117 lines
2.4 KiB
Markdown
117 lines
2.4 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# powm1
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> Evaluate `bˣ - 1`.
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<section class="intro">
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<!-- <equation class="equation" label="eq:exponential_function_minus_one" align="center" raw="y = b^x - 1" alt="Exponential function minus one"> -->
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<div class="equation" align="center" data-raw-text="y = b^x - 1" data-equation="eq:exponential_function_minus_one">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/powm1/docs/img/equation_exponential_function_minus_one.svg" alt="Exponential function minus one">
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<br>
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</div>
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<!-- </equation> -->
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When `b` is close to `1` and/or `x` is small, this implementation is more accurate than naively computing `bˣ` minus `1`.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var powm1 = require( '@stdlib/math/base/special/powm1' );
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```
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#### powm1( b, x )
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Evaluates `bˣ - 1`.
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```javascript
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var y = powm1( 2.0, 3.0 );
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// returns 7.0
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y = powm1( 4.0, 0.5 );
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// returns 1.0
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y = powm1( 0.0, 100.0 );
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// returns -1.0
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y = powm1( 100.0, 0.0 );
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// returns 0.0
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y = powm1( 0.0, 0.0 );
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// returns 0.0
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y = powm1( 3.141592653589793, 5.0 );
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// returns ~305.0197
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y = powm1( NaN, 3.0 );
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// returns NaN
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y = powm1( 5.0, NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var powm1 = require( '@stdlib/math/base/special/powm1' );
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var b;
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var x;
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var y;
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var i;
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for ( i = 0; i < 100; i++ ) {
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b = round( randu()*10.0 );
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x = round( randu()*10.0 ) - 5.0;
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y = powm1( b, x );
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console.log( '%d^%d - 1 = %d', b, x, y );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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</section>
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<!-- /.links -->
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