K can be expressed as qd+r (quotient and remainder of K/d)
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Expresión 15: "h" left parenthesis, "x" , "d" , right parenthesis equals floor left parenthesis, StartFraction, "x" floor left parenthesis, StartNestedFraction, "K" NestedOver "d" , EndNestedFraction , right parenthesis plus left parenthesis, "g" left parenthesis, "x" , "d" , right parenthesis plus 1 , right parenthesis mod left parenthesis, "K" , "d" , right parenthesis Over "K" , EndFraction , right parenthesishx,d=floorxfloorKd+gx,d+1modK,dK
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Expresión 16: "h" left parenthesis, "x" , "D" , right parenthesishx,D
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statistics
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difference
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Expresión 19: "E" left parenthesis, "x" , "d" , right parenthesis equals "h" left parenthesis, "x" , "d" , right parenthesis minus "f" left parenthesis, "x" , "d" , right parenthesisEx,d=hx,d−fx,d
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Expresión 20: "E" left parenthesis, "x" , "D" , right parenthesisEx,D
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first miss
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the refinement fails once the initial approximation drops to 2 below the target (both are floored linear functions, the target is a direct proportion while the refinement is shifted left)
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Expresión 23: "U" left parenthesis, "a" , "b" , "H" , right parenthesis equals "b" left parenthesis, floor left parenthesis, StartFraction, "a" plus "H" Over "a" minus "b" , EndFraction , right parenthesis plus 1 , right parenthesisUa,b,H=bfloora+Ha−b+1
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Expresión 24: "U" left parenthesis, StartFraction, "K" Over floor left parenthesis, StartNestedFraction, "K" NestedOver "D" , EndNestedFraction , right parenthesis , EndFraction , "D" , StartFraction, mod left parenthesis, "K" , "D" , right parenthesis Over floor left parenthesis, StartNestedFraction, "K" NestedOver "D" , EndNestedFraction , right parenthesis , EndFraction , right parenthesisUKfloorKD,D,modK,DfloorKD