c138a2bdab5855072f64be09ef (patch) | |
| tree | 494a61b3ef37e76f9235a0d10f5c93d97290a35f /Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c | |
| download | sdr-software-master.tar.gz | |
Diffstat (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c')
| -rw-r--r-- | Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c | 827 |
1 files changed, 827 insertions, 0 deletions
diff --git a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c new file mode 100644 index 0000000..b7ea7e5 --- /dev/null +++ b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c @@ -0,0 +1,827 @@ +/* ----------------------------------------------------------------------
+ * Project: CMSIS DSP Library
+ * Title: arm_cfft_radix4_q31.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_inverse_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ const q31_t * pCoef,
+ uint32_t twidCoefModifier);
+
+void arm_radix4_butterfly_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ const q31_t * pCoef,
+ uint32_t twidCoefModifier);
+
+void arm_bitreversal_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ uint16_t bitRevFactor,
+ const uint16_t * pBitRevTab);
+
+/**
+ @ingroup groupTransforms
+ */
+
+/**
+ @addtogroup ComplexFFT
+ @{
+ */
+
+/**
+ @brief Processing function for the Q31 CFFT/CIFFT.
+ @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed in the future.
+ @param[in] S points to an instance of the Q31 CFFT/CIFFT structure
+ @param[in,out] pSrc points to the complex data buffer of size <code>2*fftLen</code>. 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 CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
+ \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
+ */
+
+void arm_cfft_radix4_q31(
+ const arm_cfft_radix4_instance_q31 * S,
+ q31_t * pSrc)
+{
+ if (S->ifftFlag == 1U)
+ {
+ /* Complex IFFT radix-4 */
+ arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
+ }
+ else
+ {
+ /* Complex FFT radix-4 */
+ arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
+ }
+
+ if (S->bitReverseFlag == 1U)
+ {
+ /* Bit Reversal */
+ arm_bitreversal_q31(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)
+ *
+ * Butterfly implementation:
+ * 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 Q31 CFFT butterfly process.
+ @param[in,out] pSrc points to the in-place buffer of Q31 data type.
+ @param[in] fftLen length of the FFT.
+ @param[in] pCoef 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_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ const q31_t * pCoef,
+ uint32_t twidCoefModifier)
+{
+ uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+ q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+
+ q31_t xa, xb, xc, xd;
+ q31_t ya, yb, yc, yd;
+ q31_t xa_out, xb_out, xc_out, xd_out;
+ q31_t ya_out, yb_out, yc_out, yd_out;
+
+ q31_t *ptr1;
+
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+
+ /* start of first stage process */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+ i0 = 0U;
+ ia1 = 0U;
+
+ j = n2;
+
+ /* Calculation of first stage */
+ do
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = (pSrc[(2U * i0)] >> 4U) + (pSrc[(2U * i2)] >> 4U);
+ /* xa - xc */
+ r2 = (pSrc[(2U * i0)] >> 4U) - (pSrc[(2U * i2)] >> 4U);
+
+ /* xb + xd */
+ t1 = (pSrc[(2U * i1)] >> 4U) + (pSrc[(2U * i3)] >> 4U);
+
+ /* ya + yc */
+ s1 = (pSrc[(2U * i0) + 1U] >> 4U) + (pSrc[(2U * i2) + 1U] >> 4U);
+ /* ya - yc */
+ s2 = (pSrc[(2U * i0) + 1U] >> 4U) - (pSrc[(2U * i2) + 1U] >> 4U);
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2U * i0] = (r1 + t1);
+ /* (xa + xc) - (xb + xd) */
+ r1 = r1 - t1;
+ /* yb + yd */
+ t2 = (pSrc[(2U * i1) + 1U] >> 4U) + (pSrc[(2U * i3) + 1U] >> 4U);
+
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2U * i0) + 1U] = (s1 + t2);
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* yb - yd */
+ t1 = (pSrc[(2U * i1) + 1U] >> 4U) - (pSrc[(2U * i3) + 1U] >> 4U);
+ /* xb - xd */
+ t2 = (pSrc[(2U * i1)] >> 4U) - (pSrc[(2U * i3)] >> 4U);
+
+ /* index calculation for the coefficients */
+ ia2 = 2U * ia1;
+ co2 = pCoef[(ia2 * 2U)];
+ si2 = pCoef[(ia2 * 2U) + 1U];
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1U;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1U;
+
