add basecase _fmpz_poly_sqrlow

fmpz_poly/sqrlow.c

@@ -21,6 +21,7 @@
 
     Copyright (C) 2008, 2009 William Hart
     Copyright (C) 2010, 2011 Sebastian Pancratz
+    Copyright (C) 2014 Fredrik Johansson
 
 ******************************************************************************/
 
@@ -31,19 +32,133 @@
 #include "fmpz_vec.h"
 #include "fmpz_poly.h"
 
+void _fmpz_poly_sqrlow_tiny1(fmpz * res, const fmpz * poly, slong len, slong n)
+{
+    slong i, j, c;
+
+    _fmpz_vec_zero(res, n);
+
+    for (i = 0; i < len; i++)
+    {
+        c = poly[i];
+
+        if (c != 0)
+        {
+            if (2 * i < n)
+                res[2 * i] += c * c;
+
+            c *= 2;
+
+            for (j = i + 1; j < FLINT_MIN(len, n - i); j++)
+                res[i + j] += poly[j] * c;
+        }
+    }
+}
+
+void _fmpz_poly_sqrlow_tiny2(fmpz * res, const fmpz * poly, slong len, slong n)
+{
+    slong i, j, k, c, d;
+    mp_limb_t hi, lo;
+    mp_ptr tmp;
+    TMP_INIT;
+
+    TMP_START;
+
+    tmp = TMP_ALLOC(2 * n * sizeof(mp_limb_t));
+
+    flint_mpn_zero(tmp, 2 * n);
+
+    for (i = 0; i < len; i++)
+    {
+        c = poly[i];
+
+        if (c != 0)
+        {
+            if (2 * i < n)
+            {
+                smul_ppmm(hi, lo, c, c);
+                add_ssaaaa(tmp[4 * i + 1], tmp[4 * i],
+                           tmp[4 * i + 1], tmp[4 * i], hi, lo);
+            }
+
+            c *= 2;  /* does not overflow */
+
+            for (j = i + 1; j < FLINT_MIN(len, n - i); j++)
+            {
+                k = i + j;
+
+                d = poly[j];
+
+                if (d != 0)
+                {
+                    smul_ppmm(hi, lo, c, d);
+                    add_ssaaaa(tmp[2 * k + 1], tmp[2 * k],
+                               tmp[2 * k + 1], tmp[2 * k], hi, lo);
+                }
+            }
+        }
+    }
+
+    for (i = 0; i < n; i++)
+    {
+        lo = tmp[2 * i];
+        hi = tmp[2 * i + 1];
+
+        if (((mp_limb_signed_t) hi) >= 0)
+        {
+            fmpz_set_uiui(res + i, hi, lo);
+        }
+        else
+        {
+            sub_ddmmss(hi, lo, 0, 0, hi, lo);
+            fmpz_neg_uiui(res + i, hi, lo);
+        }
+    }
+
+    TMP_END;
+    return;
+}
+
 void _fmpz_poly_sqrlow(fmpz * res, const fmpz * poly, slong len, slong n)
 {
     mp_size_t limbs;
+    slong bits, rbits;
 
     len = FLINT_MIN(len, n);
 
+    if (len == 1)
+    {
+        fmpz_mul(res, poly, poly);
+        return;
+    }
+
+    bits = _fmpz_vec_max_bits(poly, len);
+    bits = FLINT_ABS(bits);
+
+    if (bits <= FLINT_BITS - 2 &&
+        (len < 50 + 2 * bits || (4 * len >= 3 * n && n < 140 + 6 * bits)))
+    {
+        rbits = 2 * bits + FLINT_BIT_COUNT(len);
+
+        if (rbits <= FLINT_BITS - 2)
+        {
+            _fmpz_poly_sqrlow_tiny1(res, poly, len, n);
+            return;
+        }
+        else if (rbits <= 2 * FLINT_BITS - 1)
+        {
+            _fmpz_poly_sqrlow_tiny2(res, poly, len, n);
+            return;
+        }
+    }
+
     if (n < 7)
     {
         _fmpz_poly_sqrlow_classical(res, poly, len, n);
         return;
     }
 
-    limbs = _fmpz_vec_max_limbs(poly, len);
+    limbs = (bits + FLINT_BITS - 1) / FLINT_BITS;
 
     if (n < 16 && limbs > 12)
     {