Task: Polynomial long division
C: #include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <assert.h>
#include <gsl/gsl_vector.h>

#define MAX(A,B) (((A)>(B))?(A):(B))

void reoshift(gsl_vector *v, int h)
{
  if ( h > 0 ) {
    gsl_vector *temp = gsl_vector_alloc(v->size);
    gsl_vector_view p = gsl_vector_subvector(v, 0, v->size - h);
    gsl_vector_view p1 = gsl_vector_subvector(temp, h, v->size - h);
    gsl_vector_memcpy(&p1.vector, &p.vector);
    p = gsl_vector_subvector(temp, 0, h);
    gsl_vector_set_zero(&p.vector);
    gsl_vector_memcpy(v, temp);
    gsl_vector_free(temp);
  }
}

gsl_vector *poly_long_div(gsl_vector *n, gsl_vector *d, gsl_vector **r)
{
  gsl_vector *nt = NULL, *dt = NULL, *rt = NULL, *d2 = NULL, *q = NULL;
  int gn, gt, gd;

  if ( (n->size >= d->size) && (d->size > 0) && (n->size > 0) ) {
    nt = gsl_vector_alloc(n->size); assert(nt != NULL);
    dt = gsl_vector_alloc(n->size); assert(dt != NULL);
    rt = gsl_vector_alloc(n->size); assert(rt != NULL);
    d2 = gsl_vector_alloc(n->size); assert(d2 != NULL);
    gsl_vector_memcpy(nt, n);
    gsl_vector_set_zero(dt); gsl_vector_set_zero(rt);
    gsl_vector_view p = gsl_vector_subvector(dt, 0, d->size);
    gsl_vector_memcpy(&p.vector, d);
    gsl_vector_memcpy(d2, dt);
    gn = n->size - 1;
    gd = d->size - 1;
    gt = 0;

    while( gsl_vector_get(d, gd) == 0 ) gd--;
    
    while ( gn >= gd ) {
      reoshift(dt, gn-gd);
      double v = gsl_vector_get(nt, gn)/gsl_vector_get(dt, gn);
      gsl_vector_set(rt, gn-gd, v);
      gsl_vector_scale(dt, v);
      gsl_vector_sub(nt, dt);
      gt = MAX(gt, gn-gd);
      while( (gn>=0) && (gsl_vector_get(nt, gn) == 0.0) ) gn--;
      gsl_vector_memcpy(dt, d2);
    }

    q = gsl_vector_alloc(gt+1); assert(q != NULL);
    p = gsl_vector_subvector(rt, 0, gt+1);
    gsl_vector_memcpy(q, &p.vector);
    if ( r != NULL ) {
      if ( (gn+1) > 0 ) {
	*r = gsl_vector_alloc(gn+1); assert( *r != NULL );
	p = gsl_vector_subvector(nt, 0, gn+1);
	gsl_vector_memcpy(*r, &p.vector);
      } else {
	*r = gsl_vector_alloc(1); assert( *r != NULL );
	gsl_vector_set_zero(*r);
      }
    }
    gsl_vector_free(nt); gsl_vector_free(dt);
    gsl_vector_free(rt); gsl_vector_free(d2);
    return q;
  } else {
    q = gsl_vector_alloc(1); assert( q != NULL );
    gsl_vector_set_zero(q);
    if ( r != NULL ) {
      *r = gsl_vector_alloc(n->size); assert( *r != NULL );
      gsl_vector_memcpy(*r, n);
    }
    return q;
  } 
}

void poly_print(gsl_vector *p)
{
  int i;
  for(i=p->size-1; i >= 0; i--) {
    if ( i > 0 ) 
      printf("%lfx^%d + ", 
	     gsl_vector_get(p, i), i);
    else
      printf("%lf\n", gsl_vector_get(p, i));
  }
}

gsl_vector *create_poly(int d, ...)
{
  va_list al;
  int i;
  gsl_vector *r = NULL;

  va_start(al, d);
  r = gsl_vector_alloc(d); assert( r != NULL );
  
  for(i=0; i < d; i++)
    gsl_vector_set(r, i, va_arg(al, double));

  return r;
}

VB: Option Base 1
Function degree(p As Variant)
    For i = UBound(p) To 1 Step -1
        If p(i) <> 0 Then
            degree = i
            Exit Function
        End If
    Next i
    degree = -1
End Function
 
