Method and apparatus for finding arctangents

Details Method and apparatus for finding arctangents Method and apparatus for finding arctangents

1995-04-18

1997-07-15

Malzahn, David H.

Boots, shoes, and leggings

G06F 7548

Patent

active

056489242

ABSTRACT:
Arctangents (tan.sup.-1) are calculated utilizing binary floating point numbers through much of the function's range by extracting into an Integer Register (54) as an index ("i") the exponent and a specified number of fraction bits from a Floating Point Register(s) (60). The index is utilized by an Integer Unit (52) to index into tables of polynomial coefficients and reference values. The floating point difference between the absolute value of the argument(s) and the reference value selected by the index is a polynomial linear term. The coefficients in the table entry selected by the index are multiplied in a Floating Point Unit (58) by integral powers of the linear term. The Floating Point Unit (58) then sums the high order polynomial terms. The zero.sup.th level term added to the product of the first level term multiplied by the linear term forms a "big" term. The rounding error resulting from the computation of the "Big" Term is calculated as a "Small" Term, which is added to the high order polynomial terms before the Big Term is added.

REFERENCES:
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patent: 5235535 (1993-08-01), Nakayama
patent: 5305246 (1994-04-01), Lindsley et al.
"High Speed Floating Point Multi-Function Generator," IBM technical disclosure bulletin vol. 31 No. 2, Armonk, NY, USA, Jul. 1988, pp. 331-334.
Shmuel Gal et al., "An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard" ACM Transactions on Mathematical Software, vol. 17, No. 1, Mar. 1991, pp. 26-45.

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