The CORE-MATH project

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CORE-MATH Mission: provide on-the-shelf high performance open-source mathematical functions with correct rounding that can be integrated into current mathematical libraries (GNU libc, Intel Math Library, AMD Libm, Newlib, OpenLibm, Musl, Apple Libm, llvm-libc, Microsoft libm, CUDA libm, ROCm)

Average number of clock cycles needed by CORE-MATH functions (revision 55c872b, f5d9e09 for log2l, f8f982e for expl) on an Intel Xeon Silver 4214, with GCC 13.2.0, compared to GNU libc 2.37, the Intel Math Library from icx 2023.2.0 and LLVM libc (revision d099dbb):

CORE-MATH GNU libm Intel icx LLVM

Usages of CORE-MATH:

branch core-math of LibmCS, the Mathematical Library for Critical Systems developed by the European Space Agency

Available CORE-MATH functions (under MIT license):

function	binary32	binary64	binary80	binary128
acos	code	code
acosh	code	code
acospi	code	code
asin	code	code
asinh	code	code
asinpi	code	code
atan	code	code
atan2	code	code
atan2pi	code	code
atanh	code	code
atanpi	code	code
cbrt	code	code (proof)	code
cos	code	code
cosh	code	code
cospi	code	code
erf	code	code
erfc	code	code
exp	code	code	code
exp10	code	code
exp10m1	code	code
exp2	code	code	code
exp2m1	code	code
expm1	code	code
hypot	code	code
lgamma	code
log	code	code (with Gappa proof)
log10	code	code
log10p1	code	code
log1p	code	code
log2	code	code	code
log2p1	code	code
pow	code	code	code
rsqrt	code	code	code
sin	code	code
sincos	code
sinh	code	code
sinpi	code	code
tan	code	code
tanh	code	code
tanpi	code	code
tgamma	code

Caption:

code: pointer to the main CORE-MATH code foo.c. Note that it might require some header files present in the same directory. For example the log function needs the dint.h header file available from the [git] link on top of this page, then follow src, binary64, and log.
llvm: pointer to a correctly-rounded implementation in llvm-libc
proof: a paper proof of the correctness of the algorithm
(1) tested on hard-to-round cases |x| < 2^-34
(2) only for rounding to nearest

Notes:

correct rounding is claimed for all IEEE-754 rounding modes. For univariate binary32 functions it is checked by exhaustive search. For bivariate functions or larger formats it is checked only with respect to known hard-to-round cases. If you find an input which is not correctly rounded, please send it to paul dot zimmermann @ inria dot fr.
these implementations only care about correct rounding for regular numbers, they do not necessarily correctly deal with NaN, infinities or zero, set the underflow and overflow exceptions, nor the inexact flag.
these implementations were tested on x86_64-linux, with and without the use of fma (fused multiply add).

Other correctly-rounded implementations:

CRlibm this is a mirror of the original CRlibm project (which is no more available). CRlibm is no longer maintained, but contains very useful resources: provides binary64 exp, log, cos, sin, tan, cospi, sinpi, tanpi, atan, atanpi, cosh, sinh, log2, log10, asin, acos, asinpi, acospi, expm1, log1p, exp2, pow (only for rounding to nearest for pow).
RLIBM provides binary32 log, log2, log10, exp, exp2, exp10, sinh, cosh, sinpi, cospi, sin, cos, tan, atan, asin, acos for all rounding modes.
LLVM-libc provides some correctly rounded functions (see links below): claimed accuracy of LLVM functions
JuliaIntervals provides elementary functions with directed rounding wrapping CRlibm.

function	binary32	binary64	binary80	binary128
acos	rlibm llvm	crlibm
acosh	llvm
acospi		crlibm
asin	rlibm llvm	crlibm
asinh	llvm
asinpi		crlibm
atan	rlibm llvm	crlibm
atan2	llvm
atan2pi
atanh	llvm	crlibm
atanpi		crlibm
cbrt	llvm	llvm
cos	rlibm llvm,llvm	crlibm,llvm
cosh	rlibm llvm llvm	crlibm
cospi	rlibm,llvm	crlibm
erf	llvm
erfc
exp	rlibm llvm,llvm	crlibm, llvm
exp10	rlibm llvm	llvm
exp10m1
exp2	rlibm llvm llvm llvm	crlibm, llvm
exp2m1	llvm
expm1	llvm,llvm	crlibm,llvm
hypot	llvm,llvm	llvm
lgamma
log	rlibm llvm	crlibm, llvm
log10	rlibm llvm	crlibm, llvm
log10p1
log1p	llvm	crlibm, llvm
log2	rlibm llvm	crlibm, llvm
log2p1
pow	llvm (see this)	crlibm (2)
rsqrt
sin	rlibm llvm,llvm	crlibm,llvm
sincos	llvm	llvm
sinh	rlibm llvm llvm	crlibm
sinpi	rlibm,llvm	crlibm
tan	rlibm llvm,llvm	crlibm,llvm
tanh	llvm llvm
tanpi		crlibm
tgamma