diff --git a/CHANGELOG.md b/CHANGELOG.md
index 475fa24a3..6c6ffb8e2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -494,6 +494,40 @@
+
+
+#### [@stdlib/math/base/special/sec](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sec)
+
+
+
+
+
+##### Features
+
+- [`ed4c8d6`](https://github.com/stdlib-js/stdlib/commit/ed4c8d65a020d119c4baa1eb6716751c75cf8a07) - add support for secant functionality `math/base/special/sec` [(#3027)](https://github.com/stdlib-js/stdlib/pull/3027)
+
+
+
+
+
+
+
+##### Closed Issues
+
+This release closes the following issue:
+
+[#225](https://github.com/stdlib-js/stdlib/issues/225)
+
+
+
+
+
+
+
+
+
+
+
#### [@stdlib/math/base/special/xlogyf](https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/xlogyf)
@@ -520,13 +554,26 @@
+
+
+### Closed Issues
+
+This release closes the following issue:
+
+[#225](https://github.com/stdlib-js/stdlib/issues/225)
+
+
+
+
+
### Contributors
-A total of 6 people contributed to this release. Thank you to the following contributors:
+A total of 7 people contributed to this release. Thank you to the following contributors:
- Aayush Khanna
+- AbhijitRaut04
- Aman Bhansali
- Athan Reines
- Ayaka
@@ -543,6 +590,7 @@ A total of 6 people contributed to this release. Thank you to the following cont
+- [`ed4c8d6`](https://github.com/stdlib-js/stdlib/commit/ed4c8d65a020d119c4baa1eb6716751c75cf8a07) - **feat:** add support for secant functionality `math/base/special/sec` [(#3027)](https://github.com/stdlib-js/stdlib/pull/3027) _(by AbhijitRaut04, Athan Reines, Philipp Burckhardt)_
- [`b18921a`](https://github.com/stdlib-js/stdlib/commit/b18921a136da2755efccfd6ae23c8b3f5aaa8f4a) - **feat:** add `math/base/special/acosdf` [(#3015)](https://github.com/stdlib-js/stdlib/pull/3015) _(by Aayush Khanna, Athan Reines)_
- [`60522bf`](https://github.com/stdlib-js/stdlib/commit/60522bfc0b5574d348301e788400178156731024) - **docs:** fix operator [(#3039)](https://github.com/stdlib-js/stdlib/pull/3039) _(by Gunj Joshi)_
- [`84b8294`](https://github.com/stdlib-js/stdlib/commit/84b8294c2d5494ff5eaaa2652dda81671e728068) - **feat:** add `math/base/special/nanmaxf` [(#3035)](https://github.com/stdlib-js/stdlib/pull/3035) _(by Gunj Joshi, Athan Reines)_
diff --git a/base/special/sec/README.md b/base/special/sec/README.md
new file mode 100644
index 000000000..4ba7829d8
--- /dev/null
+++ b/base/special/sec/README.md
@@ -0,0 +1,193 @@
+
+
+# Secant
+
+> Evaluate the [secant][trigonometric-functions] of a number.
+
+
+
+
+
+## Usage
+
+```javascript
+var sec = require( '@stdlib/math/base/special/sec' );
+```
+
+## sec( x )
+
+Evaluates the [secant][trigonometric-functions] of `x` (in radians).
+
+```javascript
+var v = sec( 0.0 );
+// returns 1.0
+
+v = sec( 3.141592653589793/2.0 );
+// returns 16331239353195370.0
+
+v = sec( -3.141592653589793/3.0 );
+// returns ~1.9999999999999996
+
+v = sec( 3.141592653589793/3.0 );
+// returns ~1.9999999999999996
+
+v = sec( NaN );
+// returns NaN
+```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var PI = require( '@stdlib/constants/float64/pi' );
+var sec = require( '@stdlib/math/base/special/sec' );
+
+var x = linspace( -PI/2.0, PI/2.0, 100 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+ console.log( sec( x[ i ] ) );
+}
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/sec.h"
+```
+
+#### stdlib_base_sec( x )
+
+Evaluates the [secant][trigonometric-functions] of `x` (in radians).
