Is integer division always equal to the floor of regular division?
For large quotients, integer division (//) doesn't seem to be necessarily equal to the floor of regular division (math.floor(a/b)).
According to Python docs (https://docs.python.org/3/reference/expressions.html - 6.7),
floor division of integers results in an integer; the result is that of mathematical division with the ‘floor’ function applied to the result.
However,
math.floor(648705536316023400 / 7) = 92672219473717632
648705536316023400 // 7 = 92672219473717628
'{0:.10f}'.format(648705536316023400 / 7) yields '92672219473717632.0000000000', but the last two digits of the decimal part should be 28 and not 32.
python integer division floating-accuracy integer-division
edited 4 hours ago
dan04
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asked 4 hours ago
Aditya Chanana
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For large quotients, integer division (//) doesn't seem to be necessarily equal to the floor of regular division (math.floor(a/b)).
According to Python docs (https://docs.python.org/3/reference/expressions.html - 6.7),
floor division of integers results in an integer; the result is that of mathematical division with the ‘floor’ function applied to the result.
However,
math.floor(648705536316023400 / 7) = 92672219473717632
648705536316023400 // 7 = 92672219473717628
'{0:.10f}'.format(648705536316023400 / 7) yields '92672219473717632.0000000000', but the last two digits of the decimal part should be 28 and not 32.
python integer division floating-accuracy integer-division
edited 4 hours ago
dan04
62.2k15134173
asked 4 hours ago
Aditya Chanana
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
For large quotients, integer division (//) doesn't seem to be necessarily equal to the floor of regular division (math.floor(a/b)).
According to Python docs (https://docs.python.org/3/reference/expressions.html - 6.7),
floor division of integers results in an integer; the result is that of mathematical division with the ‘floor’ function applied to the result.
However,
math.floor(648705536316023400 / 7) = 92672219473717632
648705536316023400 // 7 = 92672219473717628
'{0:.10f}'.format(648705536316023400 / 7) yields '92672219473717632.0000000000', but the last two digits of the decimal part should be 28 and not 32.
python integer division floating-accuracy integer-division
edited 4 hours ago
dan04
62.2k15134173
asked 4 hours ago
Aditya Chanana
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
For large quotients, integer division (//) doesn't seem to be necessarily equal to the floor of regular division (math.floor(a/b)).
According to Python docs (https://docs.python.org/3/reference/expressions.html - 6.7),
floor division of integers results in an integer; the result is that of mathematical division with the ‘floor’ function applied to the result.
However,
math.floor(648705536316023400 / 7) = 92672219473717632
648705536316023400 // 7 = 92672219473717628
'{0:.10f}'.format(648705536316023400 / 7) yields '92672219473717632.0000000000', but the last two digits of the decimal part should be 28 and not 32.
python integer division floating-accuracy integer-division
python integer division floating-accuracy integer-division
edited 4 hours ago
dan04
62.2k15134173
asked 4 hours ago
Aditya Chanana
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 4 hours ago
dan04
62.2k15134173
asked 4 hours ago
Aditya Chanana
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 4 hours ago
dan04
62.2k15134173
edited 4 hours ago
dan04
62.2k15134173
edited 4 hours ago
dan04
62.2k15134173
62.2k15134173
asked 4 hours ago
Aditya Chanana
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Aditya Chanana
362
asked 4 hours ago
Aditya Chanana
362
362
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Aditya Chanana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
2 Answers
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The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
answered 4 hours ago
trincot
117k1478109
add a comment |
You may be dealing with integral values that are too large to express exactly as floats. Your number is significantly larger than 2^53, which is where the gaps between adjacent floating point doubles start to get bigger than 1. So you lose some precision when doing the floating point division.
The integer division, on the other hand, is computed exactly.
answered 4 hours ago
interfect
1,331920
add a comment |
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2 Answers
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2 Answers
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The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
answered 4 hours ago
trincot
117k1478109
add a comment |
The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
answered 4 hours ago
trincot
117k1478109
add a comment |
The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
answered 4 hours ago
trincot
117k1478109
The reason the quotients in your test case are not equal is that in the math.floor(a/b) case, the result is calculated with floating point arithmetic (IEEE-754 64-bit), which means there is a maximum precision. The quotient you have there is larger than the 253 limit above which floating point is no longer accurate up to the unit.
With the integer division however, Python uses its unlimited integer range, and so that result is correct.
answered 4 hours ago
trincot
117k1478109
answered 4 hours ago
trincot
117k1478109
answered 4 hours ago
trincot
117k1478109
answered 4 hours ago
trincot
117k1478109
117k1478109
add a comment |
add a comment |
You may be dealing with integral values that are too large to express exactly as floats. Your number is significantly larger than 2^53, which is where the gaps between adjacent floating point doubles start to get bigger than 1. So you lose some precision when doing the floating point division.
The integer division, on the other hand, is computed exactly.
answered 4 hours ago
interfect
1,331920
add a comment |
You may be dealing with integral values that are too large to express exactly as floats. Your number is significantly larger than 2^53, which is where the gaps between adjacent floating point doubles start to get bigger than 1. So you lose some precision when doing the floating point division.
The integer division, on the other hand, is computed exactly.
answered 4 hours ago
interfect
1,331920
add a comment |
You may be dealing with integral values that are too large to express exactly as floats. Your number is significantly larger than 2^53, which is where the gaps between adjacent floating point doubles start to get bigger than 1. So you lose some precision when doing the floating point division.
The integer division, on the other hand, is computed exactly.
answered 4 hours ago
interfect
1,331920
You may be dealing with integral values that are too large to express exactly as floats. Your number is significantly larger than 2^53, which is where the gaps between adjacent floating point doubles start to get bigger than 1. So you lose some precision when doing the floating point division.
The integer division, on the other hand, is computed exactly.
answered 4 hours ago
interfect
1,331920
answered 4 hours ago
interfect
1,331920
answered 4 hours ago
interfect
1,331920
answered 4 hours ago
interfect
1,331920
1,331920
add a comment |
add a comment |
Aditya Chanana is a new contributor. Be nice, and check out our Code of Conduct.
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