Diff: TransformFunctions/arm_cfft_radix4_q31.c

Revision:

0:3d9c67d97d6f

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/TransformFunctions/arm_cfft_radix4_q31.c	Mon Jul 28 15:03:15 2014 +0000
@@ -0,0 +1,911 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014  
+* $Revision: 	V1.4.3  
+*    
+* 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    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.     
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+void arm_radix4_butterfly_inverse_q31(
+q31_t * pSrc,
+uint32_t fftLen,
+q31_t * pCoef,
+uint32_t twidCoefModifier);
+
+void arm_radix4_butterfly_q31(
+q31_t * pSrc,
+uint32_t fftLen,
+q31_t * pCoef,
+uint32_t twidCoefModifier);
+
+void arm_bitreversal_q31(
+q31_t * pSrc,
+uint32_t fftLen,
+uint16_t bitRevFactor,
+uint16_t * pBitRevTab);
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup ComplexFFT    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @brief Processing function for the Q31 CFFT/CIFFT.    
+ * @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:    
+ * \par    
+ * 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,
+  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;
+  q63_t xaya, xbyb, xcyc, xdyd;
+  /* 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
+  {
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    xa = (q31_t) xaya;
+    ya = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    xb = (q31_t) xbyb;
+    yb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    xc = (q31_t) xcyc;
+    yc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    xd = (q31_t) xdyd;
+    yd = (q31_t) (xdyd >> 32);
+
+#else
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    ya = (q31_t) xaya;
+    xa = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    yb = (q31_t) xbyb;
+    xb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    yc = (q31_t) xcyc;
+    xc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    yd = (q31_t) xdyd;
+    xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+    /* 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,
+  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;
+  q63_t xaya, xbyb, xcyc, xdyd;
+
+  /* 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
+  {
+#ifndef ARM_MATH_BIG_ENDIAN
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    xa = (q31_t) xaya;
+    ya = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    xb = (q31_t) xbyb;
+    yb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    xc = (q31_t) xcyc;
+    yc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    xd = (q31_t) xdyd;
+    yd = (q31_t) (xdyd >> 32);
+
+#else
+
+    /* Read xa (real), ya(imag) input */
+    xaya = *__SIMD64(ptr1)++;
+    ya = (q31_t) xaya;
+    xa = (q31_t) (xaya >> 32);
+
+    /* Read xb (real), yb(imag) input */
+    xbyb = *__SIMD64(ptr1)++;
+    yb = (q31_t) xbyb;
+    xb = (q31_t) (xbyb >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xcyc = *__SIMD64(ptr1)++;
+    yc = (q31_t) xcyc;
+    xc = (q31_t) (xcyc >> 32);
+
+    /* Read xc (real), yc(imag) input */
+    xdyd = *__SIMD64(ptr1)++;
+    yd = (q31_t) xdyd;
+    xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+    /* 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 */
+}