rounding1 http://www.openmath.org/cd/rounding1.ocd 2003-04-01 official 2001-03-12 2 0 quant1 logic1 relation1 arith1 alg1 set1 setname1 A CD of basic rounding concepts Written by James Davenport, inspired by the need from bigfloat.ocd. Finished 1999-10-24. ceiling The round up (to +infinity) operation. for all x | ceiling(x)-1 < x <= ceiling x floor The round down (to -infinity) operation. for all x | floor(x) <= x < floor(x)+1 trunc The round to zero operation. for all x | trunc(x) <= x < trunc(x)+1 (x>0) for all x | trunc(x) >= x > trunc(x)-1 (x<0) round The round to nearest operation. for all x | x <= round(x)+1/2 and x <= round(x)-1/2 2 2 for all x | Also round to even in event of a tie 2 2