+ /* (xa - xc) + (yb - yd) */
+ r1 = r2 + t1;
+ /* (xa - xc) - (yb - yd) */
+ r2 = r2 - t1;
+
+ /* (ya - yc) - (xb - xd) */
+ s1 = s2 - t2;
+ /* (ya - yc) + (xb - xd) */
+ s2 = s2 + t2;
+
+ co1 = pCoef[(ia1 * 2U)];
+ si1 = pCoef[(ia1 * 2U) + 1U];
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1U;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1U;
+
+ /* index calculation for the coefficients */
+ ia3 = 3U * ia1;
+ co3 = pCoef[(ia3 * 2U)];
+ si3 = pCoef[(ia3 * 2U) + 1U];
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1U;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1U;
+
+ } while (--j);
+
+ /* end of first stage process */
+
+ /* data is in 5.27(q27) format */
+
+
+ /* start of Middle stages process */
+
+
+ /* each stage in middle stages provides two down scaling of the input */
+
+ twidCoefModifier <<= 2U;
+
+
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ia1 = 0U;
+
+ /* Calculation of first stage */
+ for (j = 0U; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[(ia1 * 2U)];
+ si1 = pCoef[(ia1 * 2U) + 1U];
+ co2 = pCoef[(ia2 * 2U)];
+ si2 = pCoef[(ia2 * 2U) + 1U];
+ co3 = pCoef[(ia3 * 2U)];
+ si3 = pCoef[(ia3 * 2U) + 1U];
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = pSrc[2U * i0] + pSrc[2U * i2];
+ /* xa - xc */
+ r2 = pSrc[2U * i0] - pSrc[2U * i2];
+
+ /* ya + yc */
+ s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U];
+ /* ya - yc */
+ s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U];
+
+ /* xb + xd */
+ t1 = pSrc[2U * i1] + pSrc[2U * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2U * i0] = (r1 + t1) >> 2U;
+ /* xa + xc -(xb + xd) */
+ r1 = r1 - t1;
+
+ /* yb + yd */
+ t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U];
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2U * i0) + 1U] = (s1 + t2) >> 2U;
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* (yb - yd) */
+ t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U];
+ /* (xb - xd) */
+ t2 = pSrc[2U * i1] - pSrc[2U * i3];
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1U;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1U;
+
+ /* (xa - xc) + (yb - yd) */
+ r1 = r2 + t1;
+ /* (xa - xc) - (yb - yd) */
+ r2 = r2 - t1;
+
+ /* (ya - yc) - (xb - xd) */
+ s1 = s2 - t2;
+ /* (ya - yc) + (xb - xd) */
+ s2 = s2 + t2;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1U;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U;
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1U;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U;
+ }
+ }
+ twidCoefModifier <<= 2U;
+ }
+
+ /* End of Middle stages process */
+
+ /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+ /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+ /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+ /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+ /* start of Last stage process */
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+ /* Read xa (real), ya(imag) input */
+ xa = *ptr1++;
+ ya = *ptr1++;
+
+ /* Read xb (real), yb(imag) input */
+ xb = *ptr1++;
+ yb = *ptr1++;
+
+ /* Read xc (real), yc(imag) input */
+ xc = *ptr1++;
+ yc = *ptr1++;
+
+ /* Read xc (real), yc(imag) input */
+ xd = *ptr1++;
+ yd = *ptr1++;
+
+ /* xa' = xa + xb + xc + xd */
+ xa_out = xa + xb + xc + xd;
+
+ /* ya' = ya + yb + yc + yd */
+ ya_out = ya + yb + yc + yd;
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8U;
+
+ /* writing xa' and ya' */
+ *ptr1++ = xa_out;
+ *ptr1++ = ya_out;
+
+ xc_out = (xa - xb + xc - xd);
+ yc_out = (ya - yb + yc - yd);
+
+ /* writing xc' and yc' */
+ *ptr1++ = xc_out;
+ *ptr1++ = yc_out;
+
+ xb_out = (xa + yb - xc - yd);
+ yb_out = (ya - xb - yc + xd);
+
+ /* writing xb' and yb' */
+ *ptr1++ = xb_out;
+ *ptr1++ = yb_out;
+
+ xd_out = (xa - yb - xc + yd);
+ yd_out = (ya + xb - yc - xd);
+
+ /* writing xd' and yd' */
+ *ptr1++ = xd_out;
+ *ptr1++ = yd_out;
+
+
+ } while (--j);
+
+ /* output is in 11.21(q21) format for the 1024 point */
+ /* output is in 9.23(q23) format for the 256 point */
+ /* output is in 7.25(q25) format for the 64 point */
+ /* output is in 5.27(q27) format for the 16 point */
+
+ /* End of last stage process */
+
+}
+
+
+/**
+ @brief Core function for the Q31 CIFFT butterfly process.
