diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md
index 8f8856b436d6..b68857550bd2 100644
--- a/lib/node_modules/@stdlib/math/base/special/ellipe/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/README.md
@@ -114,6 +114,96 @@ for ( i = 0; i < 100; i++ ) {
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/ellipe.h"
+```
+
+#### stdlib_base_ellipe( m )
+
+Computes the [complete elliptic integral of the second kind][elliptic-integral].
+
+```c
+double out = stdlib_base_ellipe( 0.5 );
+// returns ~1.351
+
+out = stdlib_base_ellipe( -1.0 );
+// returns ~1.910
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] double` input value.
+
+```c
+double stdlib_base_ellipe( const double m );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+#include "stdlib/math/base/special/ellipe.h"
+#include
+#include
+
+int main( void ) {
+ double m;
+ double v;
+ int i;
+
+ for ( i = 0; i < 100; i++ ) {
+ m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 );
+ v = stdlib_base_ellipe( m );
+ printf( "ellipe(%lf) = %lf\n", m, v );
+ }
+}
+```
+
+
+
+
+
+
+
+
+
* * *
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.native.js
new file mode 100644
index 000000000000..b079507c24aa
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/benchmark.native.js
@@ -0,0 +1,58 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var ellipe = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( ellipe instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+ var y;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = ellipe( randu() );
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile
new file mode 100644
index 000000000000..f69e9da2b4d3
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c
new file mode 100644
index 000000000000..0552db4c3c1b
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/benchmark/c/native/benchmark.c
@@ -0,0 +1,136 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+/**
+* Benchmark `ellipe`.
+*/
+#include "stdlib/math/base/special/ellipe.h"
+#include
+#include
+#include
+#include
+#include
+
+#define NAME "ellipe"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+void print_version() {
+ printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total total number of tests
+* @param passing total number of passing tests
+*/
+void print_summary( int total, int passing ) {
+ printf( "#\n" );
+ printf( "1..%d\n", total ); // TAP plan
+ printf( "# total %d\n", total );
+ printf( "# pass %d\n", passing );
+ printf( "#\n" );
+ printf( "# ok\n" );
+}
+
+/**
+* Prints benchmarks results.
+*
+* @param elapsed elapsed time in seconds
+*/
+void print_results( double elapsed ) {
+ double rate = (double)ITERATIONS / elapsed;
+ printf( " ---\n" );
+ printf( " iterations: %d\n", ITERATIONS );
+ printf( " elapsed: %0.9f\n", elapsed );
+ printf( " rate: %0.9f\n", rate );
+ printf( " ...\n" );
+}
+
+/**
+* Returns a clock time.
+*
+* @return clock time
+*/
+double tic() {
+ struct timeval now;
+ gettimeofday( &now, NULL );
+ return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
+}
+
+/**
+* Generates a random number on the interval [0,1].
+*
+* @return random number
+*/
+double rand_double() {
+ int r = rand();
+ return (double)r / ( (double)RAND_MAX + 1.0 );
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+double benchmark() {
+ double elapsed;
+ double x;
+ double y;
+ double t;
+ int i;
+
+ t = tic();
+ for ( i = 0; i < ITERATIONS; i++ ) {
+ x = rand_double();
+ y = stdlib_base_ellipe( x );
+ if ( y != y ) {
+ printf( "should not return NaN\n" );
+ break;
+ }
+ }
+ elapsed = tic() - t;
+ if ( y != y ) {
+ printf( "should not return NaN\n" );
+ }
+ return elapsed;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+ double elapsed;
+ int i;
+
+ // Use the current time to seed the random number generator:
+ srand( time( NULL ) );
+
+ print_version();
+ for ( i = 0; i < REPEATS; i++ ) {
+ printf( "# c::native::%s\n", NAME );
+ elapsed = benchmark();
+ print_results( elapsed );
+ printf( "ok %d benchmark finished\n", i+1 );
+ }
+ print_summary( REPEATS, REPEATS );
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp b/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp
new file mode 100644
index 000000000000..ec3992233442
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/binding.gyp
@@ -0,0 +1,170 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A `.gyp` file for building a Node.js native add-on.
