Rational number operation unit for reduction

A rational number operation unit for reducing numerator and denominator of a rational number, comprising:

• first data hold means for holding a dividend which is initially equal to the numerator;
• second data hold means for holding a divisor which is initially equal to the denominator;
• third data hold means for holding a numerator P.sub.i-2 for an (i-2)th approximate fraction to the rational number which numerator is initially equal to a first initial data;
• fourth data hold means for holding a numerator P.sub.i-1 for an (i-1)th approximate fraction to the rational number, which numerator is initially equal to a second initial data;
• fifth data hold means for holding a denominator Q.sub.i-2 for the (i-2)th approximate fraction which denominator is initially equal to a third initial data;
• sixth data hold means for holding a denominator Q.sub.i-1 for the (i-1)th approximate fraction, which denominator is initially equal to a fourth initial data;
• divider means for carrying out division of the dividend and divisor held in said first and second data hold means respectively, to produce quotient and residue;
• first operation means for carrying out a first operation to calculate a numerator P.sub.i for an i-th approximate fraction of the rational number, the numerator P.sub.i being equal to a first sum of a product of the numerator P.sub.i-1 held in said fourth data hold means and the quotient outputted by said divider means, and the numerator P.sub.i-2 held in said third data hold means, each time division is carried out by said divider means;
• second operation means for carrying out a second operation to calculate a denominator Q.sub.i for the i-th approximate fraction, the denominator Q.sub.i being equal to a second sum of a product of the denominator Q.sub.i-1 held in said sixth data hold means and the quotient outputted by said divider means, and the denominator Q.sub.i-2 held in said fifth data hold means, each time division is carried out by said divider means;
• discrimination means responsive to the residue output by said division means for determining whether the residue is zero or not each time division is carried out by said divider means;
• first transfer means for transferring the divisor held in said second data hold means to said first data hold means as a new dividend and transferring the residue outputted by said divider means to said second data hold means as a new divisor in response to execution of division by said divider means;
• second transfer means for transferring the numerator P.sub.i-1 held in the fourth data hold means to said third data hold means to be used as a new numerator P.sub.i-2, transferring the numerator P.sub.i outputted by said first operation means to said fourth data hold means to be used as a new numerator P.sub.i-1, transferring the denominator Q.sub.i-1 held in said sixth data hold means to the fifth data hold means to be used as a new denominator Q.sub.i-2, and transferring the denominator Q.sub.i outputted by said second operation means to said sixth data hold means to be used a new denominator Q.sub.i-1, in response to the execution of the first and second operations by said first and second operation means;
• means for ordering said divider means and first and second operation means to repeat division, the first operation and the second operation, respectively, in response to the determination of non-zero residue by said discrimination means;
• and,
• means for producing the first and second sums outputted by said first and second operation means as numerator and denominator of a reduced rational number in response to the determination of zero residue by said discrimination means.