Table-driven implementation of the exponential function in IEEE floating-point arithmetic

ABSTRACT

Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.

REFERENCES

• 1: Ramesh C Agarwal , James W Cooley , Fred G Gustavson , James B Shearer , Gordon Slishman , Bryant Tuckerman, New scalar and vector elementary functions for the IBM system/370, IBM Journal of Research and Development, v.30 n.2, p.123-144, March 1986
• 2: William James Cody, Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics), Prentice-Hall, Inc., Upper Saddle River, NJ, 1980
• 3: Shmuel Gal, Computing Elementary Functions: A New Approach for Achieving High Accuracy and Good Performance, Proceedings of the Symposium on Accurate Scientific Computations, p.1-16, March 12-14, 1985
• 4: John F. Hart, Computer Approximations, Krieger Publishing Co., Inc., Melbourne, FL, 1978
• 5: HOUGH, D. Elementary functions based upon IEEE arithmetic. Mini/Micro West Conference Record, Electronic Conventions Inc., Los Angeles, 1983.
• 6: IBM Elementary Math Library. Programming RPQ P81005, Program 5799-BTB, Program Reference and Operations Manual. SH20-2230-1, Aug. 1984.
• 7: IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985. Institute of Electrical and Electronic Engineers, New York, 1985.

INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Computer arithmetic; Numerical algorithms; Error analysis
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

General Terms:
Algorithms

Keywords:
IEEE arithmetic, exponential function, implementation