Play the behavior of MAX_VALUE and MIN_VALUE

Question

The following also applies to others MIN_VALUEand MAX_VALUE, but now focus only on Integer. I know that in Java, integers are 32-bit, with Integer.MAX_VALUE = 2147483647(2 ³¹ -1) and Integer.MIN_VALUE = -2147483648(-2 ³¹ ). When calculating with these values, when you go beyond your borders, the number wraps around / overflows. Therefore, when you do something like Integer.MAX_VALUE + 1, the result will be the same as Integer.MIN_VALUE.

Here are some basic arithmetic calculations with MIN_VALUEand MAX_VALUE:

Integer.MAX_VALUE:                      2147483647
Integer.MAX_VALUE + 1:                  -2147483648
Integer.MAX_VALUE - 1:                  2147483646
Integer.MAX_VALUE * 2:                  -2
Integer.MAX_VALUE * 3:                  2147483645
Integer.MAX_VALUE * 4:                  -4
Integer.MAX_VALUE * 5:                  2147483643
Integer.MAX_VALUE / Integer.MAX_VALUE:  1
Integer.MAX_VALUE * Integer.MAX_VALUE:  1
Integer.MAX_VALUE / Integer.MIN_VALUE:  0
Integer.MAX_VALUE * Integer.MIN_VALUE:  -2147483648
Integer.MAX_VALUE - Integer.MIN_VALUE:  -1
Integer.MAX_VALUE + Integer.MIN_VALUE:  -1
-Integer.MAX_VALUE:                     -2147483647
-Integer.MAX_VALUE - 1:                 -2147483648
-Integer.MAX_VALUE + 1:                 -2147483646
Integer.MIN_VALUE:                      -2147483648
Integer.MIN_VALUE + 1:                  -2147483647
Integer.MIN_VALUE - 1:                  2147483647
Integer.MIN_VALUE * 2:                  0
Integer.MIN_VALUE * 3:                  -2147483648
Integer.MIN_VALUE * 4:                  0
Integer.MIN_VALUE * 5:                  -2147483648
Integer.MIN_VALUE / Integer.MAX_VALUE:  -1
Integer.MIN_VALUE / Integer.MIN_VALUE:  1
Integer.MIN_VALUE * Integer.MIN_VALUE:  0
Integer.MIN_VALUE - Integer.MAX_VALUE:  1
-Integer.MIN_VALUE:                     -2147483648
-Integer.MIN_VALUE - 1:                 2147483647
-Integer.MIN_VALUE + 1:                 -2147483647

Or more generally (iff MIN == -MAX-1):

MAX:                      MAX
MAX + 1:                  MIN
MAX - 1:                  MAX - 1
MAX * 2:                  -2
MAX * 3:                  MAX - 2
MAX * 4:                  -4
MAX * 5:                  MAX - 4
MAX / MAX:                1
MAX * MAX:                1
MAX / MIN:                0
MAX * MIN:                MIN
MAX - MIN:                -1
MAX + MIN:                -1
-MAX:                     MIN + 1
-MAX - 1:                 MIN
-MAX + 1                  MIN + 2
MIN:                      MIN
MIN + 1:                  MIN + 1
MIN - 1:                  MAX
MIN * 2:                  0
MIN * 3:                  MIN
MIN * 4:                  0
MIN * 5:                  MIN
MIN / MAX:                -1
MIN / MIN:                1
MIN * MIN:                0
MIN - MAX:                1
-MIN:                     MIN
-MIN - 1:                 MAX
-MIN + 1:                 MIN + 1

My question is: how can I manually reproduce all the basic arithmetic operations ( +-*/) manually?

, , modulo. :

long reproduceMinMaxFromLongToInt(long n){
  if(n > 2147483647L){
    return n % 2147483648L;
  }
  if(n < -2147483648L){
    return n % -2147483648L;
  }
  return n;
}

, . ( , TIO , - .) :

Calculation:                Should be       But is instead

MAX_VALUE + 1:              -2147483648     0
MAX_VALUE * 2:              -2              2147483646
MAX_VALUE * 4:              -4              2147483644
MAX_VALUE * MIN_VALUE:      -2147483648     0
MAX_VALUE - MIN_VALUE:      -1              2147483647
MIN_VALUE - 1:              2147483647      -1
MIN_VALUE * 3:              -2147483648     0
MIN_VALUE * 5:              -2147483648     0
-MIN_VALUE - 1:             2147483647      2147483647

.

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Answer 1

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long reproduceMinMaxFromLongToInt(long n){
    // reduce range
    n = Long.remainderUnsigned(n, 1L << 32);
    // sign-extend
    if (n < (1L << 31))
        return n;
    else
        return n - (1L << 32);
}

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Answer 2

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