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # List of files to include in this file:
+ 'includes': [
+ './include.gypi',
+ ],
+
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Target name should match the add-on export name:
+ 'addon_target_name%': 'addon',
+
+ # Set variables based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="win"',
+ {
+ # Define the object file suffix:
+ 'obj': 'obj',
+ },
+ {
+ # Define the object file suffix:
+ 'obj': 'o',
+ }
+ ], # end condition (OS=="win")
+ ], # end conditions
+ }, # end variables
+
+ # Define compile targets:
+ 'targets': [
+
+ # Target to generate an add-on:
+ {
+ # The target name should match the add-on export name:
+ 'target_name': '<(addon_target_name)',
+
+ # Define dependencies:
+ 'dependencies': [],
+
+ # Define directories which contain relevant include headers:
+ 'include_dirs': [
+ # Local include directory:
+ '<@(include_dirs)',
+ ],
+
+ # List of source files:
+ 'sources': [
+ '<@(src_files)',
+ ],
+
+ # Settings which should be applied when a target's object files are used as linker input:
+ 'link_settings': {
+ # Define libraries:
+ 'libraries': [
+ '<@(libraries)',
+ ],
+
+ # Define library directories:
+ 'library_dirs': [
+ '<@(library_dirs)',
+ ],
+ },
+
+ # C/C++ compiler flags:
+ 'cflags': [
+ # Enable commonly used warning options:
+ '-Wall',
+
+ # Aggressive optimization:
+ '-O3',
+ ],
+
+ # C specific compiler flags:
+ 'cflags_c': [
+ # Specify the C standard to which a program is expected to conform:
+ '-std=c99',
+ ],
+
+ # C++ specific compiler flags:
+ 'cflags_cpp': [
+ # Specify the C++ standard to which a program is expected to conform:
+ '-std=c++11',
+ ],
+
+ # Linker flags:
+ 'ldflags': [],
+
+ # Apply conditions based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="mac"',
+ {
+ # Linker flags:
+ 'ldflags': [
+ '-undefined dynamic_lookup',
+ '-Wl,-no-pie',
+ '-Wl,-search_paths_first',
+ ],
+ },
+ ], # end condition (OS=="mac")
+ [
+ 'OS!="win"',
+ {
+ # C/C++ flags:
+ 'cflags': [
+ # Generate platform-independent code:
+ '-fPIC',
+ ],
+ },
+ ], # end condition (OS!="win")
+ ], # end conditions
+ }, # end target <(addon_target_name)
+
+ # Target to copy a generated add-on to a standard location:
+ {
+ 'target_name': 'copy_addon',
+
+ # Declare that the output of this target is not linked:
+ 'type': 'none',
+
+ # Define dependencies:
+ 'dependencies': [
+ # Require that the add-on be generated before building this target:
+ '<(addon_target_name)',
+ ],
+
+ # Define a list of actions:
+ 'actions': [
+ {
+ 'action_name': 'copy_addon',
+ 'message': 'Copying addon...',
+
+ # Explicitly list the inputs in the command-line invocation below:
+ 'inputs': [],
+
+ # Declare the expected outputs:
+ 'outputs': [
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+
+ # Define the command-line invocation:
+ 'action': [
+ 'cp',
+ '<(PRODUCT_DIR)/<(addon_target_name).node',
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+ },
+ ], # end actions
+ }, # end target copy_addon
+ ], # end targets
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile
new file mode 100644
index 000000000000..6aed70daf167
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := example.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled examples.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c
new file mode 100644
index 000000000000..8cbeb7c8f97c
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/examples/c/example.c
@@ -0,0 +1,33 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/math/base/special/ellipe.h"
+#include
+#include
+
+int main( void ) {
+ double m;
+ double v;
+ int i;
+
+ for ( i = 0; i < 100; i++ ) {
+ m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 );
+ v = stdlib_base_ellipe( m );
+ printf( "ellipe(%lf) = %lf\n", m, v );
+ }
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi
new file mode 100644
index 000000000000..575cb043c0bf
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/include.gypi
@@ -0,0 +1,53 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A GYP include file for building a Node.js native add-on.
