fix: use log1mexp in stats/base/dists/exponential/logcdf

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

@@ -22,8 +22,9 @@
 
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var log1p = require( '@stdlib/math/base/special/log1p' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var log1mexp = require( '@stdlib/math/base/special/log1mexp' );
+var ln = require( '@stdlib/math/base/special/ln' );
+var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
@@ -66,10 +67,15 @@ function factory( lambda ) {
 	* // returns <number>
 	*/
 	function logcdf( x ) {
+		var t;
 		if ( x < 0.0 ) {
 			return NINF;
 		}
-		return log1p( -exp( -lambda * x ) );
+		t = lambda * x;
+		if ( t < FLOAT64_SMALLEST_NORMAL ) {
+			return ln( x ) + ln( lambda );
+		}
+		return log1mexp( t );
 	}
 }
 

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

@@ -21,8 +21,9 @@
 // MODULES //
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var log1p = require( '@stdlib/math/base/special/log1p' );
-var exp = require( '@stdlib/math/base/special/exp' );
+var log1mexp = require( '@stdlib/math/base/special/log1mexp' );
+var ln = require( '@stdlib/math/base/special/ln' );
+var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
@@ -62,6 +63,7 @@ var PINF = require( '@stdlib/constants/float64/pinf' );
 * // returns NaN
 */
 function logcdf( x, lambda ) {
+	var t;
 	if (
 		isnan( lambda ) ||
 		lambda < 0.0 ||
@@ -72,7 +74,11 @@ function logcdf( x, lambda ) {
 	if ( x < 0.0 ) {
 		return NINF;
 	}
-	return log1p( -exp( -lambda * x ) );
+	t = lambda * x;
+	if ( t < FLOAT64_SMALLEST_NORMAL ) {
+		return ln( x ) + ln( lambda );
+	}
+	return log1mexp( t );
 }
 
 

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

@@ -40,10 +40,11 @@
       "dependencies": [
         "@stdlib/math/base/napi/binary",
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/exp",
         "@stdlib/constants/float64/pinf",
         "@stdlib/constants/float64/ninf",
-        "@stdlib/math/base/special/log1p"
+        "@stdlib/math/base/special/log1mexp",
+        "@stdlib/math/base/special/ln",
+        "@stdlib/constants/float64/smallest-normal"
       ]
     },
     {
@@ -60,10 +61,11 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/eps",
-        "@stdlib/math/base/special/exp",
         "@stdlib/constants/float64/pinf",
         "@stdlib/constants/float64/ninf",
-        "@stdlib/math/base/special/log1p"
+        "@stdlib/math/base/special/log1mexp",
+        "@stdlib/math/base/special/ln",
+        "@stdlib/constants/float64/smallest-normal"
       ]
     },
     {
@@ -80,10 +82,11 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/eps",
-        "@stdlib/math/base/special/exp",
         "@stdlib/constants/float64/pinf",
         "@stdlib/constants/float64/ninf",
-        "@stdlib/math/base/special/log1p"
+        "@stdlib/math/base/special/log1mexp",
+        "@stdlib/math/base/special/ln",
+        "@stdlib/constants/float64/smallest-normal"
       ]
     }
   ]

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

@@ -18,8 +18,9 @@
 
 #include "stdlib/stats/base/dists/exponential/logcdf.h"
 #include "stdlib/math/base/assert/is_nan.h"
-#include "stdlib/math/base/special/log1p.h"
-#include "stdlib/math/base/special/exp.h"
+#include "stdlib/math/base/special/log1mexp.h"
+#include "stdlib/math/base/special/ln.h"
+#include "stdlib/constants/float64/smallest_normal.h"
 #include "stdlib/constants/float64/pinf.h"
 #include "stdlib/constants/float64/ninf.h"
 
@@ -35,6 +36,7 @@
 * // returns ~-1.708
 */
 double stdlib_base_dists_exponential_logcdf( const double x, const double lambda ) {
+	double t;
 	if (
 		stdlib_base_is_nan( x ) ||
 		stdlib_base_is_nan( lambda ) ||
@@ -46,5 +48,9 @@ double stdlib_base_dists_exponential_logcdf( const double x, const double lambda
 	if ( x < 0.0 ) {
 		return STDLIB_CONSTANT_FLOAT64_NINF;
 	}
-	return stdlib_base_log1p( -stdlib_base_exp( -lambda * x ) );
+	t = lambda * x;
+	if ( t < STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL ) {
+		return stdlib_base_ln( x ) + stdlib_base_ln( lambda );
+	}
+	return stdlib_base_log1mexp( t );
 }

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

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

lib/node_modules/@stdlib/stats/base/dists/exponential/logcdf/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 logarithm of the CDF is evaluated in extended precision from the textbook formula `ln(1 - exp(-lambda*x))`, as forming `1 - exp(-lambda*x)` 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.( log.( 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 = exp10.( ( rand( 1000 ) .* 41.0 ) .- 40.0 );
+gen( x, lambda, "small_x.json" );

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

@@ -31,6 +31,7 @@ var factory = require( './../lib/factory.js' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -138,3 +139,22 @@ tape( 'the created function evaluates the logcdf for `x` given parameter `lambda
 	}
 	t.end();
 });
+
+tape( 'the created function evaluates the logcdf for small `x`', function test( t ) {
+	var expected;
+	var lambda;
+	var logcdf;
+	var i;
+	var x;
+	var y;
+
+	expected = smallX.expected;
+	x = smallX.x;
+	lambda = smallX.lambda;
+	for ( i = 0; i < expected.length; i++ ) {
+		logcdf = factory( lambda[i] );
+		y = logcdf( x[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});

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

@@ -31,6 +31,7 @@ var logcdf = require( './../lib' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // TESTS //
@@ -110,3 +111,20 @@ tape( 'the function evaluates the logcdf for `x` given parameter `lambda`', func
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the logcdf 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 = logcdf( 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/logcdf/test/test.native.js

@@ -32,6 +32,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallX = require( './fixtures/julia/small_x.json' );
 
 
 // VARIABLES //
@@ -119,3 +120,20 @@ tape( 'the function evaluates the logcdf for `x` given parameter `lambda`', opts
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the logcdf 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 = logcdf( x[i], lambda[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});