+
+```c
+double out = stdlib_base_sec( 0.0 );
+// returns 1.0
+
+out = stdlib_base_cos( 3.141592653589793 / 2.0 );
+// returns 6.123233995736766e-17
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] double` input value.
+
+```c
+double stdlib_base_sec( const double x );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+#include "stdlib/math/base/special/sec.h"
+#include
+
+int main( void ) {
+ const double x[] = { 0.523, 0.785, 1.047, 3.14 };
+
+ double y;
+ int i;
+ for ( i = 0; i < 4; i++ ) {
+ y = stdlib_base_sec( x[ i ] );
+ printf( "sec(%lf) = %lf\n", x[ i ], y );
+ }
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions
+
+
+
+
+
+
+
+
diff --git a/base/special/sec/benchmark/benchmark.js b/base/special/sec/benchmark/benchmark.js
new file mode 100644
index 000000000..69c863a04
--- /dev/null
+++ b/base/special/sec/benchmark/benchmark.js
@@ -0,0 +1,73 @@
+/**
+* @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 bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( './../../../../base/assert/is-nan' );
+var cos = require( './../../../../base/special/cos' );
+var pkg = require( './../package.json' ).name;
+var sec = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var x;
+ var y;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ x = (randu() * 20.0) - 10.0;
+ y = sec( x );
+ 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();
+});
+
+bench( pkg + '::built-in', function benchmark( b ) {
+ var x;
+ var y;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ x = (randu() * 20.0) - 10.0;
+ y = 1.0 / cos( x );
+ 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/base/special/sec/benchmark/benchmark.native.js b/base/special/sec/benchmark/benchmark.native.js
new file mode 100644
index 000000000..455209831
--- /dev/null
+++ b/base/special/sec/benchmark/benchmark.native.js
@@ -0,0 +1,60 @@
+/**
+* @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( './../../../../base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var sec = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( sec instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+ var x;
+ var y;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ x = (randu() * 20.0) - 10.0;
+ y = sec( x );
+ 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/base/special/sec/benchmark/c/native/Makefile b/base/special/sec/benchmark/c/native/Makefile
new file mode 100644
index 000000000..f69e9da2b
--- /dev/null
+++ b/base/special/sec/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/base/special/sec/benchmark/c/native/benchmark.c b/base/special/sec/benchmark/c/native/benchmark.c
new file mode 100644
index 000000000..b1842520f
--- /dev/null
+++ b/base/special/sec/benchmark/c/native/benchmark.c
@@ -0,0 +1,133 @@
+/**
+* @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/sec.h"
+#include
+#include
+#include
+#include
+#include
+
+#define NAME "sec"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+static void print_version( void ) {
+ printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total total number of tests
+* @param passing total number of passing tests
+*/
+static 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
+*/
+static 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
+*/
+static double tic( void ) {
+ 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
+*/
+static double rand_double( void ) {
+ int r = rand();
+ return (double)r / ( (double)RAND_MAX + 1.0 );
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+static double benchmark( void ) {
+ double elapsed;
+ double x;
+ double y;
+ double t;
+ int i;
+
+ t = tic();
+ for ( i = 0; i < ITERATIONS; i++ ) {
+ x = ( 20.0 * rand_double() ) - 10.0;
+ y = stdlib_base_sec( 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/base/special/sec/binding.gyp b/base/special/sec/binding.gyp
new file mode 100644
index 000000000..ec3992233
--- /dev/null
+++ b/base/special/sec/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/base/special/sec/docs/repl.txt b/base/special/sec/docs/repl.txt
new file mode 100644
index 000000000..db2bae923
--- /dev/null
+++ b/base/special/sec/docs/repl.txt
@@ -0,0 +1,27 @@
+
+{{alias}}( x )
+ Computes the secant of a number.
+
+ Parameters
+ ----------
+ x: number
+ Input value (in radians).
+
+ Returns
+ -------
+ y: number
+ Secant.
