diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/lib/main.js b/lib/node_modules/@stdlib/math/base/special/acoth/lib/main.js index 43ad6149951a..2db2b449ce16 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/acoth/lib/main.js @@ -21,6 +21,7 @@ // MODULES // var atanh = require( '@stdlib/math/base/special/atanh' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); // MAIN // @@ -52,6 +53,13 @@ var atanh = require( '@stdlib/math/base/special/atanh' ); * // returns NaN */ function acoth( x ) { + // Near `|x| = 1`, `atanh( 1/x )` loses the low bits of `1-|1/x|` to the rounding of `1/x`. Use `acoth(x) = log( (x+1)/(x-1) )/2 = log1p( 2/(x-1) )/2` instead, where `x-1` is exact for `1 <= x <= 2`: + if ( x >= 1.0 && x <= 2.0 ) { + return 0.5 * log1p( 2.0 / ( x - 1.0 ) ); + } + if ( x <= -1.0 && x >= -2.0 ) { + return -0.5 * log1p( 2.0 / ( -x - 1.0 ) ); + } return atanh( 1.0/x ); } diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/manifest.json b/lib/node_modules/@stdlib/math/base/special/acoth/manifest.json index 6a549d2d5184..c9fc3ea8b69b 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/manifest.json @@ -37,7 +37,8 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", - "@stdlib/math/base/special/atanh" + "@stdlib/math/base/special/atanh", + "@stdlib/math/base/special/log1p" ] }, { @@ -51,7 +52,8 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/atanh" + "@stdlib/math/base/special/atanh", + "@stdlib/math/base/special/log1p" ] }, { @@ -65,7 +67,8 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/atanh" + "@stdlib/math/base/special/atanh", + "@stdlib/math/base/special/log1p" ] } ] diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/src/main.c b/lib/node_modules/@stdlib/math/base/special/acoth/src/main.c index 87fef1cffe7f..e874e975faf0 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/acoth/src/main.c @@ -18,6 +18,7 @@ #include "stdlib/math/base/special/acoth.h" #include "stdlib/math/base/special/atanh.h" +#include "stdlib/math/base/special/log1p.h" /** * Computes the inverse hyperbolic cotangent of a double-precision floating-point number. @@ -30,5 +31,12 @@ * // returns ~0.5493 */ double stdlib_base_acoth( const double x ) { + // Near `|x| = 1`, `atanh( 1/x )` loses the low bits of `1-|1/x|` to the rounding of `1/x`. Use `acoth(x) = log( (x+1)/(x-1) )/2 = log1p( 2/(x-1) )/2` instead, where `x-1` is exact for `1 <= x <= 2`: + if ( x >= 1.0 && x <= 2.0 ) { + return 0.5 * stdlib_base_log1p( 2.0 / ( x - 1.0 ) ); + } + if ( x <= -1.0 && x >= -2.0 ) { + return -0.5 * stdlib_base_log1p( 2.0 / ( -x - 1.0 ) ); + } return stdlib_base_atanh( 1.0 / x ); } diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_negative.json index c89cf620f300..22feaaf7b385 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_positive.json index c29f87a25b44..ce518b02ddda 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/huge_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_negative.json index 858d296135d4..744e59d0c5f7 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_positive.json index 16c792fc30d0..16c9cb43ded4 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_negative.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_negative.json index 111c68ecb2d3..d4551fc644da 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_positive.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_positive.json index e5729a14c883..df698e53b4ce 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/larger_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_negative.json index 0d507fa9335e..81bac69b95aa 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_positive.json index f8fef44dfda1..6ce8f6ca75b5 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_negative_one.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_negative_one.json new file mode 100644 index 000000000000..0dcd73315cea --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_negative_one.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_positive_one.json b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_positive_one.json new file mode 100644 index 000000000000..436693e0fe0d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/near_positive_one.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/runner.jl index 49076634b7e0..505a5c7952d3 100755 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/fixtures/julia/runner.jl @@ -37,7 +37,9 @@ julia> gen( x, \"data.json\" ); """ function gen( domain, name ) x = collect( domain ); - y = acoth.( x ); + y = setprecision( BigFloat, 256 ) do + Float64.( acoth.( BigFloat.