- initial import

git-svn-id: http://moon:8086/svn/mips@1 a8ebac50-d88d-4704-bea3-6648445a41b3
2014-07-20 15:01:37 +00:00
commit 26291bca3d
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+/* +++Date last modified: 05-Jul-1997 */
+
+#include <string.h>
+#include "snipmath.h"
+
+#define BITSPERLONG 32
+
+#define TOP2BITS(x) ((x & (3L << (BITSPERLONG-2))) >> (BITSPERLONG-2))
+
+
+/* usqrt:
+    ENTRY x: unsigned long
+    EXIT  returns floor(sqrt(x) * pow(2, BITSPERLONG/2))
+
+    Since the square root never uses more than half the bits
+    of the input, we use the other half of the bits to contain
+    extra bits of precision after the binary point.
+
+    EXAMPLE
+        suppose BITSPERLONG = 32
+        then    usqrt(144) = 786432 = 12 * 65536
+                usqrt(32) = 370727 = 5.66 * 65536
+
+    NOTES
+        (1) change BITSPERLONG to BITSPERLONG/2 if you do not want
+            the answer scaled.  Indeed, if you want n bits of
+            precision after the binary point, use BITSPERLONG/2+n.
+            The code assumes that BITSPERLONG is even.
+        (2) This is really better off being written in assembly.
+            The line marked below is really a "arithmetic shift left"
+            on the double-long value with r in the upper half
+            and x in the lower half.  This operation is typically
+            expressible in only one or two assembly instructions.
+        (3) Unrolling this loop is probably not a bad idea.
+
+    ALGORITHM
+        The calculations are the base-two analogue of the square
+        root algorithm we all learned in grammar school.  Since we're
+        in base 2, there is only one nontrivial trial multiplier.
+
+        Notice that absolutely no multiplications or divisions are performed.
+        This means it'll be fast on a wide range of processors.
+*/
+
+void usqrt(unsigned long x, struct int_sqrt *q)
+{
+      unsigned long a = 0L;                   /* accumulator      */
+      unsigned long r = 0L;                   /* remainder        */
+      unsigned long e = 0L;                   /* trial product    */
+
+      int i;
+
+      for (i = 0; i < BITSPERLONG; i++)   /* NOTE 1 */
+      {
+            r = (r << 2) + TOP2BITS(x); x <<= 2; /* NOTE 2 */
+            a <<= 1;
+            e = (a << 1) + 1;
+            if (r >= e)
+            {
+                  r -= e;
+                  a++;
+            }
+      }
+      memcpy(q, &a, sizeof(long));
+}
+
+#ifdef TEST
+
+#include <stdio.h>
+#include <stdlib.h>
+
+main(void)
+{
+      int i;
+      unsigned long l = 0x3fed0169L;
+      struct int_sqrt q;
+
+      for (i = 0; i < 101; ++i)
+      {
+            usqrt(i, &q);
+            printf("sqrt(%3d) = %2d, remainder = %2d\n",
+                  i, q.sqrt, q.frac);
+      }
+      usqrt(l, &q);
+      printf("\nsqrt(%lX) = %X, remainder = %X\n", l, q.sqrt, q.frac);
+      return 0;
+}
+
+#endif /* TEST */