The elementary functions in libm and libsunmath on SPARC-based systems are implemented with table-driven and polynomial/rational approximation algorithms. These algorithms are subject to change between releases for better performance or accuracy. Some elementary functions in libm and libsunmath on x86-based systems are implemented using the elementary function kernel instructions provided in the x86 instruction set; other functions are implemented using the same table-driven or polynomial/rational approximation algorithms used on SPARC-based systems.
Both the table-driven and polynomial/rational approximation algorithms for the common elementary functions in libm and the common single precision elementary functions in libsunmath deliver results that are accurate to within one unit in the last place (ulp). On SPARC-based systems, the common quadruple precision elementary functions in libsunmath deliver results that are accurate to within one ulp, except for the expm1l and log1pl functions, which deliver results accurate to within two ulps. (The common functions include the exponential, logarithm, and power functions and circular trigonometric functions of radian arguments. Other functions, such as the hyperbolic trig functions and higher transcendental functions, are less accurate.) These error bounds have been obtained by direct analysis of the algorithms. Users can also test the accuracy of these routines using BeEF, the Berkeley Elementary Function test programs, available from netlib in the ucbtest package http://www.netlib.org/fp/ucbtest.tgzhttp://www.netlib.org/fp/ucbtest.tgz.