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

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

@@ -21,7 +21,7 @@
 // MODULES //
 
 var constantFunction = require( '@stdlib/utils/constant-function' );
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 
@@ -69,7 +69,7 @@ function factory( k, lambda ) {
 		if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
 			return NaN;
 		}
-		return lambda * pow( -ln( 1.0 - p ), 1.0/k );
+		return lambda * pow( -log1p( -p ), 1.0/k );
 	}
 }
 

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

@@ -20,7 +20,7 @@
 
 // MODULES //
 
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 
@@ -79,7 +79,7 @@ function quantile( p, k, lambda ) {
 	) {
 		return NaN;
 	}
-	return lambda * pow( -ln( 1.0 - p ), 1.0/k );
+	return lambda * pow( -log1p( -p ), 1.0/k );
 }
 
 

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

@@ -40,7 +40,7 @@
       "dependencies": [
         "@stdlib/math/base/napi/ternary",
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow"
       ]
     },
@@ -57,7 +57,7 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow"
       ]
     },
@@ -74,7 +74,7 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
         "@stdlib/math/base/special/pow"
       ]
     }

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

@@ -18,7 +18,7 @@
 
 #include "stdlib/stats/base/dists/weibull/quantile.h"
 #include "stdlib/math/base/assert/is_nan.h"
-#include "stdlib/math/base/special/ln.h"
+#include "stdlib/math/base/special/log1p.h"
 #include "stdlib/math/base/special/pow.h"
 
 /**
@@ -37,5 +37,5 @@ double stdlib_base_dists_weibull_quantile( const double p, const double k, const
 	if ( stdlib_base_is_nan( k ) || stdlib_base_is_nan( lambda ) || stdlib_base_is_nan( p ) || k <= 0.0 || lambda <= 0.0 || p < 0.0 || p > 1.0 ) {
 		return 0.0 / 0.0; // NaN
 	}
-	return lambda * stdlib_base_pow( -stdlib_base_ln( 1.0 - p ), 1.0 / k );
+	return lambda * stdlib_base_pow( -stdlib_base_log1p( -p ), 1.0 / k );
 }

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

@@ -1,3 +1,2 @@
-Distributions 0.23.8
 julia 1.5
 JSON 0.21

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

@@ -16,14 +16,15 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import Distributions: quantile, Weibull
 import JSON
 
 """
 	gen( p, k, lambda, name )
 
 Generate fixture data and write to file.
 