+#
+# Main documentation:
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Source directory:
+ 'src_dir': './src',
+
+ # Include directories:
+ 'include_dirs': [
+ '
+
+/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */
+
+// BEGIN: poly_p1
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p1( const double x ) {
+ return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322)))))))))))))))))));
+}
+
+// END: poly_p1
+
+// BEGIN: poly_p2
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p2( const double x ) {
+ return 1.63525673226458 + (x * (0.4711906261487323 + (x * (0.3097284108314996 + (x * (0.2522083117731357 + (x * (0.22672562321968465 + (x * (0.21577444672958598 + (x * (0.21310877187734892 + (x * (0.21602912460518828 + (x * (0.2232558316330579 + (x * (0.23418050129420992 + (x * (0.24855768297226408 + (x * 0.26636380989261754)))))))))))))))))))));
+}
+
+// END: poly_p2
+
+// BEGIN: poly_p3
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p3( const double x ) {
+ return 1.685750354812596 + (x * (0.5417318486132803 + (x * (0.40152443839069024 + (x * (0.3696424734208891 + (x * (0.37606071535458363 + (x * (0.4052358870851259 + (x * (0.45329438175399905 + (x * (0.5205189476511842 + (x * (0.609426039204995 + (x * (0.7242635222829089 + (x * (0.8710138477098124 + (x * 1.057652872753547)))))))))))))))))))));
+}
+
+// END: poly_p3
+
+// BEGIN: poly_p4
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p4( const double x ) {
+ return 1.7443505972256133 + (x * (0.6348642753719353 + (x * (0.5398425641644455 + (x * (0.5718927051937874 + (x * (0.6702951362654062 + (x * (0.8325865900109772 + (x * (1.0738574482479333 + (x * (1.4220914606754977 + (x * (1.9203871834023047 + (x * (2.6325525483316543 + (x * (3.6521097473190394 + (x * (5.115867135558866 + (x * 7.224080007363877)))))))))))))))))))))));
+}
+
+// END: poly_p4
+
+// BEGIN: poly_p5
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p5( const double x ) {
+ return 1.8138839368169826 + (x * (0.7631632457005573 + (x * (0.7619286053215958 + (x * (0.9510746536684279 + (x * (1.315180671703161 + (x * (1.9285606934774109 + (x * (2.9375093425313787 + (x * (4.594894405442878 + (x * (7.33007122188172 + (x * (11.871512597425301 + (x * (19.45851374822938 + (x * (32.20638657246427 + (x * (53.73749198700555 + (x * 90.27388602941)))))))))))))))))))))))));
+}
+
+// END: poly_p5
+
+// BEGIN: poly_p6
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p6( const double x ) {
+ return 1.8989249102715535 + (x * (0.9505217946182445 + (x * (1.1510775899590158 + (x * (1.7502391069863006 + (x * (2.952676812636875 + (x * (5.285800396121451 + (x * (9.83248571665998 + (x * (18.787148683275596 + (x * (36.61468615273698 + (x * (72.45292395127771 + (x * (145.1079577347069 + (x * (293.4786396308497 + (x * (598.385181505501 + (x * (1228.4200130758634 + (x * 2536.5297553827645)))))))))))))))))))))))))));
+}
+
+// END: poly_p6
+
+// BEGIN: poly_p7
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p7( const double x ) {
+ return 2.0075983984243764 + (x * (1.2484572312123474 + (x * (1.9262346570764797 + (x * (3.7512896400875877 + (x * (8.119944554932045 + (x * (18.665721308735552 + (x * (44.603924842914374 + (x * (109.50920543094983 + (x * (274.2779548232414 + (x * (697.5598008606327 + (x * (1795.7160145002472 + (x * (4668.38171679039 + (x * (12235.762468136643 + (x * (32290.17809718321 + (x * (85713.07608195965 + (x * (228672.1890493117 + (x * 612757.2711915852)))))))))))))))))))))))))))))));