+
+ Examples
+ --------
+ > var y = {{alias}}( 0.0 )
+ 1.0
+ > y = {{alias}}( {{alias:@stdlib/constants/float64/pi}}/2.0 )
+ 16331239353195370.0
+ > y = {{alias}}( -{{alias:@stdlib/constants/float64/pi}}/3.0 )
+ ~1.9999999999999996
+ > y = {{alias}}( NaN )
+ NaN
+
+ See Also
+ --------
diff --git a/base/special/sec/docs/types/index.d.ts b/base/special/sec/docs/types/index.d.ts
new file mode 100644
index 000000000..96254288f
--- /dev/null
+++ b/base/special/sec/docs/types/index.d.ts
@@ -0,0 +1,48 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Computes the secant of a number.
+*
+* @param x - input value (in radians)
+* @returns secant
+*
+* @example
+* var v = sec( 0.0 );
+* // returns 1.0
+*
+* @example
+* var v = sec( 3.141592653589793/2.0 );
+* // returns 16331239353195370.0
+*
+* @example
+* var v = sec( -3.141592653589793/3.0 );
+* // returns ~1.9999999999999996
+*
+* @example
+* var v = sec( NaN );
+* // returns NaN
+*/
+declare function sec( x: number ): number;
+
+
+// EXPORTS //
+
+export = sec;
diff --git a/base/special/sec/docs/types/test.ts b/base/special/sec/docs/types/test.ts
new file mode 100644
index 000000000..4019a606c
--- /dev/null
+++ b/base/special/sec/docs/types/test.ts
@@ -0,0 +1,44 @@
+/*
+* @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.
+*/
+
+import sec = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ sec( 2 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number...
+{
+ sec( true ); // $ExpectError
+ sec( false ); // $ExpectError
+ sec( null ); // $ExpectError
+ sec( undefined ); // $ExpectError
+ sec( '5' ); // $ExpectError
+ sec( [] ); // $ExpectError
+ sec( {} ); // $ExpectError
+ sec( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+ sec(); // $ExpectError
+}
diff --git a/base/special/sec/examples/c/Makefile b/base/special/sec/examples/c/Makefile
new file mode 100644
index 000000000..6aed70daf
--- /dev/null
+++ b/base/special/sec/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/base/special/sec/examples/c/example.c b/base/special/sec/examples/c/example.c
new file mode 100644
index 000000000..e341d8bdf
--- /dev/null
+++ b/base/special/sec/examples/c/example.c
@@ -0,0 +1,31 @@
+/**
+* @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/sec.h"
+#include
+
+int main( void ) {
+ const double x[] = { 0.523, 0.785, 1.047, 3.14 };
+
+ double y;
+ int i;
+ for ( i = 0; i < 4; i++ ) {
+ y = stdlib_base_sec( x[ i ] );
+ printf( "sec(%lf) = %lf\n", x[ i ], y );
+ }
+}
diff --git a/base/special/sec/examples/index.js b/base/special/sec/examples/index.js
new file mode 100644
index 000000000..ec7bc015f
--- /dev/null
+++ b/base/special/sec/examples/index.js
@@ -0,0 +1,30 @@
+/**
+* @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';
+
+var linspace = require( '@stdlib/array/base/linspace' );
+var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
+var sec = require( './../lib' );
+
+var x = linspace( -TWO_PI, TWO_PI, 100 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+ console.log( 'sec(%d) = %d', x[ i ], sec( x[ i ] ) );
+}
diff --git a/base/special/sec/include.gypi b/base/special/sec/include.gypi
new file mode 100644
index 000000000..575cb043c
--- /dev/null
+++ b/base/special/sec/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': [
+ '=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "mathematics",
+ "math",
+ "math.cos",
+ "cos",
+ "cosine",
+ "sec",
+ "trig",
+ "trigonometry",
+ "radians",
+ "angle"
+ ]
+}
diff --git a/base/special/sec/src/Makefile b/base/special/sec/src/Makefile
new file mode 100644
index 000000000..bcf18aa46
--- /dev/null
+++ b/base/special/sec/src/Makefile
@@ -0,0 +1,70 @@
+#/
+# @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
+
+
+# RULES #
+
+#/
+# Removes generated files for building an add-on.
+#
+# @example
+# make clean-addon
+#/
+clean-addon:
+ $(QUIET) -rm -f *.o *.node
+
+.PHONY: clean-addon
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean: clean-addon
+
+.PHONY: clean
diff --git a/base/special/sec/src/addon.c b/base/special/sec/src/addon.c
new file mode 100644
index 000000000..40bb3e327
--- /dev/null
+++ b/base/special/sec/src/addon.c
@@ -0,0 +1,23 @@
+/**
+* @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/sec.h"
+#include "stdlib/math/base/napi/unary.h"
+
+// cppcheck-suppress shadowFunction
+STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_sec )
diff --git a/base/special/sec/src/main.c b/base/special/sec/src/main.c
new file mode 100644
index 000000000..4d139884a
--- /dev/null
+++ b/base/special/sec/src/main.c
@@ -0,0 +1,34 @@
+/**
+* @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/sec.h"
+#include "stdlib/math/base/special/cos.h"
+
+/**
+* Evaluates the cosecant of a number.
+*
+* @param x input value (in radians)
+* @return secant
+*
+* @example
+* double y = stdlib_base_sec( 3.141592653589793 / 2.0 );
+* // returns 16331239353195370.0
+*/
+double stdlib_base_sec( const double x ) {
+ return 1.0 / stdlib_base_cos( x );
+}
diff --git a/base/special/sec/test/fixtures/julia/REQUIRE b/base/special/sec/test/fixtures/julia/REQUIRE
new file mode 100644
index 000000000..ae40bf736
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/REQUIRE
@@ -0,0 +1,2 @@
+julia 1.5
+JSON 0.21
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/huge_negative.json b/base/special/sec/test/fixtures/julia/huge_negative.json
new file mode 100644
index 000000000..5a75ae723
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/huge_negative.json
@@ -0,0 +1,2006 @@
+{
+ "expected": [
+ 11.156638017887909,
+ 1.2704068118116802,
+ 4.180454226467146,
+ -2.4356748521961293,
+ -1.1292307102493453,
+ -1.0167043383157772,
+ -1.5085807766926251,
+ -16.668682554839517,
+ 1.759237224924984,
+ 1.0419856300916297,
+ 1.0697242743423312,
+ 1.9903772529758692,
+ -8.251212008916879,
+ -1.3901609015744856,
+ -1.0072504491967709,
+ -1.1812479596472234,
+ -2.8266247875432193,
+ 3.18135505274521,
+ 1.1875472965575062,
+ 1.0030655706531908,
+ 1.3372951115845477,
+ 7.721483596232872,
+ -2.019575020053436,
+ -1.0879711039687816,
+ -1.0302651989803502,
+ -1.7382140877380639,
+ 28.65042106115765,
+ 1.5848750567251442,
+ 1.0295367976358973,
+ 1.1243275731938096,
+ 2.307680847003251,
+ -5.04108048417328,
+ -1.333900536320725,
+ -1.0000351182745697,
+ -1.2462744836224302,
+ -3.576183231724687,
+ 2.391374340024271,
+ 1.1342568117106437,
+ 1.0123569564328885,
+ 1.4417039707939896,
+ 8.449929768934275,
+ -1.78090173540327,
+ -1.034709381602863,
+ -1.0538950064229076,
+ -1.9621475464413132,
+ 21.670536349739198,
+ 1.4500229708323564,
+ 1.0045259895709842,
+ 1.130938454523418,
+ 2.765449005209118,
+ -2.9581193232878142,
+ -1.2514218375125001,
+ -1.0024424598381412,
+ -1.413166356010486,
+ -4.907555478953208,
+ 2.04978828004182,
+ 1.127537394265044,
+ 1.0281654033035077,
+ 1.717806699846439,
+ 24.746726568004977,
+ -1.601433054091961,
+ -1.0167087443281366,
+ -1.085424480304672,
+ -2.2682266357623715,
+ 8.061690936984334,
+ 1.343889954642629,
+ 1.0001404854322504,
+ 1.183388925589299,
+ 3.476276625508969,
+ -2.43580257367371,
+ -1.1853725057007105,
+ -1.0110563162238937,
+ -1.5378265176135644,
+ -7.8950505097576515,
+ 1.803234711055636,
+ 1.0866386160630845,
+ 1.05100144743814,
+ 1.9348414018822968,
+ -26.474351724934383,
+ -1.462947987882786,
+ -1.0288178985478338,
+ -1.2213108831797752,
