다시 생각해 보는 Java 의 Native Number

Java 에는 부호 없는 native 정수 타입이 없다.

Java 8에 와서야 부호 없는 정수를 처리하기 위한 메서드 몇 개가 추가되었다.

예를 들어, String을 native 타입 number로 변환하는 스태틱 메서드

        Long.parseUnsignedLong(String),  Integer.parseUnsignedint(String),

       Short.parseUnsignedShort(String),  Byte.parseUnsignedByte(String),

들과 역으로 native 타입 number를 String으로 변환하는 스태틱 메서드

        Long.toUnsignedString(long),  Integer.toUnsignedString(int)

가 있는데 이들은 타입 캐스팅할 댸 주의해야 할 부분이 있다.

아래의 Java 소스는 overflow 와 관련하여 심각한 문제가 발생할 수

있음을 보여 준다.

 

 

//  Filename: About_Java_Native_Number.java
//
//       Re-consider Java's native numbers (int or long or double) near to theirs maximal valuea
//
//
//  Compile: javac -d . About_Java_Native_Number.java
//  Execute: java About_Java_Native_Number
//
//
// Date: 2023.10.22


public class About_Java_Native_Number
{

    public static void main(String[] args)
    { 
        System.out.printf("What is pow(2, 30) = 2**30 (using Python's integer power operator expression)\n");
        System.out.printf("                   = 1 << 30 (using intege's shift opertor expression)\n");
        System.out.printf("                   = 2^30 (in LaTeX' math expression)\n");
        System.out.printf("\n");

        System.out.printf("Math.pow(2, 30) == %s\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %e\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %.9e\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %g\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %.0g\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %.9g\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %f\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %.0f\n", Math.pow(2, 30));
        System.out.printf("Math.pow(2, 30) == %a\n", Math.pow(2, 30));
        System.out.printf("\n");

        System.out.printf("1 << 30 = %d\n", 1 << 30);
        System.out.printf("(1 << 30) + (1 << 30) = %d\n", (1 << 30) + (1 << 30) );
        System.out.printf("(1 << 30)*2 = %d\n", (1 << 30)*2);
        System.out.printf("1 << (1 << 30) << 1 = %d\n", (1 << 30) << 1 );
        System.out.printf("0x7FFFFFFF = %d\n", 0x7FFFFFFF);
        System.out.printf("0x7FFFFFFF + 1 = %d\n", 0x7FFFFFFF + 1);
        System.out.printf("0x7FFFFFFF + 2 = %d\n", 0x7FFFFFFF + 2);
        System.out.printf("0x7FFFFFFF + 2 = %d\n", 0x7FFFFFFF + 2);
        System.out.printf("0x7FFFFFFF + 1 - 1 = %d\n", 0x7FFFFFFF + 1 - 1);
        System.out.printf("0x7FFFFFFF + 2 - 2 = %d\n", 0x7FFFFFFF + 2 - 2);
        System.out.printf("0x7FFFFFFF + 3 - 3 = %d\n", 0x7FFFFFFF + 3 - 3);
        System.out.printf("\n");

        System.out.printf("Is it true that (0x7FFFFFFF + 1) - 1 = (%d + 1) - 1 = %d - 1 = %d ?\n", 0x7FFFFFFF, 0x7FFFFFFF + 1, (0x7FFFFFFF + 1) - 1);
        System.out.printf("Is it true that (0x7FFFFFFF + 2) - 2 = (%d + 2) - 2 = %d - 2 = %d ?\n", 0x7FFFFFFF, 0x7FFFFFFF + 2, (0x7FFFFFFF + 1) - 2);
        System.out.printf("Is it true that (0x7FFFFFFF + 3) - 3 = (%d + 3) - 3 = %d - 3 = %d ?\n", 0x7FFFFFFF, 0x7FFFFFFF + 3, (0x7FFFFFFF + 1) - 3);
        System.out.printf("\n");

        System.out.printf("It is true that 1 << 30 = %d\n", 1 << 30);
        System.out.printf("But, is it true that (1 << 30)*2/2 = (%d)*2/2 = %d/2 = %d ?\n", 1 << 30, (1 << 30)*2,  (1 << 30)*2/2);
        System.out.printf("And, is it true that (1 << 30)*2/4 = (%d)*2/4 = %d/4 = %d ?\n", 1 << 30, (1 << 30)*2,  (1 << 30)*2/4);
        System.out.printf("And, is it true that (1 << 30)*2/8 = (%d)*2/8 = %d/8 = %d ?\n", 1 << 30, (1 << 30)*2,  (1 << 30)*2/8);
        System.out.printf("\n");

        System.out.printf("Also, is it true that (1 << 30)*4/2 = (%d)*4/2 = %d/2 = %d ?\n", 1 << 30, (1 << 30)*4,  (1 << 30)*4/2);
        System.out.printf("Also, is it true that ((1 << 30)*4 + 1234567)/2 = ((%d)*4 + 1234567)/2 = (%d + 1234567)/2 = %d ?\n", 1 << 30, (1 << 30)*4,  ((1 << 30)*4 + 1234567)/2);
        System.out.printf("Then, is it true that (Math.pow(2, 30)*4 + 1234567)/2 = ((%.0f)*4 + 1234567)/2 = (%.0f + 1234567)/2 = %.0f ?\n", Math.pow(2, 30), Math.pow(2, 30)*4,  (Math.pow(2, 30)*4 + 1234567)/2);


        System.out.printf("In is known that Math.pow(2, 30) == (1 << 30) ? %s\n", Math.pow(2, 30) == (1 << 30));
        System.out.printf("\n");

        System.out.printf("Long.toUnsignedString((byte)0xFFL) = %s\n", Long.toUnsignedString((byte)0xFFL));
        System.out.printf("Long.toUnsignedString(0xFFL) = %s\n", Long.toUnsignedString(0xFFL));
        System.out.printf("Integer.toUnsignedString((byte)0xFFL) = %s\n", Integer.toUnsignedString((byte)0xFFL));
        System.out.printf("Integer.toUnsignedString(0xFF) = %s\n", Integer.toUnsignedString(0xFF));
        System.out.printf("Integer.toUnsignedString(0xFFFFFFFFFF) = %s\n", Integer.toUnsignedString(0xFFFFFFFF));
        System.out.printf("Long.toUnsignedString(0xFFFFFFFFFF) = %s\n", Long.toUnsignedString(0xFFFFFFFF));
        System.out.printf("Long.toUnsignedString(0x100000000L) = %s\n", Long.toUnsignedString(0x100000000L));
        System.out.printf("Long.toUnsignedString(0xFFFFFFFFFFFFFFFFL) = %s\n", Long.toUnsignedString(0xFFFFFFFFFFFFFFFFL));
        System.out.printf("Long.toUnsignedString(0x8000000000000000L) = %s\n", Long.toUnsignedString(0x8000000000000000L));
        System.out.printf("Long.toString(0xFFFFFFFFFFFFFFFFL) = %s\n", Long.toString(0xFFFFFFFFFFFFFFFFL));
        System.out.printf("Long.toString(0x8000000000000000L) = %s\n", Long.toString(0x8000000000000000L));
        System.out.printf("\n");

    }
}

/*
---------
 Output:
---------

What is pow(2, 30) = 2**30 (using Python's integer power operator expression)
                   = 1 << 30 (using intege's shift opertor expression)
                   = 2^30 (in LaTeX' math expression)

Math.pow(2, 30) == 1.073741824E9
Math.pow(2, 30) == 1.073742e+09
Math.pow(2, 30) == 1.073741824e+09
Math.pow(2, 30) == 1.07374e+09
Math.pow(2, 30) == 1e+09
Math.pow(2, 30) == 1.07374182e+09
Math.pow(2, 30) == 1073741824.000000
Math.pow(2, 30) == 1073741824
Math.pow(2, 30) == 0x1.0p30

1 << 30 = 1073741824
(1 << 30) + (1 << 30) = -2147483648
(1 << 30)*2 = -2147483648
1 << (1 << 30) << 1 = -2147483648
0x7FFFFFFF = 2147483647
0x7FFFFFFF + 1 = -2147483648
0x7FFFFFFF + 2 = -2147483647
0x7FFFFFFF + 2 = -2147483647
0x7FFFFFFF + 1 - 1 = 2147483647
0x7FFFFFFF + 2 - 2 = 2147483647
0x7FFFFFFF + 3 - 3 = 2147483647

Is it true that (0x7FFFFFFF + 1) - 1 = (2147483647 + 1) - 1 = -2147483648 - 1 = 2147483647 ?
Is it true that (0x7FFFFFFF + 2) - 2 = (2147483647 + 2) - 2 = -2147483647 - 2 = 2147483646 ?
Is it true that (0x7FFFFFFF + 3) - 3 = (2147483647 + 3) - 3 = -2147483646 - 3 = 2147483645 ?

It is true that 1 << 30 = 1073741824
But, is it true that (1 << 30)*2/2 = (1073741824)*2/2 = -2147483648/2 = -1073741824 ?
And, is it true that (1 << 30)*2/4 = (1073741824)*2/4 = -2147483648/4 = -536870912 ?
And, is it true that (1 << 30)*2/8 = (1073741824)*2/8 = -2147483648/8 = -268435456 ?

Also, is it true that (1 << 30)*4/2 = (1073741824)*4/2 = 0/2 = 0 ?
Also, is it true that ((1 << 30)*4 + 1234567)/2 = ((1073741824)*4 + 1234567)/2 = (0 + 1234567)/2 = 617283 ?
Then, is it true that (Math.pow(2, 30)*4 + 1234567)/2 = ((1073741824)*4 + 1234567)/2 = (4294967296 + 1234567)/2 = 2148100932 ?
In is known that Math.pow(2, 30) == (1 << 30) ? true

Long.toUnsignedString((byte)0xFFL) = 18446744073709551615
Long.toUnsignedString(0xFFL) = 255
Integer.toUnsignedString((byte)0xFFL) = 4294967295
Integer.toUnsignedString(0xFF) = 255
Integer.toUnsignedString(0xFFFFFFFFFF) = 4294967295
Long.toUnsignedString(0xFFFFFFFFFF) = 18446744073709551615
Long.toUnsignedString(0x100000000L) = 4294967296
Long.toUnsignedString(0xFFFFFFFFFFFFFFFFL) = 18446744073709551615
Long.toUnsignedString(0x8000000000000000L) = 9223372036854775808
Long.toString(0xFFFFFFFFFFFFFFFFL) = -1
Long.toString(0x8000000000000000L) = -9223372036854775808
*/