feat: add C implementation of math/base/special/kernel-betainc

lib/node_modules/@stdlib/math/base/special/kernel-betainc/README.md

@@ -18,7 +18,7 @@ limitations under the License.
 
 -->
 
-# Kernel Betainc
+# kernelBetainc
 
 > [Incomplete beta function][incomplete-beta-function] and its first derivative.
 
@@ -135,6 +135,111 @@ for ( i = 0; i < 100; i++ ) {
 
 <!-- /.examples -->
 
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/kernel_betainc.h"
+```
+
+#### stdlib_base_kernel_betainc( x, a, b, regularized, upper, &out, &derivative )
+
+Evaluates the incomplete beta function and its first derivative.
+
+```c
+double out;
+double derivative;
+
+stdlib_base_kernel_betainc( 0.2, 1.0, 2.0, true, false, &out, &derivative );
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] double` function input.
+-   **a**: `[in] double` function parameter.
+-   **b**: `[in] double` function parameter.
+-   **regularized**: `[in] bool` indicating if the function should evaluate the regularized incomplete beta function.
+-   **upper**: `[in] bool` indicating if the function should return the upper tail of the incomplete beta function.
+-   **out**: `[out] double*` destination pointer to store the function value.
+-   **derivative**: `[out] double*` destination pointer to store the first derivative.
+
+```c
+void stdlib_base_kernel_betainc( double x, double a, double b, const bool regularized, const bool upper, double *out, double *derivative );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/math/base/special/kernel_betainc.h"
+#include "stdlib/random/base/randu.h"
+#include <stdio.h>
+#include <stdint.h>
+#include <stdbool.h>
+
+int main( void ) {
+    struct BasePRNGObject *obj = stdlib_base_random_randu_allocate( 0 );
+    double deriv;
+    double out;
+    int32_t i;
+    double x;
+    double a;
+    double b;
+
+    for ( i = 0; i < 100; i++ ) {
+        x = stdlib_base_random_randu( obj );
+        a = stdlib_base_random_randu( obj ) * 10.0;
+        b = stdlib_base_random_randu( obj ) * 10.0;
+        stdlib_base_kernel_betainc( x, a, b, true, false, &out, &deriv );
+        printf( "x: %lf, a: %lf, b: %lf, f(x,a,b): %lf, f^1(x,a,b): %lf\n", x, a, b, out, deriv );
+    }
+
+    stdlib_base_random_randu_free( obj );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
 <!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
 
 <section class="related">

lib/node_modules/@stdlib/math/base/special/kernel-betainc/benchmark/benchmark.js

@@ -31,7 +31,7 @@
 
 // MAIN //
 
-bench( format( '%s::regularized,upper', pkg ), function benchmark( assert ) {
+bench( format( '%s::regularized=true,upper=true', pkg ), function benchmark( assert ) {
 	var out;
 	var x;
 	var a;
@@ -45,7 +45,7 @@
 	out = [ 0.0, 0.0 ];
 	assert.tic();
 	for ( i = 0; i < assert.iterations; i++ ) {
 		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], true, true, out, 1, 0 );
 		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
 			assert.fail( 'should not return NaN' );
 		}
@@ -58,7 +58,7 @@
 	assert.end();
 });
 
-bench( format( '%s::unregularized,upper', pkg ), function benchmark( assert ) {
+bench( format( '%s::regularized=false,upper=true', pkg ), function benchmark( assert ) {
 	var out;
 	var x;
 	var a;
@@ -72,7 +72,7 @@
 	out = [ 0.0, 0.0 ];
 	assert.tic();
 	for ( i = 0; i < assert.iterations; i++ ) {
 		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], false, true, out, 1, 0 );
 		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
 			assert.fail( 'should not return NaN' );
 		}
@@ -85,7 +85,7 @@
 	assert.end();
 });
 
-bench( format( '%s::regularized,lower', pkg ), function benchmark( assert ) {
+bench( format( '%s::regularized=true,upper=false', pkg ), function benchmark( assert ) {
 	var out;
 	var x;
 	var a;
@@ -99,7 +99,7 @@
 	out = [ 0.0, 0.0 ];
 	assert.tic();
 	for ( i = 0; i < assert.iterations; i++ ) {
 		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], true, false, out, 1, 0 );
 		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
 			assert.fail( 'should not return NaN' );
 		}
@@ -112,7 +112,7 @@
 	assert.end();
 });
 
-bench( format( '%s::unregularized,lower', pkg ), function benchmark( assert ) {
+bench( format( '%s::regularized=false,upper=false', pkg ), function benchmark( assert ) {
 	var out;
 	var x;
 	var a;
@@ -126,7 +126,7 @@
 	out = [ 0.0, 0.0 ];
 	assert.tic();
 	for ( i = 0; i < assert.iterations; i++ ) {
 		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], false, false, out, 1, 0 );
 		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
 			assert.fail( 'should not return NaN' );
 		}

lib/node_modules/@stdlib/math/base/special/kernel-betainc/benchmark/benchmark.native.js

@@ -0,0 +1,149 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var format = require( '@stdlib/string/format' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var kernelBetainc = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( kernelBetainc instanceof Error )
+};
+
+
+// MAIN //
+
+bench( format( '%s::native:regularized=true,upper=true', pkg ), opts, function benchmark( assert ) {
+	var out;
+	var x;
+	var a;
+	var b;
+	var i;
+
+	x = uniform( 100, 0.0, 1.0 );
+	a = uniform( 100, EPS, 1000.0 );
+	b = uniform( 100, EPS, 1000.0 );
+
+	out = [ 0.0, 0.0 ];
+	assert.tic();
+	for ( i = 0; i < assert.iterations; i++ ) {
+		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], true, true );
+		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+			assert.fail( 'should not return NaN' );
+		}
+	}
+	assert.toc();
+	if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+		assert.fail( 'should not return NaN' );
+	}
+	assert.pass( 'benchmark finished' );
+	assert.end();
+});
+
+bench( format( '%s::native:regularized=false,upper=true', pkg ), opts, function benchmark( assert ) {
+	var out;
+	var x;
+	var a;
+	var b;
+	var i;
+
+	x = uniform( 100, 0.0, 1.0 );
+	a = uniform( 100, EPS, 1000.0 );
+	b = uniform( 100, EPS, 1000.0 );
+
+	out = [ 0.0, 0.0 ];
+	assert.tic();
+	for ( i = 0; i < assert.iterations; i++ ) {
+		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], false, true );
+		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+			assert.fail( 'should not return NaN' );
+		}
+	}
+	assert.toc();
+	if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+		assert.fail( 'should not return NaN' );
+	}
+	assert.pass( 'benchmark finished' );
+	assert.end();
+});
+
+bench( format( '%s::native:regularized=true,upper=false', pkg ), opts, function benchmark( assert ) {
+	var out;
+	var x;
+	var a;
+	var b;
+	var i;
+
+	x = uniform( 100, 0.0, 1.0 );
+	a = uniform( 100, EPS, 1000.0 );
+	b = uniform( 100, EPS, 1000.0 );
+
+	out = [ 0.0, 0.0 ];
+	assert.tic();
+	for ( i = 0; i < assert.iterations; i++ ) {
+		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], true, false );
+		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+			assert.fail( 'should not return NaN' );
+		}
+	}
+	assert.toc();
+	if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+		assert.fail( 'should not return NaN' );
+	}
+	assert.pass( 'benchmark finished' );
+	assert.end();
+});
+
+bench( format( '%s::native:regularized=false,upper=false', pkg ), opts, function benchmark( assert ) {
+	var out;
+	var x;
+	var a;
+	var b;
+	var i;
+
+	x = uniform( 100, 0.0, 1.0 );
+	a = uniform( 100, EPS, 1000.0 );
+	b = uniform( 100, EPS, 1000.0 );
+
+	out = [ 0.0, 0.0 ];
+	assert.tic();
+	for ( i = 0; i < assert.iterations; i++ ) {
+		out = kernelBetainc( x[ i%x.length ], a[ i%a.length ], b[ i%b.length ], false, false );
+		if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+			assert.fail( 'should not return NaN' );
+		}
+	}
+	assert.toc();
+	if ( isnan( out[ 0 ] ) || isnan( out[ 1 ] ) ) {
+		assert.fail( 'should not return NaN' );
+	}
+	assert.pass( 'benchmark finished' );
+	assert.end();
+});