Update tsub-ok.c

chapter2/code/floats/float-twice.c

@@ -18,8 +18,8 @@ float_bits float_twice(float_bits f) {
   if (exp == 0) {
     /* Denormalized */
     frac <<= 1;
-  } else if (exp == 0xFF - 1) {
-    /* twice to oo */
+  } else if (exp == 0xFE || exp == 0xFF) {
+    /* twice to INF */
     exp = 0xFF;
     frac = 0;
   } else {

chapter2/code/tsub-ok.c

@@ -2,27 +2,60 @@
  * tsub-ok.c
  */
 #include <stdio.h>
-#include <assert.h>
 #include <limits.h>
+#include <assert.h>
 
-/* Determine whether arguments can be substracted without overflow */
-int tsub_ok(int x, int y) {
-  if (y == INT_MIN) {
-    return 0;
-  }
+int tsub_ok(int x, int y)
+{
+    int is_ok = 1;
 
-  int neg_y = -y;
-  int sum = x + neg_y;
-  int pos_over = x > 0 && neg_y > 0 && sum < 0;
-  int neg_over = x < 0 && neg_y < 0 && sum >= 0;
+    is_ok &= (y != INT_MIN);
 
-  return !(pos_over || neg_over);
-}
+    int sub = x - y;
+    int sig_mask = INT_MIN;
+
+    int x_is_neg = x & sig_mask;
+    int x_is_pos = !x_is_neg && x != 0;
+    int y_is_neg = y & sig_mask;
+    int y_is_pos = !y_is_neg && y != 0;
+    int sub_is_not_neg = !(sub & sig_mask);
+    int sub_is_not_pos = (sub & sig_mask) | sub == 0;
+
+    int pos_over = x_is_pos && y_is_neg && sub_is_not_pos;
+    int neg_over = x_is_neg && y_is_pos && sub_is_not_neg;
+
+    is_ok &= !pos_over;
+    is_ok &= !neg_over;
 
-int main(int argc, char* argv[]) {
-  assert(!tsub_ok(0x00, INT_MIN));
-  assert(tsub_ok(0x00, 0x00));
-  return 0;
+    return is_ok;
 }
 
+int main()
+{
 
+    // y 为 INT_MIN 导致溢出
+    int x = 0x12345678;
+    int y = INT_MIN;
+    printf("tsub_ok(0x%08x, 0x%08x) = %d\n", x, y, tsub_ok(x, y));
+    assert(!tsub_ok(x, y));
+
+    // sub 为正溢出
+    x = INT_MAX;
+    y = INT_MIN + 1;
+    printf("tsub_ok(0x%08x, 0x%08x) = %d\n", x, y, tsub_ok(x, y));
+    assert(!tsub_ok(x, y));
+
+    // sub 为负溢出
+    x = INT_MIN;
+    y = INT_MAX;
+    printf("tsub_ok(0x%08x, 0x%08x) = %d\n", x, y, tsub_ok(x, y));
+    assert(!tsub_ok(x, y));
+
+    // sub is ok
+    x = 0x77654321;
+    y = 0x12345678;
+    printf("tsub_ok(0x%08x, 0x%08x) = %d\n", x, y, tsub_ok(x, y));
+    assert(tsub_ok(x, y));
+
+    return 0;
+}

chapter2/code/unsigned-high-prod.c

@@ -3,33 +3,47 @@
  */
 #include <stdio.h>
 #include <assert.h>
+#include <limits.h>
 #include <inttypes.h>
 
-int signed_high_prod(int x, int y) {
-  int64_t mul = (int64_t) x * y;
-  return mul >> 32;
+int signed_high_prod(int x, int y)
+{
+    int64_t mul = (int64_t)x * y;
+    int res = mul >> 32;
+    return res;
 }
 
-unsigned unsigned_high_prod(unsigned x, unsigned y) {
-  /* TODO calculations */
-  int sig_x = x >> 31;
-  int sig_y = y >> 31;
-  int signed_prod = signed_high_prod(x, y);
-  return signed_prod + x * sig_y + y * sig_x;
-}
+unsigned unsigned_high_prod(unsigned x, unsigned y)
+{
 
-/* a theorically correct version to test unsigned_high_prod func */
-unsigned another_unsigned_high_prod(unsigned x, unsigned y) {
-  uint64_t mul = (uint64_t) x * y;
-  return mul >> 32;
-}
+    unsigned hp = signed_high_prod(x, y);
+
+    int sig_mask = INT_MIN;
+
+    /**
+     * 68 页的 (2-18) 中
+     * 带有 2^w 权重的项会出现在高 w 位中
+     */
 
-int main(int argc, char* argv[]) {
-  unsigned x = 0x12345678;
-  unsigned y = 0xFFFFFFFF;
+    (x & sig_mask) && (hp += y);
+    (y & sig_mask) && (hp += x);
 
-  assert(another_unsigned_high_prod(x, y) == unsigned_high_prod(x, y));
-  return 0;
+    return hp;
 }
 
+unsigned unsigned_high_prod_2(unsigned x, unsigned y)
+{
+    uint64_t mul = (uint64_t)x * y;
+    return mul >> 32;
+}
+
+int main(int argc, char *argv[])
+{
+    unsigned x = 0x12345678;
+    unsigned y = 0xFFFFFFFF;
 
+    printf("unsigned(%X, %X) = %X\n", x, y, unsigned_high_prod(x, y));
+    assert(unsigned_high_prod_2(x, y) == unsigned_high_prod(x, y));
+
+    return 0;
+}