diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/lib/main.js b/lib/node_modules/@stdlib/math/base/special/erfcx/lib/main.js index 490a808083da..be84c6da8bbe 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/lib/main.js @@ -49,6 +49,7 @@ var exp = require( '@stdlib/math/base/special/exp' ); var PINF = require( '@stdlib/constants/float64/pinf' ); +var floor = require( '@stdlib/math/base/special/floor' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var erfcxY100 = require( './erfcx_y100.js' ); @@ -100,7 +101,9 @@ var INV_SQRT_PI = 0.56418958354775628694807945156; // 1 / sqrt(pi) * // returns NaN */ function erfcx( x ) { + var ex2; var x2; + var xh; if ( isnan( x ) ) { return x; @@ -120,11 +123,13 @@ function erfcx( x ) { if ( x < -26.7 ) { return PINF; } - x2 = x * x; + // Forming `x*x` rounds away bits that `exp` then amplifies by a factor of `x^2` (several hundred ULPs near `x = -26`). Split `x = xh + xl`, with `xh` holding the leading bits of `x` so that `xh*xh` is exact, and use `exp(x^2) = exp(xh^2) * exp(xl*(x+xh))`, whose second factor is close to one: + xh = floor( x * 65536.0 ) / 65536.0; + ex2 = exp( xh * xh ) * exp( ( x - xh ) * ( x + xh ) ); if ( x < -6.1 ) { - return 2.0 * exp( x2 ); + return 2.0 * ex2; } - return ( 2.0*exp( x2 ) ) - erfcxY100( 400.0/(4.0-x) ); + return ( 2.0*ex2 ) - erfcxY100( 400.0/(4.0-x) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/manifest.json b/lib/node_modules/@stdlib/math/base/special/erfcx/manifest.json index 33c79807e930..43f3aba3cbfc 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/manifest.json @@ -40,7 +40,8 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/floor", "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/exp" + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/floor" ] }, { @@ -57,7 +58,8 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/floor", "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/exp" + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/floor" ] }, { @@ -74,7 +76,8 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/floor", "@stdlib/constants/float64/pinf", - "@stdlib/math/base/special/exp" + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/floor" ] } ] diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/src/main.c b/lib/node_modules/@stdlib/math/base/special/erfcx/src/main.c index eb24d37a2ae5..dee9b0e9f2df 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/src/main.c @@ -45,6 +45,7 @@ #include "stdlib/math/base/special/erfcx.h" #include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/floor.h" #include "stdlib/constants/float64/pinf.h" #include "stdlib/math/base/special/floor.h" #include "stdlib/math/base/assert/is_nan.h" @@ -1133,7 +1134,9 @@ static double erfcxY100( const double y100 ) { * // returns +Infinity */ double stdlib_base_erfcx( const double x ) { + double ex2; double x2; + double xh; if( stdlib_base_is_nan( x ) ) { return x; @@ -1153,9 +1156,11 @@ double stdlib_base_erfcx( const double x ) { if ( x < -26.7 ) { return STDLIB_CONSTANT_FLOAT64_PINF; } - x2 = x * x; + // Forming `x*x` rounds away bits that `exp` then amplifies by a factor of `x^2` (several hundred ULPs near `x = -26`). Split `x = xh + xl`, with `xh` holding the leading bits of `x` so that `xh*xh` is exact, and use `exp(x^2) = exp(xh^2) * exp(xl*(x+xh))`, whose second factor is close to one: + xh = stdlib_base_floor( x * 65536.0 ) / 65536.0; + ex2 = stdlib_base_exp( xh * xh ) * stdlib_base_exp( ( x - xh ) * ( x + xh ) ); if ( x < -6.1 ) { - return 2.0 * stdlib_base_exp( x2 ); + return 2.0 * ex2; } - return ( 2.0 * stdlib_base_exp( x2 ) ) - erfcxY100( 400.0 / ( 4.0 - x ) ); + return ( 2.0 * ex2 ) - erfcxY100( 400.0 / ( 4.0 - x ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..32b7aa2b920c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/REQUIRE @@ -0,0 +1,3 @@ +julia 1.5 +JSON 0.21 +SpecialFunctions 0.10 diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/medium_negative.json new file mode 100644 index 000000000000..e6a3a7bdf623 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/medium_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/negative.json b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/negative.json new file mode 100644 index 000000000000..49106c143371 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..674103137e0e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/julia/runner.jl @@ -0,0 +1,75 @@ +#!