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License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>\n  <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>\n  <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# kernelTan\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Compute the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-special-kernel-tan\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar kernelTan = require( '@stdlib/math-base-special-kernel-tan' );\n```\n\n#### kernelTan( x, y, k )\n\nComputes the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.\n\n```javascript\nvar out = kernelTan( 3.141592653589793/4.0, 0.0, 1 );\n// returns ~1.0\n\nout = kernelTan( 3.141592653589793/6.0, 0.0, 1 );\n// returns ~0.577\n\nout = kernelTan( 0.664, 5.288e-17, 1 );\n// returns ~0.783\n```\n\nIf `k = 1`, the function returns `tan(x+y)`. To return the negative inverse `-1/tan(x+y)`, set `k = -1`.\n\n```javascript\nvar out = kernelTan( 3.141592653589793/4.0, 0.0, -1 );\n// returns ~-1.0\n```\n\nIf either `x` or `y` is `NaN`, the function returns `NaN`.\n\n```javascript\nvar out = kernelTan( NaN, 0.0, 1 );\n// returns NaN\n\nout = kernelTan( 3.0, NaN, 1 );\n// returns NaN\n\nout = kernelTan( NaN, NaN, 1 );\n// returns NaN\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"notes\">\n\n## Notes\n\n-   For increased accuracy, the number for which the [tangent][tangent] should be evaluated can be supplied as a [double-double number][double-double-arithmetic] (i.e., a non-evaluated sum of two [double-precision floating-point numbers][ieee754] `x` and `y`).\n\n-   As components of a [double-double number][double-double-arithmetic], the two [double-precision floating-point numbers][ieee754] `x` and `y` must satisfy\n\n    <!-- <equation class=\"equation\" label=\"eq:double_double_inequality\" align=\"center\" raw=\"|y| \\leq \\frac{1}{2} \\operatorname{ulp}(x)\" alt=\"Inequality for the two components of a double-double number.\"> -->\n\n    <div class=\"equation\" align=\"center\" data-raw-text=\"|y| \\leq \\frac{1}{2} \\operatorname{ulp}(x)\" data-equation=\"eq:double_double_inequality\">\n        <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/kernel-tan/docs/img/equation_double_double_inequality.svg\" alt=\"Inequality for the two components of a double-double number.\">\n        <br>\n    </div>\n\n    <!-- </equation> -->\n\n    where `ulp` stands for [units in the last place][ulp].\n\n</section>\n\n<!-- /.notes -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar linspace = require( '@stdlib/array-base-linspace' );\nvar binomial = require( '@stdlib/random-base-binomial' ).factory;\nvar PI = require( '@stdlib/constants-float64-pi' );\nvar kernelTan = require( '@stdlib/math-base-special-kernel-tan' );\n\nvar x = linspace( -PI/4.0, PI/4.0, 100 );\nvar rbinom = binomial( 1, 0.5 );\n\nvar descr;\nvar i;\nvar k;\n\nfor ( i = 0; i < x.length; i++ ) {\n    k = rbinom();\n    descr = ( k === 1 ) ? 'tan(%d) = %d' : '-1/tan(%d) = %d';\n    console.log( descr, x[ i ], kernelTan( x[ i ], 0.0, k ) );\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n<!-- C interface documentation. -->\n\n* * *\n\n<section class=\"c\">\n\n## C APIs\n\n<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->\n\n<section class=\"intro\">\n\n</section>\n\n<!-- /.intro -->\n\n<!-- C usage documentation. -->\n\n<section class=\"usage\">\n\n### Usage\n\n```c\n#include \"stdlib/math/base/special/kernel_tan.h\"\n```\n\n#### stdlib_base_kernel_tan( x, y, k )\n\nComputes the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.\n\n```c\ndouble out = stdlib_base_kernel_tan( 3.141592653589793/4.0, 0.0, 1 );\n// returns ~1.0\n\nout = stdlib_base_kernel_tan( 3.141592653589793/6.0, 0.0, 1 );\n// returns ~0.577\n```\n\nThe function accepts the following arguments:\n\n-   **x**: `[in] double` input value (in radians, assumed to be bounded by `~pi/4` in magnitude).