refactor: decrease tolerance and clean-up math/base/special/asind

PR-URL: 	#2138
Co-authored-by: Athan Reines <[email protected]>
Reviewed-by: Athan Reines <[email protected]>

Author: gunjjoshi

lib/node_modules/@stdlib/math/base/special/asind/README.md

@@ -20,7 +20,7 @@ limitations under the License.
 
 # asind
 
-> Compute the [arcsine][arcsine] in degrees of a double-precision floating-point number.
+> Compute the [arcsine][arcsine] (in degrees) of a double-precision floating-point number.
 
 <section class="usage">
 
@@ -36,6 +36,7 @@ Computes the [arcsine][arcsine] (in degrees) of a double-precision floating-poin
 
 ```javascript
 var sqrt = require( '@stdlib/math/base/special/sqrt' );
+
 var v = asind( 0.0 );
 // returns 0.0
 
@@ -154,7 +155,7 @@ double stdlib_base_asind( const double x );
 #include <stdio.h>
 
 int main( void ) {
-    const double x[] = { 1.0, 1.45, 1.89, 2.33, 2.78, 3.22, 3.66, 4.11, 4.55, 5.0 };
+    const double x[] = { 1.0, 0.45, -0.89, 0.33, -0.78, -0.22, 0.66, 0.11, -0.55, 0.0 };
     
     double v;
     int i;

lib/node_modules/@stdlib/math/base/special/asind/benchmark/benchmark.js

@@ -36,7 +36,7 @@ bench( pkg, function benchmark( b ) {
 
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		x = ( randu()*2.0 ) - 1.0;
+		x = ( randu() * 2.0 ) - 1.0;
 		y = asind( x );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );

lib/node_modules/@stdlib/math/base/special/asind/docs/repl.txt

@@ -19,7 +19,7 @@
     --------
     > var y = {{alias}}( 0.0 )
     0.0
-    > y = {{alias}}( {{alias:@stdlib/constants/float64/pi}}/6.0 )
+    > y = {{alias}}( {{alias:@stdlib/constants/float64/pi}} / 6.0 )
     ~31.57
     > y = {{alias}}( NaN )
     NaN

lib/node_modules/@stdlib/math/base/special/asind/docs/types/index.d.ts

@@ -33,11 +33,15 @@
 * // returns ~30.0
 *
 * @example
-* var v = asind( Math.sqrt( 2.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+* var v = asindf( sqrt( 2.0 ) / 2.0 );
 * // returns ~45.0
 *
 * @example
-* var v = asind( Math.sqrt( 3.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+** var v = asindf( sqrt( 3.0 ) / 2.0 );
 * // returns ~60.0
 *
 * @example

lib/node_modules/@stdlib/math/base/special/asind/examples/c/example.c

@@ -20,7 +20,7 @@
 #include <stdio.h>
 
 int main( void ) {
-	const double x[] = { 1.0, 1.45, 1.89, 2.33, 2.78, 3.22, 3.66, 4.11, 4.55, 5.0 };
+	const double x[] = { 1.0, 0.45, -0.89, 0.33, -0.78, -0.22, 0.66, 0.11, -0.55, 0.0 };
 
 	double v;
 	int i;

lib/node_modules/@stdlib/math/base/special/asind/lib/index.js

@@ -24,6 +24,7 @@
 * @module @stdlib/math/base/special/asind
 *
 * @example
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
 * var asind = require( '@stdlib/math/base/special/asind' );
 *
 * var v = asind( 0.0 );
@@ -32,10 +33,10 @@
 * var v = asind( 0.5  );
 * // returns ~30.0
 *
-* var v = asind( Math.sqrt( 2.0 ) / 2.0 );
+* var v = asind( sqrt( 2.0 ) / 2.0 );
 * // returns ~45.0
 *
-* var v = asind( Math.sqrt( 3.0 ) / 2.0 );
+* var v = asind( sqrt( 3.0 ) / 2.0 );
 * // returns ~60.0
 *
 * var v = asind( NaN );

lib/node_modules/@stdlib/math/base/special/asind/lib/main.js

@@ -41,20 +41,23 @@ var asin = require( '@stdlib/math/base/special/asin' );
 * // returns ~30.0
 *
 * @example
-* var v = asind( Math.sqrt( 2.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+* var v = asind( sqrt( 2.0 ) / 2.0 );
 * // returns ~45.0
 *
 * @example
-* var v = asind( Math.sqrt( 3.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+* var v = asind( sqrt( 3.0 ) / 2.0 );
 * // returns ~60.0
 *
 * @example
 * var v = asind( NaN );
 * // returns NaN
 */
 function asind( x ) {
-	var rad = asin( x );
-	return rad2deg( rad );
+	return rad2deg( asin( x ) );
 }
 
 

lib/node_modules/@stdlib/math/base/special/asind/lib/native.js

