CoreMath

CoreMath.jl is a Julia package wrapping the CORE-MATH functions. This project provides correctly-rounded mathematical functions.

See also: CRlibm.jl.

What is correct rounding?

Suppose that we ask Julia to calculate the cosine of a number

julia> cos(0.5) # Julia build-in `cos` function
0.8775825618903728

The result is a floating-point number that is a very good approximation to the true value. However, we do not know if the result that Julia gives is below or above the true value, nor how far away it is.

Correctly-rounded functions guarantee that when the result is not exactly representable as a floating-point number, the value returned is the next largest floating-point number when rounding up, or the next smallest when rounding down. This is equivalent to doing the calculation in infinite precision and then performing the rounding.

List of implemented functions

All functions from CORE-MATH are wrapped:

• exponential: cr_cbrt (Float16 and Float32), cr_cbrt, cr_pow, cr_exp, cr_exp2, cr_exp10, cr_expm1, cr_exp2m1, cr_exp10m1
• logarithmic: cr_log, cr_log2, cr_log10, cr_log1p, cr_log2p1, cr_log10p1
• trigonometric: cr_sin, cr_cos, cr_tan, cr_asin, cr_acos, cr_atan, cr_atan2, cr_sinpi, cr_cospi, cr_tanpi, cr_asinpi, cr_acospi, cr_atanpi, cr_atan2pi
• hyperbolic: cr_sinh, cr_cosh, cr_tanh, cr_asinh, cr_acosh, cr_atanh
• others: cr_hypot, cr_rsqrt, cr_erf, cr_erfc, cr_lgamma, cr_tgamma

Installation

The CoreMath.jl package requires to install Julia (v1.6 or above).

Then, start Julia and execute the following command in the REPL:

using Pkg; Pkg.add("CoreMath")

Usage

All functions use the cr_ prefix, and are used as follows:

using CoreMath

# Float64
cr_sin(1.0)          # 0.8414709848078965
cr_exp(1.0)          # 2.718281828459045
cr_log(2.0)          # 0.6931471805599453
cr_cbrt(27.0)        # 3.0

# Float32 — same function names, dispatch on type
cr_sin(1.0f0)        # 0.84147096f0
cr_exp(1.0f0)        # 2.7182817f0

# Float16 (Linux only)
cr_sin(Float16(1.0)) # Float16(0.8413)
cr_exp(Float16(1.0)) # Float16(2.719)

Precision support

Type	Platforms	C suffix
Float64	All	(none)
Float32	All	f
Float16	Linux only	f16

Float16 requires GCC 12+ for _Float16 support and is not available on macOS, FreeBSD, or Windows.