From 988673e609983fd08bbdbcf2b0755d48ce11810a Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Tue, 13 Oct 2026 18:53:31 +0530 Subject: [PATCH] fix: avoid cancellation for large negative `m` in `math/base/special/ellipk` For `m < 0` the parameter is transformed to `x = m/(m-1)`, and `1 - x` was then formed by subtraction, which cancels as `m` grows more negative. The relative error reached 2e-5 at `m = -1e15`, 5e-3 at `-3.7e15`, and `x` rounds to one below `-2^53`, so the function returned `Infinity`. Form `1 - x` as `1/(1-m)` instead. The C++ fixture for large negative values was computed through the same transformation in Boost and was itself off by up to 6e-8, which is what the 204773163-ULP tolerance and its FIXME were covering. It is replaced by a Julia runner evaluating `pi/(2*agm(1, sqrt(1-m)))` in BigFloat. Signed-off-by: Abhist17 --- .../math/base/special/ellipk/lib/main.js | 7 +- .../math/base/special/ellipk/src/main.c | 7 +- .../test/fixtures/cpp/large_negative.json | 1 - .../ellipk/test/fixtures/cpp/runner.cpp | 2 - .../ellipk/test/fixtures/julia/REQUIRE | 2 + .../test/fixtures/julia/huge_negative.json | 1 + .../test/fixtures/julia/large_negative.json | 1 + .../ellipk/test/fixtures/julia/runner.jl | 96 +++++++++++++++++++ .../math/base/special/ellipk/test/test.js | 21 +++- .../base/special/ellipk/test/test.native.js | 21 +++- 10 files changed, 148 insertions(+), 11 deletions(-) delete mode 100644 lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/large_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/REQUIRE create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/huge_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/large_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/runner.jl diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/lib/main.js b/lib/node_modules/@stdlib/math/base/special/ellipk/lib/main.js index 10fd87df0524..afac2760323d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/lib/main.js @@ -137,14 +137,18 @@ function ellipk( m ) { var x; x = m; + td = 1.0 - m; if ( m < 0.0 ) { x = m / ( m - 1.0 ); + + // Form `1-x` as `1/(1-m)` rather than by subtracting `x` from one, which cancels as `m` grows more negative and gives `x = 1` once `m < -2^53`: + td = 1.0 / ( 1.0 - m ); FLG = true; } if ( x === 0.0 ) { return HALF_PI; } - if ( x === 1.0 ) { + if ( td === 0.0 && !FLG ) { return PINF; } if ( x > 1.0 ) { @@ -171,7 +175,6 @@ function ellipk( m ) { } else if ( x < 0.9 ) { t = poly10( x - 0.875 ); } else { - td = 1.0 - x; qd = poly11( td ); kdm = poly12( td - 0.05 ); t = -ln( qd ) * ( kdm * ONE_DIV_PI ); diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/src/main.c b/lib/node_modules/@stdlib/math/base/special/ellipk/src/main.c index 384320054227..01e4f45bae86 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/src/main.c @@ -348,14 +348,18 @@ double stdlib_base_ellipk( const double m ) { FLG = 0; x = m; + td = 1.0 - m; if ( m < 0.0 ) { x = m / ( m - 1.0 ); + + // Form `1-x` as `1/(1-m)` rather than by subtracting `x` from one, which cancels as `m` grows more negative and gives `x = 1` once `m < -2^53`: + td = 1.0 / ( 1.0 - m ); FLG += 1; } if ( x == 0.0 ) { return STDLIB_CONSTANT_FLOAT64_HALF_PI; } - if ( x == 1.0 ) { + if ( td == 0.0 && FLG == 0 ) { return STDLIB_CONSTANT_FLOAT64_PINF; } if ( x > 1.0 ) { @@ -382,7 +386,6 @@ double stdlib_base_ellipk( const double m ) { } else if ( x < 0.9 ) { t = poly_p10( x - 0.875 ); } else { - td = 1.0 - x; qd = poly_p11( td ); kdm = poly_p12( td - 0.05 ); t = -stdlib_base_ln( qd ) * ( kdm * ONE_DIV_PI ); diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/large_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/large_negative.json deleted file mode 100644 index f94cb3166c54..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/large_negative.json +++ /dev/null @@ -1 +0,0 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/runner.cpp b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/runner.cpp index 629e991bf1e8..54d9d62ad164 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/runner.cpp +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/cpp/runner.cpp @@ -330,8 +330,6 @@ int main( void ) { rand_array_f64( x, len, -1.0, 0.0); generate( x, len, "medium_negative.json" ); - rand_array_f64( x, len, -1.0e10, -1.0); - generate( x, len, "large_negative.json" ); // Free allocated memory: free( x ); diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..308c3be89c85 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/REQUIRE @@ -0,0 +1,2 @@ +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/huge_negative.json new file mode 100644 index 000000000000..205d75537bb6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/huge_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/large_negative.json new file mode 100644 index 000000000000..afe9b09c680b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/large_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..fba2500f4945 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/fixtures/julia/runner.jl @@ -0,0 +1,96 @@ +#!