Exponential function computing apparatus

Apparatus for computing an expontential function a.sup.X with an N radix computer where a represents a positive constant and X a variable, comprising:

• generating means for generating a logarithmic value log.sub.a (1+N).sup.-k or N.sup.k .multidot.log.sub.a (1+N.sup.-k) where k=0, 1, 2 . . . m and where said positive constant a (a.noteq.1) is the base of the logarithm;
• first memory means;
• subtracting means carrying out a subtraction operation wherein said logarithmic value is subtracted from the contents of said first memory means and the remainder is stored in said first memory means;
• second memory means;
• third memory means;
• first shifting means for carrying out a first shift operation wherein a value corresponding to the contents of said second memory means is stored in said third memory means, said contents of said third memory means are shifted in a first predetermined direction k number of digits, and the shifted contents are added to said contents of said second memory means;
• second shifting means for carrying out a second shift operation wherein the contents of said first memory means are shifted by one digit in a second direction opposite said first direction;
• sequencing means for storing an initial value I in said second memory means, for storing a value corresponding to said variable X in said first memory means, for causing said generating means to sequentially generate said logarithmic value in a range from k=o to k=m and, for each logarithmic value generated, for carrying out a sequence wherein said subtracting means and said first shifting means are repeatedly caused to carry out said subtraction operation and said first shift operation, respectively, until said contents of said first memory means are reduced to a value less than said logarithmic value, at which time said second shift means is caused to carry out said second shift operation;
• whereby upon termination of the final second shift operation for k=m, the contents of said second memory means correspond to the value a.sup.X.

Apparatus for computing an expotential function a.sup.X with an N radix computer where a represents a positive constant and X a variable comprising:

• generating means for generating a logarithmic value log.sub.a (1+N.sup.-k) or N.sup.k.multidot. log.sub.a (1+N.sup.-k) where k=0, 1, 2 . . . m and where said positive constant a (a.noteq.1) is the base of the logarithm;
• first memory means;
• subtracting means for carrying out a subtraction operation wherein said logarithmic value is subtracted from the contents of said first memory means and the remainder is stored in said first memory means;
• second memory means;
• third memory means;
• shifting means for carrying out a shift operation wherein a value corresponding to the contents of said second memory means is stored in said third memory means, the contents of said third memory means are shifted in a predetermined direction k number of digits and the shifted contents are added to said contents of said second memory means;
• sequencing means for storing on initial value I in said second memory means, for storing a value corresponding to said variable X in said first memory means, for causing said generating means to sequentially generate said logarithmic value in a range from k=o to k=m and, for each logarithmic value generated, for carrying out a sequence wherein said subtracting means and said shifting means are repeatedly caused to carry out said subtraction operation and said shift operation, respectively, with each of said sequences terminating when said remainder stored in said first memory means is less than the particular logarithmic value used in such sequence;
• whereby upon termination of the final one of said sequences where k=m, the contents of said second memory means corresponds to the value a.sup.X.