Data commit

Task/Isqrt-integer-square-root-of-X/UNIX-Shell/isqrt-integer-square-root-of-x.sh

@@ -0,0 +1,58 @@
+function isqrt {
+  typeset -i x
+  for x; do
+    typeset -i q=1
+    while (( q <= x )); do
+      (( q <<= 2 ))
+      if (( q <= 0 )); then
+        return 1
+      fi
+    done
+    typeset -i z=x
+    typeset -i r=0
+    typeset -i t
+    while (( q > 1 )); do
+      (( q >>= 2 ))
+      (( t = z - r - q ))
+      (( r >>= 1 ))
+      if (( t >= 0 )); then
+        (( z = t ))
+        (( r = r + q ))
+      fi
+    done
+    printf '%d\n' "$r"
+  done
+}
+
+# demo
+printf 'isqrt(n) for n from 0 to 65:\n'
+for i in {1..4}; do
+  for n in {0..65}; do
+    case $i in
+     1)
+      (( tens=n/10 ))
+      if (( tens )); then
+        printf '%2d' "$tens"
+      else
+        printf '  '
+      fi
+      ;;
+     2) printf '%2d' $(( n%10 ));;
+     3) printf -- '--';;
+     4) printf '%2d' "$(isqrt "$n")";;
+    esac
+  done
+  printf '\n'
+done
+printf '\n'
+
+printf 'isqrt(7ⁿ) for odd n up to the limit of integer precision:\n'
+printf '%2s|%27sⁿ|%14sⁿ)\n' "n" "7" "isqrt(7"
+for (( i=0;i<48; ++i )); do printf '-'; done; printf '\n'
+for (( p=1; p<=73 && (n=7**p) > 0; p+=2)); do
+  if r=$(isqrt $n); then
+    printf "%2d|%'28d|%'16d\n" "$p" "$n" "$r"
+  else
+    break
+  fi
+done