@@ -28,6 +28,7 @@ var addon = require( './../src/addon.node' );
 /**
 * Computes the arcsine (in degrees) of a double-precision floating-point number.
 *
+* @private
 * @param {number} x - input value
 * @returns {number} arcsine (in degrees)
 *
@@ -40,11 +41,15 @@ var addon = require( './../src/addon.node' );
 * // returns ~30.0
 *
 * @example
-* var v = asind( Math.sqrt( 2.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+* var v = asind( sqrt( 2.0 ) / 2.0 );
 * // returns ~45.0
 *
 * @example
-* var v = asind( Math.sqrt( 3.0 ) / 2.0 );
+* var sqrt = require( '@stdlib/math/base/special/sqrt' );
+*
+* var v = asind( sqrt( 3.0 ) / 2.0 );
 * // returns ~60.0
 *
 * @example

lib/node_modules/@stdlib/math/base/special/asind/src/main.c

@@ -27,12 +27,9 @@
 * @return     arcsine (in degrees)
 *
 * @example
-* double v = stdlib_base_acotd( 0.0 );
+* double v = stdlib_base_asind( 0.0 );
 * // returns 0.0
 */
 double stdlib_base_asind( const double x ) {
-	double rad;
-
-	rad = stdlib_base_asin( x );
-	return stdlib_base_rad2deg( rad );
+	return stdlib_base_rad2deg( stdlib_base_asin( x ) );
 }

lib/node_modules/@stdlib/math/base/special/asind/test/test.js

@@ -22,7 +22,7 @@
 
 var tape = require( 'tape' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
+var uniform = require( '@stdlib/random/base/uniform' );
 var abs = require( '@stdlib/math/base/special/abs' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 var asind = require( './../lib' );
@@ -54,13 +54,13 @@ tape( 'the function computes the arcsine in degrees (negative values)', function
 	expected = negative.expected;
 
 	for ( i = 0; i < x.length; i++ ) {
-		y = asind( x[i] );
+		y = asind( x[ i ] );
 		if ( y === expected[ i ] ) {
-			t.equal( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
+			t.equal( y, expected[ i ], 'x: '+x[ i ]+'. E: '+expected[ i ] );
 		} else {
-			delta = abs( y - expected[i] );
-			tol = 1.4 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
+			delta = abs( y - expected[ i ] );
+			tol = 1.2 * EPS * abs( expected[ i ] );
+			t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. tol: '+tol+'. Δ: '+delta+'.' );
 		}
 	}
 	t.end();
@@ -78,21 +78,21 @@ tape( 'the function computes the arcsine in degrees (positive values)', function
 	expected = positive.expected;
 
 	for ( i = 0; i < x.length; i++ ) {
-		y = asind( x[i] );
+		y = asind( x[ i ] );
 		if ( y === expected[ i ] ) {
-			t.equal( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
+			t.equal( y, expected[ i ], 'x: '+x[ i ]+'. E: '+expected[ i ] );
 		} else {
-			delta = abs( y - expected[i] );
-			tol = 1.4 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
+			delta = abs( y - expected[ i ] );
+			tol = 1.2 * EPS * abs( expected[ i ] );
+			t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. tol: '+tol+'. Δ: '+delta+'.' );
 		}
 	}
 	t.end();
 });
 
 tape( 'the function returns `NaN` if provided `NaN`', function test( t ) {
 	var v = asind( NaN );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 	t.end();
 });
 
@@ -101,8 +101,8 @@ tape( 'the function returns `NaN` if provided a value less than `-1`', function
 	var i;
 
 	for ( i = 0; i < 1e3; i++ ) {
-		v = -(randu()*1.0e6) - (1.0-EPS);
-		t.equal( isnan( asind( v ) ), true, 'returns NaN when provided '+v );
+		v = uniform( -1.0e6, -1.0 - EPS );
+		t.equal( isnan( asind( v ) ), true, 'returns expected value when provided '+v );
 	}
 	t.end();
 });
@@ -112,8 +112,8 @@ tape( 'the function returns `NaN` if provided a value greater than `+1`', functi
 	var i;
 
 	for ( i = 0; i < 1e3; i++ ) {
-		v = (randu()*1.0e6) + 1.0 + EPS;
-		t.equal( isnan( asind( v ) ), true, 'returns NaN when provided '+v );
+		v = uniform( 1.0 + EPS, 1.0e6 );
+		t.equal( isnan( asind( v ) ), true, 'returns expected value when provided '+v );
 	}
 	t.end();
 });