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convolution.cpp
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convolution.cpp
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#include "stdafx.h"
/* Copyright (c) Colorado School of Mines, 1995.*/
/* All rights reserved. */
/*********************** self documentation **********************/
/*****************************************************************************
CONVOLUTION - Compute z = x convolved with y
conv compute the convolution of two input vector arrays
******************************************************************************
Input:
lx length of x array
ifx sample index of first x
x array[lx] to be convolved with y
ly length of y array
ify sample index of first y
y array[ly] with which x is to be convolved
lz length of z array
ifz sample index of first z
Output:
z array[lz] containing x convolved with y
******************************************************************************
Function Prototype:
void conv (int lx, int ifx, float *x, int ly, int ify, float *y,
int lz, int ifz, float *z);
******************************************************************************
Notes:
The operation z = x convolved with y is defined to be
ifx+lx-1
z[i] = sum x[j]*y[i-j] ; i = ifz,...,ifz+lz-1
j=ifx
The x samples are contained in x[0], x[1], ..., x[lx-1]; likewise for
the y and z samples. The sample indices of the first x, y, and z values
determine the location of the origin for each array. For example, if
z is to be a weighted average of the nearest 5 samples of y, one might
use
...
x[0] = x[1] = x[2] = x[3] = x[4] = 1.0/5.0;
conv(5,-2,x,lx,0,y,ly,0,z);
...
In this example, the filter x is symmetric, with index of first sample = -2.
This function is optimized for architectures that can simultaneously perform
a multiply, add, and one load from memory; e.g., the IBM RISC System/6000.
Because, for each value of i, it accumulates the convolution sum z[i] in a
scalar, this function is not likely to be optimal for vector architectures.
******************************************************************************
Author: Dave Hale, Colorado School of Mines, 11/23/91
*****************************************************************************/
/**************** end self doc ********************************/
/* prototype of function used internally */
static void convs(int,int,float*,int,int,float*,int,int,float*);
void conv (int lx, int ifx, float *x,int ly, int ify, float *y,int lz, int ifz, float *z)
/*****************************************************************************
Compute z = x convolved with y; i.e.,
ifx+lx-1
z[i] = sum x[j]*y[i-j] ; i = ifz,...,ifz+lz-1
j=ifx
******************************************************************************
Input:
lx length of x array
ifx sample index of first x
x array[lx] to be convolved with y
ly length of y array
ify sample index of first y
y array[ly] with which x is to be convolved
lz length of z array
ifz sample index of first z
Output:
z array[lz] containing x convolved with y
******************************************************************************
Notes:
The x samples are contained in x[0], x[1], ..., x[lx-1]; likewise for
the y and z samples. The sample indices of the first x, y, and z values
determine the location of the origin for each array. For example, if
z is to be a weighted average of the nearest 5 samples of y, one might
use
...
x[0] = x[1] = x[2] = x[3] = x[4] = 1.0/5.0;
conv(5,-2,x,lx,0,y,ly,0,z);
...
In this example, the filter x is symmetric, with index of first sample = -2.
This function is optimized for architectures that can simultaneously perform
a multiply, add, and one load from memory; e.g., the IBM RISC System/6000.
Because, for each value of i, it accumulates the convolution sum z[i] in a
scalar, this function is not likely to be optimal for vector architectures.
******************************************************************************
Author: Dave Hale, Colorado School of Mines, 11/23/91
*****************************************************************************/
#ifdef SIMPLE_CONV
{
