diff --git a/lib/node_modules/@stdlib/math/base/special/asec/lib/main.js b/lib/node_modules/@stdlib/math/base/special/asec/lib/main.js index fc5a0fe7ee91..bbb3ff192a6f 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/asec/lib/main.js @@ -22,6 +22,8 @@ // MODULES // var acos = require( '@stdlib/math/base/special/acos' ); +var atan = require( '@stdlib/math/base/special/atan' ); +var sqrt = require( '@stdlib/math/base/special/sqrt' ); // MAIN // @@ -51,6 +53,10 @@ var acos = require( '@stdlib/math/base/special/acos' ); * // returns NaN */ function asec( x ) { + // Near `x = 1`, `acos( 1/x )` loses the low bits of `1-1/x` to the rounding of `1/x`, and those bits are most of the (small) result. Use `asec(x) = atan( sqrt(x^2-1) ) = atan( sqrt((x-1)*(x+1)) )` instead, where `x-1` is exact for `1 <= x <= 2`: + if ( x >= 1.0 && x <= 2.0 ) { + return atan( sqrt( ( x - 1.0 ) * ( x + 1.0 ) ) ); + } return acos( 1.0 / x ); } diff --git a/lib/node_modules/@stdlib/math/base/special/asec/manifest.json b/lib/node_modules/@stdlib/math/base/special/asec/manifest.json index 1b2dd7efd454..935e87a37672 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/manifest.json +++ b/lib/node_modules/@stdlib/math/base/special/asec/manifest.json @@ -37,7 +37,9 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/unary", - "@stdlib/math/base/special/acos" + "@stdlib/math/base/special/acos", + "@stdlib/math/base/special/atan", + "@stdlib/math/base/special/sqrt" ] }, { @@ -51,7 +53,9 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/acos" + "@stdlib/math/base/special/acos", + "@stdlib/math/base/special/atan", + "@stdlib/math/base/special/sqrt" ] }, { @@ -65,7 +69,9 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/acos" + "@stdlib/math/base/special/acos", + "@stdlib/math/base/special/atan", + "@stdlib/math/base/special/sqrt" ] } ] diff --git a/lib/node_modules/@stdlib/math/base/special/asec/src/main.c b/lib/node_modules/@stdlib/math/base/special/asec/src/main.c index 850b339970cb..3441d24553c7 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/asec/src/main.c @@ -18,6 +18,8 @@ #include "stdlib/math/base/special/asec.h" #include "stdlib/math/base/special/acos.h" +#include "stdlib/math/base/special/atan.h" +#include "stdlib/math/base/special/sqrt.h" /** * Computes the inverse (arc) secant of a double-precision floating-point number. @@ -30,5 +32,9 @@ * // returns 0.0 */ double stdlib_base_asec( const double x ) { + // Near `x = 1`, `acos( 1/x )` loses the low bits of `1-1/x` to the rounding of `1/x`, and those bits are most of the (small) result. Use `asec(x) = atan( sqrt(x^2-1) ) = atan( sqrt((x-1)*(x+1)) )` instead, where `x-1` is exact for `1 <= x <= 2`: + if ( x >= 1.0 && x <= 2.0 ) { + return stdlib_base_atan( stdlib_base_sqrt( ( x - 1.0 ) * ( x + 1.0 ) ) ); + } return stdlib_base_acos( 1.0 / x ); } diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_negative.json b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_negative.json index dcea66021c74..c73caf3b5f4a 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_positive.json b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_positive.json index e3868921ffe7..b8f6019dfaa7 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/large_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_negative.json index 2d77453a9f7a..8eaa93a9eae0 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_negative.json +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_negative.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_positive.json index 48c79d89c757..d53a08d33e75 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_positive.json +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/medium_positive.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/near_one.json b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/near_one.json new file mode 100644 index 000000000000..72f0bca18ed5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/near_one.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/runner.jl index 9fc9863bb9e5..66017730adf7 100755 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/fixtures/julia/runner.jl @@ -37,7 +37,9 @@ julia> gen( x, \"data.json\" ); """ function gen( domain, name ) x = collect( domain ); - y = asec.( x ); + y = setprecision( BigFloat, 256 ) do + Float64.( asec.( BigFloat.( x ) ) ); + end # Store data to be written to file as a collection: data = Dict([ @@ -92,3 +94,8 @@ gen( x, "huge_negative.json" ); # Huge positive values: x = range( 1e300, stop = 1e308, length = 503 ); gen( x, "huge_positive.json" ); + +# Values close to one (in `Float64`, `asec` is `acos(1/x)` and loses the low bits of `1-1/x`): +x = 1.0 .+ exp10.( range( -15.0, stop = -1.0, length = 1000 ) ); +gen( x, "near_one.json" ); + diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/test.js b/lib/node_modules/@stdlib/math/base/special/asec/test/test.js index 03c968f0d74f..38c99960d339 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/test.js @@ -36,6 +36,7 @@ var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var hugeNegative = require( './fixtures/julia/huge_negative.json' ); var hugePositive = require( './fixtures/julia/huge_positive.json' ); +var nearOne = require( './fixtures/julia/near_one.json' ); // TESTS // @@ -174,6 +175,22 @@ tape( 'the function computes the inverse (arc) secant on the interval `[1e300,1e t.end(); }); +tape( 'the function computes the inverse (arc) secant close to `1`', function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOne.x; + expected = nearOne.expected; + + for ( i = 0; i < x.length; i++ ) { + y = asec( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { var v = asec( NaN ); t.strictEqual( isnan( v ), true, 'returns expected value' ); diff --git a/lib/node_modules/@stdlib/math/base/special/asec/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/asec/test/test.native.js index f00958473e2e..b254de5c8113 100644 --- a/lib/node_modules/@stdlib/math/base/special/asec/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/asec/test/test.native.js @@ -37,6 +37,7 @@ var mediumNegative = require( './fixtures/julia/medium_negative.json' ); var mediumPositive = require( './fixtures/julia/medium_positive.json' ); var hugeNegative = require( './fixtures/julia/huge_negative.json' ); var hugePositive = require( './fixtures/julia/huge_positive.json' ); +var nearOne = require( './fixtures/julia/near_one.json' ); // VARIABLES // @@ -183,6 +184,22 @@ tape( 'the function computes the inverse (arc) secant on the interval `[1e300,1e t.end(); }); +tape( 'the function computes the inverse (arc) secant close to `1`', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + x = nearOne.x; + expected = nearOne.expected; + + for ( i = 0; i < x.length; i++ ) { + y = asec( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + tape( 'the function returns `NaN` if provided `NaN`', opts, function test( t ) { var v = asec( NaN ); t.strictEqual( isnan( v ), true, 'returns expected value' );