From 2e7bf2e2a03f2f48240270a85a974d4f663d9407 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 04:46:35 +0530 Subject: [PATCH 1/3] fix: avoid cancellation in `math/base/special/versin` and `haversin` `1 - cos(x)` loses significant digits as `cos(x)` approaches one: the relative error is about `2e-16/x^2`, so `versin(1e-6)` has 4 correct digits, `versin(1e-7)` has 3, and below `|x| ~ 1.5e-8` the result is exactly `0` (e.g., `versin(1e-10)` returns `0` instead of `5e-21`). Use the half-angle identities `versin(x) = 2*sin(x/2)^2` and `haversin(x) = sin(x/2)^2`, which are within 2 ULP everywhere. Regenerate the fixtures in extended precision and add fixtures for small `|x|`. --- .../math/base/special/haversin/lib/main.js | 8 ++- .../math/base/special/haversin/manifest.json | 6 +-- .../math/base/special/haversin/src/main.c | 8 ++- .../test/fixtures/julia/huge_negative.json | 2 +- .../test/fixtures/julia/huge_positive.json | 2 +- .../test/fixtures/julia/large_negative.json | 2 +- .../test/fixtures/julia/large_positive.json | 2 +- .../test/fixtures/julia/medium_negative.json | 2 +- .../test/fixtures/julia/medium_positive.json | 2 +- .../haversin/test/fixtures/julia/runner.jl | 13 ++++- .../test/fixtures/julia/small_negative.json | 1 + .../test/fixtures/julia/small_positive.json | 1 + .../math/base/special/haversin/test/test.js | 49 ++++++++++++++++--- .../base/special/haversin/test/test.native.js | 36 ++++++++++++++ .../math/base/special/versin/lib/main.js | 8 ++- .../math/base/special/versin/manifest.json | 6 +-- .../math/base/special/versin/src/main.c | 8 ++- .../test/fixtures/julia/huge_negative.json | 2 +- .../test/fixtures/julia/huge_positive.json | 2 +- .../test/fixtures/julia/large_negative.json | 2 +- .../test/fixtures/julia/large_positive.json | 2 +- .../test/fixtures/julia/medium_negative.json | 2 +- .../test/fixtures/julia/medium_positive.json | 2 +- .../versin/test/fixtures/julia/runner.jl | 13 ++++- .../test/fixtures/julia/small_negative.json | 1 + .../test/fixtures/julia/small_positive.json | 1 + .../math/base/special/versin/test/test.js | 49 ++++++++++++++++--- .../base/special/versin/test/test.native.js | 36 ++++++++++++++ 28 files changed, 228 insertions(+), 40 deletions(-) create mode 100644 lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_positive.json create mode 100644 lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_negative.json create mode 100644 lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_positive.json diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js b/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js index 4c5e647e2ec0..8807ed08735d 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js @@ -20,7 +20,7 @@ // MODULES // -var cos = require( '@stdlib/math/base/special/cos' ); +var sin = require( '@stdlib/math/base/special/sin' ); // MAIN // @@ -48,7 +48,11 @@ var cos = require( '@stdlib/math/base/special/cos' ); * // returns NaN */ function haversin( x ) { - return (1.0 - cos( x )) / 2.0; + var s; + + // Use the half-angle identity `(1 - cos(x))/2 = sin(x/2)^2`, as evaluating `(1 - cos(x))/2` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): + s = sin( x / 2.0 ); + return s * s; } diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json b/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json index fec32d6cb6ec..083d8fc81535 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json @@ -37,7 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] }, { @@ -51,7 +51,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] }, { @@ -65,7 +65,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] } ] diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c b/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c index 63377a7393ca..04131aa4a6d9 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c @@ -17,7 +17,7 @@ */ #include "stdlib/math/base/special/haversin.h" -#include "stdlib/math/base/special/cos.h" +#include "stdlib/math/base/special/sin.h" /** * Computes the half-value versed sine. @@ -30,5 +30,9 @@ * // returns 0.0 */ double stdlib_base_haversin( const double x ) { - return ( 1.0 - stdlib_base_cos( x ) ) / 2.0; + double s; + + // Use the half-angle identity `(1 - cos(x))/2 = sin(x/2)^2`, as evaluating `(1 - cos(x))/2` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): + s = stdlib_base_sin( x / 2.0 ); + return s * s; } diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_negative.json