fix: use log1p for small p in stats/base/dists/exponential/quantile

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

@@ -22,7 +22,7 @@
 
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -63,7 +63,7 @@ function factory( lambda ) {
 		if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
 			return NaN;
 		}
-		return -ln( 1.0 - p ) / lambda;
+		return -log1p( -p ) / lambda;
 	}
 }
 

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

@@ -21,7 +21,7 @@
 // MODULES //
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -74,7 +74,7 @@ function quantile( p, lambda ) {
 	) {
 		return NaN;
 	}
-	return -ln( 1.0 - p ) / lambda;
+	return -log1p( -p ) / lambda;
 }
 
 

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

@@ -41,7 +41,7 @@
         "@stdlib/math/base/napi/binary",
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/pinf",
-        "@stdlib/math/base/special/ln"
+        "@stdlib/math/base/special/log1p"
       ]
     },
     {
@@ -59,7 +59,7 @@
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/eps",
         "@stdlib/constants/float64/pinf",
-        "@stdlib/math/base/special/ln"
+        "@stdlib/math/base/special/log1p"
       ]
     },
     {
@@ -76,7 +76,7 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/constants/float64/pinf",
-        "@stdlib/math/base/special/ln"
+        "@stdlib/math/base/special/log1p"
       ]
     }
   ]

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

@@ -19,7 +19,7 @@
 #include "stdlib/stats/base/dists/exponential/quantile.h"
 #include "stdlib/math/base/assert/is_nan.h"
 #include "stdlib/constants/float64/pinf.h"
-#include "stdlib/math/base/special/ln.h"
+#include "stdlib/math/base/special/log1p.h"
 
 /**
 * Evaluates the quantile function for an exponential distribution with rate parameter `lambda` at a probability `p`.
@@ -42,5 +42,5 @@ double stdlib_base_dists_exponential_quantile( const double p, const double lamb
 	) {
 		return 0.0 / 0.0; // NaN
 	}
-	return -stdlib_base_ln( 1.0 - p ) / lambda;
+	return -stdlib_base_log1p( -p ) / lambda;
 }

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

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

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

@@ -0,0 +1,73 @@
+#!/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( p, lambda, name )
+
+Generate fixture data and write to file.
+
+The quantile is evaluated in extended precision from the textbook formula `-ln(1-p) / lambda`, as forming `1-p` in double precision rounds away the low-order bits of `p` (all of them for `p < 2^-53`).
+
+# Arguments
+
+* `p`: input value
+* `lambda`: rate parameter
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> p = rand( 1000 );
+julia> lambda = rand( 1000 ) .* 100.0;
+julia> gen( p, lambda, "data.json" );
+```
+"""
+function gen( p, lambda, name )
+	z = setprecision( BigFloat, 2048 ) do
+		Float64.( .-log.( 1 .- BigFloat.( p ) ) ./ BigFloat.( lambda ) )
+	end
+
+	# Store data to be written to file as a collection:
+	data = Dict([
+		("p", p),
+		("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 `p`:
+p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) );
+lambda = ( rand( 1000 ) .* 100.0 ) .+ 0.1;
+gen( p, lambda, "small_p.json" );

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

@@ -31,6 +31,7 @@ var factory = require( './../lib/factory.js' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 var i;
 for ( i = 0; i < data.expected.length; i++ ) {
 	if ( data.expected[ i ] === 'Inf' ) {
@@ -135,7 +136,26 @@ tape( 'the created function evaluates the quantile for `x` given parameter `lamb
 	for ( i = 0; i < x.length; i++ ) {
 		quantile = factory( lambda[i] );
 		y = quantile( x[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 172 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the created function evaluates the quantile for small `x`', function test( t ) {
+	var expected;
+	var quantile;
+	var lambda;
+	var x;
+	var y;
+	var i;
+
+	expected = smallP.expected;
+	x = smallP.p;
+	lambda = smallP.lambda;
+	for ( i = 0; i < x.length; i++ ) {
+		quantile = factory( lambda[i] );
+		y = quantile( x[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });

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

@@ -40,6 +40,7 @@ var opts = {
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 var i;
 for ( i = 0; i < data.expected.length; i++ ) {
 	if ( data.expected[ i ] === 'Inf' ) {
@@ -120,7 +121,24 @@ tape( 'the function evaluates the quantile for `x` given parameter `lambda`', op
 	lambda = data.lambda;
 	for ( i = 0; i < x.length; i++ ) {
 		y = quantile( x[i], lambda[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 172 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the quantile for small `x`', opts, function test( t ) {
+	var expected;
+	var lambda;
+	var x;
+	var y;
+	var i;
+
+	expected = smallP.expected;
+	x = smallP.p;
+	lambda = smallP.lambda;
+	for ( i = 0; i < x.length; i++ ) {
+		y = quantile( 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/quantile/test/test.quantile.js

@@ -31,6 +31,7 @@ var quantile = require( './../lib' );
 // FIXTURES //
 
 var data = require( './fixtures/r/data.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 var i;
 for ( i = 0; i < data.expected.length; i++ ) {
 	if ( data.expected[ i ] === 'Inf' ) {
@@ -111,7 +112,24 @@ tape( 'the function evaluates the quantile for `x` given parameter `lambda`', fu
 	lambda = data.lambda;
 	for ( i = 0; i < x.length; i++ ) {
 		y = quantile( x[i], lambda[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 172 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the quantile for small `x`', function test( t ) {
+	var expected;
+	var lambda;
+	var x;
+	var y;
+	var i;
+
+	expected = smallP.expected;
+	x = smallP.p;
+	lambda = smallP.lambda;
+	for ( i = 0; i < x.length; i++ ) {
+		y = quantile( x[i], lambda[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });