b'@techreport{BurnikelZiegler98,'b'\nTITLE = {Fast recursive division},\nAUTHOR = {Burnikel, Christoph and Ziegler, Joachim},\nLANGUAGE = {eng},\nNUMBER = {MPI-I-1998-1-022},\nINSTITUTION = {Max-Planck-Institut f{\\"u}r Informatik},\nADDRESS = {Saarbr{\\"u}cken},\nYEAR = {1998},\nDATE = {1998},\nABSTRACT = {We present a new recursive method for division with remainder of integers. Its running time is $2K(n)+O(n \\log n)$ for division of a $2n$-digit number by an $n$-digit number where $K(n)$ is the Karatsuba multiplication time. It pays in p ractice for numbers with 860 bits or more. Then we show how we can lower this bo und to $3/2 K(n)+O(n\\log n)$ if we are not interested in the remainder. As an application of division with remainder we show how to speedup modular multiplication. We also give practical results of an implementation that allow u s to say that we have the fastest integer division on a SPARC architecture compa red to all other integer packages we know of.},\nTYPE = {Research Report / Max-Planck-Institut f\xc3\xbcr Informatik},\n}\n'