When does a floating point number overflow?
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Why is
Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE
=> false
but
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE
=> true
?
My expectation was, that everything I add to the maximum value must overflow.
javascript floating-point
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
add a comment |
Why is
Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE
=> false
but
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE
=> true
?
My expectation was, that everything I add to the maximum value must overflow.
javascript floating-point
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
4
The number overflows when the mantissa and exponent are as "big" as possible. AddingMIN_VALUEdoesn't do that because it's vanishingly small in comparison toMAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
– Pointy
Nov 22 '18 at 14:39
add a comment |
Why is
Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE
=> false
but
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE
=> true
?
My expectation was, that everything I add to the maximum value must overflow.
javascript floating-point
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
Why is
Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE
=> false
but
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE
=> true
?
My expectation was, that everything I add to the maximum value must overflow.
javascript floating-point
javascript floating-point
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
asked Nov 22 '18 at 14:36
cevingceving
10.5k360104
10.5k360104
4
The number overflows when the mantissa and exponent are as "big" as possible. AddingMIN_VALUEdoesn't do that because it's vanishingly small in comparison toMAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
– Pointy
Nov 22 '18 at 14:39
add a comment |
4
The number overflows when the mantissa and exponent are as "big" as possible. AddingMIN_VALUEdoesn't do that because it's vanishingly small in comparison toMAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
– Pointy
Nov 22 '18 at 14:39
4
4
The number overflows when the mantissa and exponent are as "big" as possible. Adding
MIN_VALUE doesn't do that because it's vanishingly small in comparison to MAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.– Pointy
Nov 22 '18 at 14:39
The number overflows when the mantissa and exponent are as "big" as possible. Adding
MIN_VALUE doesn't do that because it's vanishingly small in comparison to MAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.– Pointy
Nov 22 '18 at 14:39
add a comment |
2 Answers
2
active
oldest
votes
Imagine it like this:
MAX_VALUE = Infinite
MIN_VALUE = 0
So, when you add MAX_VALUE with MIN_VALUE it's like you added 0. So it's still MAX_VALUE.
Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
add a comment |
JavaScript’s Number.MAX_VALUE is misnamed. It is not the maximum representable value. It is the maximum representable finite value. The actual maximum representable value is infinity.
If the name were correct, so that Number.MAX_VALUE were infinity, then Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE would be true, because infinity plus infinity is true.
As it is the mathematical value of Number.MAX_VALUE + Number.MAX_VALUE is beyond the representable finite values, so it is rounded to infinity.
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE is true because arithmetic rounds to the nearest representable value, and adding a small value to the maximum finite value produces a result very close to the maximum finite value, so it rounds to the maximum finite value.
(Note: The rule about rounding to the nearest representable value treats infinity as if it were in a normal place at the end of the finite values, so any result that is greater than or equal to Number.MAX_VALUE plus half a “step” beyond it rounds to infinity.)
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
Imagine it like this:
MAX_VALUE = Infinite
MIN_VALUE = 0
So, when you add MAX_VALUE with MIN_VALUE it's like you added 0. So it's still MAX_VALUE.
Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
add a comment |
Imagine it like this:
MAX_VALUE = Infinite
MIN_VALUE = 0
So, when you add MAX_VALUE with MIN_VALUE it's like you added 0. So it's still MAX_VALUE.
Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
add a comment |
Imagine it like this:
MAX_VALUE = Infinite
MIN_VALUE = 0
So, when you add MAX_VALUE with MIN_VALUE it's like you added 0. So it's still MAX_VALUE.
Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
Imagine it like this:
MAX_VALUE = Infinite
MIN_VALUE = 0
So, when you add MAX_VALUE with MIN_VALUE it's like you added 0. So it's still MAX_VALUE.
Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
answered Nov 22 '18 at 14:41
Santiago Mendoza RamirezSantiago Mendoza Ramirez
305321
305321
add a comment |
add a comment |
JavaScript’s Number.MAX_VALUE is misnamed. It is not the maximum representable value. It is the maximum representable finite value. The actual maximum representable value is infinity.
If the name were correct, so that Number.MAX_VALUE were infinity, then Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE would be true, because infinity plus infinity is true.
As it is the mathematical value of Number.MAX_VALUE + Number.MAX_VALUE is beyond the representable finite values, so it is rounded to infinity.
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE is true because arithmetic rounds to the nearest representable value, and adding a small value to the maximum finite value produces a result very close to the maximum finite value, so it rounds to the maximum finite value.
(Note: The rule about rounding to the nearest representable value treats infinity as if it were in a normal place at the end of the finite values, so any result that is greater than or equal to Number.MAX_VALUE plus half a “step” beyond it rounds to infinity.)
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
add a comment |
JavaScript’s Number.MAX_VALUE is misnamed. It is not the maximum representable value. It is the maximum representable finite value. The actual maximum representable value is infinity.
If the name were correct, so that Number.MAX_VALUE were infinity, then Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE would be true, because infinity plus infinity is true.
As it is the mathematical value of Number.MAX_VALUE + Number.MAX_VALUE is beyond the representable finite values, so it is rounded to infinity.
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE is true because arithmetic rounds to the nearest representable value, and adding a small value to the maximum finite value produces a result very close to the maximum finite value, so it rounds to the maximum finite value.
(Note: The rule about rounding to the nearest representable value treats infinity as if it were in a normal place at the end of the finite values, so any result that is greater than or equal to Number.MAX_VALUE plus half a “step” beyond it rounds to infinity.)
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
add a comment |
JavaScript’s Number.MAX_VALUE is misnamed. It is not the maximum representable value. It is the maximum representable finite value. The actual maximum representable value is infinity.
If the name were correct, so that Number.MAX_VALUE were infinity, then Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE would be true, because infinity plus infinity is true.
As it is the mathematical value of Number.MAX_VALUE + Number.MAX_VALUE is beyond the representable finite values, so it is rounded to infinity.
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE is true because arithmetic rounds to the nearest representable value, and adding a small value to the maximum finite value produces a result very close to the maximum finite value, so it rounds to the maximum finite value.
(Note: The rule about rounding to the nearest representable value treats infinity as if it were in a normal place at the end of the finite values, so any result that is greater than or equal to Number.MAX_VALUE plus half a “step” beyond it rounds to infinity.)
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
JavaScript’s Number.MAX_VALUE is misnamed. It is not the maximum representable value. It is the maximum representable finite value. The actual maximum representable value is infinity.
If the name were correct, so that Number.MAX_VALUE were infinity, then Number.MAX_VALUE + Number.MAX_VALUE == Number.MAX_VALUE would be true, because infinity plus infinity is true.
As it is the mathematical value of Number.MAX_VALUE + Number.MAX_VALUE is beyond the representable finite values, so it is rounded to infinity.
Number.MAX_VALUE + Number.MIN_VALUE == Number.MAX_VALUE is true because arithmetic rounds to the nearest representable value, and adding a small value to the maximum finite value produces a result very close to the maximum finite value, so it rounds to the maximum finite value.
(Note: The rule about rounding to the nearest representable value treats infinity as if it were in a normal place at the end of the finite values, so any result that is greater than or equal to Number.MAX_VALUE plus half a “step” beyond it rounds to infinity.)
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
answered Nov 22 '18 at 16:00
Eric PostpischilEric Postpischil
81.2k890169
81.2k890169
add a comment |
add a comment |
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4
The number overflows when the mantissa and exponent are as "big" as possible. Adding
MIN_VALUEdoesn't do that because it's vanishingly small in comparison toMAX_VALUE. Think of it as all the non-zero digits being far, far to the right, and therefore they have no net effect.– Pointy
Nov 22 '18 at 14:39