index 6ad2aee4cbe8..b92210c23514 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_positive.json index f62b02a87e8a..67bb8c1fed2d 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/huge_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_negative.json index b1fef57abfd6..150de538268c 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_positive.json index f0aa7ad9341c..e32bb4c31f1b 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_negative.json index 60f118064065..c0b5a06215e1 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_positive.json index 30cbe30a3845..a1af0f2dccc7 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl index 1211b5b3299e..f8c04f7deb36 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl @@ -37,7 +37,8 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - y = (1.0 .- cos.( x )) ./ 2.0; + # Evaluate the half-angle form in extended precision, which avoids the cancellation in `1 - cos(x)`: + y = Float64.( sin.( big.( x ) ./ 2 ).^2 ); data = Dict([ ("x", x), ("expected", y) @@ -54,6 +55,16 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); +# Negative small values: +x = -exp10.( range( -300.0, stop = 0.0, length = 4000 ) ) +out = joinpath( dir, "small_negative.json" ); +gen( x, out ); + +# Positive small values: +x = exp10.( range( -300.0, stop = 0.0, length = 4000 ) ) +out = joinpath( dir, "small_positive.json" ); +gen( x, out ); + # Negative medium sized values: x = range( -256.0*pi, stop = 0.0, length = 4000 ) out = joinpath( dir, "medium_negative.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_negative.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_negative.json new file mode 100644 index 000000000000..30aa7ce4f255 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_positive.json new file mode 100644 index 000000000000..c793137fe6f6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/small_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/test.js b/lib/node_modules/@stdlib/math/base/special/haversin/test/test.js index 83fd6ccb85c2..11737830047e 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/test.js @@ -21,6 +21,7 @@ // MODULES // var tape = require( 'tape' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); @@ -29,6 +30,8 @@ var haversin = require( './../lib' ); // FIXTURES // +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); @@ -45,6 +48,40 @@ tape( 'main export is a function', function test( t ) { t.end(); }); +tape( 'the function computes the half-value versed sine (for -1 <= x <= -1e-300)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = haversin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + +tape( 'the function computes the half-value versed sine (for 1e-300 <= x <= 1)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = haversin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the half-value versed sine (for -256*pi < x < 0 )', function test( t ) { var expected; var x; @@ -56,7 +93,7 @@ tape( 'the function computes the half-value versed sine (for -256*pi < x < 0 )', for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -73,7 +110,7 @@ tape( 'the function computes the half-value versed sine (for 0 < x < 256*pi )', for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -90,7 +127,7 @@ tape( 'the function computes the half-value versed sine (for -2**60 (pi/2) < x < for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -107,7 +144,7 @@ tape( 'the function computes the half-value versed sine (for 2**20 (pi/2) < x < for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -124,7 +161,7 @@ tape( 'the function computes the half-value versed sine (for x <= -2**60 (PI/2) for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -141,7 +178,7 @@ tape( 'the function computes the half-value versed sine (for x >= 2**60 (PI/2) ) for ( i = 0; i < x.length; i++ ) { y = haversin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/haversin/test/test.native.js index 272d2d2f8901..649e5c05975d 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/test.native.js @@ -39,6 +39,8 @@ var opts = { // FIXTURES // +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); @@ -55,6 +57,40 @@ tape( 'main export is a function', opts, function test( t ) { t.end(); }); +tape( 'the function computes the half-value versed sine (for -1 <= x <= -1e-300)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = haversin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + +tape( 'the function computes