Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance

Jean-Michel Muller (1, 2) , Nicolas Brisebarre (3) , Saurabh Raina (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 ARENAIRE - Computer arithmetic
3 LArAl - Laboratoire d'Arithmétique et d'Algèbre

We present techniques for accelerating the floating-point computation of x/y when y is known before x. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with usual division with rounding to nearest. It is known that the advanced computation of 1/y allows performing correctly rounded division in one multiplication plus two fused-macs. We show algorithms that reduce this latency to one multiplication and one fused-mac. This is achieved if a precision of at least n+1 bits is available, where n is the number of mantissa bits in the target format, or if y satisfies some properties that can be easily checked at compile-time. This requires a double-word approximation of 1/y (we also show how to get it). Compilers to accelerate some numerical programs without loss of accuracy can use these techniques.

Keywords: floating point arithmetic; optimising compilers; roundoff error; computer arithmetic; double-word approximation; fused-mac operation; rounded floating-point division

Domains: Computer Science [cs]; Other [cs.OH]

Jean-Michel Muller, Nicolas Brisebarre, Saurabh Raina. Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in Advance. IEEE Transactions on Computers, 2004, 53 (8), pp.1069- 1072. ⟨10.1109/TC.2004.37⟩. ⟨ensl-00087465⟩