Data Length Independent Real Number Representation Based on Double Exponential Cut
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A new internal representation is proposed for real numbers. It has been named URR for Universal Representation of Real numbers. This approach is based on a bisection method which is applied to real number intervals. With this method the point of division increases or decreases in a double exponential manner in the globalrange. The main characteristics of the method are as follows. First overflow/underflow does not in practice occur. Second since the data format does not depend on the length but on the value of the data a transformation operation is virtually not needed between systems of long and short data. Finally only one bit of resolution is lost compared with the fixed point form. In addition arithmetic operations are slightly complicated compared with conventional representation but they present no special difficulties. This new method is thus the most suitable internal form as an interface not only between computers but also between computers and digital systems which deal with real numbers or physical (scalar) values.A new internal representation is proposed for real numbers. It has been named URR for Universal Representation of Real numbers. This approach is based on a bisection method which is applied to real number intervals. With this method, the point of division increases or decreases in a double exponential manner in the globalrange. The main characteristics of the method are as follows. First, overflow/underflow does not, in practice, occur. Second, since the data format does not depend on the length but on the value of the data, a transformation operation is virtually not needed between systems of long and short data. Finally, only one bit of resolution is lost compared with the fixed point form. In addition, arithmetic operations are slightly complicated compared with conventional representation, but they present no special difficulties. This new method is thus the most suitable internal form as an interface not only between computers but also between computers and digital systems which deal with real numbers or physical (scalar) values.
A new internal representation is proposed for real numbers. It has been named URR for Universal Representation of Real numbers. This approach is based on a bisection method which is applied to real number intervals. With this method, the point of division increases or decreases in a double exponential manner in the globalrange. The main characteristics of the method are as follows. First, overflow/underflow does not, in practice, occur. Second, since the data format does not depend on the length but on the value of the data, a transformation operation is virtually not needed between systems of long and short data. Finally, only one bit of resolution is lost compared with the fixed point form. In addition, arithmetic operations are slightly complicated compared with conventional representation, but they present no special difficulties. This new method is thus the most suitable internal form as an interface not only between computers but also between computers and digital systems which deal with real numbers or physical (scalar) values.
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 Journal of Information Processing

Journal of Information Processing 10(1), 16, 19870331
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