Apparatus and method useful for evaluating periodic functions

Details Apparatus and method useful for evaluating periodic functions Apparatus and method useful for evaluating periodic functions

1997-09-30

2000-10-31

Mai, Tan V.

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

708495, 708510, G06F 102, G06F 738

Patent

active

061416703

ABSTRACT:
A computer and a method of using the computer to reduce an original argument to obtain a periodic function of the argument. A special number P.sub.j is employed that is close to a nontrivial even-integral multiple .pi.. The technique subtracts a non-negative integral multiple of P.sub.j from the original argument to obtain a first reduced argument. Then, a second non-negative integer multiple of a floating-point representation of .pi./2 is subtracted from the first reduced argument to obtain a second reduced argument. Next, a periodic function of a third argument equal to a sum of the second reduced argument plus the product of the first non-negative integral multiple and a floating-point representation of an offset .delta..sub.j is evaluated to obtain a result.

REFERENCES:
patent: 5068816 (1991-11-01), Noetzel
patent: 5452241 (1995-09-01), Desrosiers et al.
patent: 5463574 (1995-10-01), Desrosiers et al.
J. M. Muller, "Elementary Functions: Algorithms & Implementation" (1997 Birkhauser), Chapter 8, pp. 143-148, 154-162.
Roger Alan Smith, "A Continued-Fraction Analysis of Trigonometric Argument Reduction", IEEE Transactions on Computers, Nov. 11, 1995, vol. 44 No. 11.
Ping Tak Peter Tang, Table-Driven Implementation of the Logarithm Function in IEEE Floating-Point Arithmetic, ACM Transactions on Mathematical Software, Dec. 1990, vol. 16, No. 4, pp. 378-400.

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