This module provides Julia-language wrappers to the free/open-source MPFR library for "multiple-precision floating-point computations with correct rounding".

MPFR_wrap.jl does not introduce new types and instead makes use of Julia's BigFloat but allows the user to perform in-place operations to minimize garbage collection. MPFR_wrap.jl's functions that modify their input have names terminating with a bang (!) following the standard Julia convention.

Compute a = sqrt(3.5 + 0.8). Using operations defined in Julia's Base for BigFloats

a = BigFloat("3.5", precision=1000)
b = BigFloat("0.8", precision=1000)
c = sqrt(a + b)

creates a temporary variable to hold the intermediate result of the computation a + b.

Using MPFR_wrap for in-place computation

a = BigFloat("3.5", precision=1000)
b = BigFloat("0.8", precision=1000)
# add a and b and store the result in a
add!(a, a, b)
# take the square root of a and store it in a
sqrt!(a, a)

The last two operations can be combined into sqrt!(a, add!(a, a, b)) relying on add! to return the modified input a.

The file examples/pi_iterative.jl contains two methods for the computation of π using the iterative method Brent-Salamin and the Borwein cubic iteration taken from "A catalogue of mathematical formulas involving π, with analysis" by David H. Bailey available online.

The following shows the difference in execution time and memory allocation for the Brent-Salamin method using standard and in-place operations.

julia> @btime brent_salamin();
  336.484 ms (870 allocations: 11.88 MiB)

julia> @btime inplace_brent_salamin();
  129.504 ms (158 allocations: 413.14 KiB)

The following functions are exported:

1. Assignment functions

• set!

2. Basic arithmetic functions

• add!, sub!, mul!, div!
• sqrt!, rec_sqrt!, cbrt!, root!, pow!
• neg!, abs!
• dim!
• mul_2!

3. Comparison functions

• cmp_2exp
• number_p, regular_p
• cmpabs
• unordered_p

4. Special functions

• log!, log2!, log10!, log1p!
• exp!, exp2!, exp10!, exp1p!
• cos!, sin!, tan!, sin_cos!
• sec!, csc!, cot!
• acos!, asin!, atan!, atan2!
• cosh!, sinh!, atanh!
• eint!, li!
• gamma!, gamma_inc!, lngamma!, lgamma!, digamma!
• beta!, zeta!, erf!
• j0!, j1!, jn!, y0!, y1, yn!
• fma!, fms!, fmma!, fmms!
• agm!, hypot!, ai!

5. Integer and reminder related functions

• ceil!, floor!, round!, roundeven!, trunc!
• rint!, frac!
• modf!, fmod!
• integer_p