+ @param[in,out] pSrc points to the in-place buffer of Q31 data type.
+ @param[in] fftLen length of the FFT.
+ @param[in] pCoef 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_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ const q31_t * pCoef,
+ uint32_t twidCoefModifier)
+{
+ uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+ q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+ q31_t xa, xb, xc, xd;
+ q31_t ya, yb, yc, yd;
+ q31_t xa_out, xb_out, xc_out, xd_out;
+ q31_t ya_out, yb_out, yc_out, yd_out;
+
+ q31_t *ptr1;
+
+ /* input is be 1.31(q31) format for all FFT sizes */
+ /* Total process is divided into three stages */
+ /* process first stage, middle stages, & last stage */
+
+ /* Start of first stage process */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+ /* n2 = fftLen/4 */
+ n2 >>= 2U;
+ i0 = 0U;
+ ia1 = 0U;
+
+ j = n2;
+
+ do
+ {
+ /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = (pSrc[2U * i0] >> 4U) + (pSrc[2U * i2] >> 4U);
+ /* xa - xc */
+ r2 = (pSrc[2U * i0] >> 4U) - (pSrc[2U * i2] >> 4U);
+
+ /* xb + xd */
+ t1 = (pSrc[2U * i1] >> 4U) + (pSrc[2U * i3] >> 4U);
+
+ /* ya + yc */
+ s1 = (pSrc[(2U * i0) + 1U] >> 4U) + (pSrc[(2U * i2) + 1U] >> 4U);
+ /* ya - yc */
+ s2 = (pSrc[(2U * i0) + 1U] >> 4U) - (pSrc[(2U * i2) + 1U] >> 4U);
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2U * i0] = (r1 + t1);
+ /* (xa + xc) - (xb + xd) */
+ r1 = r1 - t1;
+ /* yb + yd */
+ t2 = (pSrc[(2U * i1) + 1U] >> 4U) + (pSrc[(2U * i3) + 1U] >> 4U);
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2U * i0) + 1U] = (s1 + t2);
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* yb - yd */
+ t1 = (pSrc[(2U * i1) + 1U] >> 4U) - (pSrc[(2U * i3) + 1U] >> 4U);
+ /* xb - xd */
+ t2 = (pSrc[2U * i1] >> 4U) - (pSrc[2U * i3] >> 4U);
+
+ /* index calculation for the coefficients */
+ ia2 = 2U * ia1;
+ co2 = pCoef[ia2 * 2U];
+ si2 = pCoef[(ia2 * 2U) + 1U];
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1U;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[2U * i1 + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1U;
+
+ /* (xa - xc) - (yb - yd) */
+ r1 = r2 - t1;
+ /* (xa - xc) + (yb - yd) */
+ r2 = r2 + t1;
+
+ /* (ya - yc) + (xb - xd) */
+ s1 = s2 + t2;
+ /* (ya - yc) - (xb - xd) */
+ s2 = s2 - t2;
+
+ co1 = pCoef[ia1 * 2U];
+ si1 = pCoef[(ia1 * 2U) + 1U];
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1U;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1U;
+
+ /* index calculation for the coefficients */
+ ia3 = 3U * ia1;
+ co3 = pCoef[ia3 * 2U];
+ si3 = pCoef[(ia3 * 2U) + 1U];
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1U;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1U;
+
+ } while (--j);
+
+ /* data is in 5.27(q27) format */
+ /* each stage provides two down scaling of the input */
+
+
+ /* Start of Middle stages process */
+
+ twidCoefModifier <<= 2U;
+
+ /* Calculation of second stage to excluding last stage */
+ for (k = fftLen / 4U; k > 4U; k >>= 2U)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2U;
+ ia1 = 0U;
+
+ for (j = 0; j <= (n2 - 1U); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[(ia1 * 2U)];
+ si1 = pCoef[(ia1 * 2U) + 1U];
+ co2 = pCoef[(ia2 * 2U)];
+ si2 = pCoef[(ia2 * 2U) + 1U];