int ilx=ifx+lx-1,ily=ify+ly-1,ilz=ifz+lz-1,i,j,jlow,jhigh;
float sum;
x -= ifx; y -= ify; z -= ifz;
for (i=ifz; i<=ilz; ++i) {
jlow = i-ily; if (jlow<ifx) jlow = ifx;
jhigh = i-ify; if (jhigh>ilx) jhigh = ilx;
for (j=jlow,sum=0.0; j<=jhigh; ++j)
sum += x[j]*y[i-j];
z[i] = sum;
}
}
#else
{
int ilx=ifx+lx-1,ily=ify+ly-1,ilz=ifz+lz-1,
i,j,ilow,ihigh,jlow,jhigh;
float sa,sb,xa,xb,ya,yb,*t;
/* if x is longer than y, swap x and y */
if (lx>ly) {
i = ifx; ifx = ify; ify = i;
i = ilx; ilx = ily; ily = i;
i = lx; lx = ly; ly = i;
t = x; x = y; y = t;
}
/* handle short x with special code */
if (lx>=1 && lx<=30) {
convs(lx,ifx,x,ly,ify,y,lz,ifz,z);
return;
}
/* adjust pointers for indices of first samples */
x -= ifx;
y -= ify;
z -= ifz;
/* OFF LEFT: i < ify+ifx */
/* zero output for all i */
ilow = ifz;
ihigh = ify+ifx-1; if (ihigh>ilz) ihigh = ilz;
for (i=ilow; i<=ihigh; ++i)
z[i] = 0.0;
/* ROLLING ON: ify+ifx <= i < ify+ilx */
/* if necessary, do one i so that number of j in overlap is odd */
if (i<ify+ilx && i<=ilz) {
jlow = ifx;
jhigh = i-ify;
if ((jhigh-jlow)%2) {
sa = 0.0;
for (j=jlow; j<=jhigh; ++j)
sa += x[j]*y[i-j];
z[i++] = sa;
}
}
/* loop over pairs of i and j */
ilow = i;
ihigh = ilx+ify-1; if (ihigh>ilz) ihigh = ilz;
jlow = ifx;
jhigh = ilow-ify;
for (i=ilow; i<ihigh; i+=2,jhigh+=2) {
sa = sb = 0.0;
xb = x[jhigh+1];
yb = 0.0;
for (j=jhigh; j>=jlow; j-=2) {
sa += xb*yb;
ya = y[i-j];
sb += xb*ya;
xa = x[j];
sa += xa*ya;
yb = y[i+1-j];
sb += xa*yb;
xb = x[j-1];
}
z[i] = sa;
z[i+1] = sb;
}
/* if number of i is odd */
if (i==ihigh) {
jlow = ifx;
jhigh = i-ify;
sa = 0.0;
for (j=jlow; j<=jhigh; ++j)
sa += x[j]*y[i-j];
z[i++] = sa;
}
/* MIDDLE: ify+ilx <= i <= ily+ifx */
/* determine limits for i and j */
ilow = i;
ihigh = ily+ifx; if (ihigh>ilz) ihigh = ilz;
jlow = ifx;
jhigh = ilx;
/* if number of j is even, do j in pairs with no leftover */
if ((jhigh-jlow)%2) {
for (i=ilow; i<ihigh; i+=2) {
sa = sb = 0.0;
yb = y[i+1-jlow];
xa = x[jlow];
for (j=jlow; j<jhigh; j+=2) {
sb += xa*yb;
ya = y[i-j];
sa += xa*ya;
xb = x[j+1];
sb += xb*ya;
yb = y[i-1-j];
sa += xb*yb;
xa = x[j+2];
}
z[i] = sa;
z[i+1] = sb;
}
/* else, number of j is odd, so do j in pairs with leftover */
} else {
for (i=ilow; i<ihigh; i+=2) {
sa = sb = 0.0;
yb = y[i+1-jlow];
xa = x[jlow];
for (j=jlow; j<jhigh; j+=2) {
sb += xa*yb;
ya = y[i-j];
sa += xa*ya;
xb = x[j+1];
sb += xb*ya;
yb = y[i-1-j];
sa += xb*yb;
xa = x[j+2];
}
z[i] = sa+x[jhigh]*y[i-jhigh];
z[i+1] = sb+x[jhigh]*y[i+1-jhigh];
}
}
/* if number of i is odd */
if (i==ihigh) {
sa = 0.0;
for (j=jlow; j<=jhigh; ++j)
sa += x[j]*y[i-j];
z[i++] = sa;
}
/* ROLLING OFF: ily+ifx < i <= ily+ilx */
/* if necessary, do one i so that number of j in overlap is even */
if (i<=ily+ilx && i<=ilz) {
jlow = i-ily;
jhigh = ilx;
if (!((jhigh-jlow)%2)) {
sa = 0.0;
for (j=jlow; j<=jhigh; ++j)
sa += x[j]*y[i-j];
z[i++] = sa;
}
}
/* number of j is now even, so loop over both i and j in pairs */
ilow = i;
ihigh = ily+ilx; if (ihigh>ilz) ihigh = ilz;
jlow = ilow-ily;
jhigh = ilx;
for (i=ilow; i<ihigh; i+=2,jlow+=2) {
sa = sb = 0.0;
xa = x[jlow];
yb = 0.0;
for (j=jlow; j<jhigh; j+=2) {
sb += xa*yb;
ya = y[i-j];
sa += xa*ya;
xb = x[j+1];
sb += xb*ya;
yb = y[i-1-j];
sa += xb*yb;
xa = x[j+2];
}
z[i] = sa;
z[i+1] = sb;
}
/* if number of i is odd */
if (i==ihigh) {
jlow = i-ily;
jhigh = ilx;
sa = 0.0;
for (j=jlow; j<=jhigh; ++j)
sa += x[j]*y[i-j];
z[i++] = sa;
}
/* OFF RIGHT: ily+ilx < i */
/* zero output for all i */
ilow = i;
ihigh = ilz;
for (i=ilow; i<=ihigh; ++i)
z[i] = 0.0;
}
/* internal function optimized for short x */
static void convs (int lx, int ifx, float *x,
int ly, int ify, float *y,
int lz, int ifz, float *z)
{
int ilx=ifx+lx-1,ily=ify+ly-1,ilz=ifz+lz-1,
i,j,ilow,ihigh,jlow,jhigh;
float x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,
x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,
x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,
ya,yb,z0,z1,sum;
x -= ifx;
y -= ify;
z -= ifz;
/* OFF LEFT: i < ifx+ify */
ilow = ifz;
ihigh = ify+ifx-1; if (ihigh>ilz) ihigh = ilz;
for (i=ilow; i<=ihigh; ++i)
z[i] = 0.0;
/* ROLLING ON: ify+ifx <= i < ify+ilx */
