fix: use expm1 in stats/base/dists/exponential/cdf

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/lib/factory.js

@@ -22,7 +22,7 @@
 
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -64,10 +64,10 @@ function factory( lambda ) {
 	* // returns <number>
 	*/
 	function cdf( x ) {
-		if ( x < 0.0 ) {
+		if ( x <= 0.0 ) {
 			return 0.0;
 		}
-		return 1.0 - exp( -lambda * x );
+		return -expm1( -lambda * x );
 	}
 }
 

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/lib/main.js

@@ -21,7 +21,7 @@
 // MODULES //
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -67,10 +67,10 @@ function cdf( x, lambda ) {
 	) {
 		return NaN;
 	}
-	if ( x < 0.0 ) {
+	if ( x <= 0.0 ) {
 		return 0.0;
 	}
-	return 1.0 - exp( -lambda * x );
+	return -expm1( -lambda * x );
 }
 
 

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/manifest.json

@@ -40,7 +40,7 @@
       "dependencies": [
         "@stdlib/math/base/napi/binary",
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/constants/float64/pinf"
       ]
     },
@@ -58,7 +58,7 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/eps",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/constants/float64/pinf"
       ]
     },
@@ -76,7 +76,7 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/eps",
-        "@stdlib/math/base/special/exp",
+        "@stdlib/math/base/special/expm1",
         "@stdlib/constants/float64/pinf"
       ]
     }

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/src/main.c

@@ -18,7 +18,7 @@
 
 #include "stdlib/stats/base/dists/exponential/cdf.h"
 #include "stdlib/math/base/assert/is_nan.h"
-#include "stdlib/math/base/special/exp.h"
+#include "stdlib/math/base/special/expm1.h"
 #include "stdlib/constants/float64/pinf.h"
 
 /**
@@ -41,8 +41,8 @@ double stdlib_base_dists_exponential_cdf( const double x, const double lambda )
 	) {
 		return 0.0/0.0; // NaN
 	}
-	if ( x < 0.0 ) {
+	if ( x <= 0.0 ) {
 		return 0.0;
 	}
-	return 1.0 - stdlib_base_exp( -lambda * x );
+	return -stdlib_base_expm1( -lambda * x );
 }

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/test/fixtures/julia/REQUIRE

@@ -0,0 +1,2 @@
+julia 1.5
+JSON 0.21

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/test/fixtures/julia/runner.jl

@@ -0,0 +1,65 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2026 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.
+
+import JSON
+
+"""
+	gen( x, lambda, name )
+
+Generate fixture data and write to file.
+
+The CDF is evaluated in extended precision from the textbook formula `1 - exp(-lambda*x)`, as subtracting `exp(-lambda*x)` from `1` in double precision cancels for small `lambda*x` (to `0` for `lambda*x < 2^-53`).
+
+# Arguments
+
+* `x`: input value
+* `lambda`: rate parameter
+* `name::AbstractString`: output filename
+"""
+function gen( x, lambda, name )
+	z = setprecision( BigFloat, 2048 ) do
+		Float64.( 1 .- exp.( .-BigFloat.( lambda ) .* BigFloat.( x ) ) )
+	end
+
+	# Store data to be written to file as a collection:
+	data = Dict([
+		("x", x),
+		("lambda", lambda),
+		("expected", z)
+	]);
+
+	# Based on the script directory, create an output filepath:
+	filepath = joinpath( dir, name );
+
+	# Write the data to the output filepath as JSON:
+	outfile = open( filepath, "w" );
+	write( outfile, JSON.json(data) );
+	write( outfile, "\n" );
+	close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Small `x`:
+x = exp10.( range( -300.0, stop = -1.0, length = 1000 ) );
+lambda = ( rand( 1000 ) .* 10.0 ) .+ 0.1;
+gen( x, lambda, "small_x.json" );

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/test/test.cdf.js

@@ -23,6 +23,7 @@
 var tape = require( 'tape' );
 var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 var cdf = require( './../lib' );
@@ -31,6 +32,7 @@ var cdf = require( './../lib' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -61,6 +63,18 @@ tape( 'if provided `-infinity` for `x` and a finite `lambda`, the function retur
 	t.end();
 });
 
+tape( 'if provided `-0` or `+0` for `x` and a finite `lambda`, the function returns `+0`', function test( t ) {
+	var y;
+
+	y = cdf( -0.0, 1.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	y = cdf( 0.0, 1.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'if provided `+infinity` for `lambda`, the function returns `NaN`', function test( t ) {
 	var y;
 
@@ -110,3 +124,20 @@ tape( 'the function evaluates the cdf for `x` given parameter `lambda`', functio
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for small `x`', function test( t ) {
+	var expected;
+	var lambda;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	lambda = smallX.lambda;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = cdf( x[i], lambda[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/test/test.factory.js

@@ -23,6 +23,7 @@
 var tape = require( 'tape' );
 var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 var factory = require( './../lib/factory.js' );
@@ -31,6 +32,7 @@ var factory = require( './../lib/factory.js' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -84,6 +86,21 @@ tape( 'if provided a finite `lambda`, the function returns a function which retu
 	t.end();
 });
 
+tape( 'if provided a finite `lambda`, the function returns a function which returns `+0` when provided `-0` or `+0` for `x`', function test( t ) {
+	var cdf;
+	var y;
+
+	cdf = factory( 1.0 );
+
+	y = cdf( -0.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	y = cdf( 0.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'if provided `+infinity` for `lambda`, the function returns a function which returns `NaN` for any `x`', function test( t ) {
 	var cdf;
 	var y;
@@ -138,3 +155,22 @@ tape( 'the created function evaluates the cdf for `x` given parameter `lambda`',
 	}
 	t.end();
 });
+
+tape( 'the created function evaluates the cdf for small `x`', function test( t ) {
+	var expected;
+	var lambda;
+	var cdf;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	lambda = smallX.lambda;
+	for ( i = 0; i < expected.length; i++ ) {
+		cdf = factory( lambda[i] );
+		y = cdf( x[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/test/test.native.js

@@ -25,13 +25,15 @@ var tape = require( 'tape' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 
 
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // VARIABLES //
@@ -70,6 +72,18 @@ tape( 'if provided `-infinity` for `x` and a finite `lambda`, the function retur
 	t.end();
 });
 
+tape( 'if provided `-0` or `+0` for `x` and a finite `lambda`, the function returns `+0`', opts, function test( t ) {
+	var y;
+
+	y = cdf( -0.0, 1.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	y = cdf( 0.0, 1.0 );
+	t.strictEqual( isPositiveZero( y ), true, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'if provided `+infinity` for `lambda`, the function returns `NaN`', opts, function test( t ) {
 	var y;
 
@@ -119,3 +133,20 @@ tape( 'the function evaluates the cdf for `x` given parameter `lambda`', opts, f
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for small `x`', opts, function test( t ) {
+	var expected;
+	var lambda;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	lambda = smallX.lambda;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = cdf( x[i], lambda[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});