the half-value versed sine (for 1e-300 <= x <= 1)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = haversin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the half-value versed sine (for -256*pi < x < 0 )', opts, function test( t ) { var expected; var x; diff --git a/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js b/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js index fb56284b6a22..92bce1bfbf32 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js @@ -20,7 +20,7 @@ // MODULES // -var cos = require( '@stdlib/math/base/special/cos' ); +var sin = require( '@stdlib/math/base/special/sin' ); // MAIN // @@ -48,7 +48,11 @@ var cos = require( '@stdlib/math/base/special/cos' ); * // returns NaN */ function versin( x ) { - return 1.0 - cos( x ); + var s; + + // Use the half-angle identity `1 - cos(x) = 2*sin(x/2)^2`, as evaluating `1 - cos(x)` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): + s = sin( x / 2.0 ); + return 2.0 * s * s; } diff --git a/lib/node_modules/@stdlib/math/base/special/versin/manifest.json b/lib/node_modules/@stdlib/math/base/special/versin/manifest.json index fec32d6cb6ec..083d8fc81535 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/manifest.json @@ -37,7 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] }, { @@ -51,7 +51,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] }, { @@ -65,7 +65,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/cos" + "@stdlib/math/base/special/sin" ] } ] diff --git a/lib/node_modules/@stdlib/math/base/special/versin/src/main.c b/lib/node_modules/@stdlib/math/base/special/versin/src/main.c index 04ac99470c30..4d2299da98fb 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/versin/src/main.c @@ -17,7 +17,7 @@ */ #include "stdlib/math/base/special/versin.h" -#include "stdlib/math/base/special/cos.h" +#include "stdlib/math/base/special/sin.h" /** * Computes the versed sine. @@ -30,5 +30,9 @@ * // returns 0.0 */ double stdlib_base_versin( const double x ) { - return 1.0 - stdlib_base_cos( x ); + double s; + + // Use the half-angle identity `1 - cos(x) = 2*sin(x/2)^2`, as evaluating `1 - cos(x)` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): + s = stdlib_base_sin( x / 2.0 ); + return 2.0 * s * s; } diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_negative.json index 31a985388f70..dad88b0c277f 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_negative.json @@ -1 +1 @@ -{"expected":[0.910367263113076,0.9277943241428723,1.9895726807480307,0.18066768764982066,0.04149181903431176,0.0005249102343740653,0.6573891238778162,0.3780964409889961,0.16252413404369503,0.03275978919982292,0.0020990898759878363,1.3806191180989815,1.7652355751255793,1.8503664647509315,1.2264719265788935,0.004720886318832163,0.5972683478814744,1.7439785203898401,0.12889274922245808,0.8134170964507066,0.00838754714733636,0.5678264775120259,1.710258173875107,1.890400207539686,0.828829029124448,0.010533745074159273,0.5537537512540057,1.6991444153283375,1.8974209329432885,0.8608374279024325,0.018838971740057886,0.5103342829727712,1.6756144327637656,1.9112424838311215,0.8929919223970885,0.025612763384810222,0.4823443152855855,1.6513751763386968,1.9303736402062301,0.9252587561619334,0.03340948669504795,0.45489779313197687,1.626452092920673,1.9360021567265147,0.9910666528871964,0.03754319010123486,0.41437494082656834,1.6141656837899365,1.9414009974590418,1.0067312388129697,0.04191306072606238,0.40174974033881317,1.6017285709602564,1.9568323243197328,1.022394173030394,0.05714141958443508,0.38927133823039517,1.5337665339001016,1.9612675570543785,1.0714749934566943,0.07464607324778638,0.35111324967237323,1.5204549711364197,1.9654669143887114,1.0870902764825903,0.0806979388689123,0.33927427132257637,1.5070156993662693,1.9770985426554586,1.1026841893356578,0.10113902624282833,0.3275974215545726,1.4640651841657015,1.9863712123436894,1.1514207592994634,0.10811385345237956,0.26880977921881655,1.4501329586078238,1.9888274929390772,1.166885679811075,0.13140555917773888,0.25821384263607927,1.405727168135222,1.9860159023177704,1.2151155505506168,0.13927406639735074,0.24779992520662653,1.3913604787768539,1.9998403906187243,1.2303865542046146,0.14735377815898476,0.23757058229282801,1.3140865801362294,1.9999975752107695,1.2456010257096795,0.15564271186660694,0.2275283239662419,1.2991766227959318,1.9999093808480857,1.260755231745644,0.16413883358539638,0.17775796833604818,1.284193253630645,1.9995758291717656,1.2758454537802553,0.21228895262384384,0.16894380627379557,1.269140149252748,1.9989970020285694,1.3542241629025642,0.2220353946734912,0.16033356840615376,1.2540210033862151,1.9981730414508414,1.4301865745765432,0.23197273332769386,0.15192936750941388,1.2388395259602514,1.989782650620731,1.44427441823601,0.2874402204885177,0.1437332658026076,1.1578919704985042,1.987427756341669,1.458253246038777,0.2985177659470275,0.13574727444148127,1.1424049683464452,1.984830567484372,1.4721196278663715,0.30976744080026775,0.09718203808553771,1.1268830229273752,1.9819917213458724,1.4858701611922653,0.37183291931279105,0.09055687588115824,1.1113299430092716,1.9789119145209575,1.4995014719167818,0.3840978997126183,0.05934405543369514,1.0957495449998818,1.9755919027312392,1.5692870096905072,0.3965140098924874,0.05414366291928041,1.0801456520102537,1.9541435073063478,1.582095241554355,0.40907820319287314,0.049175364206961,0.9307217220679285,1.9493373975187382,1.5947606391499343,0.4217873966176807,0.04444037841563786,0.9151037418744369,1.9442983397479907,1.6072800946476864,0.4910873947453269,0.03993986741399236,0.8995065934865374,1.8847188049870753,1.6707709300739468,0.5638588788930783,0.05554528075294607,0.9506423614435212,1.9074505998226101,1.6318689278413134,0.5183017344476956,0.03164662930688755,0.8683900949616868,1.8696835642374265,1.6936739513031034,0.592261040855061,0.0006383865747935369,0.9193803755691702,1.8938440712834486,1.6558376082284885,0.5459888407604843,0.003783807060553701,0.8374027660294054,1.8537947656068268,1.802699240356656,0.6210633814754207,9.699145162911371e-6,0.8881975144691877,1.8793602723407068,1.7710713137502236,0.5741215399520445,0.0015502860454711387,0.8065750194511935,1.8370680032836078,1.8209866967448414,0.650237632466889,0.0003624601839964381,0.6003199714553271,1.864013418234551,1.7906386919166288,0.6026722209600368,0.00029670147753357856,0.6478360827302736,1.8195196938822615,1.8384683891816556,0.6797551605277932,0.0016963234711548925,0.5718024595584339,1.8478185712575301,1.8094300914234138,0.7590226116831181,2.4283697328653098e-5,0.6186912057386267,1.8011670603312213,1.855127160120417,0.8399338610585421,0.004009979875860381,0.5437052055579495,1.7490504848319555,1.8274270693014318,0.7895421457183388,0.0007333000714626614,0.5899205673089136,1.691824351700204,1.8709466596773208,0.8709329088880807,0.007301158641553673,0.5160557857282472,1.6298790221082005,1.90852519235075,0.8202682352957326,0.002423054730151919,0.5615524046140344,1.668866584411369,1.8859113616781649,0.9020586306451491,0.04066060906039981,0.4888813368132757,1.6052404826021096,1.9211676234692137,0.9845171212450954,0.027452683643038656,0.5336145598138644,1.6452523526705125,1.950140251304199,0.9332804777415038,0.04997285201211543,0.4622085293929862,1.5800079249898484,1.972631611893129,1.0158453506161014,0.03521928886614012,0.5061344527293437,1.6210048328540019,1.9594416499804959,0.9645678072459191,0.0602175066968198,0.33086397125378864,1.55420611396663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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_positive.json index 6522f3b53ade..79f24be361d9 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/huge_positive.json @@ -1 +1 @@ -{"expected":[0.910367263113076,0.9277943241428723,1.9895726807480307,0.18066768764982066,0.04149181903431176,0.0005249102343740653,0.6573891238778162,0.3780964409889961,0.16252413404369503,0.03275978919982292,0.0020990898759878363,1.3806191180989815,1.7652355751255793,1.8503664647509315,1.2264719265788935,0.004720886318832163,0.5972683478814744,1.7439785203898401,0.12889274922245808,0.8134170964507066,0.00838754714733636,0.5678264775120259,1.710258173875107,1.890400207539686,0.828829029124448,0.010533745074159273,0.5537537512540057,1.6991444153283375,1.8974209329432885,0.8608374279024325,0.018838971740057886,0.5103342829727712,1.6756144327637656,1.9112424838311215,0.8929919223970885,0.025612763384810222,0.4823443152855855,1.6513751763386968,1.9303736402062301,0.9252587561619334,0.03340948669504795,0.45489779313197687,1.626452092920673,1.9360021567265147,0.9910666528871964,0.03754319010123486,0.41437494082656834,1.6141656837899365,1.9414009974590418,1.0067312388129697,0.04191306072606238,0.40174974033881317,1.6017285709602564,1.9568323243197328,1.022394173030394,0.05714141958443508,0.38927133823039517,1.5337665339001016,1.9612675570543785,1.0714749934566943,0.07464607324778638,0.35111324967237323,1.5204549711364197