feat: add C implementation for math/base/special/ellipj

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---

Author: anandkaranubc

lib/node_modules/@stdlib/math/base/special/ellipj/README.md

@@ -24,7 +24,7 @@ limitations under the License.
 
 <section class="intro">
 
-The [Jacobi elliptic functions][jacobi-elliptic] may be defined as the inverse of the [incomplete elliptic integral of the first kind][incomplete-elliptic]. Accordingly, they compute the value `φ` which satisfies the equation 
+The [Jacobi elliptic functions][jacobi-elliptic] may be defined as the inverse of the [incomplete elliptic integral of the first kind][incomplete-elliptic]. Accordingly, they compute the value `φ` which satisfies the equation
 
 <!-- <equation class="equation" label="eq:incomplete_elliptic_integral_first_kind" align="center" raw="u=\int_{0}^{\varphi}{\frac {\mathrm{d} \theta }{\sqrt {1-m\sin^{2}\theta }}}" alt="Incomplete elliptic integral of the first kind"> -->
 
@@ -166,6 +166,105 @@ 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/ellipj.h"
+```
+
+#### stdlib_base_ellipj( x, m, &sn, &cn, &dn, &am )
+
+Computes the [Jacobi elliptic functions][jacobi-elliptic] functions `sn`, `cn`, and `dn`, and the Jacobi amplitude `am`.
+
+```c
+double sn;
+double cn;
+double dn;
+double am;
+
+stdlib_base_ellipj( 0.3, 0.5, &sn, &cn, &dn, &am );
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] double` input value.
+-   **m**: `[in] double` modulus `m`, equivalent to `k²`.
+-   **sn**: `[out] double*` destination for the sine amplitude.
+-   **cn**: `[out] double*` destination for the cosine amplitude.
+-   **dn**: `[out] double*` destination for the delta amplitude.
+-   **am**: `[out] double*` destination for the Jacobi amplitude.
+
+```c
+void stdlib_base_ellipj( const double u, const double m, double* sn, double* cn, double* dn, double* am );
+```
+
+</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/ellipj.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+int main( void ) {
+    double sn;
+    double cn;
+    double dn;
+    double am;
+    double x;
+    int i;
+
+    for ( i = 0; i < 100; i++ ) {
+        x = 2.0 * ( (double)rand() / (double)RAND_MAX );
+        stdlib_base_ellipj( x, 0.7, &sn, &cn, &dn, &am );
+        printf( "x: %lf, m: %lf => sn: %lf, cn: %lf, dn: %lf, am: %lf\n", x, 0.7, sn, cn, dn, am );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
 * * *
 
 <section class="references">

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

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2022 The Stdlib Authors.
+* 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.
@@ -23,7 +23,7 @@
 var bench = require( '@stdlib/bench' );
 var isArray = require( '@stdlib/assert/is-array' );
 var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
-var randu = require( '@stdlib/random/base/randu' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var pkg = require( './../package.json' ).name;
 var ellipj = require( './../lib' );
 
@@ -32,15 +32,16 @@ var ellipj = require( './../lib' );
 
 bench( pkg, function benchmark( b ) {
 	var out;
-	var u;
+	var x;
 	var m;
 	var i;
 
+	x = uniform( 100, -50.0, 50.0 );
+	m = uniform( 100, 0.0, 1.0 );
+
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		u = (randu() * 100.0) - 50.0;
-		m = randu();
-		out = ellipj( u, m );
+		out = ellipj( x[ i%x.length ], m[ i%m.length ] );
 		if ( typeof out !== 'object' ) {
 			b.fail( 'should return an object' );
 		}

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

@@ -0,0 +1,69 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var isFloat64Array = require( '@stdlib/assert/is-float64array' );
+var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var uniform = require( '@stdlib/random/array/uniform' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var ellipj = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( ellipj instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var out;
+	var x;
+	var m;
+	var i;
+
+	x = uniform( 100, -50.0, 50.0 );
+	m = uniform( 100, 0.0, 1.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		out = ellipj( x[ i%x.length ], m[ i%m.length ] );
+		if ( typeof out !== 'object' ) {
+			b.fail( 'should return an object' );
+		}
+	}
+	b.toc();
+	if ( !isFloat64Array( out ) ) {
+		b.fail( 'should return an array' );
+	}
+	for ( i = 0; i < 4; i++ ) {
+		if ( !isNumber( out[ i ] ) ) {
+			b.fail( 'should return a number' );
+		}
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/ellipj/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