/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 + +""" + ellipk( m ) + +Evaluate the complete elliptic integral of the first kind in extended precision. + +# Arguments + +* `m`: parameter + +# Examples + +``` julia +julia> y = ellipk( BigFloat( -1.0 ) ); +``` +""" +function ellipk( m ) + # Use `K(m) = π / ( 2 * agm( 1, sqrt(1-m) ) )`, which holds for all `m < 1` without transforming a negative `m` into a parameter close to one: + a = BigFloat( 1 ); + b = sqrt( 1 - m ); + while abs( a - b ) > eps( a ) * 4 + a, b = ( a + b ) / 2, sqrt( a * b ); + end + return BigFloat( pi ) / ( a + b ); +end + +""" + gen( x, name ) + +Generate fixture data and write to file. + +# Arguments + +* `x`: input values +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> x = -rand( 1000 ) .* 1.0e10; +julia> gen( x, "data.json" ); +``` +""" +function gen( x, name ) + y = setprecision( BigFloat, 2048 ) do + Float64.( ellipk.( BigFloat.( x ) ) ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("expected", y) + ]); + + # 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 ); + +# Large negative values: +x = -( rand( 4000 ) .* ( 1.0e10 - 1.0 ) .+ 1.0 ); +gen( x, "large_negative.json" ); + +# Huge negative values (below `-2^53`, `m/(m-1)` rounds to one): +x = -exp10.( range( 10.0, stop = 300.0, length = 1000 ) ); +gen( x, "huge_negative.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.js b/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.js index 37a2d16e57de..634a0d2f1c70 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.js @@ -34,7 +34,8 @@ var ellipk = require( './../lib' ); var mediumPositive = require( './fixtures/cpp/medium_positive.json' ); var closeToUnity = require( './fixtures/cpp/close_to_unity.json' ); var mediumNegative = require( './fixtures/cpp/medium_negative.json' ); -var largeNegative = require( './fixtures/cpp/large_negative.json' ); +var largeNegative = require( './fixtures/julia/large_negative.json' ); +var hugeNegative = require( './fixtures/julia/huge_negative.json' ); // TESTS // @@ -104,7 +105,23 @@ tape( 'the function evaluates the complete elliptic integral of the first kind ( for ( i = 0; i < x.length; i++ ) { y = ellipk( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 204773163 ), true, 'returns expected value' ); // FIXME: investigate the reason for this large discrepancy + t.strictEqual( isAlmostSameValue( y, expected[ i ], 5 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (huge negative values)', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = hugeNegative.expected; + x = hugeNegative.x; + + for ( i = 0; i < x.length; i++ ) { + y = ellipk( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.native.js index de505efb136c..6186ca53180d 100644 --- a/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/ellipk/test/test.native.js @@ -35,7 +35,8 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var mediumPositive = require( './fixtures/cpp/medium_positive.json' ); var closeToUnity = require( './fixtures/cpp/close_to_unity.json' ); var mediumNegative = require( './fixtures/cpp/medium_negative.json' ); -var largeNegative = require( './fixtures/cpp/large_negative.json' ); +var largeNegative = require( './fixtures/julia/large_negative.json' ); +var hugeNegative = require( './fixtures/julia/huge_negative.json' ); // VARIABLES // @@ -113,7 +114,23 @@ tape( 'the function evaluates the complete elliptic integral of the first kind ( for ( i = 0; i < x.length; i++ ) { y = ellipk( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 204773163 ), true, 'returns expected value' ); // FIXME: investigate the reason for this large discrepancy + t.strictEqual( isAlmostSameValue( y, expected[ i ], 5 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the complete elliptic integral of the first kind (huge negative values)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = hugeNegative.expected; + x = hugeNegative.x; + + for ( i = 0; i < x.length; i++ ) { + y = ellipk( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); } t.end(); });