diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/factory.js index 435ab5fa490a..31fbaea10950 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/factory.js @@ -68,6 +68,13 @@ function factory( x0, gamma ) { if ( isnan( p ) || p < 0.0 || p > 1.0 ) { return NaN; } + // `p-0.5` rounds away the low-order bits of a `p` close to `0` (`tan(PI*(p-0.5)) = -1/tan(PI*p)`), so evaluate each tail from its own probability, which is exact (`1-p` for `p > 0.75`): + if ( p < 0.25 ) { + return x0 - ( gamma / tan( PI*p ) ); + } + if ( p > 0.75 ) { + return x0 + ( gamma / tan( PI*( 1.0-p ) ) ); + } return x0 + ( gamma * tan( PI*( p-0.5 ) ) ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/main.js index 429670074264..d5aa8ee66614 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/lib/main.js @@ -83,6 +83,13 @@ function quantile( p, x0, gamma ) { ) { return NaN; } + // `p-0.5` rounds away the low-order bits of a `p` close to `0` (`tan(PI*(p-0.5)) = -1/tan(PI*p)`), so evaluate each tail from its own probability, which is exact (`1-p` for `p > 0.75`): + if ( p < 0.25 ) { + return x0 - ( gamma / tan( PI*p ) ); + } + if ( p > 0.75 ) { + return x0 + ( gamma / tan( PI*( 1.0-p ) ) ); + } return x0 + ( gamma * tan( PI*( p-0.5 ) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/src/main.c index 82d6b5356437..d35396d57e20 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/src/main.c @@ -44,5 +44,12 @@ double stdlib_base_dists_cauchy_quantile( const double p, const double x0, const ) { return 0.0/0.0; // NaN } + // `p-0.5` rounds away the low-order bits of a `p` close to `0` (`tan(PI*(p-0.5)) = -1/tan(PI*p)`), so evaluate each tail from its own probability, which is exact (`1-p` for `p > 0.75`): + if ( p < 0.25 ) { + return x0 - ( gamma / stdlib_base_tan( STDLIB_CONSTANT_FLOAT64_PI * p ) ); + } + if ( p > 0.75 ) { + return x0 + ( gamma / stdlib_base_tan( STDLIB_CONSTANT_FLOAT64_PI * ( 1.0 - p ) ) ); + } return x0 + gamma * stdlib_base_tan( STDLIB_CONSTANT_FLOAT64_PI * ( p - 0.5 ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/REQUIRE @@ -1,3 +1,2 @@ -Distributions 0.23.8 julia 1.5 JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/large_gamma.json b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/large_gamma.json index 05469b529869..fa60a845b515 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/large_gamma.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/large_gamma.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/negative_median.json b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/negative_median.json index 4849b3ad12b0..1b7f3504727c 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/negative_median.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/negative_median.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/positive_median.json b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/positive_median.json index 2c6d07eeb8f2..7a7ca18412fb 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/positive_median.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/positive_median.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/runner.jl index 17a588bbca74..4c6cecf89732 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/runner.jl @@ -16,7 +16,6 @@ # See the License for the specific language governing permissions and # limitations under the License. -import Distributions: quantile, Cauchy import JSON """ @@ -24,6 +23,8 @@ import JSON Generate fixture data and write to file. +The quantile is evaluated in extended precision from the textbook formula `x0 + gamma*tan(pi*(p - 0.5))`, as forming `p - 0.5` in double precision rounds away the low-order bits of a `p` close to `0`. + # Arguments * `p`: input value @@ -41,9 +42,8 @@ julia> gen( p, x0, gamma, \"data.json\" ); ``` """ function gen( p, x0, gamma, name ) - z = Array{Float64}( undef, length(p) ); - for i in eachindex(p) - z[ i ] = quantile( Cauchy( x0[i], gamma[i] ), p[i] ); + z = setprecision( BigFloat, 2048 ) do + Float64.( BigFloat.( x0 ) .+ ( BigFloat.( gamma ) .* tan.( BigFloat( pi ) .* ( BigFloat.( p ) .- 0.5 ) ) ) ) end # Store data to be written to file as a collection: @@ -87,3 +87,9 @@ p = rand( 1000 ); x0 = rand( 1000 ) .* 1.0; gamma = rand( 1000 ) .* 50.0; gen( p, x0, gamma, "large_gamma.json" ); + +# Tails (`p` and `1-p` log-spaced; `x0 = 0`, so that the result does not also measure the rounding of `x0 + ...`): +p = vcat( exp10.( range( -300.0, stop = -1.0, length = 500 ) ), 1.0 .- exp10.( range( -16.0, stop = -1.0, length = 500 ) ) ); +x0 = zeros( 1000 ); +gamma = ( rand( 1000 ) .* 20.0 ) .+ 0.1; +gen( p, x0, gamma, "tails.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/tails.json b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/tails.json new file mode 100644 index 000000000000..ed9ce252bbcd --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/fixtures/julia/tails.