+ co3 = pCoef[(ia3 * 2U)];
+ si3 = pCoef[(ia3 * 2U) + 1U];
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = pSrc[2U * i0] + pSrc[2U * i2];
+ /* xa - xc */
+ r2 = pSrc[2U * i0] - pSrc[2U * i2];
+
+ /* ya + yc */
+ s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U];
+ /* ya - yc */
+ s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U];
+
+ /* xb + xd */
+ t1 = pSrc[2U * i1] + pSrc[2U * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2U * i0] = (r1 + t1) >> 2U;
+ /* xa + xc -(xb + xd) */
+ r1 = r1 - t1;
+ /* yb + yd */
+ t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U];
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2U * i0) + 1U] = (s1 + t2) >> 2U;
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* (yb - yd) */
+ t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U];
+ /* (xb - xd) */
+ t2 = pSrc[2U * i1] - pSrc[2U * i3];
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32U)) -
+ ((int32_t) (((q63_t) s1 * si2) >> 32U))) >> 1U;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32U)) +
+ ((int32_t) (((q63_t) r1 * si2) >> 32U))) >> 1U;
+
+ /* (xa - xc) - (yb - yd) */
+ r1 = r2 - t1;
+ /* (xa - xc) + (yb - yd) */
+ r2 = r2 + t1;
+
+ /* (ya - yc) + (xb - xd) */
+ s1 = s2 + t2;
+ /* (ya - yc) - (xb - xd) */
+ s2 = s2 - t2;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1U;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U;
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[(2U * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1U;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U;
+ }
+ }
+ twidCoefModifier <<= 2U;
+ }
+
+ /* End of Middle stages process */
+
+ /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+ /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+ /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+ /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+ /* Start of last stage process */
+
+
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+ /* Read xa (real), ya(imag) input */
+ xa = *ptr1++;
+ ya = *ptr1++;
+
+ /* Read xb (real), yb(imag) input */
+ xb = *ptr1++;
+ yb = *ptr1++;
+
+ /* Read xc (real), yc(imag) input */
+ xc = *ptr1++;
+ yc = *ptr1++;
+
+ /* Read xc (real), yc(imag) input */
+ xd = *ptr1++;
+ yd = *ptr1++;
+
+ /* xa' = xa + xb + xc + xd */
+ xa_out = xa + xb + xc + xd;
+
+ /* ya' = ya + yb + yc + yd */
+ ya_out = ya + yb + yc + yd;
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8U;
+
+ /* writing xa' and ya' */
+ *ptr1++ = xa_out;
+ *ptr1++ = ya_out;
+
+ xc_out = (xa - xb + xc - xd);
+ yc_out = (ya - yb + yc - yd);
+
+ /* writing xc' and yc' */
+ *ptr1++ = xc_out;
+ *ptr1++ = yc_out;
+
+ xb_out = (xa - yb - xc + yd);
+ yb_out = (ya + xb - yc - xd);
+
+ /* writing xb' and yb' */
+ *ptr1++ = xb_out;
+ *ptr1++ = yb_out;
+
+ xd_out = (xa + yb - xc - yd);
+ yd_out = (ya - xb - yc + xd);
+
+ /* writing xd' and yd' */
+ *ptr1++ = xd_out;
+ *ptr1++ = yd_out;
+
+ } while (--j);
+
+ /* output is in 11.21(q21) format for the 1024 point */
+ /* output is in 9.23(q23) format for the 256 point */
+ /* output is in 7.25(q25) format for the 64 point */
+ /* output is in 5.27(q27) format for the 16 point */
+
+ /* End of last stage process */
+}
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