magicu.c.txt

// Computes the magic number for unsigned division.
// Max line length is 57, to fit in hacker.book.
#include <stdlib.h>
#include <stdio.h>
// ------------------------------ cut ----------------------------------
struct mu {unsigned M;     // Magic number,
          int a;           // "add" indicator,
          int s;};         // and shift amount.
// ---------------------------- end cut --------------------------------

int main() {
   struct mu magicu(unsigned);
   struct mu magicu2(unsigned);
   struct mu mag;

   mag = magicu(3);
   printf("M = %08x a = %d s = %d\n", mag.M, mag.a, mag.s);
   if (mag.M + mag.a + mag.s != 0xAAAAAAAB + 0 + 1) return 1;
   mag = magicu(7);
   printf("M = %08x a = %d s = %d\n", mag.M, mag.a, mag.s);
   if (mag.M + mag.a + mag.s != 0x24924925 + 1 + 3) return 2;

   mag = magicu2(3);
   printf("M = %08x a = %d s = %d\n", mag.M, mag.a, mag.s);
   if (mag.M + mag.a + mag.s != 0xAAAAAAAB + 0 + 1) return 11;
   mag = magicu2(7);
   printf("M = %08x a = %d s = %d\n", mag.M, mag.a, mag.s);
   if (mag.M + mag.a + mag.s != 0x24924925 + 1 + 3) return 12;
   return 0;
}

// ------------------------------ cut ----------------------------------
struct mu magicu(unsigned d) {
                           // Must have 1 <= d <= 2**32-1.
   int p;
   unsigned nc, delta, q1, r1, q2, r2;
   struct mu magu;

   magu.a = 0;             // Initialize "add" indicator.
   nc = -1 - (-d)%d;       // Unsigned arithmetic here.
   p = 31;                 // Init. p.
   q1 = 0x80000000/nc;     // Init. q1 = 2**p/nc.
   r1 = 0x80000000 - q1*nc;// Init. r1 = rem(2**p, nc).
   q2 = 0x7FFFFFFF/d;      // Init. q2 = (2**p - 1)/d.
   r2 = 0x7FFFFFFF - q2*d; // Init. r2 = rem(2**p - 1, d).
   do {
      p = p + 1;
      if (r1 >= nc - r1) {
         q1 = 2*q1 + 1;            // Update q1.
         r1 = 2*r1 - nc;}          // Update r1.
      else {
         q1 = 2*q1;
         r1 = 2*r1;}
      if (r2 + 1 >= d - r2) {
         if (q2 >= 0x7FFFFFFF) magu.a = 1;
         q2 = 2*q2 + 1;            // Update q2.
         r2 = 2*r2 + 1 - d;}       // Update r2.
      else {
         if (q2 >= 0x80000000) magu.a = 1;
         q2 = 2*q2;
         r2 = 2*r2 + 1;}
      delta = d - 1 - r2;
   } while (p < 64 &&
           (q1 < delta || (q1 == delta && r1 == 0)));

   magu.M = q2 + 1;        // Magic number
   magu.s = p - 32;        // and shift amount to return
   return magu;            // (magu.a was set above).
}
// ---------------------------- end cut --------------------------------

// ------------------------------ cut ----------------------------------
struct mu magicu2(unsigned d) {
                           // Must have 1 <= d <= 2**32-1.
   int p;
   unsigned p32, q, r, delta;
   struct mu magu;
   magu.a = 0;             // Initialize "add" indicator.
   p = 31;                 // Initialize p.
   q = 0x7FFFFFFF/d;       // Initialize q = (2**p - 1)/d.
   r = 0x7FFFFFFF - q*d;   // Init. r = rem(2**p - 1, d).
   do {
      p = p + 1;
      if (p == 32) p32 = 1;     // Set p32 = 2**(p-32).
      else p32 = 2*p32;
      if (r + 1 >= d - r) {
         if (q >= 0x7FFFFFFF) magu.a = 1;
         q = 2*q + 1;           // Update q.
         r = 2*r + 1 - d;       // Update r.
      }
      else {
         if (q >= 0x80000000) magu.a = 1;
         q = 2*q;
         r = 2*r + 1;
      }
      delta = d - 1 - r;
   } while (p < 64 && p32 < delta);
   magu.M = q + 1;         // Magic number and
   magu.s = p - 32;        // shift amount to return
   return magu;            // (magu.a was set above).
}
// ---------------------------- end cut --------------------------------