ilow = ify+ifx; if (ilow<ifz) ilow = ifz;
ihigh = ify+ilx-1; if (ihigh>ilz) ihigh = ilz;
jlow = ifx;
jhigh = ilow-ify;
for (i=ilow; i<=ihigh; ++i,++jhigh) {
for (j=jlow,sum=0.0; j<=jhigh; ++j)
sum += x[j]*y[i-j];
z[i] = sum;
}
/* MIDDLE: ify+ilx <= i <= ily+ifx */
ilow = ify+ilx; if (ilow<ifz) ilow = ifz;
ihigh = ily+ifx; if (ihigh>ilz) ihigh = ilz;
if (lx==1) {
x0 = x[ifx];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==2) {
x0 = x[ifx];
x1 = x[ifx+1];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==3) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==4) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==5) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==6) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==7) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==8) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==9) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==10) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==11) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==12) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==13) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==14) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==15) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==16) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==17) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==18) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
x17 = x[ifx+17];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb; z1 += x17*yb;
ya = y[i-ifx-17]; z0 += x17*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==19) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
x17 = x[ifx+17];
x18 = x[ifx+18];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb; z1 += x17*yb;
ya = y[i-ifx-17]; z0 += x17*ya; z1 += x18*ya;
yb = y[i-ifx-18]; z0 += x18*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==20) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
x17 = x[ifx+17];
x18 = x[ifx+18];
x19 = x[ifx+19];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb; z1 += x17*yb;
ya = y[i-ifx-17]; z0 += x17*ya; z1 += x18*ya;
yb = y[i-ifx-18]; z0 += x18*yb; z1 += x19*yb;
ya = y[i-ifx-19]; z0 += x19*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==21) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
x17 = x[ifx+17];
x18 = x[ifx+18];
x19 = x[ifx+19];
x20 = x[ifx+20];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb; z1 += x17*yb;
ya = y[i-ifx-17]; z0 += x17*ya; z1 += x18*ya;
yb = y[i-ifx-18]; z0 += x18*yb; z1 += x19*yb;
ya = y[i-ifx-19]; z0 += x19*ya; z1 += x20*ya;
yb = y[i-ifx-20]; z0 += x20*yb;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==22) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];
x17 = x[ifx+17];
x18 = x[ifx+18];
x19 = x[ifx+19];
x20 = x[ifx+20];
x21 = x[ifx+21];
for (i=ilow; i<=ihigh-1; i+=2) {
ya = y[i+1-ifx]; z1 = x0*ya;
yb = y[i-ifx]; z0 = x0*yb; z1 += x1*yb;
ya = y[i-ifx-1]; z0 += x1*ya; z1 += x2*ya;
yb = y[i-ifx-2]; z0 += x2*yb; z1 += x3*yb;
ya = y[i-ifx-3]; z0 += x3*ya; z1 += x4*ya;
yb = y[i-ifx-4]; z0 += x4*yb; z1 += x5*yb;
ya = y[i-ifx-5]; z0 += x5*ya; z1 += x6*ya;
yb = y[i-ifx-6]; z0 += x6*yb; z1 += x7*yb;
ya = y[i-ifx-7]; z0 += x7*ya; z1 += x8*ya;
yb = y[i-ifx-8]; z0 += x8*yb; z1 += x9*yb;
ya = y[i-ifx-9]; z0 += x9*ya; z1 += x10*ya;
yb = y[i-ifx-10]; z0 += x10*yb; z1 += x11*yb;
ya = y[i-ifx-11]; z0 += x11*ya; z1 += x12*ya;
yb = y[i-ifx-12]; z0 += x12*yb; z1 += x13*yb;
ya = y[i-ifx-13]; z0 += x13*ya; z1 += x14*ya;
yb = y[i-ifx-14]; z0 += x14*yb; z1 += x15*yb;
ya = y[i-ifx-15]; z0 += x15*ya; z1 += x16*ya;
yb = y[i-ifx-16]; z0 += x16*yb; z1 += x17*yb;
ya = y[i-ifx-17]; z0 += x17*ya; z1 += x18*ya;
yb = y[i-ifx-18]; z0 += x18*yb; z1 += x19*yb;
ya = y[i-ifx-19]; z0 += x19*ya; z1 += x20*ya;
yb = y[i-ifx-20]; z0 += x20*yb; z1 += x21*yb;
ya = y[i-ifx-21]; z0 += x21*ya;
z[i+1] = z1;
z[i] = z0;
}
} else if (lx==23) {
x0 = x[ifx];
x1 = x[ifx+1];
x2 = x[ifx+2];
x3 = x[ifx+3];
x4 = x[ifx+4];
x5 = x[ifx+5];
x6 = x[ifx+6];
x7 = x[ifx+7];
x8 = x[ifx+8];
x9 = x[ifx+9];
x10 = x[ifx+10];
x11 = x[ifx+11];
x12 = x[ifx+12];
x13 = x[ifx+13];
x14 = x[ifx+14];
x15 = x[ifx+15];
x16 = x[ifx+16];