feat: add math/base/special/sincospif

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

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+<!--
+
+@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.
+
+-->
+
+# sincospif
+
+> Simultaneously compute the [sinef][@stdlib/math/base/special/sinf] and [cosinef][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi].
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var sincospif = require( '@stdlib/math/base/special/sincospif' );
+```
+
+#### sincospif( x )
+
+Simultaneously computes the [sinef][@stdlib/math/base/special/sinf] and [cosinef][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi] more accurately than `sincos(pi*x)` when operating on single-precision floating-point values, especially for large `x`.
+
+```javascript
+var v = sincospif( 0.0 );
+// returns <Float32Array>[ 0.0, 1.0 ]
+
+v = sincospif( 0.5 );
+// returns <Float32Array>[ 1.0, 0.0 ]
+
+v = sincospif( 0.1 );
+// returns <Float32Array>[ ~0.309, ~0.951 ]
+
+v = sincospif( NaN );
+// returns <Float32Array>[ NaN, NaN ]
+```
+
+#### sincospif( x, out, stride, offset )
+
+Simultaneously computes the [sinef][@stdlib/math/base/special/sinf] and [cosinef][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi] more accurately than `sincos(pi*x)`, especially for large `x`, and assigns results to a provided output array.
+
+<!-- eslint-disable stdlib/doctest -->
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var out = new Float32Array( 2 );
+
+var v = sincospif.assign( 0.0, out, 1, 0 );
+// returns <Float32Array>[ 0.0, 1.0 ]
+
+var bool = ( v === out );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var sincospif = require( '@stdlib/math/base/special/sincospif' );
+
+var x = linspace( 0.0, 2.0, 101 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+    console.log( sincospif( x[ i ] ) );
+}
+```
+
+</section>
+
+<!-- /.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/sincospif.h"
+```
+
+#### stdlib_base_sincospif( x, &sine, &cosine )
+
+Simultaneously computes the [sinef][@stdlib/math/base/special/sinf] and [cosinef][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi] more accurately than `sincos(pi*x)`, especially for large `x`.
+
+```c
+float cosine;
+float sine;
+
+stdlib_base_sincospif( 4.0, &sine, &cosine );
+```
+
+The function accepts the following arguments:
+
+-   **x**:      `[in] float` input value.
+-   **sine**:   `[out] float*` destination for the sine.
+-   **cosine**: `[out] float*` destination for the cosine.
+
+```c
+void stdlib_base_sincospif( const float x, float *sine, float *cosine );
+```
+
+</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/sincospif.h"
+#include <stdio.h>
+
+int main( void ) {
+    const float x[] = { 0.0f, 0.5f, 1.0f, 2.0f };
+
+    float cosine;
+    float sine;
+    int i;
+    for ( i = 0; i < 4; i++ ) {
+        stdlib_base_sincospif( x[ i ], &sine, &cosine );
+        printf( "x: %f => sine: %f, cosine: %f\n", x[ i ], sine, cosine );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/math/base/special/cospif`][@stdlib/math/base/special/cospif]</span><span class="delimiter">: </span><span class="description">compute cos(πx).</span>
+-   <span class="package-name">[`@stdlib/math/base/special/sincosf`][@stdlib/math/base/special/sincosf]</span><span class="delimiter">: </span><span class="description">simultaneously compute the sine and cosine of an angle measured in radians.</span>
+-   <span class="package-name">[`@stdlib/math/base/special/sinpif`][@stdlib/math/base/special/sinpif]</span><span class="delimiter">: </span><span class="description">compute sin(πx).</span>
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
+
+[@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
+
+[@stdlib/constants/float32/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/pi
+
+<!-- <related-links> -->
+
+[@stdlib/math/base/special/cospif]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cospif
+
+[@stdlib/math/base/special/sincosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sincosf
+
+[@stdlib/math/base/special/sinpif]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinpif
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->