IEEE 754 machine numbers












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$begingroup$


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







share|cite|improve this question









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    0












    $begingroup$


    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







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      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







      share|cite|improve this question









      $endgroup$




      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






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 24 at 3:12









      hallo97hallo97

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