Patent ID: 11334317

Abstract:
An information processing apparatus, program, and information processing method performing validated numerics. Arithmetic operation of definite numbers a1 and b1 of the computer numbers in which real numbers A and B are defined by formulas (1) and (2) is performed to determine an absolute effective digit γ satisfying formula (3), A=a1+a2,|a1|≤Cha,−Cea≤a2<Cea  formula (1),B=b1+b2,|a1|≤Chb,−Ceb≤b2<Ceb  formula (2),(A,B)=(a,b)1+(a,b)2,−Cγ≤(a,b)2<Cγ  formula (3). a1 and b1 are definite numbers whose numerical values are definite, and a2 and b2 are uncertain numbers whose numerical values are uncertain; C denotes a radix; ha and hb denote extended high order maxes that are minimum extended digits satisfying |a1|≤Cha and |b1|≤Chb, and ha and hb denote high order maxes that are integers; and ea, eb and γ denote the absolute effective digits that are integers.