Names:
tripledouble,
TD
represents a number as the sum of three IEEE doubles.
Library names:
sollya_obj_t sollya_lib_triple_double(sollya_obj_t)
sollya_obj_t sollya_lib_triple_double_obj()
int sollya_lib_is_triple_double_obj(sollya_obj_t)
sollya_obj_t sollya_lib_build_function_triple_double(sollya_obj_t)
#define SOLLYA_TD(x) sollya_lib_build_function_triple_double(x)
Description:
- tripledouble is both a function and a constant.
- As a function, it rounds its argument to the nearest number that can be written
as the sum of three double precision numbers.
- The algorithm used to compute tripledouble(x) is the following: let xh = double(x),
let xm = double(x - xh) and let xl = double(x - xh - xm).
Return the number xh + xm + xl. Note that if the
current precision is not sufficient to represent exactly xh + xm + xl, a rounding will
occur and the result of tripledouble(x) will be useless.
- As a constant, it symbolizes the triple-double precision format. It is used in
contexts when a precision format is necessary, e.g. in the commands
roundcoefficients and implementpoly.
See the corresponding help pages for examples.
Example 1:
> verbosity=1!;
> a = 1+ 2^(-55)+2^(-115);
> TD(a);
Warning: For at least 1 of the constants displayed in decimal, rounding has happened.
1.00000000000000002775557561562891353466491600711096
> prec=110!;
> TD(a);
1.0000000000000000277555756156289135346649160071109559756997242823115914817262706026923524404992349445819854736328125