/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 +import SpecialFunctions: erfcx + +""" + gen( domain, name ) + +Generate fixture data and write to file. + +The scaled complementary error function is evaluated in extended precision, as `Float64` implementations form `x^2` before exponentiating it. + +# Arguments + +* `domain`: domain +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> x = range( -26.0, stop = -1.0, length = 2001 ); +julia> gen( x, "data.json" ); +``` +""" +function gen( domain, name ) + x = collect( domain ); + y = setprecision( BigFloat, 256 ) do + Float64.( erfcx.( 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 ); + +# Medium negative values (previously generated with SciPy, whose `erfcx` forms `x^2` in double precision as well): +x = range( -10.0, stop = -1.0, length = 1707 ); +gen( x, "medium_negative.json" ); + +# Negative values, down to where the function overflows: +x = range( -26.6, stop = -1.0, length = 2001 ); +gen( x, "negative.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/medium_negative.json deleted file mode 100644 index 5065e27b6e3b..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/medium_negative.json +++ /dev/null @@ -1 +0,0 @@ -{"x": [-10.0, -9.9947245017585, -9.989449003516999, -9.984173505275498, -9.978898007033997, -9.973622508792497, -9.968347010550996, -9.963071512309496, -9.957796014067995, -9.952520515826494, 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5.378576171271032, 5.314575508035581, 5.251558418152361, 5.1895073569585914, 5.128405128251391, 5.068234876754934, 5.008980080762283]} diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/runner.py b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/runner.py index 07bedc4e46e6..ec65fc7bb06c 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/runner.py +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/fixtures/runner.py @@ -72,10 +72,6 @@ def main(): x = np.linspace(2.0**-54, 1.0, 1653) generate(x, "small_positive.json") - # Medium negative values: - x = np.linspace(-10.0, -1.0, 1707) - generate(x, "medium_negative.json") - # Small negative values: x = np.linspace(-1.0, -2.0**-54, 1653) generate(x, "small_negative.json") diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.js b/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.js index ea62627dc4c9..a9e90f66d009 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.js @@ -37,9 +37,10 @@ var INV_SQRT_PI = 0.56418958354775628694807945156; // 1 / sqrt(pi) var mediumPositive = require( './fixtures/medium_positive.json' ); var smallPositive = require( './fixtures/small_positive.json' ); var smallNegative = require( './fixtures/small_negative.json' ); -var mediumNegative = require( './fixtures/medium_negative.json' ); +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var largePositive = require( './fixtures/large_positive.json' ); var tiny = require( './fixtures/tiny.json' ); +var negative = require( './fixtures/julia/negative.json' ); // TESTS // @@ -148,7 +149,22 @@ tape( 'the function computes the scaled complementary error function for negativ x = mediumNegative.x; for ( i = 0; i < expected.length; i++ ) { y = erfcx( x[ i ] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function computes the scaled complementary error function for negative numbers (extended-precision reference)', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = negative.expected; + x = negative.x; + for ( i = 0; i < expected.length; i++ ) { + y = erfcx( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.native.js index 2da9e281ce41..52d3d25c29bd 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcx/test/test.native.js @@ -33,9 +33,10 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var mediumPositive = require( './fixtures/medium_positive.json' ); var smallPositive = require( './fixtures/small_positive.json' ); var smallNegative = require( './fixtures/small_negative.json' ); -var mediumNegative = require( './fixtures/medium_negative.json' ); +var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var largePositive = require( './fixtures/large_positive.json' ); var tiny = require( './fixtures/tiny.json' ); +var negative = require( './fixtures/julia/negative.json' ); // VARIABLES // @@ -157,7 +158,22 @@ tape( 'the function computes the scaled complementary error function for negativ x = mediumNegative.x; for ( i = 0; i < expected.length; i++ ) { y = erfcx( x[ i ] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function computes the scaled complementary error function for negative numbers (extended-precision reference)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = negative.expected; + x = negative.x; + for ( i = 0; i < expected.length; i++ ) { + y = erfcx( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); });