+ -2.7070512440445453,
+ 4.970596372230001,
+ 1.1519803969856925,
+ 1.0018904458745699,
+ 1.2489464138843316,
+ 12.562797388133538,
+ -2.0810676442834932,
+ -1.1325211122331236,
+ -1.004277048871493,
+ -1.6979908075505181,
+ -20.499522155833425,
+ 1.9709352210713396,
+ 1.0183110538186402,
+ 1.0816365089075841,
+ 1.7740089318781982,
+ -4.0438105335843275,
+ -1.3541259443705087,
+ -1.0127819488917504,
+ -1.296275669768132,
+ -3.382031503513602,
+ 3.6088961624755087,
+ 1.1059495672446507,
+ 1.0098298472278604,
+ 1.3308048809512305,
+ 674.48164812617,
+ -1.8262648177123793,
+ -1.0905628904710256,
+ -1.0147177937410943,
+ -1.9084170317118503,
+ 34.01758868100464,
+ 1.744766529684393,
+ 1.0062737733871185,
+ 1.121169915025429,
+ 2.0102736037923585,
+ -3.103359378455869,
+ -1.2675841156247938,
+ -1.0032765374195936,
+ -1.3900975167118756,
+ -4.542407231048973,
+ 2.846494785697001,
+ 1.0697434641376224,
+ 1.0242064529134087,
+ 1.4335231513214022,
+ -13.047347987936382,
+ -1.6359599608284174,
+ -1.0578375143794956,
+ -1.0317506377236285,
+ -2.1936811357050625,
+ 9.311415587491846,
+ 1.5737906064890832,
+ 1.0005621391571347,
+ 1.171132813364961,
+ 2.335609048200104,
+ -2.5303529146481507,
+ -1.198324177025028,
+ -1.0000034821583816,
+ -1.5085003230324534,
+ -6.9798636871924105,
+ 2.361954646535407,
+ 1.0420000377994112,
+ 1.045481013789673,
+ 1.563782265765834,
+ -6.480797503858046,
+ -1.4898204735730145,
+ -1.0331500013660062,
+ -1.0559295203517456,
+ -2.597883860845052,
+ 5.413097475894072,
+ 1.44135702327655,
+ 1.000998954241362,
+ 1.2336486816650807,
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/huge_positive.json b/base/special/sec/test/fixtures/julia/huge_positive.json
new file mode 100644
index 000000000..5a340a449
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/huge_positive.json
@@ -0,0 +1,2006 @@
+{
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/large_negative.json b/base/special/sec/test/fixtures/julia/large_negative.json
new file mode 100644
index 000000000..15d3eea82
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/large_negative.json
@@ -0,0 +1,2004 @@
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\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/large_positive.json b/base/special/sec/test/fixtures/julia/large_positive.json
new file mode 100644
index 000000000..e3868c9dd
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/large_positive.json
@@ -0,0 +1,2006 @@
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\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/medium_negative.json b/base/special/sec/test/fixtures/julia/medium_negative.json
new file mode 100644
index 000000000..c88ddc4cd
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/medium_negative.json
@@ -0,0 +1,2006 @@
+{
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\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/medium_positive.json b/base/special/sec/test/fixtures/julia/medium_positive.json
new file mode 100644
index 000000000..fe2d5c968
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/medium_positive.json
@@ -0,0 +1,2006 @@
+{
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+ 37.69911184307752
+ ]
+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/runner.jl b/base/special/sec/test/fixtures/julia/runner.jl
new file mode 100644
index 000000000..54f5cec55
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/runner.jl
@@ -0,0 +1,113 @@
+#!/usr/bin/env julia
+#
+# @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.