,1.9654669143887114,1.0870902764825903,0.0806979388689123,0.33927427132257637,1.5070156993662693,1.9770985426554586,1.1026841893356578,0.10113902624282833,0.3275974215545726,1.4640651841657015,1.9863712123436894,1.1514207592994634,0.10811385345237956,0.26880977921881655,1.4501329586078238,1.9888274929390772,1.166885679811075,0.13140555917773888,0.25821384263607927,1.405727168135222,1.9860159023177704,1.2151155505506168,0.13927406639735074,0.24779992520662653,1.3913604787768539,1.9998403906187243,1.2303865542046146,0.14735377815898476,0.23757058229282801,1.3140865801362294,1.9999975752107695,1.2456010257096795,0.15564271186660694,0.2275283239662419,1.2991766227959318,1.9999093808480857,1.260755231745644,0.16413883358539638,0.17775796833604818,1.284193253630645,1.9995758291717656,1.2758454537802553,0.21228895262384384,0.16894380627379557,1.269140149252748,1.9989970020285694,1.3542241629025642,0.2220353946734912,0.16033356840615376,1.2540210033862151,1.9981730414508414,1.4301865745765432,0.23197273332769386,0.15192936750941388,1.2388395259602514,1.989782650620731,1.44427441823601,0.2874402204885177,0.1437332658026076,1.1578919704985042,1.987427756341669,1.458253246038777,0.2985177659470275,0.13574727444148127,1.1424049683464452,1.984830567484372,1.4721196278663715,0.30976744080026775,0.09718203808553771,1.1268830229273752,1.9819917213458724,1.4858701611922653,0.37183291931279105,0.09055687588115824,1.1113299430092716,1.9789119145209575,1.4995014719167818,0.3840978997126183,0.05934405543369514,1.0957495449998818,1.9755919027312392,1.5692870096905072,0.3965140098924874,0.05414366291928041,1.0801456520102537,1.9541435073063478,1.582095241554355,0.40907820319287314,0.049175364206961,0.9307217220679285,1.9493373975187382,1.5947606391499343,0.4217873966176807,0.04444037841563786,0.9151037418744369,1.9442983397479907,1.6072800946476864,0.4910873947453269,0.03993986741399236,0.8995065934865374,1.8847188049870753,1.6707709300739468,0.5638588788930783,0.05554528075294607,0.9506423614435212,1.9074505998226101,1.6318689278413134,0.5183017344476956,0.03164662930688755,0.8683900949616868,1.8696835642374265,1.6936739513031034,0.592261040855061,0.0006383865747935369,0.9193803755691702,1.8938440712834486,1.6558376082284885,0.5459888407604843,0.003783807060553701,0.8374027660294054,1.8537947656068268,1.802699240356656,0.6210633814754207,9.699145162911371e-6,0.8881975144691877,1.8793602723407068,1.7710713137502236,0.5741215399520445,0.0015502860454711387,0.8065750194511935,1.8370680032836078,1.8209866967448414,0.650237632466889,0.0003624601839964381,0.6003199714553271,1.864013418234551,1.7906386919166288,0.6026722209600368,0.00029670147753357856,0.6478360827302736,1.8195196938822615,1.8384683891816556,0.6797551605277932,0.0016963234711548925,0.5718024595584339,1.8478185712575301,1.8094300914234138,0.7590226116831181,2.4283697328653098e-5,0.6186912057386267,1.8011670603312213,1.855127160120417,0.8399338610585421,0.004009979875860381,0.5437052055579495,1.7490504848319555,1.8274270693014318,0.7895421457183388,0.0007333000714626614,0.5899205673089136,1.691824351700204,1.8709466596773208,0.8709329088880807,0.007301158641553673,0.5160557857282472,1.6298790221082005,1.90852519235075,0.8202682352957326,0.002423054730151919,0.5615524046140344,1.668866584411369,1.8859113616781649,0.9020586306451491,0.04066060906039981,0.4888813368132757,1.6052404826021096,1.9211676234692137,0.9845171212450954,0.027452683643038656,0.5336145598138644,1.6452523526705125,1.950140251304199,0.9332804777415038,0.04997285201211543,0.4622085293929862,1.5800079249898484,1.972631611893129,1.0158453506161014,0.03521928886614012,0.5061344527293437,1.6210048328540019,1.9594416499804959,0.9645678072459191,0.0602175066968198,0.33086397125378864,1.55420611396663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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_negative.json index afcf9109880c..ebb55e4cd229 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_positive.json index 49877f423bd8..8484c0e580fa 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_negative.json index b96e54b26e02..38d6aafa3b44 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_positive.json index e97036d8e169..a38d13a18ea7 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl index 118b9d501849..ef65e9449455 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl @@ -37,7 +37,8 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - y = 1.0 .- cos.( x ); + # Evaluate the half-angle form in extended precision, which avoids the cancellation in `1 - cos(x)`: + y = Float64.( 2 .* sin.( big.( x ) ./ 2 ).^2 ); data = Dict([ ("x", x), ("expected", y) @@ -54,6 +55,16 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); +# Negative small values: +x = -exp10.( range( -300.0, stop = 0.0, length = 4000 ) ) +out = joinpath( dir, "small_negative.json" ); +gen( x, out ); + +# Positive small values: +x = exp10.( range( -300.0, stop = 0.0, length = 4000 ) ) +out = joinpath( dir, "small_positive.json" ); +gen( x, out ); + # Negative medium sized values: x = range( -256.0*pi, stop = 0.0, length = 4000 ) out = joinpath( dir, "medium_negative.json" ); diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_negative.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_negative.json new file mode 100644 index 000000000000..c65862160403 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_negative.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_positive.json b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_positive.json new file mode 100644 index 000000000000..35b97bb6a62c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/small_positive.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/test.js b/lib/node_modules/@stdlib/math/base/special/versin/test/test.js index 241e411bfc2f..8b5096050f71 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/test.js @@ -21,6 +21,7 @@ // MODULES // var tape = require( 'tape' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); @@ -29,6 +30,8 @@ var versin = require( './../lib' ); // FIXTURES // +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); @@ -45,6 +48,40 @@ tape( 'main export is a function', function test( t ) { t.end(); }); +tape( 'the function computes the versed sine (for -1 <= x <= -1e-300)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = versin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + +tape( 'the function computes the versed sine (for 1e-300 <= x <= 1)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = versin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the versed sine (for -256*pi < x < 0 )', function test( t ) { var expected; var x; @@ -56,7 +93,7 @@ tape( 'the function computes the versed sine (for -256*pi < x < 0 )', function t for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -73,7 +110,7 @@ tape( 'the function computes the versed sine (for 0 < x < 256*pi )', function te for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -90,7 +127,7 @@ tape( 'the function computes the versed sine (for -2**60 (pi/2) < x < -2**20 (pi for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -107,7 +144,7 @@ tape( 'the function computes the versed sine (for 2**20 (pi/2) < x < 2**60 (pi/2 for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -124,7 +161,7 @@ tape( 'the function computes the versed sine (for x <= -2**60 (PI/2) )', functio for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); @@ -141,7 +178,7 @@ tape( 'the function computes the versed sine (for x >= 2**60 (PI/2) )', function for ( i = 0; i < x.length; i++ ) { y = versin( x[i] ); - t.strictEqual( y, expected[ i ], 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/versin/test/test.native.js index d5e22b7fcfa6..fac8daec7c39 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/test.native.js @@ -39,6 +39,8 @@ var opts = { // FIXTURES // +var smallNegative = require( './fixtures/julia/small_negative.json' ); +var smallPositive = require( './fixtures/julia/small_positive.json' ); var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var largeNegative = require( './fixtures/julia/large_negative.json' ); @@ -55,6 +57,40 @@ tape( 'main export is a function', opts, function test( t ) { t.end(); }); +tape( 'the function computes the versed sine (for -1 <= x <= -1e-300)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + y = versin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + +tape( 'the function computes the versed sine (for 1e-300 <= x <= 1)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + y = versin( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the versed sine (for -256*pi < x < 0 )', opts, function test( t ) { var expected; var x; From 19c471297cae5ef505306d01e7a9247c75ab94b3 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 05:10:22 +0530 Subject: [PATCH 2/3] chore: use tab indentation in the `versin` and `haversin` fixture runner