CuInterval

CuInterval is a CUDA interval arithmetic library. It includes all fundamental and set-based interval operations of the IEEE Standard for Interval Arithmetic. Other flavors, including decorations are not supported.

Supported Operations

The following operations are implemented as CUDA kernels. All operations are correctly-rounded, given the limitations of the precision of the underlying CUDA operation. The tightest interval is always a subset of the computed interval. The lower and upper bounds of the basic operations are at most 3 ulps away from the lower and upper bounds of the correct interval, respectively. The error for a paricular operation is given below.

Basic Operations

Operation	Function Description	Error [ulps]
pos	$\mathbb{IR} \rightarrow \mathbb{IR}$	0
neg	$\mathbb{IR} \rightarrow \mathbb{IR}$	0
add	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
sub	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
mul	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
div	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
recip	$\mathbb{IR} \rightarrow \mathbb{IR}$	0
sqr	$\mathbb{IR} \rightarrow \mathbb{IR}$	0
sqrt	$\mathbb{IR} \rightarrow \mathbb{IR}$	0
fma	$\mathbb{IR}^3 \rightarrow \mathbb{IR}$	0

Power functions

Operation	Function Description	Error [ulps]
pown	$\mathbb{IR} \times \mathbb{N} \rightarrow \mathbb{IR}_{\ge \mathbf{0}}$	1
pow	$\mathbb{IR}^2 \rightarrow \mathbb{IR}_{\ge \mathbf{0}}$	1
rootn	$\mathbb{IR}_{\ge \mathbf{0}} \times \mathbb{N} \rightarrow \mathbb{IR}$	2
cbrt	$\mathbb{IR}_{\ge \mathbf{0}} \rightarrow \mathbb{IR}$	1
exp	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
exp2	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
exp10	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
expm1	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
log	$\mathbb{IR}_{\ge \mathbf{0}} \rightarrow \mathbb{IR}$	3
log2	$\mathbb{IR}_{\ge \mathbf{0}} \rightarrow \mathbb{IR}$	3
log10	$\mathbb{IR}_{\ge \mathbf{0}} \rightarrow \mathbb{IR}$	3
log1p	$\mathbb{IR}_{\ge \mathbf{-1}} \rightarrow \mathbb{IR}$	3

Trigonometric functions

Operation	Function Description	Error [ulps]
sin	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
cos	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
tan	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
asin	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
acos	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
atan	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
atan2	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	3
cot	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
sinpi	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
cospi	$\mathbb{IR} \rightarrow \mathbb{IR}$	3

Hyperbolic functions

Operation	Function Description	Error [ulps]
sinh	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
cosh	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
tanh	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
asinh	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
acosh	$\mathbb{IR} \rightarrow \mathbb{IR}$	3
atanh	$\mathbb{IR} \rightarrow \mathbb{IR}$	3

Special functions

Operation	Function Description	Error [ulps]
erf	$\mathbb{IR} \rightarrow \mathbb{IR}$	2
erfc	$\mathbb{IR} \rightarrow \mathbb{IR}$	5

Integer functions

Operation	Function Description	Error [ulps]
sign	$\mathbb{IR} \rightarrow \{-1, 0, 1\}$	0
ceil	$\mathbb{IR} \rightarrow \mathbb{Z}$	0
floor	$\mathbb{IR} \rightarrow \mathbb{Z}$	0
trunc	$\mathbb{IR} \rightarrow \mathbb{Z}$	0
roundTiesToEven	$\mathbb{IR} \rightarrow \mathbb{Z}$	0
roundTiesToAway	$\mathbb{IR} \rightarrow \mathbb{Z}$	0

Absmax functions

Operation	Function Description	Error [ulps]
abs	$\mathbb{IR} \rightarrow \mathbb{IR}_{\ge \mathbf{0}}$	0
min	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
max	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0

Numeric functions

Operation	Function Description	Error [ulps]
inf	$\mathbb{IR} \rightarrow \mathbb{R}$	0
sup	$\mathbb{IR} \rightarrow \mathbb{R}$	0
mid	$\mathbb{IR} \rightarrow \mathbb{R}$	0
wid	$\mathbb{IR} \rightarrow \mathbb{R}$	0
rad	$\mathbb{IR} \rightarrow \mathbb{R}$	0
mag	$\mathbb{IR} \rightarrow \mathbb{R}$	0
mig	$\mathbb{IR} \rightarrow \mathbb{R}$	0

Boolean functions

Operation	Function Description	Error [ulps]
equal	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
subset	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
interior	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
disjoint	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
isEmpty	$\mathbb{IR} \rightarrow \mathbb{B}$	0
isEntire	$\mathbb{IR} \rightarrow \mathbb{B}$	0
less	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
strictLess	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
precedes	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
strictPrecedes	$\mathbb{IR}^2 \rightarrow \mathbb{B}$	0
isMember	$\mathbb{R} \times \mathbb{IR} \rightarrow \mathbb{B}$	0
isSingleton	$\mathbb{IR} \rightarrow \mathbb{B}$	0
isCommonInterval	$\mathbb{IR} \rightarrow \mathbb{B}$	0

Set operations

Operation	Function Description	Error [ulps]
intersection	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
convexHull	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0

Cancellative add and subtract

Operation	Function Description	Error [ulps]
cancelMinus	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0
cancelPlus	$\mathbb{IR}^2 \rightarrow \mathbb{IR}$	0

Installation

Please make sure that you have installed everything mentioned in the section Build Requirements.

System-wide

git clone https://github.com/neilkichler/cuinterval.git
cd cuinterval
cmake --preset release
cmake --build build
cmake --install build

CMake Project

CPM.cmake

CPMAddPackage("gh:neilkichler/[email protected]")

FetchContent

include(FetchContent)
FetchContent_Declare(
  cuinterval
  GIT_REPOSITORY [email protected]:neilkichler/cuinterval.git
  GIT_TAG main
)
FetchContent_MakeAvailable(cuinterval)

In either case, you can link to the library using:

target_link_libraries(${PROJECT_NAME} PUBLIC cuinterval)

Example

Have a look at the examples folder.

Documentation

The documentation is available here.

Build

Build Requirements

We use C++20, CMake v3.25.2+, Ninja (optional), and a recent C++ and CUDA compiler.

Ubuntu

apt install cmake gcc ninja-build

Cluster

module load CMake CUDA GCC Ninja

Build and run tests

Using Workflows

cmake --workflow --preset dev

Using Presets

cmake --preset debug
cmake --build --preset debug
ctest --preset debug

Using regular CMake

cmake -S . -B build -GNinja
cmake --build build
./build/tests/tests