bench: clean-up and add julia benchmarks

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: passed
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: passed
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: na
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---

Author: anandkaranubc

lib/node_modules/@stdlib/math/base/special/sech/benchmark/benchmark.js

@@ -21,7 +21,7 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/array/uniform' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pkg = require( './../package.json' ).name;
 var sech = require( './../lib' );
@@ -34,11 +34,11 @@ bench( pkg, function benchmark( b ) {
 	var y;
 	var i;
 
-	x = randu( 100, -5.0, 5.0 );
+	x = uniform( 100, -5.0, 5.0 );
 
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		y = sech( x[ i % x.length ] );
+		y = sech( x[ i%x.length ] );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );
 		}

lib/node_modules/@stdlib/math/base/special/sech/benchmark/benchmark.native.js

@@ -22,7 +22,7 @@
 
 var resolve = require( 'path' ).resolve;
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/array/uniform' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var pkg = require( './../package.json' ).name;
@@ -43,11 +43,11 @@ bench( pkg+'::native', opts, function benchmark( b ) {
 	var y;
 	var i;
 
-	x = randu( 100, -5.0, 5.0 );
+	x = uniform( 100, -5.0, 5.0 );
 
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		y = sech( x[ i % x.length ] );
+		y = sech( x[ i%x.length ] );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );
 		}

lib/node_modules/@stdlib/math/base/special/sech/benchmark/c/native/benchmark.c

@@ -90,19 +90,19 @@ static double rand_double( void ) {
 * @return elapsed time in seconds
 */
 static double benchmark( void ) {
-	double elapsed;
 	double x[ 100 ];
+	double elapsed;
 	double y;
 	double t;
 	int i;
 
 	for ( i = 0; i < 100; i++ ) {
-		x[ i ] = ( 10.0 * rand_double() ) - 5.0;
+		x[ i ] = ( 10.0*rand_double() ) - 5.0;
 	}
 
 	t = tic();
 	for ( i = 0; i < ITERATIONS; i++ ) {
-		y = stdlib_base_sech( x[ i % 100 ] );
+		y = stdlib_base_sech( x[ i%100 ] );
 		if ( y != y ) {
 			printf( "should not return NaN\n" );
 			break;

lib/node_modules/@stdlib/math/base/special/sech/benchmark/julia/REQUIRE

@@ -0,0 +1,2 @@
+julia 1.5
+BenchmarkTools 0.5.0

lib/node_modules/@stdlib/math/base/special/sech/benchmark/julia/benchmark.jl

@@ -0,0 +1,144 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2025 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 BenchmarkTools
+using Printf
+
+# Benchmark variables:
+name = "sech";
+repeats = 3;
+
+"""
+	print_version()
+
+Prints the TAP version.
+
+# Examples
+
+``` julia
+julia> print_version()
+```
+"""
+function print_version()
+	@printf( "TAP version 13\n" );
+end
+
+"""
+	print_summary( total, passing )
+
+Print the benchmark summary.
+
+# Arguments
+
+* `total`: total number of tests
+* `passing`: number of passing tests
+
+# Examples
+
+``` julia
+julia> print_summary( 3, 3 )
+```
+"""
+function print_summary( total, 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" );
+end
+
+"""
+	print_results( iterations, elapsed )
+
+Print benchmark results.
+
+# Arguments
+
+* `iterations`: number of iterations
+* `elapsed`: elapsed time (in seconds)
+
+# Examples
+
+``` julia
+julia> print_results( 1000000, 0.131009101868 )
+```
+"""
+function print_results( iterations, elapsed )
+	rate = iterations / elapsed
+
+	@printf( "  ---\n" );
+	@printf( "  iterations: %d\n", iterations );
+	@printf( "  elapsed: %0.9f\n", elapsed );
+	@printf( "  rate: %0.9f\n", rate );
+	@printf( "  ...\n" );
+end
+
+"""
+	benchmark()
+
+Run a benchmark.
+
+# Notes
+
+* Benchmark results are returned as a two-element array: [ iterations, elapsed ].
+* The number of iterations is not the true number of iterations. Instead, an 'iteration' is defined as a 'sample', which is a computed estimate for a single evaluation.
+* The elapsed time is in seconds.
+
+# Examples
+
+``` julia
+julia> out = benchmark();
+```
+"""
+function benchmark()
+	t = BenchmarkTools.@benchmark sech( (10.0*rand()) - 5.0 ) samples=1e6
+
+	# Compute the total "elapsed" time and convert from nanoseconds to seconds:
+	s = sum( t.times ) / 1.0e9;
+
+	# Determine the number of "iterations":
+	iter = length( t.times );
+
+	# Return the results:
+	[ iter, s ];
+end
+
+"""
+	main()
+
+Run benchmarks.
+
+# Examples
+
+``` julia
+julia> main();
+```
+"""
+function main()
+	print_version();
+	for i in 1:repeats
+		@printf( "# julia::%s\n", name );
+		results = benchmark();
+		print_results( results[ 1 ], results[ 2 ] );
+		@printf( "ok %d benchmark finished\n", i );
+	end
+	print_summary( repeats, repeats );
+end
+
+main();