<!-- @license Apache-2.0 Copyright (c) 2018 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. --> # negaFibonacci > Compute the nth [negaFibonacci number][fibonacci-number]. <section class="intro"> The [negaFibonacci numbers][fibonacci-number] are the integer sequence <!-- <equation class="equation" label="eq:negafibonacci_sequence" align="center" raw="0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots" alt="NegaFibonacci sequence"> --> <div class="equation" align="center" data-raw-text="0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots" data-equation="eq:negafibonacci_sequence"> <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_sequence.svg" alt="NegaFibonacci sequence"> <br> </div> <!-- </equation> --> The sequence is defined by the recurrence relation <!-- <equation class="equation" label="eq:negafibonacci_recurrence_relation" align="center" raw="F_{n-2} = F_{n} - F_{n-1}" alt="NegaFibonacci sequence recurrence relation"> --> <div class="equation" align="center" data-raw-text="F_{n-2} = F_{n} - F_{n-1}" data-equation="eq:negafibonacci_recurrence_relation"> <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_recurrence_relation.svg" alt="NegaFibonacci sequence recurrence relation"> <br> </div> <!-- </equation> --> which yields <!-- <equation class="equation" label="eq:negafibonacci_fibonacci" align="center" raw="F_{-n} = (-1)^{n+1} F_n" alt="NegaFibonacci relationship to Fibonacci numbers"> --> <div class="equation" align="center" data-raw-text="F_{-n} = (-1)^{n+1} F_n" data-equation="eq:negafibonacci_fibonacci"> <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_fibonacci.svg" alt="NegaFibonacci relationship to Fibonacci numbers"> <br> </div> <!-- </equation> --> with seed values `F_0 = 0` and `F_{-1} = 1`. </section> <!-- /.intro --> <section class="usage"> ## Usage ```javascript var negafibonacci = require( '@stdlib/math/base/special/negafibonacci' ); ``` #### negafibonacci( n ) Computes the nth [negaFibonacci number][fibonacci-number]. ```javascript var v = negafibonacci( 0 ); // returns 0 v = negafibonacci( -1 ); // returns 1 v = negafibonacci( -2 ); // returns -1 v = negafibonacci( -3 ); // returns 2 v = negafibonacci( -78 ); // returns -8944394323791464 ``` If `n < -78`, the function returns `NaN`, as larger [negaFibonacci numbers][fibonacci-number] cannot be safely represented in [double-precision floating-point format][ieee754]. ```javascript var v = negafibonacci( -79 ); // returns NaN ``` If not provided a nonpositive integer value, the function returns `NaN`. ```javascript var v = negafibonacci( -3.14 ); // returns NaN v = negafibonacci( 1 ); // returns NaN ``` If provided `NaN`, the function returns `NaN`. ```javascript var v = negafibonacci( NaN ); // returns NaN ``` </section> <!-- /.usage --> <section class="notes"> </section> <!-- /.notes --> <section class="examples"> ## Examples <!-- eslint no-undef: "error" --> ```javascript var negafibonacci = require( '@stdlib/math/base/special/negafibonacci' ); var v; var i; for ( i = 0; i > -79; i-- ) { v = negafibonacci( i ); console.log( v ); } ``` </section> <!-- /.examples --> <section class="links"> [fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number [ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985 </section> <!-- /.links -->