\n-   **y**: `[in] double` tail of `x`.\n-   **k**: `[in] int32_t` indicates whether `tan(x+y)` (if `k = 1`) or `-1/tan(x+y)` (if `k = -1`) is returned.\n\n```c\ndouble stdlib_base_kernel_tan( const double x, const double y, const int32_t k );\n```\n\n</section>\n\n<!-- /.usage -->\n\n<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"notes\">\n\n### Notes\n\n-   For increased accuracy, the number for which the [tangent][tangent] should be evaluated can be supplied as a [double-double number][double-double-arithmetic] (i.e., a non-evaluated sum of two [double-precision floating-point numbers][ieee754] `x` and `y`).\n\n</section>\n\n<!-- /.notes -->\n\n<!-- C API usage examples. -->\n\n<section class=\"examples\">\n\n### Examples\n\n```c\n#include \"stdlib/math/base/special/kernel_tan.h\"\n#include <stdio.h>\n\nint main( void ) {\n    const double x[] = { -0.7853981633974483, -0.6108652381980153, -0.4363323129985824, -0.26179938779914946, -0.08726646259971649, 0.08726646259971649, 0.26179938779914935, 0.43633231299858233, 0.6108652381980153, 0.7853981633974483 };\n\n    double out;\n    int i;\n    for ( i = 0; i < 10; i++ ) {\n        out = stdlib_base_kernel_tan( x[ i ], 0.0, 1 );\n        printf( \"tan(%lf) = %lf\\n\", x[ i ], out );\n    }\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n</section>\n\n<!-- /.c -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n* * *\n\n## See Also\n\n-   <span class=\"package-name\">[`@stdlib/math-base/special/kernel-cos`][@stdlib/math/base/special/kernel-cos]</span><span class=\"delimiter\">: </span><span class=\"description\">compute the cosine of a double-precision floating-point number on \\[-π/4, π/4].</span>\n-   <span class=\"package-name\">[`@stdlib/math-base/special/kernel-sin`][@stdlib/math/base/special/kernel-sin]</span><span class=\"delimiter\">: </span><span class=\"description\">compute the sine of a double-precision floating-point number on \\[-π/4, π/4].</span>\n-   <span class=\"package-name\">[`@stdlib/math-base/special/tan`][@stdlib/math/base/special/tan]</span><span class=\"delimiter\">: </span><span class=\"description\">evaluate the tangent of a number.</span>\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## Copyright\n\nCopyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-kernel-tan.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-kernel-tan\n\n[test-image]: https://github.com/stdlib-js/math-base-special-kernel-tan/actions/workflows/test.yml/badge.svg?branch=v0.2.4\n[test-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/actions/workflows/test.yml?query=branch:v0.2.4\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-kernel-tan/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-kernel-tan?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-base-special-kernel-tan.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-base-special-kernel-tan/main\n\n-->\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/main/branches.md\n\n[tangent]: https://en.wikipedia.org/wiki/Tangent\n\n[double-double-arithmetic]: https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic\n\n[ieee754]: https://en.wikipedia.org/wiki/IEEE_floating_point\n\n[ulp]: https://en.wikipedia.org/wiki/Unit_in_the_last_place\n\n<!-- <related-links> -->\n\n[@stdlib/math/base/special/kernel-cos]: https://www.npmjs.com/package/@stdlib/math-base-special-kernel-cos\n\n[@stdlib/math/base/special/kernel-sin]: https://www.npmjs.com/package/@stdlib/math-base-special-kernel-sin\n\n[@stdlib/math/base/special/tan]: https://www.npmjs.com/package/@stdlib/math-base-special-tan\n\n<!-- </related-links> -->\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}