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.factory.js index 2a8374c744a5..6bf2b6a2396a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.factory.js @@ -22,10 +22,9 @@ var tape = require( 'tape' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); var factory = require( './../lib/factory.js' ); @@ -34,6 +33,7 @@ var factory = require( './../lib/factory.js' ); var largeGamma = require( './fixtures/julia/large_gamma.json' ); var negativeMedian = require( './fixtures/julia/negative_median.json' ); var positiveMedian = require( './fixtures/julia/positive_median.json' ); +var tails = require( './fixtures/julia/tails.json' ); // TESTS // @@ -131,36 +131,11 @@ tape( 'if provided a nonpositive `gamma`, the created function always returns `N tape( 'the created function evaluates the quantile function at `p` given parameters `x0` and `gamma` (large `gamma`)', function test( t ) { var expected; var quantile; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; - - /* - * Higher tolerance than EPS because Julia gives slightly different results for - * |x| ~<= 3*pi/4: - * - * Example 1: - * x = -1.35646279095478; - * Julia (tan): -4.593961172862999 - * stdlib (tan): -4.593961172863 - * Mathematica: -4.59396117286300026311049650877442413097818001966176559315 - * - * Example 2: - * x = 1.4710248292410089 - * Julia (tan): 9.989623320530624 - * stdlib (tan): 9.989623320530626 - * Mathematica: 9.989623320530629158499137574831736702146195199133529403233 - * - * Example 3: - * x = 1.528545878614728 - * Julia (tan): 23.654302824341386 - * stdlib (tan): 23.65430282434139 - * Mathematica: 23.65430282434144042648214719732782590575979471046811610915... - */ expected = largeGamma.expected; p = largeGamma.p; @@ -169,13 +144,7 @@ tape( 'the created function evaluates the quantile function at `p` given paramet for ( i = 0; i < p.length; i++ ) { quantile = factory( x0[i], gamma[i] ); y = quantile( p[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0: '+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 50.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 28 ), true, 'returns expected value' ); } t.end(); }); @@ -183,13 +152,11 @@ tape( 'the created function evaluates the quantile function at `p` given paramet tape( 'the created function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 > 0`)', function test( t ) { var expected; var quantile; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = positiveMedian.expected; p = positiveMedian.p; @@ -198,13 +165,7 @@ tape( 'the created function evaluates the quantile function at `p` given `x0` an for ( i = 0; i < p.length; i++ ) { quantile = factory( x0[i], gamma[i] ); y = quantile( p[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0: '+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 125.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 162 ), true, 'returns expected value' ); } t.end(); }); @@ -212,13 +173,11 @@ tape( 'the created function evaluates the quantile function at `p` given `x0` an tape( 'the created function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 < 0`)', function test( t ) { var expected; var quantile; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = negativeMedian.expected; p = negativeMedian.p; @@ -227,13 +186,28 @@ tape( 'the created function evaluates the quantile function at `p` given `x0` an for ( i = 0; i < p.length; i++ ) { quantile = factory( x0[i], gamma[i] ); y = quantile( p[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0: '+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 50.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 326 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the created function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', function test( t ) { + var expected; + var quantile; + var gamma; + var x0; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + x0 = tails.x0; + gamma = tails.gamma; + for ( i = 0; i < p.length; i++ ) { + quantile = factory( x0[i], gamma[i] ); + y = quantile( p[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.native.js index c78e6b0beab5..3369327b3a62 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.native.js @@ -24,10 +24,9 @@ var resolve = require( 'path' ).resolve; var tape = require( 'tape' ); var tryRequire = require( '@stdlib/utils/try-require' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); // FIXTURES // @@ -35,6 +34,7 @@ var EPS = require( '@stdlib/constants/float64/eps' ); var largeGamma = require( './fixtures/julia/large_gamma.json' ); var negativeMedian = require( './fixtures/julia/negative_median.json' ); var positiveMedian = require( './fixtures/julia/positive_median.json' ); +var tails = require( './fixtures/julia/tails.json' ); // VARIABLES // @@ -104,35 +104,10 @@ tape( 'if provided a nonpositive `gamma`, the function always returns `NaN`', op tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (large `gamma`)', opts, function test( t ) { var expected; var gamma; - var delta; - var tol; var x0; + var i; var p; var y; - var i; - - /* - * Higher tolerance than EPS because Julia gives slightly different results for - * |x| ~<= 3*pi/4: - * - * Example 1: - * x = -1.35646279095478; - * Julia (tan): -4.593961172862999 - * stdlib (tan): -4.593961172863 - * Mathematica: -4.59396117286300026311049650877442413097818001966176559315 - * - * Example 2: - * x = 1.4710248292410089 - * Julia (tan): 9.989623320530624 - * stdlib (tan): 9.989623320530626 - * Mathematica: 9.989623320530629158499137574831736702146195199133529403233 - * - * Example 3: - * x = 1.528545878614728 - * Julia (tan): 23.654302824341386 - * stdlib (tan): 23.65430282434139 - * Mathematica: 23.65430282434144042648214719732782590575979471046811610915... - */ expected = largeGamma.expected; p = largeGamma.p; @@ -140,26 +115,18 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = largeGamma.