What is the smallest decimal that can be represented using IEEE754 single precision?
Is seems like it would be IE-38, which would make the exponent 127-127. But when I add 1E10 and 1E-32, I get 1E10 which makes me think that 1E-32 is so small it's not being properly represented.
math architecture ieee-754
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
add a comment |
Is seems like it would be IE-38, which would make the exponent 127-127. But when I add 1E10 and 1E-32, I get 1E10 which makes me think that 1E-32 is so small it's not being properly represented.
math architecture ieee-754
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
add a comment |
Is seems like it would be IE-38, which would make the exponent 127-127. But when I add 1E10 and 1E-32, I get 1E10 which makes me think that 1E-32 is so small it's not being properly represented.
math architecture ieee-754
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
Is seems like it would be IE-38, which would make the exponent 127-127. But when I add 1E10 and 1E-32, I get 1E10 which makes me think that 1E-32 is so small it's not being properly represented.
math architecture ieee-754
math architecture ieee-754
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
asked Nov 15 '18 at 1:08
ShagalabagalaShagalabagala
205
205
add a comment |
add a comment |
1 Answer
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You are mixing two different terms:
- minimal value representable in given format (
~10^-38) and
machine epsilon - such minimal value that1.0 + eps != 1.0, for single precision it is about2^-23
For bigger value 1e10 minimal summand is ~1e10 * macheps
Simplified example: for 4 decimal digits you can represent values 100.0 and 0.001, but 100.0 + 0.001 = 100.0 because true sum 100.001 cannot fit into 4 decimal places.
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
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1 Answer
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1 Answer
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You are mixing two different terms:
- minimal value representable in given format (
~10^-38) and
machine epsilon - such minimal value that1.0 + eps != 1.0, for single precision it is about2^-23
For bigger value 1e10 minimal summand is ~1e10 * macheps
Simplified example: for 4 decimal digits you can represent values 100.0 and 0.001, but 100.0 + 0.001 = 100.0 because true sum 100.001 cannot fit into 4 decimal places.
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
add a comment |
You are mixing two different terms:
- minimal value representable in given format (
~10^-38) and
machine epsilon - such minimal value that1.0 + eps != 1.0, for single precision it is about2^-23
For bigger value 1e10 minimal summand is ~1e10 * macheps
Simplified example: for 4 decimal digits you can represent values 100.0 and 0.001, but 100.0 + 0.001 = 100.0 because true sum 100.001 cannot fit into 4 decimal places.
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
add a comment |
You are mixing two different terms:
- minimal value representable in given format (
~10^-38) and
machine epsilon - such minimal value that1.0 + eps != 1.0, for single precision it is about2^-23
For bigger value 1e10 minimal summand is ~1e10 * macheps
Simplified example: for 4 decimal digits you can represent values 100.0 and 0.001, but 100.0 + 0.001 = 100.0 because true sum 100.001 cannot fit into 4 decimal places.
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
You are mixing two different terms:
- minimal value representable in given format (
~10^-38) and
machine epsilon - such minimal value that1.0 + eps != 1.0, for single precision it is about2^-23
For bigger value 1e10 minimal summand is ~1e10 * macheps
Simplified example: for 4 decimal digits you can represent values 100.0 and 0.001, but 100.0 + 0.001 = 100.0 because true sum 100.001 cannot fit into 4 decimal places.
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
answered Nov 15 '18 at 2:46
MBoMBo
49.8k23051
49.8k23051
add a comment |
add a comment |
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