+The quantile is evaluated in extended precision from the textbook formula `lambda * (-ln(1-p))^(1/k)`, 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
@@ -41,9 +42,8 @@ julia> gen( p, k, lambda, "data.json" );
 ```
 """
 function gen( p, k, lambda, name )
-	z = Array{Float64}( undef, length(p) );
-	for i in eachindex(p)
-		z[ i ] = quantile( Weibull( k[i], lambda[i] ), p[i] );
+	z = setprecision( BigFloat, 2048 ) do
+		Float64.( BigFloat.( lambda ) .* ( .-log.( 1 .- BigFloat.( p ) ) ) .^ ( 1 ./ BigFloat.( k ) ) )
 	end
 
 	# Store data to be written to file as a collection:
@@ -87,3 +87,9 @@ p = rand( 1000 );
 lambda = ( rand( 1000 ) .* 20.0 ) .+ 10.0;
 k = ( rand( 1000 ) .* 20.0 ) .+ 10.0;
 gen( p, k, lambda, "both_large.json" );
+
+# Small `p` (shape parameters are powers of two, so that `1/k` is exact and the test measures the error from `1-p`):
+p = exp10.( range( -300.0, stop = -1.0, length = 1000 ) );
+lambda = ( rand( 1000 ) .* 10.0 ) .+ 0.1;
+k = repeat( [ 1.0, 2.0, 4.0, 8.0 ], 250 );
+gen( p, k, lambda, "small_p.json" );

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

@@ -33,6 +33,7 @@ var factory = require( './../lib/factory.js' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
 var largeShape = require( './fixtures/julia/large_shape.json' );
 var bothLarge = require( './fixtures/julia/both_large.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 
 
 // TESTS //
@@ -180,7 +181,7 @@ tape( 'the created function evaluates the quantile for `p` given large `lambda`
 	for ( i = 0; i < p.length; i++ ) {
 		quantile = factory( k[i], lambda[i] );
 		y = quantile( p[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -222,7 +223,28 @@ tape( 'the created function evaluates the quantile for `p` given large scale par
 	for ( i = 0; i < p.length; i++ ) {
 		quantile = factory( k[i], lambda[i] );
 		y = quantile( p[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 6 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 56 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the created function evaluates the quantile for small `p`', function test( t ) {
+	var expected;
+	var quantile;
+	var lambda;
+	var i;
+	var k;
+	var p;
+	var y;
+
+	expected = smallP.expected;
+	p = smallP.p;
+	lambda = smallP.lambda;
+	k = smallP.k;
+	for ( i = 0; i < p.length; i++ ) {
+		quantile = factory( k[i], lambda[i] );
+		y = quantile( p[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });

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

@@ -34,6 +34,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
 var bothLarge = require( './fixtures/julia/both_large.json' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
 var largeShape = require( './fixtures/julia/large_shape.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 
 
 // VARIABLES //
@@ -106,7 +107,7 @@ tape( 'the function evaluates the quantile for `p` given large `k` and `lambda`'
 	lambda = bothLarge.lambda;
 	for ( i = 0; i < p.length; i++ ) {
 		y = quantile( p[ i ], k[ i ], lambda[ i ] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -125,7 +126,7 @@ tape( 'the function evaluates the quantile for `p` given large `lambda`', opts,
 	lambda = largeScale.lambda;
 	for ( i = 0; i < p.length; i++ ) {
 		y = quantile( p[ i ], k[ i ], lambda[ i ] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 6 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 56 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -148,3 +149,22 @@ tape( 'the function evaluates the quantile for `p` given large `k`', opts, funct
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the quantile for small `p`', opts, function test( t ) {
+	var expected;
+	var lambda;
+	var p;
+	var k;
+	var y;
+	var i;
+
+	expected = smallP.expected;
+	p = smallP.p;
+	lambda = smallP.lambda;
+	k = smallP.k;
+	for ( i = 0; i < p.length; i++ ) {
+		y = quantile( p[ i ], k[ i ], lambda[ i ] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
+	}
+	t.end();
+});

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

@@ -33,6 +33,7 @@ var quantile = require( './../lib' );
 var largeScale = require( './fixtures/julia/large_scale.json' );
 var largeShape = require( './fixtures/julia/large_shape.json' );
 var bothLarge = require( './fixtures/julia/both_large.json' );
+var smallP = require( './fixtures/julia/small_p.json' );
 
 
 // TESTS //
@@ -129,7 +130,7 @@ tape( 'the function evaluates the p-th quantile given large parameters `lambda`
 	k = bothLarge.k;
 	for ( i = 0; i < p.length; i++ ) {
 		y = quantile( p[i], k[i], lambda[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
@@ -167,7 +168,26 @@ tape( 'the function evaluates the p-th quantile given large scale parameter `k`'
 	k = largeScale.k;
 	for ( i = 0; i < p.length; i++ ) {
 		y = quantile( p[i], k[i], lambda[i] );
-		t.strictEqual( isAlmostSameValue( y, expected[ i ], 6 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 56 ), true, 'returns expected value' );
+	}
+	t.end();
+});
+
+tape( 'the function evaluates the p-th quantile for small `p`', function test( t ) {
+	var expected;
+	var lambda;
+	var p;
+	var k;
+	var y;
+	var i;
+
+	expected = smallP.expected;
+	p = smallP.p;
+	lambda = smallP.lambda;
+	k = smallP.k;
+	for ( i = 0; i < p.length; i++ ) {
+		y = quantile( p[i], k[i], lambda[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });