diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/lib/main.js b/lib/node_modules/@stdlib/math/base/special/havercos/lib/main.js index a6d7cdff70a5..d661748557fc 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/havercos/lib/main.js @@ -20,6 +20,7 @@ // MODULES // +var abs2 = require( '@stdlib/math/base/special/abs2' ); var cos = require( '@stdlib/math/base/special/cos' ); @@ -28,6 +29,22 @@ var cos = require( '@stdlib/math/base/special/cos' ); /** * Computes the half-value versed cosine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{havercos}(x) = \frac{1 + \cos(x)}{2} +* ``` +* +* loses significant digits when \\(\cos(x)\\) is close to negative one (i.e., for `x` near odd multiples of π). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{havercos}(x) = \cos^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param {number} x - input value (in radians) * @returns {number} half-value versed cosine * @@ -48,7 +65,7 @@ var cos = require( '@stdlib/math/base/special/cos' ); * // returns NaN */ function havercos( x ) { - return (1.0 + cos( x )) / 2.0; + return abs2( cos( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/manifest.json b/lib/node_modules/@stdlib/math/base/special/havercos/manifest.json index fec32d6cb6ec..607b0b364cc3 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/manifest.json @@ -37,6 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] }, @@ -51,6 +52,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] }, @@ -65,6 +67,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] } diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/src/main.c b/lib/node_modules/@stdlib/math/base/special/havercos/src/main.c index ecc5f1b53a65..ff2b5014445b 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/havercos/src/main.c @@ -17,11 +17,28 @@ */ #include "stdlib/math/base/special/havercos.h" +#include "stdlib/math/base/special/abs2.h" #include "stdlib/math/base/special/cos.h" /** * Computes the half-value versed cosine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{havercos}(x) = \frac{1 + \cos(x)}{2} +* ``` +* +* loses significant digits when `cos(x)` is close to negative one (i.e., for `x` near odd multiples of π). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{havercos}(x) = \cos^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param x input value (in radians) * @return half-value versed cosine * @@ -30,5 +47,5 @@ * // returns 0.5 */ double stdlib_base_havercos( const double x ) { - return ( 1.0 + stdlib_base_cos( x ) ) / 2.0; + return stdlib_base_abs2( stdlib_base_cos( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_negative.json index dacbef79136d..b2bb51c054a9 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_positive.json index 6af7c74bbb13..d500b7e8748d 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/huge_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_negative.json index d0679beef8fe..b5e246a073cb 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_positive.json index bb3fb004461e..e61946057e36 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_negative.json index d2193462c651..dbd86daab81f 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_positive.json index 50457294e449..80b8ebd9ad0f 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/near_odd_pi.json b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/near_odd_pi.json new file mode 100644 index 000000000000..4d2114dab1d8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/near_odd_pi.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/runner.jl index 594e88e7b63f..15b616b1e380 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/fixtures/julia/runner.jl @@ -19,7 +19,7 @@ import JSON """ - gen( domain, filepath ) + gen( domain, filepath ) Generate fixture data and write to file. @@ -37,7 +37,12 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - y = (1.0 .+ cos.( x )) ./ 2.0; + + # Evaluate the textbook formula in extended precision (4096 bits resolve the cancellation even for `x` closest to an odd multiple of pi), 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) @@ -54,6 +59,11 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); +# Values near odd multiples of pi, where `1 + cos(x)` is close to zero: +x = vec( [ (2*k+1)*pi + s*d for d in exp10.( range( -12.0, stop = -1.0, length = 100 ) ), k in -10:9, s in (-1, 1) ] ) +out = joinpath( dir, "near_odd_pi.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/havercos/test/test.js b/lib/node_modules/@stdlib/math/base/special/havercos/test/test.js index 6ea8177fe2f3..18118bf096e0 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/havercos/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 +30,7 @@ var havercos = require( './../lib' ); // FIXTURES // +var nearOddPi = require( './fixtures/julia/near_odd_pi.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 +47,23 @@ tape( 'main export is a function', function test( t ) { t.end(); }); +tape( 'the function computes the half-value versed cosine (for x near odd multiples of pi)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOddPi.x; + expected = nearOddPi.expected; + + for ( i = 0; i < x.length; i++ ) { + y = havercos( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the half-value versed cosine (for -256*pi < x < 0 )', function test( t ) { var expected; var x; @@ -56,7 +75,7 @@ tape( 'the function computes the half-value versed cosine (for -256*pi < x < 0 ) for ( i = 0; i < x.length; i++ ) { y = havercos( 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 +92,7 @@ tape( 'the function computes the half-value versed cosine (for 0 < x < 256*pi )' for ( i = 0; i < x.length; i++ ) { y = havercos( 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 +109,7 @@ tape( 'the function computes the half-value versed cosine (for -2**60 (pi/2) < x for ( i = 0; i < x.length; i++ ) { y = havercos( 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 +126,7 @@ tape( 'the function computes the half-value versed cosine (for 2**20 (pi/2) < x for ( i = 0; i < x.length; i++ ) { y = havercos( 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 +143,7 @@ tape( 'the function computes the half-value versed cosine (for x <= -2**60 (PI/2 for ( i = 0; i < x.length; i++ ) { y = havercos( 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 +160,7 @@ tape( 'the function computes the half-value versed cosine (for x >= 2**60 (PI/2) for ( i = 0; i < x.length; i++ ) { y = havercos( 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/havercos/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/havercos/test/test.native.js index 824e3a8bfc3e..f2d3e135db0a 100644 --- a/lib/node_modules/@stdlib/math/base/special/havercos/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/havercos/test/test.native.js @@ -39,6 +39,7 @@ var opts = { // FIXTURES // +var nearOddPi = require( './fixtures/julia/near_odd_pi.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 +56,23 @@ tape( 'main export is a function', opts, function test( t ) { t.end(); }); +tape( 'the function computes the half-value versed cosine (for x near odd multiples of pi)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOddPi.x; + expected = nearOddPi.expected; + + for ( i = 0; i < x.length; i++ ) { + y = havercos( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the half-value versed cosine (for -256*pi < x < 0 )', opts, function test( t ) { var expected; var x; diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/lib/main.js b/lib/node_modules/@stdlib/math/base/special/vercos/lib/main.js index 0931b7ab9a26..f8bae0117bc5 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/vercos/lib/main.js @@ -20,6 +20,7 @@ // MODULES // +var abs2 = require( '@stdlib/math/base/special/abs2' ); var cos = require( '@stdlib/math/base/special/cos' ); @@ -28,6 +29,22 @@ var cos = require( '@stdlib/math/base/special/cos' ); /** * Computes the versed cosine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{vercos}(x) = 1 + \cos(x) +* ``` +* +* loses significant digits when \\(\cos(x)\\) is close to negative one (i.e., for `x` near odd multiples of π). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{vercos}(x) = 2 \cos^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param {number} x - input value (in radians) * @returns {number} versed cosine * @@ -48,7 +65,7 @@ var cos = require( '@stdlib/math/base/special/cos' ); * // returns NaN */ function vercos( x ) { - return 1.0 + cos( x ); + return 2.0 * abs2( cos( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/manifest.json b/lib/node_modules/@stdlib/math/base/special/vercos/manifest.json index fec32d6cb6ec..607b0b364cc3 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/manifest.json @@ -37,6 +37,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] }, @@ -51,6 +52,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] }, @@ -65,6 +67,7 @@ "libraries": [], "libpath": [], "dependencies": [ + "@stdlib/math/base/special/abs2", "@stdlib/math/base/special/cos" ] } diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/src/main.c b/lib/node_modules/@stdlib/math/base/special/vercos/src/main.c index 570c50b26766..933b4430ec1b 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/vercos/src/main.c @@ -17,11 +17,28 @@ */ #include "stdlib/math/base/special/vercos.h" +#include "stdlib/math/base/special/abs2.h" #include "stdlib/math/base/special/cos.h" /** * Computes the versed cosine. * +* ## Method +* +* Evaluating the textbook formula +* +* ```tex +* \operatorname{vercos}(x) = 1 + \cos(x) +* ``` +* +* loses significant digits when `cos(x)` is close to negative one (i.e., for `x` near odd multiples of π). Accordingly, we use the equivalent half-angle identity +* +* ```tex +* \operatorname{vercos}(x) = 2 \cos^2\left(\tfrac{x}{2}\right) +* ``` +* +* which does not suffer from cancellation. +* * @param x input value (in radians) * @return versed cosine * @@ -30,5 +47,5 @@ * // returns 1.0 */ double stdlib_base_vercos( const double x ) { - return 1.0 + stdlib_base_cos( x ); + return 2.0 * stdlib_base_abs2( stdlib_base_cos( x / 2.0 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_negative.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_negative.json index ea8d8a541f4b..edc4bb1b2f1f 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_negative.json @@ -1 +1 @@ -{"expected":[1.089632736886924,1.0722056758571277,0.010427319251969158,1.8193323123501792,1.9585081809656884,1.999475089765626,1.3426108761221838,1.6219035590110038,1.8374758659563049,1.9672402108001772,1.9979009101240122,0.6193808819010185,0.23476442487442084,0.14963353524906853,0.7735280734211065,1.9952791136811678,1.4027316521185256,0.25602147961015986,1.871107250777542,1.1865829035492934,1.9916124528526638,1.4321735224879741,0.28974182612489296,0.10959979246031404,1.171170970875552,1.9894662549258406,1.4462462487459944,0.3008555846716624,0.10257906705671149,1.1391625720975675,1.9811610282599421,1.4896657170272287,0.32438556723623435,0.0887575161688785,1.1070080776029116,1.9743872366151898,1.5176556847144145,0.3486248236613032,0.06962635979376985,1.0747412438380666,1.966590513304952,1.5451022068680231,0.37354790707932695,0.06399784327348546,1.0089333471128037,1.9624568098987651,1.5856250591734318,0.3858343162100635,0.05859900254095807,0.9932687611870303,1.9580869392739375,1.598250259661187,0.39827142903974355,0.04316767568026725,0.977605826969606,1.942858580415565,1.6107286617696048,0.46623346609989835,0.03873244294562139,0.9285250065433057,1.9253539267522135,1.6488867503276268,0.4795450288635802,0.03453308561128865,0.9129097235174097,1.9193020611310878,1.6607257286774235,0.49298430063373055,0.02290145734454152,0.8973158106643422,1.8988609737571718,1.6724025784454275,0.5359348158342985,0.013628787656310482,0.8485792407005366,1.8918861465476204,1.7311902207811833,0.5498670413921762,0.011172507060922654,0.8331143201889251,1.8685944408222612,1.7417861573639208,0.5942728318647781,0.013984097682229635,0.7848844494493832,1.8607259336026494,1.7522000747933735,0.6086395212231461,0.0001596093812756827,0.7696134457953854,1.8526462218410154,1.762429417707172,0.6859134198637706,2.4247892305151453e-6,0.7543989742903207,1.8443572881333932,1.7724716760337582,0.7008233772040682,9.061915191443948e-5,0.7392447682543559,1.8358611664146036,1.8222420316639518,0.7158067463693549,0.000424170828234538,0.7241545462197447,1.7877110473761562,1.8310561937262044,0.7308598507472519,0.0010029979714304416,0.6457758370974358,1.7779646053265088,1.8396664315938462,0.7459789966137848,0.0018269585491585971,0.5698134254234567,1.768027266672306,1.848070632490586,0.7611604740397486,0.010217349379268992,0.5557255817639899,1.7125597795114822,1.8562667341973924,0.8421080295014957,0.012572243658331095,0.5417467539612231,1.7014822340529725,1.8642527255585186,0.8575950316535548,0.015169432515628078,0.5278803721336284,1.6902325591997323,1.9028179619144623,0.8731169770726249,0.018008278654127574,0.5141298388077347,1.6281670806872088,1.9094431241188419,0.8886700569907284,0.021088085479042507,0.5004985280832182,1.6159021002873817,1.9406559445663047,0.9042504550001182,0.024408097268760698,0.43071299030949284,1.6034859901075125,1.9458563370807196,0.9198543479897463,0.04585649269365211,0.417904758445645,1.5909217968071268,1.950824635793039,1.0692782779320715,0.05066260248126164,0.4052393608500656,1.5782126033823194,1.9555596215843623,1.084896258125563,0.05570166025200929,0.3927199053523136,1.508912605254673,1.9600601325860076,1.1004934065134626,0.11528119501292466,0.32922906992605316,1.4361411211069217,1.9444547192470538,1.049357638556479,0.09254940017739,0.36813107215868646,1.4816982655523043,1.9683533706931124,1.1316099050383133,0.13031643576257346,0.3063260486968965,1.407738959144939,1.9993616134252066,1.0806196244308297,0.10615592871655155,0.3441623917715114,1.4540111592395157,1.9962161929394462,1.1625972339705946,0.14620523439317323,0.19730075964334404,1.3789366185245793,1.999990300854837,1.1118024855308122,0.1206397276592932,0.22892868624977625,1.4258784600479555,1.9984497139545288,1.1934249805488064,0.16293199671639225,0.17901330325515863,1.349762367533111,1.9996375398160036,1.3996800285446729,0.1359865817654491,0.20936130808337128,1.3973277790399632,1.9997032985224665,1.3521639172697264,0.18048030611773858,0.16153161081834433,1.3202448394722068,1.998303676528845,1.428197540441566,0.15218142874246987,0.19056990857658618,1.2409773883168818,1.9999757163026715,1.3813087942613733,0.19883293966877869,0.1448728398795831,1.160066138941458,1.9959900201241396,1.4562947944420506,0.25094951516804453,0.17257293069856805,1.2104578542816613,1.9992666999285373,1.4100794326910864,0.30817564829979605,0.12905334032267912,1.1290670911119194,1.9926988413584463,1.483944214271753,0.37012097789179965,0.09147480764924987,1.1797317647042673,1.9975769452698482,1.4384475953859654,0.33113341558863096,0.11408863832183513,1.097941369354851,1.9593393909396002,1.5111186631867244,0.3947595173978905,0.07883237653078645,1.0154828787549046,1.9725473163569613,1.4663854401861356,0.3547476473294874,0.04985974869580112,1.0667195222584962,1.9500271479878846,1.5377914706070137,0.41999207501015157,0.027368388106870922,0.9841546493838986,1.96478071113386,1.4938655472706563,0.37899516714599824,0.04055835001950414,1.035432192754081,1.9397824933031802,1.6691360287462114,0.44579388603336245,0.02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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_positive.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_positive.json index dfc87d737444..684018910678 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/huge_positive.json @@ -1 +1 @@ -{"expected":[1.089632736886924,1.0722056758571277,0.010427319251969158,1.8193323123501792,1.9585081809656884,1.999475089765626,1.3426108761221838,1.6219035590110038,1.8374758659563049,1.9672402108001772,1.9979009101240122,0.6193808819010185,0.23476442487442084,0.14963353524906853,0.7735280734211065,1.9952791136811678,1.4027316521185256,0.25602147961015986,1.871107250777542,1.1865829035492934,1.9916124528526638,1.4321735224879741,0.28974182612489296,0.10959979246031404,1.171170970875552,1.9894662549258406,1.4462462487459944,0.3008555846716624,0.10257906705671149,1.1391625720975675,1.9811610282599421,1.4896657170272287,0.32438556723623435,0.0887575161688785,1.1070080776029116,1.9743872366151898,1.5176556847144145,0.3486248236613032,0.06962635979376985,1.0747412438380666,1.966590513304952,1.5451022068680231,0.37354790707932695,0.06399784327348546,1.0089333471128037,1.9624568098987651,1.5856250591734318,0.3858343162100635,0.05859900254095807,0.9932687611870303,1.9580869392739375,1.598250259661187,0.39827142903974355,0.04316767568026725,0.977605826969606,1.942858580415565,1.6107286617696048,0.46623346609989835,0.03873244294562139,0.9285250065433057,1.9253539267522135,1.6488867503276268,0.4795450288635802,0.03453308561128865,0.9129097235174097,1.9193020611310878,1.6607257286774235,0.49298430063373055,0.02290145734454152,0.8973158106643422,1.8988609737571718,1.6724025784454275,0.5359348158342985,0.013628787656310482,0.8485792407005366,1.8918861465476204,1.7311902207811833,0.5498670413921762,0.011172507060922654,0.8331143201889251,1.8685944408222612,1.7417861573639208,0.5942728318647781,0.013984097682229635,0.7848844494493832,1.8607259336026494,1.7522000747933735,0.6086395212231461,0.0001596093812756827,0.7696134457953854,1.8526462218410154,1.762429417707172,0.6859134198637706,2.4247892305151453e-6,0.7543989742903207,1.8443572881333932,1.7724716760337582,0.7008233772040682,9.061915191443948e-5,0.7392447682543559,1.8358611664146036,1.8222420316639518,0.7158067463693549,0.000424170828234538,0.7241545462197447,1.7877110473761562,1.8310561937262044,0.7308598507472519,0.0010029979714304416,0.6457758370974358,1.7779646053265088,1.8396664315938462,0.7459789966137848,0.0018269585491585971,0.5698134254234567,1.768027266672306,1.848070632490586,0.7611604740397486,0.010217349379268992,0.5557255817639899,1.7125597795114822,1.8562667341973924,0.8421080295014957,0.012572243658331095,0.5417467539612231,1.7014822340529725,1.8642527255585186,0.8575950316535548,0.015169432515628078,0.5278803721336284,1.6902325591997323,1.9028179619144623,0.8731169770726249,0.018008278654127574,0.5141298388077347,1.6281670806872088,1.9094431241188419,0.8886700569907284,0.021088085479042507,0.5004985280832182,1.6159021002873817,1.9406559445663047,0.9042504550001182,0.024408097268760698,0.43071299030949284,1.6034859901075125,1.9458563370807196,0.9198543479897463,0.04585649269365211,0.417904758445645,1.5909217968071268,1.950824635793039,1.0692782779320715,0.05066260248126164,0.4052393608500656,1.5782126033823194,1.9555596215843623,1.084896258125563,0.05570166025200929,0.3927199053523136,1.508912605254673,1.9600601325860076,1.1004934065134626,0.11528119501292466,0.32922906992605316,1.4361411211069217,1.9444547192470538,1.049357638556479,0.09254940017739,0.36813107215868646,1.4816982655523043,1.9683533706931124,1.1316099050383133,0.13031643576257346,0.3063260486968965,1.407738959144939,1.9993616134252066,1.0806196244308297,0.10615592871655155,0.3441623917715114,1.4540111592395157,1.9962161929394462,1.1625972339705946,0.14620523439317323,0.19730075964334404,1.3789366185245793,1.999990300854837,1.1118024855308122,0.1206397276592932,0.22892868624977625,1.4258784600479555,1.9984497139545288,1.1934249805488064,0.16293199671639225,0.17901330325515863,1.349762367533111,1.9996375398160036,1.3996800285446729,0.1359865817654491,0.20936130808337128,1.3973277790399632,1.9997032985224665,1.3521639172697264,0.18048030611773858,0.16153161081834433,1.3202448394722068,1.998303676528845,1.428197540441566,0.15218142874246987,0.19056990857658618,1.2409773883168818,1.9999757163026715,1.3813087942613733,0.19883293966877869,0.1448728398795831,1.160066138941458,1.9959900201241396,1.4562947944420506,0.25094951516804453,0.17257293069856805,1.2104578542816613,1.9992666999285373,1.4100794326910864,0.30817564829979605,0.12905334032267912,1.1290670911119194,1.9926988413584463,1.483944214271753,0.37012097789179965,0.09147480764924987,1.1797317647042673,1.9975769452698482,1.4384475953859654,0.33113341558863096,0.11408863832183513,1.097941369354851,1.9593393909396002,1.5111186631867244,0.3947595173978905,0.07883237653078645,1.0154828787549046,1.9725473163569613,1.4663854401861356,0.3547476473294874,0.04985974869580112,1.0667195222584962,1.9500271479878846,1.5377914706070137,0.41999207501015157,0.027368388106870922,0.9841546493838986,1.96478071113386,1.4938655472706563,0.37899516714599824,0.04055835001950414,1.035432192754081,1.9397824933031802,1.6691360287462114,0.44579388603336245,0.02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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_negative.json index 9fa7518ae10b..6a13f46a68b7 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_positive.json index 77e66a9aed43..ef5e3d43ea32 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_negative.json index ea3395a4dfaa..7d416c37328d 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_positive.json index e5bc0abbc1af..79b4cb0d1949 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/near_odd_pi.json b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/near_odd_pi.json new file mode 100644 index 000000000000..40ce5023ff10 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/near_odd_pi.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/runner.jl index 2905f43c585c..cca3b30933b5 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/fixtures/julia/runner.jl @@ -19,7 +19,7 @@ import JSON """ - gen( domain, filepath ) + gen( domain, filepath ) Generate fixture data and write to file. @@ -37,7 +37,12 @@ julia> gen( x, \"./data.json\" ); """ function gen( domain, filepath ) x = collect( domain ); - y = 1.0 .+ cos.( x ); + + # Evaluate the textbook formula in extended precision (4096 bits resolve the cancellation even for `x` closest to an odd multiple of pi), and round the result to double precision: + y = setprecision( BigFloat, 4096 ) do + Float64.( 1 .+ cos.( big.( x ) ) ) + end + data = Dict([ ("x", x), ("expected", y) @@ -54,6 +59,11 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); +# Values near odd multiples of pi, where `1 + cos(x)` is close to zero: +x = vec( [ (2*k+1)*pi + s*d for d in exp10.( range( -12.0, stop = -1.0, length = 100 ) ), k in -10:9, s in (-1, 1) ] ) +out = joinpath( dir, "near_odd_pi.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/vercos/test/test.js b/lib/node_modules/@stdlib/math/base/special/vercos/test/test.js index 2ad49b0980ec..86ab51183433 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/vercos/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 +30,7 @@ var vercos = require( './../lib' ); // FIXTURES // +var nearOddPi = require( './fixtures/julia/near_odd_pi.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 +47,23 @@ tape( 'main export is a function', function test( t ) { t.end(); }); +tape( 'the function computes the versed cosine (for x near odd multiples of pi)', function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOddPi.x; + expected = nearOddPi.expected; + + for ( i = 0; i < x.length; i++ ) { + y = vercos( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the versed cosine (for -256*pi < x < 0 )', function test( t ) { var expected; var x; @@ -56,7 +75,7 @@ tape( 'the function computes the versed cosine (for -256*pi < x < 0 )', function for ( i = 0; i < x.length; i++ ) { y = vercos( 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 +92,7 @@ tape( 'the function computes the versed cosine (for 0 < x < 256*pi )', function for ( i = 0; i < x.length; i++ ) { y = vercos( 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 +109,7 @@ tape( 'the function computes the versed cosine (for -2**60 (pi/2) < x < -2**20 ( for ( i = 0; i < x.length; i++ ) { y = vercos( 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 +126,7 @@ tape( 'the function computes the versed cosine (for 2**20 (pi/2) < x < 2**60 (pi for ( i = 0; i < x.length; i++ ) { y = vercos( 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 +143,7 @@ tape( 'the function computes the versed cosine (for x <= -2**60 (PI/2) )', funct for ( i = 0; i < x.length; i++ ) { y = vercos( 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 +160,7 @@ tape( 'the function computes the versed cosine (for x >= 2**60 (PI/2) )', functi for ( i = 0; i < x.length; i++ ) { y = vercos( 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/vercos/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/vercos/test/test.native.js index ce9357a1825d..8399eed74777 100644 --- a/lib/node_modules/@stdlib/math/base/special/vercos/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/vercos/test/test.native.js @@ -39,6 +39,7 @@ var opts = { // FIXTURES // +var nearOddPi = require( './fixtures/julia/near_odd_pi.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 +56,23 @@ tape( 'main export is a function', opts, function test( t ) { t.end(); }); +tape( 'the function computes the versed cosine (for x near odd multiples of pi)', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOddPi.x; + expected = nearOddPi.expected; + + for ( i = 0; i < x.length; i++ ) { + y = vercos( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + + t.end(); +}); + tape( 'the function computes the versed cosine (for -256*pi < x < 0 )', opts, function test( t ) { var expected; var x;