refactor: made some changes to the implementation

1. Switched from pow()-1 to powm1()
2. Updated the ulp values of the test cases
They were failing in test.native.js because of compiler optimisations

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Author: nirmaljb

lib/node_modules/@stdlib/math/base/special/kernel-betainc/lib/assign.js

@@ -45,6 +45,7 @@ var beta = require( '@stdlib/math/base/special/beta' );
 var sqrt = require( '@stdlib/math/base/special/sqrt' );
 var exp = require( '@stdlib/math/base/special/exp' );
 var pow = require( '@stdlib/math/base/special/pow' );
+var powm1 = require( '@stdlib/math/base/special/powm1' );
 var max = require( '@stdlib/math/base/special/max' );
 var min = require( '@stdlib/math/base/special/min' );
 var MAX_FLOAT64 = require( '@stdlib/constants/float64/max' );
@@ -210,7 +211,7 @@ function ibetaImp( x, a, b, regularized, upper, out, stride, offset ) {
 		if ( y < 0.5 ) {
 			p = ( upper ) ? -expm1( a * log1p(-y) ) : exp( a * log1p(-y) );
 		} else {
-			p = ( upper ) ? -( pow( x, a ) - 1.0 ) : pow( x, a );
+			p = ( upper ) ? -powm1( x, a ) : pow( x, a );
 		}
 		if ( !regularized ) {
 			p /= a;

lib/node_modules/@stdlib/math/base/special/kernel-betainc/manifest.json

@@ -57,6 +57,7 @@
         "@stdlib/math/base/special/sqrt",
         "@stdlib/math/base/special/exp",
         "@stdlib/math/base/special/pow",
+        "@stdlib/math/base/special/powm1",
         "@stdlib/math/base/special/max",
         "@stdlib/math/base/special/min",
         "@stdlib/math/base/special/factorial",
@@ -103,6 +104,7 @@
         "@stdlib/math/base/special/sqrt",
         "@stdlib/math/base/special/exp",
         "@stdlib/math/base/special/pow",
+        "@stdlib/math/base/special/powm1",
         "@stdlib/math/base/special/max",
         "@stdlib/math/base/special/min",
         "@stdlib/math/base/special/factorial",
@@ -150,6 +152,7 @@
         "@stdlib/math/base/special/sqrt",
         "@stdlib/math/base/special/exp",
         "@stdlib/math/base/special/pow",
+        "@stdlib/math/base/special/powm1",
         "@stdlib/math/base/special/max",
         "@stdlib/math/base/special/min",
         "@stdlib/math/base/special/factorial",

lib/node_modules/@stdlib/math/base/special/kernel-betainc/test/test.native.js

@@ -252,11 +252,11 @@ tape( 'the function evaluates the lower regularized incomplete beta function for
 
 	val = kernelBetainc( 8391/100000, 9713/1000, 9940/100, true, false );
 	expected = 0.46116895440368248909937863372410093344466819447476;
-	t.strictEqual( isAlmostEqual( val[0], expected, 4 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[0], expected, 1 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( 0.75, 72.5, 1.125, true, false );
 	expected = 1.3423066982487051710597194786268004978931316494920e-9;
-	t.strictEqual( isAlmostEqual( val[0], expected, 13 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[0], expected, 11 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( 7599/10000, 4985/1000, 1066/1000, true, false );
 	expected = 0.27533431334486812211032939156910472371928659321347;
@@ -268,7 +268,7 @@ tape( 'the function evaluates the lower regularized incomplete beta function for
 
 	val = kernelBetainc( 2003/10000, 4898/10000, 2251/10000, true, false );
 	expected = 0.17089223868046209692215231702890838878342349377008;
-	t.strictEqual( isAlmostEqual( val[0], expected, 3 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[0], expected, 2 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( 6537/10000, 4049/1000, 1540/10000, true, false );
 	expected = 0.017273988301528087878279199511703371301647583919670;
@@ -280,7 +280,7 @@ tape( 'the function evaluates the lower regularized incomplete beta function for
 
 	val = kernelBetainc( 8665/100000, 2726/1000, 1151/100000, true, false );
 	expected = 5.8218877068298586420691288375690562915515260230173e-6;
-	t.strictEqual( isAlmostEqual( val[0], expected, 7 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[0], expected, 5 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( 7582/10000, 3431/10000, 4634/100000, true, false );
 	expected = 0.15132819929418661038699397753916091907278005695387;
@@ -403,7 +403,7 @@ tape( 'the function handles extreme x values (Rocco Romeo bug cases)', opts, fun
 	x0 = ldexp( 1.0, -52 );
 	val = kernelBetainc( x0, 2, 24, false, false );
 	expected=2.46519032881565349871772482100516780410072110983579277754743e-32;
-	t.strictEqual( isAlmostEqual( val[ 0 ], expected, 4 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[ 0 ], expected, 2 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( x0, 2, 24, true, false );
 	expected=1.47911419728939209923063489260310068246043266590147566652846e-29;
@@ -421,7 +421,7 @@ tape( 'the function handles extreme x values (Rocco Romeo bug cases)', opts, fun
 	x0 = ldexp( 1.0, -373 );
 	val = kernelBetainc( x0, 2, 31, false, false );
 	expected=1.35080680244581673116149460571129957689952846520037541640260e-225;
-	t.strictEqual( isAlmostEqual( val[ 0 ], expected, 14 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[ 0 ], expected, 12 ), true, 'within tolerance.' );
 
 	val = kernelBetainc( x0, 2, 31, true, false );
 	expected=1.34000034802625019731220264886560918028433223747877241307138e-222;
@@ -436,7 +436,7 @@ tape( 'the function returns the correct derivative for a naive analytical check'
 
 	val = kernelBetainc( 0.5, 2, 3, true, false );
 	expected = 1.5;
-	t.strictEqual( isAlmostEqual( val[ 1 ], expected, 2 ), true, 'within tolerance.' );
+	t.strictEqual( isAlmostEqual( val[ 1 ], expected, 1 ), true, 'within tolerance.' );
 
 	t.end();
 });
@@ -476,7 +476,7 @@ tape( 'the function evaluates the lower regularized incomplete beta function for
 	sb = smallRange.b;
 	for ( i = 0; i < sv.length; i++ ) {
 		y = kernelBetainc( sv[i], sa[i], sb[i], true, false )[0];
-		t.strictEqual( isAlmostEqual( y, expected[ i ], 21 ), true, 'within tolerance' );
+		t.strictEqual( isAlmostEqual( y, expected[ i ], 19 ), true, 'within tolerance' );
 	}
 	t.end();
 });
@@ -514,7 +514,7 @@ tape( 'the function evaluates the lower regularized incomplete beta function for
 	mb = mediumRange.b;
 	for ( i = 0; i < mv.length; i++ ) {
 		y = kernelBetainc( mv[i], ma[i], mb[i], true, false )[0];
-		t.strictEqual( isAlmostEqual( y, expected[ i ], 167 ), true, 'within tolerance' );
+		t.strictEqual( isAlmostEqual( y, expected[ i ], 162 ), true, 'within tolerance' );
 	}
 	t.end();
 });