+}
+
+// END: poly_p7
+
+// BEGIN: poly_p8
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p8( const double x ) {
+ return 2.1565156474996434 + (x * (1.7918056418494632 + (x * (3.8267512874657132 + (x * (10.386724683637972 + (x * (31.403314054680703 + (x * (100.92370394986955 + (x * (337.3268282632273 + (x * (1158.7079305678278 + (x * (4060.9907421936323 + (x * (14454.001840343448 + (x * (52076.661075994045 + (x * (189493.65914621568 + (x * (695184.5762413896 + (x * (2567994.048255285 + (x * (9541921.966748387 + (x * (35634927.44218076 + (x * (133669298.46120408 + (x * (503352186.68662846 + (x * (1901975729.53866 + (x * 7208915015.330104)))))))))))))))))))))))))))))))))))));
+}
+
+// END: poly_p8
+
+// BEGIN: poly_p9
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p9( const double x ) {
+ return 2.3181226217125106 + (x * (2.6169201502912327 + (x * (7.897935075731356 + (x * (30.502397154466724 + (x * (131.48693655235286 + (x * (602.9847637356492 + (x * (2877.024617809973 + (x * (14110.519919151804 + (x * (70621.4408815654 + (x * (358977.266582531 + (x * (1847238.2637239718 + (x * (9600515.416049214 + (x * (50307677.08502367 + (x * (265444188.6527128 + (x * (1408862325.0287027 + (x * 7515687935.373775)))))))))))))))))))))))))))));
+}
+
+// END: poly_p9
+
+// BEGIN: poly_p10
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p10( const double x ) {
+ return 2.473596173751344 + (x * (3.727624244118099 + (x * (15.607393035549306 + (x * (84.12850842805888 + (x * (506.98181970406137 + (x * (3252.2770581451236 + (x * (21713.242419574344 + (x * (149037.04518909327 + (x * (1043999.3310899908 + (x * (7427974.817042039 + (x * (53503839.67558661 + (x * (389249886.99487084 + (x * (2855288351.1008105 + (x * (21090077038.76684 + (x * (156699833947.7902 + (x * (1170222242422.44 + (x * (8777948323668.9375 + (x * (66101242752484.95 + (x * (499488053713388.8 + (x * 37859743397240296.0)))))))))))))))))))))))))))))))))))));
+}
+
+// END: poly_p10
+
+// BEGIN: poly_p11
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p11( const double x ) {
+ return 0.0 + (x * (0.0625 + (x * (0.03125 + (x * (0.0205078125 + (x * (0.01513671875 + (x * (0.011934280395507812 + (x * (0.009816169738769531 + (x * (0.008315593004226685 + (x * (0.007199153304100037 + (x * (0.00633745662344154 + (x * (0.00565311038371874 + (x * (0.005097046040418718 + (x * (0.004636680381850056 + (x * (0.004249547423822886 + (x * 0.003919665602267974)))))))))))))))))))))))))));
+}
+
+// END: poly_p11
+
+// BEGIN: poly_p12
+
+/**
+* Evaluates a polynomial.
+*
+* ## Notes
+*
+* - The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x value at which to evaluate the polynomial
+* @return evaluated polynomial
+*/
+static double poly_p12( const double x ) {
+ return 1.5910034537907922 + (x * (0.41600074399178694 + (x * (0.24579151426410342 + (x * (0.17948148291490615 + (x * (0.14455605708755515 + (x * (0.12320099331242772 + (x * (0.10893881157429353 + (x * (0.09885340987159291 + (x * (0.09143962920174975 + (x * (0.0858425915954139 + (x * 0.08154111871830322)))))))))))))))))));
+}
+
+// END: poly_p12
+
+/* End auto-generated functions. */
+
+/**
+* Computes the complete elliptic integral of the second kind.