docstrings --- .../math/base/special/haversin/test/fixtures/julia/runner.jl | 2 +- .../math/base/special/versin/test/fixtures/julia/runner.jl | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl index f8c04f7deb36..095387941d3c 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl @@ -19,7 +19,7 @@ import JSON """ - gen( domain, filepath ) + gen( domain, filepath ) Generate fixture data and write to file. diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl index ef65e9449455..de47bdec227d 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl @@ -19,7 +19,7 @@ import JSON """ - gen( domain, filepath ) + gen( domain, filepath ) Generate fixture data and write to file. From 814681be8c43d200b9a11bcbae9bb8f659223f6a Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Mon, 28 Sep 2026 09:30:46 +0530 Subject: [PATCH 3/3] refactor: address review feedback - document the half-angle method in the JSDoc and C doc comments instead of an inline comment - use `abs2` to square - generate fixtures from the textbook formula `1 - cos(x)` evaluated at 4096 bits, rather than from the identity used by the implementation, and separate comments from expressions in the Julia runners --- .../math/base/special/haversin/lib/main.js | 23 +++++++++++++++---- .../math/base/special/haversin/manifest.json | 3 +++ .../math/base/special/haversin/src/main.c | 23 +++++++++++++++---- .../haversin/test/fixtures/julia/runner.jl | 8 +++++-- .../math/base/special/versin/lib/main.js | 23 +++++++++++++++---- .../math/base/special/versin/manifest.json | 3 +++ .../math/base/special/versin/src/main.c | 23 +++++++++++++++---- .../versin/test/fixtures/julia/runner.jl | 8 +++++-- 8 files changed, 90 insertions(+), 24 deletions(-) diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js b/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js index 8807ed08735d..40f40e42e9e8 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/haversin/lib/main.js @@ -20,6 +20,7 @@ // MODULES // +var abs2 = require( '@stdlib/math/base/special/abs2' ); var sin = require( '@stdlib/math/base/special/sin' ); @@ -28,6 +29,22 @@ var sin = require( '@stdlib/math/base/special/sin' ); /** * Computes the half-value versed sine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{haversin}(x) = \frac{1 - \cos(x)}{2} +* ``` +* +* loses significant digits when \\(\cos(x)\\) is close to one (i.e., for `x` near multiples of 2π, including small `x`). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{haversin}(x) = \sin^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param {number} x - input value (in radians) * @returns {number} half-value versed sine * @@ -48,11 +65,7 @@ var sin = require( '@stdlib/math/base/special/sin' ); * // returns NaN */ function haversin( x ) { - var s; - - // Use the half-angle identity `(1 - cos(x))/2 = sin(x/2)^2`, as evaluating `(1 - cos(x))/2` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): - s = sin( x / 2.0 ); - return s * s; + return abs2( sin( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json b/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json index 083d8fc81535..df48666b0a68 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/haversin/manifest.json @@ -37,6 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] }, @@ -51,6 +52,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] }, @@ -65,6 +67,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] } diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c b/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c index 04131aa4a6d9..e199235e00fd 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/haversin/src/main.c @@ -17,11 +17,28 @@ */ #include "stdlib/math/base/special/haversin.h" +#include "stdlib/math/base/special/abs2.h" #include "stdlib/math/base/special/sin.h" /** * Computes the half-value versed sine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{haversin}(x) = \frac{1 - \cos(x)}{2} +* ``` +* +* loses significant digits when `cos(x)` is close to one (i.e., for `x` near multiples of 2π, including small `x`). