System for obtaining strict solution in accordance with accuracy of approximate solutions

A hybrid type function calculating system for obtaining a strict solution y of n-bit length to a function f(x) where y equals a root of x, wherein the accuracy of approximate solutions is insufficient and the function f(x) has an inverse function f.sup.-1 (y), comprising:

• a first multiplier for multiplying a value x normalized from an approximate solution y'=g(x) having an error smaller than said strict solution y from said inverse function f.sup.-1 (y) in a domain of said approximate solution y' with an initial value x.sub.o obtained from a parameter ROM by use of a normalized value x;
• a second multiplier for multiplying said initial value x.sub.o with upper n-bits obtained through a feed-back path from an output of said first multiplier to obtain said approximate solution y'=g(x);
• an adder/subtracter for comparing an inverse function f(y') with said value x;
• first means for determining y" by correcting a bit string of y' up to an m-th bit in accordance with results from said adder/subtracter and determining a difference between f.sup.-1 (y") and x;
• and
• second means for obtaining said strict solution y by starting a dichotomy on the basis of the remainder (m-n) bit string.

A hybrid type function calculating system for obtaining a strict solution y of n-bit length to a function f(x) where y equals 1/x, wherein accuracy of approximate solutions is sufficient and the function f(x) has an inverse function f.sup.-1 x(y) comprising:

• a first multiplier for multiplying a value x normalized from an approximate solution y'=g(x) having an error smaller than a value E.sub.o which is smaller than a resolution of said strict solution y from said inverse function f.sup.-1 (y) in a domain of said approximate solution y' with an initial value Xo obtained from a parameter ROM by use of a normalized value x;
• a second multiplier for multiplying said initial value X.sub.o with upper n-bits obtained through a feed-back path from an output of said first multiplier to obtain an approximate solution y'=g(x) of (n+2)-bit length;
• an adder/subtractor for comparing a normalization number 1.0 with an output from said second multiplier;
• first means for determining y" by correcting a bit string of said approximate solution y' in accordance with results from said adder/subtractor;
• and
• second means for determining y"' by correcting a bit string of y" in accordance with results of the comparison in said adder/subtractor and obtaining said strict solution y by rounding y"'.

A hybrid type function calculating system for obtaining a strict solution y of n-bit length to a function f(x) where y equals 1/x wherein the accuracy of approximate solutions is insufficient and the function f(x) has an inverse function f.sup.-1 (y), comprising:

• a first multiplier for multiplying a value x normalized from an approximate solution y'=g(x) having an error smaller than a value E.sub.o which is smaller than a resolution of said strict solution y from said inverse function f.sup.-1 (y) in a domain of said approximate solution y' with an initial value x.sub.o obtained from a parameter ROM by use of a normalized value x;
• a second multiplier for multiplying said initial value x.sub.o with upper n-bits obtained through a feed-back path from an output of said first multiplier to obtain an approximate solution y'=g(X);
• an adder/subtractor for comparing an inverse function f.sup.-1 (y') with said value x;
• first means for determining y" by correcting a bit string of y' up to an m-th bit in accordance with results from said adder/subtractor and determining a difference between f.sup.-1 (y") and x;
• and
• second means for obtaining said strict solution y by starting a dichotomy on the basis of the remainder (m-n) bit string.