Implement expit

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2019 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.
+
+-->
+
+# expit
+
+> Compute the [standard logistic][logistic-function] function.
+
+<section class="intro">
+
+The [standard Logistic][logistic-function] function, also called the expit function, inverse logit, or sigmoid function, is defined as the [logistic][logistic-function] function with parameters (`k = 1`, `x0 = 0`, `L = 1`).
+
+<!-- <equation class="equation" label="eq:expit_function" align="center" raw="{\displaystyle {\begin{aligned}\operatorname{expit}(x)&={\frac {1}{1+e^{-x}}}\\&={\frac {e^{x}}{e^{x}+1}}\\&={\tfrac {1}{2}}+{\tfrac {1}{2}}\tanh({\tfrac {x}{2}})\\\end{aligned}}}" alt="Expit function."> -->
+
+<div class="equation" align="center" data-raw-text="{\displaystyle {\begin{aligned}\operatorname{expit}(x)&={\frac {1}{1+e^{-x}}}\\&={\frac {e^{x}}{e^{x}+1}}\\&={\tfrac {1}{2}}+{\tfrac {1}{2}}\tanh({\tfrac {x}{2}})\\\end{aligned}}}" data-equation="eq:expit_function">
+    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/special/expit/docs/img/equation_expit_function.svg" alt="Expit function.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var expit = require( '@stdlib/math/base/special/expit' );
+```
+
+#### expit( x )
+
+Computes the [standard logistic][logistic-function] function.
+
+```javascript
+var v = expit( 0.0 );
+// returns ~0.5
+
+v = expit( 1.0 );
+// returns ~0.731
+
+v = expit( -1.0 );
+// returns ~0.269
+
+v = expit( Infinity );
+// returns 1.0
+
+v = expit( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var expit = require( '@stdlib/math/base/special/expit' );
+
+var x;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+    x = randu();
+    console.log( 'expit(%d) = %d', x, expit( x ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[logistic-function]: https://en.wikipedia.org/wiki/Logistic_function
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 expit = 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();
+		y = expit( 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/expit/benchmark/c/Makefile

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+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2019 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.
+#/
+
+
+# VARIABLES #
+
+ifndef VERBOSE
+	QUIET := @
+endif
+
+# Determine the OS:
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+	OS := WINNT
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+	CC := $(C_COMPILER)
+else
+	CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+	-std=c99 \
+	-O3 \
+	-Wall \
+	-pedantic
+
+# Determine whether to generate [position independent code][1]:
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+	fPIC ?=
+else
+	fPIC ?= -fPIC
+endif
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# TARGETS #
+
+# Default target.
+#
+# This target is the default target.
+
+all: $(c_targets)
+
+.PHONY: all
+
+
+# Compile C source.
+#
+# This target compiles C source files.
+
+$(c_targets): %.out: %.c
+	$(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm
+
+
+# Run a benchmark.
+#
+# This target runs a benchmark.
+
+run: $(c_targets)
+	$(QUIET) ./$<
+
+.PHONY: run
+
+
+# Perform clean-up.
+#
+# This target removes generated files.
+
+clean:
+	$(QUIET) -rm -f *.o *.out
+
+.PHONY: clean