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 50.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 28 ), true, 'returns expected value' ); } t.end(); }); tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 > 0`)', opts, function test( t ) { var expected; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = positiveMedian.expected; p = positiveMedian.p; @@ -167,26 +134,18 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = positiveMedian.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 125.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 162 ), true, 'returns expected value' ); } t.end(); }); tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 < 0`)', opts, function test( t ) { var expected; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = negativeMedian.expected; p = negativeMedian.p; @@ -194,13 +153,26 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = negativeMedian.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 90.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 326 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', opts, function test( t ) { + var expected; + var gamma; + var x0; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + x0 = tails.x0; + gamma = tails.gamma; + for ( i = 0; i < p.length; i++ ) { + y = quantile( p[i], x0[i], gamma[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.quantile.js b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.quantile.js index 96e2b96e6263..55780caf1092 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.quantile.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.quantile.js @@ -22,10 +22,9 @@ var tape = require( 'tape' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); var quantile = require( './../lib' ); @@ -34,6 +33,7 @@ var quantile = require( './../lib' ); var largeGamma = require( './fixtures/julia/large_gamma.json' ); var negativeMedian = require( './fixtures/julia/negative_median.json' ); var positiveMedian = require( './fixtures/julia/positive_median.json' ); +var tails = require( './fixtures/julia/tails.json' ); // TESTS // @@ -95,35 +95,10 @@ tape( 'if provided a nonpositive `gamma`, the function always returns `NaN`', fu tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` ( large `gamma`)', function test( t ) { var expected; var gamma; - var delta; - var tol; var x0; + var i; var p; var y; - var i; - - /* - * Higher tolerance than EPS because Julia gives slightly different results for - * |x| ~<= 3*pi/4: - * - * Example 1: - * x = -1.35646279095478; - * Julia (tan): -4.593961172862999 - * stdlib (tan): -4.593961172863 - * Mathematica: -4.59396117286300026311049650877442413097818001966176559315 - * - * Example 2: - * x = 1.4710248292410089 - * Julia (tan): 9.989623320530624 - * stdlib (tan): 9.989623320530626 - * Mathematica: 9.989623320530629158499137574831736702146195199133529403233 - * - * Example 3: - * x = 1.528545878614728 - * Julia (tan): 23.654302824341386 - * stdlib (tan): 23.65430282434139 - * Mathematica: 23.65430282434144042648214719732782590575979471046811610915... - */ expected = largeGamma.expected; p = largeGamma.p; @@ -131,26 +106,18 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = largeGamma.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 50.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 28 ), true, 'returns expected value' ); } t.end(); }); tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 > 0`)', function test( t ) { var expected; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = positiveMedian.expected; p = positiveMedian.p; @@ -158,26 +125,18 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = positiveMedian.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 125.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 162 ), true, 'returns expected value' ); } t.end(); }); tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (`x0 < 0`)', function test( t ) { var expected; - var delta; var gamma; - var tol; var x0; + var i; var p; var y; - var i; expected = negativeMedian.expected; p = negativeMedian.p; @@ -185,13 +144,26 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma gamma = negativeMedian.gamma; for ( i = 0; i < p.length; i++ ) { y = quantile( p[i], x0[i], gamma[i] ); - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'p: '+p[i]+', x0:'+x0[i]+', gamma: '+gamma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 50.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. p: '+p[ i ]+'. x0: '+x0[i]+'. gamma: '+gamma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 326 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', function test( t ) { + var expected; + var gamma; + var x0; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + x0 = tails.x0; + gamma = tails.gamma; + for ( i = 0; i < p.length; i++ ) { + y = quantile( p[i], x0[i], gamma[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); } t.end(); });