+
+import JSON
+
+"""
+ gen( domain, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `domain`: domain
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> x = range( -1000.0, stop = 1000.0, length = 2022 );
+julia> gen( x, \"data.json\" );
+```
+"""
+function gen( domain, name )
+ x = collect( domain );
+ y = sec.( x );
+
+ # Store data to be written to file as a collection:
+ data = Dict([
+ ("x", x),
+ ("expected", y)
+ ]);
+
+ # Based on the script directory, create an output filepath:
+ filepath = joinpath( dir, name );
+
+ # Write the data to the output filepath as JSON:
+ outfile = open( filepath, "w" );
+ write( outfile, JSON.json(data) );
+ close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Negative tiny values:
+x = range( -1.0e-300, stop = -1.0e-308, length = 500 );
+gen( x, "tiny_negative.json" );
+
+# Positive tiny values:
+x = range( 1.0e-300, stop = 1.0e-308, length = 500 );
+gen( x, "tiny_positive.json" );
+
+# Small(er) values:
+x = range( -pi, stop = pi, length = 2022 );
+gen( x, "smaller.json" );
+
+# Negative small values:
+x = range( -4.0*pi, stop = -pi, length = 1000 );
+gen( x, "small_negative.json" );
+
+# Positive small values:
+x = range( pi, stop = 4.0*pi, length = 1000 );
+gen( x, "small_positive.json" );
+
+# Negative medium values:
+x = range( -4.0*pi, stop = -12.0*pi, length = 1000 );
+gen( x, "medium_negative.json" );
+
+# Positive medium values:
+x = range( 4.0*pi, stop = 12.0*pi, length = 1000 );
+gen( x, "medium_positive.json" );
+
+# Large negative values:
+x = range( -12.0*pi, stop = -256.0*pi, length = 1000 );
+gen( x, "large_negative.json" );
+
+# Large positive values:
+x = range( 12.0*pi, stop = 256.0*pi, length = 1000 );
+gen( x, "large_positive.json" );
+
+# Very large negative values:
+x = range( -2.0^20*(pi/2.0), stop = -2.0^60*(pi/2.0), length = 500 );
+gen( x, "very_large_negative.json" );
+
+# Very large positive values:
+x = range( 2.0^20*(pi/2.0), stop = 2.0^60*(pi/2.0), length = 500 );
+gen( x, "very_large_positive.json" );
+
+# Huge negative values:
+x = range( -2.0^60*(pi/2.0), stop = -2.0^1000*(pi/2.0), length = 1000 )
+gen( x, "huge_negative.json" );
+
+# Huge positive values:
+x = range( 2.0^20*(pi/2.0), stop = 2.0^60*(pi/2.0), length = 1000 )
+gen( x, "huge_positive.json" );
diff --git a/base/special/sec/test/fixtures/julia/small_negative.json b/base/special/sec/test/fixtures/julia/small_negative.json
new file mode 100644
index 000000000..fd1b49c06
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/small_negative.json
@@ -0,0 +1,2004 @@
+{
+ "expected": [1,
+ 1.0000445038300918,
+ 1.0001780351283918,
+ 1.0004006533404892,
+ 1.0007124576141289,
+ 1.0011135869070056,
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/small_positive.json b/base/special/sec/test/fixtures/julia/small_positive.json
new file mode 100644
index 000000000..7958855f2
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/small_positive.json
@@ -0,0 +1,2004 @@
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/smaller.json b/base/special/sec/test/fixtures/julia/smaller.json
new file mode 100644
index 000000000..9215e9653
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/smaller.json
@@ -0,0 +1,4050 @@
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\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/tiny_negative.json b/base/special/sec/test/fixtures/julia/tiny_negative.json
new file mode 100644
index 000000000..6944fa287
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/tiny_negative.json
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\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/tiny_positive.json b/base/special/sec/test/fixtures/julia/tiny_positive.json
new file mode 100644
index 000000000..61d010b87
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/tiny_positive.json
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/very_large_negative.json b/base/special/sec/test/fixtures/julia/very_large_negative.json
new file mode 100644
index 000000000..866f6c50f
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/very_large_negative.json
@@ -0,0 +1,1004 @@
+{
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+}
\ No newline at end of file
diff --git a/base/special/sec/test/fixtures/julia/very_large_positive.json b/base/special/sec/test/fixtures/julia/very_large_positive.json
new file mode 100644
index 000000000..a45a5d709
--- /dev/null
+++ b/base/special/sec/test/fixtures/julia/very_large_positive.json
@@ -0,0 +1,1004 @@
+{
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+ 1.8001170597225815e18,
+ 1.803746327988148e18,
+ 1.8073755962537142e18,
+ 1.8110048645192806e18
+ ]
+}
\ No newline at end of file
diff --git a/base/special/sec/test/test.js b/base/special/sec/test/test.js
new file mode 100644
index 000000000..108582659
--- /dev/null
+++ b/base/special/sec/test/test.js
@@ -0,0 +1,396 @@
+/**
+* @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 tape = require( 'tape' );
