in lib/cmsis/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c [819:1404]
void arm_radix4_butterfly_inverse_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pCoef,
uint32_t twidCoefModifier)
{
#if defined(ARM_MATH_CM7)
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;
}
#else
uint32_t n1, n2, ia1, ia2, ia3, i0, 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;
q31_t *pSi0;
q31_t *pSi1;
q31_t *pSi2;
q31_t *pSi3;
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;
ia1 = 0u;
j = n2;
pSi0 = pSrc;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
do
{
/* Butterfly implementation */
/* xa + xc */
r1 = (pSi0[0] >> 4u) + (pSi2[0] >> 4u);
/* xa - xc */
r2 = (pSi0[0] >> 4u) - (pSi2[0] >> 4u);
/* xb + xd */
t1 = (pSi1[0] >> 4u) + (pSi3[0] >> 4u);
/* ya + yc */
s1 = (pSi0[1] >> 4u) + (pSi2[1] >> 4u);
/* ya - yc */
s2 = (pSi0[1] >> 4u) - (pSi2[1] >> 4u);
/* xa' = xa + xb + xc + xd */
*pSi0++ = (r1 + t1);
/* (xa + xc) - (xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = (pSi1[1] >> 4u) + (pSi3[1] >> 4u);
/* ya' = ya + yb + yc + yd */
*pSi0++ = (s1 + t2);
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* yb - yd */
t1 = (pSi1[1] >> 4u) - (pSi3[1] >> 4u);
/* xb - xd */
t2 = (pSi1[0] >> 4u) - (pSi3[0] >> 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) */
*pSi1++ = (((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) */
*pSi1++ = (((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) */
*pSi2++ = (((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) */
*pSi2++ = (((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) */
*pSi3++ = (((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) */
*pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
} 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;
pSi0 = pSrc + 2 * j;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* Butterfly implementation */
/* xa + xc */
r1 = pSi0[0] + pSi2[0];
/* xa - xc */
r2 = pSi0[0] - pSi2[0];
/* ya + yc */
s1 = pSi0[1] + pSi2[1];
/* ya - yc */
s2 = pSi0[1] - pSi2[1];
/* xb + xd */
t1 = pSi1[0] + pSi3[0];
/* xa' = xa + xb + xc + xd */
pSi0[0] = (r1 + t1) >> 2u;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSi1[1] + pSi3[1];
/* ya' = ya + yb + yc + yd */
pSi0[1] = (s1 + t2) >> 2u;
pSi0 += 2 * n1;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSi1[1] - pSi3[1];
/* (xb - xd) */
t2 = pSi1[0] - pSi3[0];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSi1[0] = (((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) */
pSi1[1] =
(((int32_t) (((q63_t) s1 * co2) >> 32u)) +
((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
pSi1 += 2 * n1;
/* (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) */
pSi2[0] = (((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) */
pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
pSi2 += 2 * n1;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSi3[0] = (((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) */
pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
pSi3 += 2 * n1;
}
}
twidCoefModifier <<= 2u;
}
#endif
/* 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 */
}