+*
+* @param x input value
+* @return output value
+*
+* @example
+* double out = stdlib_base_ellipe( 0.5 );
+* // returns ~1.351
+*/
+double stdlib_base_ellipe( const double m ) {
+ int8_t FLG;
+ double kdm;
+ double edm;
+ double td;
+ double km;
+ double t;
+ double x;
+
+ FLG = 0;
+ x = m;
+ if ( m < 0.0 ) {
+ x = m / ( m - 1.0 );
+ FLG += 1;
+ }
+ if ( x == 0.0 ) {
+ return STDLIB_CONSTANT_FLOAT64_HALF_PI;
+ }
+ if ( x == 1.0 ) {
+ return 1.0;
+ }
+ if ( x > 1.0 ) {
+ return 0.0 / 0.0; // NaN
+ }
+ if ( x < 0.1 ) {
+ t = poly_p1( x - 0.05 );
+ } else if ( x < 0.2 ) {
+ t = poly_p2( x - 0.15 );
+ } else if ( x < 0.3 ) {
+ t = poly_p3( x - 0.25 );
+ } else if ( x < 0.4 ) {
+ t = poly_p4( x - 0.35 );
+ } else if ( x < 0.5 ) {
+ t = poly_p5( x - 0.45 );
+ } else if ( x < 0.6 ) {
+ t = poly_p6( x - 0.55 );
+ } else if ( x < 0.7 ) {
+ t = poly_p7( x - 0.65 );
+ } else if ( x < 0.8 ) {
+ t = poly_p8( x - 0.75 );
+ } else if ( x < 0.85 ) {
+ t = poly_p9( x - 0.825 );
+ } else if ( x < 0.9 ) {
+ t = poly_p10( x - 0.875 );
+ } else {
+ td = 0.95 - x;
+ kdm = poly_p11( td );
+ edm = poly_p12( td );
+ km = ellipe( x );
+
+ // To avoid precision loss near 1, we use Eq. 33 from Fukushima (2009):
+ t = ( STDLIB_CONSTANT_FLOAT64_HALF_PI + ( km * (kdm - edm) ) ) / kdm;
+ }
+ if ( FLG == 1 ) {
+ // Complete the transformation mentioned above for m < 0:
+ return t * stdlib_base_sqrt( 1.0 - m );
+ }
+ return t;
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js
new file mode 100644
index 000000000000..373285710255
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/ellipe/test/test.native.js
@@ -0,0 +1,155 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+var HALF_PI = require( '@stdlib/constants/float64/half-pi' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+
+
+// FIXTURES //
+
+var mediumPositive = require( './fixtures/cpp/medium_positive.json' );
+var closeToUnity = require( './fixtures/cpp/close_to_unity.json' );
+var negativeSpotChecks = require( './fixtures/wolframalpha/negative_spot_checks.json' );
+
+
+// VARIABLES //
+
+var ellipe = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( ellipe instanceof Error )
+};
+
+
+// TESTS //
+
+tape( 'main export is a function', opts, function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof ellipe, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function evaluates the complete elliptic integral of the second kind (values close to positive unity)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = closeToUnity.expected;
+ x = closeToUnity.x;
+ for ( i = 0; i < x.length; i++ ) {
+ y = ellipe( x[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[i] );
+ tol = 4.0 * EPS * abs( expected[i] );
+ t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function evaluates the complete elliptic integral of the second kind (medium positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = mediumPositive.expected;
+ x = mediumPositive.x;
+ for ( i = 0; i < x.length; i++ ) {
+ y = ellipe( x[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[i] );
+ tol = 5.0 * EPS * abs( expected[i] );
+ t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function evaluates the complete elliptic integral of the second kind (spot checked negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ // The spot checked values are derived from Wolfram Alpha and cross-checked against Maxima. For example, to compute E(-0.1): https://www.wolframalpha.com/input/?i=EllipticE(-0.1)
+ expected = negativeSpotChecks.expected;
+ x = negativeSpotChecks.x;
+ for ( i = 0; i < x.length; i++ ) {
+ y = ellipe( x[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[i] );
+ tol = 2.2 * EPS * abs( expected[i] );
+ t.equal( delta <= tol, true, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function returns `NaN` if provided values larger than `1.0`', opts, function test( t ) {
+ var v = ellipe( 1.01 );
+ t.equal( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns `1.0` if provided `1.0`', opts, function test( t ) {
+ var v = ellipe( 1.0 );
+ t.equal( v, 1.0, 'return expected value' );
+ t.end();
+});
+
+tape( 'the function returns `NaN` if provided `+infinity`', opts, function test( t ) {
+ var v = ellipe( PINF );
+ t.equal( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns `NaN` if provided `-infinity`', opts, function test( t ) {
+ var v = ellipe( NINF );
+ t.equal( isnan( v ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns `π/2` if provided `0`', opts, function test( t ) {
+ var v = ellipe( 0 );
+ t.equal( v, HALF_PI, 'returns expected value' );
+ t.end();
+});