+var isnan = require( './../../../../base/assert/is-nan' );
+var abs = require( './../../../../base/special/abs' );
+var PI = require( '@stdlib/constants/float64/pi' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+var sec = require( './../lib' );
+
+
+// FIXTURES //
+
+var hugeNegative = require( './fixtures/julia/huge_negative.json' );
+var hugePositive = require( './fixtures/julia/huge_positive.json' );
+var veryLargeNegative = require( './fixtures/julia/very_large_negative.json' );
+var veryLargePositive = require( './fixtures/julia/very_large_positive.json' );
+var largeNegative = require( './fixtures/julia/large_negative.json' );
+var largePositive = require( './fixtures/julia/large_positive.json' );
+var mediumNegative = require( './fixtures/julia/medium_negative.json' );
+var mediumPositive = require( './fixtures/julia/medium_positive.json' );
+var smallNegative = require( './fixtures/julia/small_negative.json' );
+var smallPositive = require( './fixtures/julia/small_positive.json' );
+var smaller = require( './fixtures/julia/smaller.json' );
+var tinyNegative = require( './fixtures/julia/tiny_negative.json' );
+var tinyPositive = require( './fixtures/julia/tiny_positive.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.true( typeof sec, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function computes the secant (huge negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = hugeNegative.x;
+ expected = hugeNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (huge positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = hugePositive.x;
+ expected = hugePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (very large positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = veryLargePositive.x;
+ expected = veryLargePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (very large negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = veryLargeNegative.x;
+ expected = veryLargeNegative.expected;
+
+ for (i = 0; i < x.length; i++) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (large positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = largePositive.x;
+ expected = largePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (large negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = largeNegative.x;
+ expected = largeNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (medium positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = mediumPositive.x;
+ expected = mediumPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (medium negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = mediumNegative.x;
+ expected = mediumNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (small positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smallPositive.x;
+ expected = smallPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ]);
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (small negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smallNegative.x;
+ expected = smallNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ]);
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (smaller values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smaller.x;
+ expected = smaller.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (tiny positive values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = tinyPositive.x;
+ expected = tinyPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec(x[i]);
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (tiny negative values)', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = tinyNegative.x;
+ expected = tinyNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'if provided a multiple of `-pi/2`, the function does not return `~+infinity` due to floating-point rounding errors', function test( t ) {
+ t.notEqual( sec( -PI / 2 ), PINF, 'returns expected value');
+ t.end();
+});
+
+tape( 'if provided a multiple of `pi/2`, the function does not return `~+infinity`', function test( t ) {
+ t.notEqual( sec( PI / 2 ), NINF, 'returns expected value');
+ t.end();
+});
+
+tape( 'if provided a `NaN`, the function returns `NaN`', function test( t ) {
+ var v = sec( NaN );
+ t.equal(isnan(v), true, 'returns NaN');
+ t.end();
+});
+
+tape( 'if provided `+infinity`, the function returns `NaN`', function test( t ) {
+ var v = sec( PINF );
+ t.equal( isnan( v ), true, 'returns NaN' );
+ t.end();
+});
+
+tape( 'if provided `-infinity`, the function returns `NaN`', function test( t ) {
+ var v = sec( NINF );
+ t.equal( isnan( v ), true, 'returns NaN' );
+ t.end();
+});
diff --git a/base/special/sec/test/test.native.js b/base/special/sec/test/test.native.js
new file mode 100644
index 000000000..613114661
--- /dev/null
+++ b/base/special/sec/test/test.native.js
@@ -0,0 +1,405 @@
+/**
+* @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( './../../../../base/assert/is-nan' );