( x ) ) ); + end # Store data to be written to file as a collection: data = Dict([ @@ -92,3 +94,11 @@ gen( x, "larger_negative.json" ); # Huge negative values: x = range( -1.0e300, stop = -1.0e308, length = 1003 ); gen( x, "huge_negative.json" ); + +# Values close to one (in `Float64`, `acoth` is `atanh(1/x)` and loses the low bits of `1-1/x`): +x = 1.0 .+ exp10.( range( -15.0, stop = -1.0, length = 1000 ) ); +gen( x, "near_positive_one.json" ); + +x = -1.0 .- exp10.( range( -15.0, stop = -1.0, length = 1000 ) ); +gen( x, "near_negative_one.json" ); + diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/test.js b/lib/node_modules/@stdlib/math/base/special/acoth/test/test.js index 0eccb43b0473..d2740231f250 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/test.js @@ -37,6 +37,8 @@ var largerNegative = require( './fixtures/julia/larger_negative.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var hugeNegative = require( './fixtures/julia/huge_negative.json' ); +var nearPositiveOne = require( './fixtures/julia/near_positive_one.json' ); +var nearNegativeOne = require( './fixtures/julia/near_negative_one.json' ); // TESTS // @@ -57,7 +59,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for medium positiv expected = mediumPositive.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -72,7 +74,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for medium negativ expected = mediumNegative.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -87,7 +89,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for large positive expected = largePositive.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -102,7 +104,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for large negative expected = largeNegative.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -167,6 +169,36 @@ tape( 'the function computes the inverse hyperbolic cotangent for huge negative t.end(); }); +tape( 'the function computes the inverse hyperbolic cotangent for values close to `1`', function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearPositiveOne.x; + expected = nearPositiveOne.expected; + for ( i = 0; i < x.length; i++ ) { + y = acoth( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function computes the inverse hyperbolic cotangent for values close to `-1`', function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearNegativeOne.x; + expected = nearNegativeOne.expected; + for ( i = 0; i < x.length; i++ ) { + y = acoth( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { var v = acoth( NaN ); t.strictEqual( isnan( v ), true, 'returns expected value' ); diff --git a/lib/node_modules/@stdlib/math/base/special/acoth/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/acoth/test/test.native.js index c6a651eabf8b..d6afb7f2ff0e 100644 --- a/lib/node_modules/@stdlib/math/base/special/acoth/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/acoth/test/test.native.js @@ -38,6 +38,8 @@ var largerNegative = require( './fixtures/julia/larger_negative.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var hugeNegative = require( './fixtures/julia/huge_negative.json' ); +var nearPositiveOne = require( './fixtures/julia/near_positive_one.json' ); +var nearNegativeOne = require( './fixtures/julia/near_negative_one.json' ); // VARIABLES // @@ -66,7 +68,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for medium positiv expected = mediumPositive.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -81,7 +83,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for medium negativ expected = mediumNegative.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -96,7 +98,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for large positive expected = largePositive.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -111,7 +113,7 @@ tape( 'the function computes the inverse hyperbolic cotangent for large negative expected = largeNegative.expected; for ( i = 0; i < x.length; i++ ) { y = acoth( 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(); }); @@ -176,6 +178,36 @@ tape( 'the function computes the inverse hyperbolic cotangent for huge negative t.end(); }); +tape( 'the function computes the inverse hyperbolic cotangent for values close to `1`', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearPositiveOne.x; + expected = nearPositiveOne.expected; + for ( i = 0; i < x.length; i++ ) { + y = acoth( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function computes the inverse hyperbolic cotangent for values close to `-1`', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearNegativeOne.x; + expected = nearNegativeOne.expected; + for ( i = 0; i < x.length; i++ ) { + y = acoth( x[ i ] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { var v = acoth( NaN ); t.strictEqual( isnan( v ), true, 'returns expected value' );