| /* ---------------------------------------------------------------------- |
| * 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 It has been superseded by \ref arm_cfft_q31 and will be removed in the future.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 */ |
| } |