Function poly_div(ByVal n As Variant, ByVal d As Variant) As Variant
    If UBound(d) < UBound(n) Then
        ReDim Preserve d(UBound(n))
    End If
    Dim dn As Integer: dn = degree(n)
    Dim dd As Integer: dd = degree(d)
    If dd < 0 Then
        poly_div = CVErr(xlErrDiv0)
        Exit Function
    End If
    Dim quot() As Integer
    ReDim quot(dn)
    Do While dn >= dd
        Dim k As Integer: k = dn - dd
        Dim qk As Integer: qk = n(dn) / d(dd)
        quot(k + 1) = qk
        Dim d2() As Variant
        d2 = d
        ReDim Preserve d2(UBound(d) - k)
        For i = 1 To UBound(d2)
            n(UBound(n) + 1 - i) = n(UBound(n) + 1 - i) - d2(UBound(d2) + 1 - i) * qk
        Next i
        dn = degree(n)
    Loop
    poly_div = Array(quot, n) 
End Function
 
Function poly(si As Variant) As String

    Dim r As String
    For t = UBound(si) To 1 Step -1
        Dim sit As Integer: sit = si(t)
        If sit <> 0 Then
            If sit = 1 And t > 1 Then
                r = r & IIf(r = "", "", " + ")
            Else
                If sit = -1 And t > 1 Then
                    r = r & IIf(r = "", "-", " - ")
                Else
                    If r <> "" Then
                        r = r & IIf(sit < 0, " - ", " + ")
                        sit = Abs(sit)
                    End If
                    r = r & CStr(sit)
                End If
            End If
            r = r & IIf(t > 1, "x" & IIf(t > 2, t - 1, ""), "")
        End If
    Next t
    If r = "" Then r = "0"
    poly = r
End Function
 
Function polyn(s As Variant) As String
    Dim t() As String
    ReDim t(2 * UBound(s))
    For i = 1 To 2 * UBound(s) Step 2
        t(i) = poly(s((i + 1) / 2))
    Next i
    t(1) = String$(45 - Len(t(1)) - Len(t(3)), " ") & t(1)
    t(2) = "/"
    t(4) = "="
    t(6) = "rem"
    polyn = Join(t, " ")
End Function
 
Public Sub main()
    Dim tests(7) As Variant
    tests(1) = Array(Array(-42, 0, -12, 1), Array(-3, 1))
    tests(2) = Array(Array(-3, 1), Array(-42, 0, -12, 1))
    tests(3) = Array(Array(-42, 0, -12, 1), Array(-3, 1, 1))
    tests(4) = Array(Array(2, 3, 1), Array(1, 1))
    tests(5) = Array(Array(3, 5, 6, -4, 1), Array(1, 2, 1))
    tests(6) = Array(Array(3, 0, 7, 0, 0, 0, 0, 0, 3, 0, 0, 1), Array(1, 0, 0, 5, 0, 0, 0, 1))
    tests(7) = Array(Array(-56, 87, -94, -55, 22, -7), Array(2, 0, 1))
    Dim num As Variant, denom As Variant, quot As Variant, rmdr As Variant
    For i = 1 To 7
        num = tests(i)(1)
        denom = tests(i)(2)
        tmp = poly_div(num, denom)
        quot = tmp(1)
        rmdr = tmp(2)
        Debug.Print polyn(Array(num, denom, quot, rmdr))
    Next i
End Sub