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{haversin}(x) = \sin^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param x input value (in radians) * @return half-value versed sine * @@ -30,9 +47,5 @@ * // returns 0.0 */ double stdlib_base_haversin( const double x ) { - double s; - - // Use the half-angle identity `(1 - cos(x))/2 = sin(x/2)^2`, as evaluating `(1 - cos(x))/2` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): - s = stdlib_base_sin( x / 2.0 ); - return s * s; + return stdlib_base_abs2( stdlib_base_sin( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl index 095387941d3c..780853b6249d 100644 --- a/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/haversin/test/fixtures/julia/runner.jl @@ -37,8 +37,12 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - # Evaluate the half-angle form in extended precision, which avoids the cancellation in `1 - cos(x)`: - y = Float64.( sin.( big.( x ) ./ 2 ).^2 ); + + # Evaluate the textbook formula in extended precision (4096 bits resolve the cancellation even for the smallest `x`), and round the result to double precision: + y = setprecision( BigFloat, 4096 ) do + Float64.( ( 1 .- cos.( big.( x ) ) ) ./ 2 ) + end + data = Dict([ ("x", x), ("expected", y) diff --git a/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js b/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js index 92bce1bfbf32..2cd8d43c83c2 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/versin/lib/main.js @@ -20,6 +20,7 @@ // MODULES // +var abs2 = require( '@stdlib/math/base/special/abs2' ); var sin = require( '@stdlib/math/base/special/sin' ); @@ -28,6 +29,22 @@ var sin = require( '@stdlib/math/base/special/sin' ); /** * Computes the versed sine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{versin}(x) = 1 - \cos(x) +* ``` +* +* loses significant digits when \\(\cos(x)\\) is close to one (i.e., for `x` near multiples of 2π, including small `x`). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{versin}(x) = 2 \sin^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param {number} x - input value (in radians) * @returns {number} versed sine * @@ -48,11 +65,7 @@ var sin = require( '@stdlib/math/base/special/sin' ); * // returns NaN */ function versin( x ) { - var s; - - // Use the half-angle identity `1 - cos(x) = 2*sin(x/2)^2`, as evaluating `1 - cos(x)` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): - s = sin( x / 2.0 ); - return 2.0 * s * s; + return 2.0 * abs2( sin( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/versin/manifest.json b/lib/node_modules/@stdlib/math/base/special/versin/manifest.json index 083d8fc81535..df48666b0a68 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/versin/manifest.json @@ -37,6 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] }, @@ -51,6 +52,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] }, @@ -65,6 +67,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/sin" ] } diff --git a/lib/node_modules/@stdlib/math/base/special/versin/src/main.c b/lib/node_modules/@stdlib/math/base/special/versin/src/main.c index 4d2299da98fb..a5521653dd12 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/versin/src/main.c @@ -17,11 +17,28 @@ */ #include "stdlib/math/base/special/versin.h" +#include "stdlib/math/base/special/abs2.h" #include "stdlib/math/base/special/sin.h" /** * Computes the versed sine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{versin}(x) = 1 - \cos(x) +* ``` +* +* loses significant digits when `cos(x)` is close to one (i.e., for `x` near multiples of 2π, including small `x`). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{versin}(x) = 2 \sin^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param x input value (in radians) * @return versed sine * @@ -30,9 +47,5 @@ * // returns 0.0 */ double stdlib_base_versin( const double x ) { - double s; - - // Use the half-angle identity `1 - cos(x) = 2*sin(x/2)^2`, as evaluating `1 - cos(x)` directly loses all significant digits when `cos(x)` is close to one (e.g., for small `x`): - s = stdlib_base_sin( x / 2.0 ); - return 2.0 * s * s; + return 2.0 * stdlib_base_abs2( stdlib_base_sin( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl index de47bdec227d..ea3b3a392739 100644 --- a/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/versin/test/fixtures/julia/runner.jl @@ -37,8 +37,12 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - # Evaluate the half-angle form in extended precision, which avoids the cancellation in `1 - cos(x)`: - y = Float64.( 2 .* sin.( big.( x ) ./ 2 ).^2 ); + + # Evaluate the textbook formula in extended precision (4096 bits resolve the cancellation even for the smallest `x`), and round the result to double precision: + y = setprecision( BigFloat, 4096 ) do + Float64.( 1 .- cos.( big.( x ) ) ) + end + data = Dict([ ("x", x), ("expected", y)