+var abs = require( './../../../../base/special/abs' );
+var PI = require( '@stdlib/constants/float64/pi' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+
+
+// VARIABLES //
+
+var sec = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( sec instanceof Error )
+};
+
+
+// FIXTURES //
+
+var hugeNegative = require( './fixtures/julia/huge_negative.json' );
+var hugePositive = require( './fixtures/julia//huge_positive.json' );
+var veryLargeNegative = require( './fixtures/julia//very_large_negative.json' );
+var veryLargePositive = require( './fixtures/julia//very_large_positive.json' );
+var largeNegative = require( './fixtures/julia//large_negative.json' );
+var largePositive = require( './fixtures/julia//large_positive.json' );
+var mediumNegative = require( './fixtures/julia//medium_negative.json' );
+var mediumPositive = require( './fixtures/julia//medium_positive.json' );
+var smallNegative = require( './fixtures/julia//small_negative.json' );
+var smallPositive = require( './fixtures/julia//small_positive.json' );
+var smaller = require( './fixtures/julia//smaller.json' );
+var tinyNegative = require( './fixtures/julia//tiny_negative.json' );
+var tinyPositive = require( './fixtures/julia//tiny_positive.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', opts, function test( t ) {
+ t.ok(true, __filename);
+ t.true(typeof sec, 'function', 'main export is a function');
+ t.end();
+});
+
+tape( 'the function computes the secant (huge negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = hugeNegative.x;
+ expected = hugeNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (huge positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = hugePositive.x;
+ expected = hugePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (very large positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = veryLargePositive.x;
+ expected = veryLargePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (very large negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = veryLargeNegative.x;
+ expected = veryLargeNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs(y - expected[ i ]);
+ tol = 1.4 * EPS * abs(expected[ i ]);
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (large positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = largePositive.x;
+ expected = largePositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (large negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = largeNegative.x;
+ expected = largeNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (medium positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = mediumPositive.x;
+ expected = mediumPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (medium negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = mediumNegative.x;
+ expected = mediumNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (small positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smallPositive.x;
+ expected = smallPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (small negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smallNegative.x;
+ expected = smallNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (smaller values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = smaller.x;
+ expected = smaller.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (tiny positive values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = tinyPositive.x;
+ expected = tinyPositive.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function computes the secant (tiny negative values)', opts, function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ x = tinyNegative.x;
+ expected = tinyNegative.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ y = sec( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: ' + x[ i ] + '. E: ' + expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1.4 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + expected[ i ] + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'if provided a multiple of `-pi/2`, the function does not return `~+infinity` due to floating-point rounding errors', opts, function test( t ) {
+ t.notEqual( sec( -PI / 2 ), PINF, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided a multiple of `pi/2`, the function does not return `~+infinity`', opts, function test( t ) {
+ t.notEqual( sec( PI / 2 ), NINF, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided a `NaN`, the function returns `expected value`', opts, function test( t ) {
+ var v = sec( NaN );
+ t.equal( isnan( v ), true, 'returns NaN' );
+ t.end();
+});
+
+tape( 'if provided `+infinity`, the function returns `expected value`', opts, function test( t ) {
+ var v = sec( PINF );
+ t.equal( isnan( v ), true, 'returns NaN' );
+ t.end();
+});
+
+tape( 'if provided `-infinity`, the function returns `expected value`', opts, function test( t ) {
+ var v = sec( NINF );
+ t.equal( isnan( v ), true, 'returns NaN' );
+ t.end();
+});