Compute (approximations to) integer square roots.

diff --git a/mp-sqrt.c b/mp-sqrt.c
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+/* -*-c-*-
+ *
+ * $Id: mp-sqrt.c,v 1.1 2000/06/22 19:01:44 mdw Exp $
+ *
+ * Compute integer square roots
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------* 
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ * 
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU Library General Public License for more details.
+ * 
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mp-sqrt.c,v $
+ * Revision 1.1  2000/06/22 19:01:44  mdw
+ * Compute (approximations to) integer square roots.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mp_sqrt@ --- *
+ *
+ * Arguments:  @mp *d@ = pointer to destination integer
+ *             @mp *a@ = (nonnegative) integer to take square root of
+ *
+ * Returns:    The largest integer %$x$% such that %$x^2 \le a$%.
+ *
+ * Use:                Computes integer square roots.
+ *
+ *             The current implementation isn't very good: it uses the
+ *             Newton-Raphson method to find an approximation to %$a$%.  If
+ *             there's any demand for a better version, I'll write one.
+ */
+
+mp *mp_sqrt(mp *d, mp *a)
+{
+  unsigned long z;
+  mp *q = MP_NEW, *r = MP_NEW;
+
+  /* --- Sanity preservation --- */
+
+  assert(((void)"imaginary root in mp_sqrt", !(a->f & MP_NEG)));
+
+  /* --- Deal with trivial cases --- */
+
+  MP_SHRINK(a);
+  if (a->v == a->vl) {
+    if (d)
+      mp_drop(d);
+    return (MP_ZERO);
+  }
+
+  /* --- Find an initial guess of about the right size --- */
+
+  z = mp_bits(a);
+  z >>= 1;
+  mp_copy(a);
+  d = mp_lsr(d, a, z);
+  mp_drop(a);
+
+  /* --- Main approximation --- *
+   *
+   * We use the Newton-Raphson recurrence relation
+   *
+   *   %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
+   *
+   * We inspect the term %$q = x^2 - a$% to see when to stop.  Increasing
+   * %$x$% is pointless when %$-q < 2 x + 1$%.
+   */
+
+  for (;;) {
+    q = mp_sqr(q, d);
+    q = mp_sub(q, q, a);
+    if (q->v == q->vl)
+      break;
+    if (q->f & MP_NEG) {
+      r = mp_lsl(r, d, 1);
+      r->f |= MP_NEG;
+      if (MP_CMP(q, <=, r))
+       break;
+    }
+    mp_div(&r, &q, q, d);
+    r = mp_lsr(r, r, 1);
+    if (r->v == r->vl)
+      d = mp_sub(d, d, MP_ONE);
+    else
+      d = mp_sub(d, d, r);
+  }
+
+  /* --- Finished, at last --- */
+
+  mp_drop(q);
+  if (r)
+    mp_drop(r);
+  return (d);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include <mLib/testrig.h>
+
+static int verify(dstr *v)
+{
+  mp *a = *(mp **)v[0].buf;
+  mp *qq = *(mp **)v[1].buf;
+  mp *q = mp_sqrt(MP_NEW, a);
+  int ok = 1;
+
+  if (MP_CMP(q, !=, qq)) {
+    ok = 0;
+    fputs("\n*** sqrt failed", stderr);
+    fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 10);
+    fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10);
+    fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10);
+    fputc('\n', stderr);
+  }
+
+  mp_drop(a);
+  mp_drop(q);
+  mp_drop(qq);
+  assert(mparena_count(MPARENA_GLOBAL) == 0);
+
+  return (ok);
+}
+
+static test_chunk tests[] = {
+  { "sqrt", verify, { &type_mp, &type_mp, 0 } },
+  { 0, 0, { 0 } },
+};
+
+int main(int argc, char *argv[])
+{
+  sub_init();
+  test_run(argc, argv, tests, SRCDIR "/tests/mp");
+  return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/