Mixing
IEEE 754 machine numbers
$begingroup$
I have a machine number range $ F=F(2,5,-3,3).$ 2 is the base, 5 the mantissa, -3 the minimum exponent and 3 the maximum exponent.
I tried to find two numbers $ a,bin F $ with $ acdot bin [F_{min},F_{max}]=[0,125;15,5] $ and their roundings $ a',b' $ so that the following conditions are satisfied:
$ aneq a' $ and $ bneq b' $ but $ acdot b = a'cdot b' $. After many tries I always failed to find the right numbers.
Each rounded number here has this figure: $ z'=(1,xxxx)_2cdot 2^E. $ The positions with x are for 0 or 1. So the thrid condition could be written as:
$ acdot b= underbrace{(1,xxxx)_2cdot 2^{E_a}}_{a'}cdot underbrace{(1,xxxx)_2cdot 2^{E_b}}_{b'}. $
But the problem is there are (only for the x positions) 8^8 combinations for 0 and 1 which is quite a lot.
How I could find the right numbers a and b more efficiently?
I guess I have to choose periodical numbers else the rounded numbers a' and b' would be equal to a and b.
numerical-methods
asked Jan 24 at 3:12
hallo97hallo97
12
$endgroup$
add a comment |
$begingroup$
I have a machine number range $ F=F(2,5,-3,3).$ 2 is the base, 5 the mantissa, -3 the minimum exponent and 3 the maximum exponent.
I tried to find two numbers $ a,bin F $ with $ acdot bin [F_{min},F_{max}]=[0,125;15,5] $ and their roundings $ a',b' $ so that the following conditions are satisfied:
$ aneq a' $ and $ bneq b' $ but $ acdot b = a'cdot b' $. After many tries I always failed to find the right numbers.
Each rounded number here has this figure: $ z'=(1,xxxx)_2cdot 2^E. $ The positions with x are for 0 or 1. So the thrid condition could be written as:
$ acdot b= underbrace{(1,xxxx)_2cdot 2^{E_a}}_{a'}cdot underbrace{(1,xxxx)_2cdot 2^{E_b}}_{b'}. $
But the problem is there are (only for the x positions) 8^8 combinations for 0 and 1 which is quite a lot.
How I could find the right numbers a and b more efficiently?
I guess I have to choose periodical numbers else the rounded numbers a' and b' would be equal to a and b.
numerical-methods
asked Jan 24 at 3:12
hallo97hallo97
12
$endgroup$
add a comment |
$begingroup$
I have a machine number range $ F=F(2,5,-3,3).$ 2 is the base, 5 the mantissa, -3 the minimum exponent and 3 the maximum exponent.
I tried to find two numbers $ a,bin F $ with $ acdot bin [F_{min},F_{max}]=[0,125;15,5] $ and their roundings $ a',b' $ so that the following conditions are satisfied:
$ aneq a' $ and $ bneq b' $ but $ acdot b = a'cdot b' $. After many tries I always failed to find the right numbers.
Each rounded number here has this figure: $ z'=(1,xxxx)_2cdot 2^E. $ The positions with x are for 0 or 1. So the thrid condition could be written as:
$ acdot b= underbrace{(1,xxxx)_2cdot 2^{E_a}}_{a'}cdot underbrace{(1,xxxx)_2cdot 2^{E_b}}_{b'}. $
But the problem is there are (only for the x positions) 8^8 combinations for 0 and 1 which is quite a lot.
How I could find the right numbers a and b more efficiently?
I guess I have to choose periodical numbers else the rounded numbers a' and b' would be equal to a and b.
numerical-methods
asked Jan 24 at 3:12
hallo97hallo97
12
$endgroup$
I have a machine number range $ F=F(2,5,-3,3).$ 2 is the base, 5 the mantissa, -3 the minimum exponent and 3 the maximum exponent.
I tried to find two numbers $ a,bin F $ with $ acdot bin [F_{min},F_{max}]=[0,125;15,5] $ and their roundings $ a',b' $ so that the following conditions are satisfied:
$ aneq a' $ and $ bneq b' $ but $ acdot b = a'cdot b' $. After many tries I always failed to find the right numbers.
Each rounded number here has this figure: $ z'=(1,xxxx)_2cdot 2^E. $ The positions with x are for 0 or 1. So the thrid condition could be written as:
$ acdot b= underbrace{(1,xxxx)_2cdot 2^{E_a}}_{a'}cdot underbrace{(1,xxxx)_2cdot 2^{E_b}}_{b'}. $
But the problem is there are (only for the x positions) 8^8 combinations for 0 and 1 which is quite a lot.
How I could find the right numbers a and b more efficiently?
I guess I have to choose periodical numbers else the rounded numbers a' and b' would be equal to a and b.
numerical-methods
numerical-methods
asked Jan 24 at 3:12
hallo97hallo97
12
asked Jan 24 at 3:12
hallo97hallo97
12
asked Jan 24 at 3:12
hallo97hallo97
12
asked Jan 24 at 3:12
hallo97hallo97
12
asked Jan 24 at 3:12
hallo97hallo97
12
12
add a comment |
add a comment |
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