Add relative error exponential

lib/node_modules/@stdlib/math/base/special/expm1rel/README.md

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+<!--
+
+@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.
+
+-->
+
+# expm1rel
+
+> Compute the relative error exponential.
+
+<!-- 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">
+
+The relative error exponential is defined as
+
+<!-- <equation class="equation" label="eq:relative_error_exponential" align="center" raw="f(x) = \frac{e^x - 1}{x}" alt="Equation for the relative error exponential."> -->
+
+<div class="equation" align="center" data-raw-text="f(x) = \frac{e^x - 1}{x}" data-equation="eq:relative_error_exponential">
+    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/65a72b6be80b988ebfa5e581849691524b01a533/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/img/equation_relative_error_exponential.svg" alt="Equation for the relative error exponential.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var expm1rel = require( '@stdlib/math/base/special/expm1rel' );
+```
+
+#### expm1rel( x )
+
+Computes the relative error exponential.
+
+```javascript
+var v = expm1rel( 0.0 );
+// returns 1.0
+
+v = expm1rel( 1.0 );
+// returns ~1.718
+
+v = expm1rel( -1.0 );
+// returns ~0.632
+
+v = expm1rel( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+## Notes
+
+-   When `x` is near zero, `exp(x)-1` can suffer catastrophic cancellation (i.e., a significant loss in precision). `expm1rel` avoids such a loss in precision.
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var expm1rel = require( '@stdlib/math/base/special/expm1rel' );
+
+var x;
+var y;
+var a;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+    x = (randu()*100.0) - 50.0;
+    a = x.toFixed( 3 );
+    y = expm1rel( x );
+    console.log( '(e^%d - 1)/%d = %d', a, a, y );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/benchmark.js

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+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var expm1rel = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = ( randu()*10.0 ) - 5.0;
+		y = expm1rel( x );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/python/scipy/benchmark.py

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+#!/usr/bin/env python
+#
+# @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.
+
+"""Benchmark scipy.special.exprel."""
+
+from __future__ import print_function
+import timeit
+
+NAME = "expm1rel"
+REPEATS = 3
+ITERATIONS = 1000000
+COUNT = [0]  # use a list to allow modification within nested scopes
+
+
+def print_version():
+    """Print the TAP version."""
+    print("TAP version 13")
+
+
+def print_summary(total, passing):
+    """Print the benchmark summary.
+
+    # Arguments
+
+    * `total`: total number of tests
+    * `passing`: number of passing tests
+
+    """
+    print("#")
+    print("1.." + str(total))  # TAP plan
+    print("# total " + str(total))
+    print("# pass  " + str(passing))
+    print("#")
+    print("# ok")
+
+
+def print_results(iterations, elapsed):
+    """Print benchmark results.
+
+    # Arguments
+
+    * `iterations`: number of iterations
+    * `elapsed`: elapsed time (in seconds)
+
+    # Examples
+
+    ``` python
+    python> print_results(100000, 0.131009101868)
+    ```
+    """
+    rate = iterations / elapsed
+
+    print("  ---")
+    print("  iterations: " + str(iterations))
+    print("  elapsed: " + str(elapsed))
+    print("  rate: " + str(rate))
+    print("  ...")
+
+
+def benchmark(name, setup, stmt, iterations):
+    """Run the benchmark and print benchmark results.
+
+    # Arguments
+
+    * `name`: benchmark name (suffix)
+    * `setup`: benchmark setup
+    * `stmt`: statement to benchmark
+    * `iterations`: number of iterations
+
+    # Examples
+
+    ``` python
+    python> benchmark("::random", "from random import random;", "y = random()", 1000000)
+    ```
+    """
+    t = timeit.Timer(stmt, setup=setup)
+
+    i = 0
+    while i < REPEATS:
+        print("# python::scipy::" + NAME + name)
+        COUNT[0] += 1
+        elapsed = t.timeit(number=iterations)
+        print_results(iterations, elapsed)
+        print("ok " + str(COUNT[0]) + " benchmark finished")
+        i += 1
+
+
+def main():
+    """Run the benchmarks."""
+    print_version()
+
+    name = ""
+    setup = "from scipy.special import exprel; from random import random;"
+    stmt = "y = exprel(random())"
+    benchmark(name, setup, stmt, ITERATIONS)
+
+    print_summary(COUNT[0], COUNT[0])
+
+
+if __name__ == "__main__":
+    main()

lib/node_modules/@stdlib/math/base/special/expm1rel/docs/repl.txt

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+
+{{alias}}( x )
+    Relative error exponential.
+
+    When `x` is near zero,
+
+        e^x - 1
+
+    can suffer catastrophic cancellation (i.e., significant loss of precision).
+    This function avoids the loss of precision when `x` is near zero.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    Returns
+    -------
+    y: number
+        Function value.
+
+    Examples
+    --------
+    > var y = {{alias}}( 0.0 )
+    1.0
+    > y = {{alias}}( 1.0 )
+    ~1.718
+    > y = {{alias}}( -1.0 )
+    ~0.632
+    > y = {{alias}}( NaN )
+    NaN
+
+    See Also
+    --------
+