feat!: update the return value for n=1 in math/base/special/bernoulli

BREAKING CHANGE: update return value for `n=1`

In order to migrate and preserve prior behavior, users should special case `n=1` and return `0`. The change in this commit aligns return values with SymPy and R; although, other libraries and envs choose to return `-0.5`.

PR-URL: #3108
Ref: #3037 (comment)
Co-authored-by: Athan Reines <[email protected]>
Reviewed-by: Athan Reines <[email protected]> 
Signed-off-by: Gunj Joshi <[email protected]>
Signed-off-by: Athan Reines <[email protected]>

Author: gunjjoshi

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

@@ -43,7 +43,7 @@ var v = bernoulli( 0 );
 // returns 1.0
 
 v = bernoulli( 1 );
-// returns 0.0
+// returns 0.5
 
 v = bernoulli( 2 );
 // returns ~0.167
@@ -158,7 +158,7 @@ double out = stdlib_base_bernoulli( 0 );
 // returns 1.0
 
 out = stdlib_base_bernoulli( 1 );
-// returns 0.0
+// returns 0.5
 ```
 
 The function accepts the following arguments:

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

@@ -21,8 +21,7 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
-var floor = require( '@stdlib/math/base/special/floor' );
+var randu = require( '@stdlib/random/array/discrete-uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pkg = require( './../package.json' ).name;
 var bernoulli = require( './../lib' );
@@ -35,10 +34,11 @@ bench( pkg, function benchmark( b ) {
 	var y;
 	var i;
 
+	x = randu( 100, 0, 500 );
+
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		x = floor( randu()*500.0 );
-		y = bernoulli( x );
+		y = bernoulli( x[ i % x.length ] );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );
 		}

lib/node_modules/@stdlib/math/base/special/bernoulli/benchmark/benchmark.native.js

@@ -22,8 +22,7 @@
 
 var resolve = require( 'path' ).resolve;
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
-var floor = require( '@stdlib/math/base/special/floor' );
+var randu = require( '@stdlib/random/array/discrete-uniform' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var pkg = require( './../package.json' ).name;
@@ -44,10 +43,11 @@ bench( pkg+'::native', opts, function benchmark( b ) {
 	var y;
 	var i;
 
+	x = randu( 100, 0, 500 );
+
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		x = floor( randu() * 500.0 );
-		y = bernoulli( x );
+		y = bernoulli( x[ i % x.length ] );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );
 		}

lib/node_modules/@stdlib/math/base/special/bernoulli/benchmark/c/native/benchmark.c

@@ -91,15 +91,18 @@ static double rand_double( void ) {
 */
 static double benchmark( void ) {
 	double elapsed;
-	double x;
+	double x[ 100 ];
 	double y;
 	double t;
 	int i;
 
+	for ( i = 0; i < 100; i++ ) {
+		x[ i ] = ( 500.0 * rand_double() );
+	}
+
 	t = tic();
 	for ( i = 0; i < ITERATIONS; i++ ) {
-		x = ( 500.0 * rand_double() );
-		y = stdlib_base_bernoulli( x );
+		y = stdlib_base_bernoulli( (int)( x[ i % 100 ] ) );
 		if ( y != y ) {
 			printf( "should not return NaN\n" );
 			break;

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

@@ -21,7 +21,7 @@
     > var y = {{alias}}( 0 )
     1.0
     > y = {{alias}}( 1 )
-    0.0
+    0.5
     > y = {{alias}}( 2 )
     ~0.167
     > y = {{alias}}( 3 )

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

@@ -30,7 +30,7 @@
 *
 * @example
 * var y = bernoulli( 1 );
-* // returns 0.0
+* // returns 0.5
 *
 * @example
 * var y = bernoulli( 2 );

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

@@ -30,7 +30,7 @@
 * // returns 1.0
 *
 * y = bernoulli( 1 );
-* // returns 0.0
+* // returns 0.5
 *
 * y = bernoulli( 2 );
 * // returns ~0.166

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

@@ -47,7 +47,7 @@ var MAX_BERNOULLI = 258|0; // asm type annotation
 *
 * @example
 * var y = bernoulli( 1 );
-* // returns 0.0
+* // returns 0.5
 *
 * @example
 * var y = bernoulli( 2 );
@@ -85,6 +85,9 @@ function bernoulli( n ) {
 	if ( isnan( n ) || !isNonNegativeInteger( n ) ) {
 		return NaN;
 	}
+	if ( n === 1 ) {
+		return 0.5;
+	}
 	if ( isOdd( n ) ) {
 		return 0.0;
 	}

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

@@ -37,7 +37,7 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var y = bernoulli( 1 );
-* // returns 0.0
+* // returns 0.5
 *
 * @example
 * var y = bernoulli( 2 );

lib/node_modules/@stdlib/math/base/special/bernoulli/manifest.json

@@ -37,8 +37,6 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/napi/unary",
-        "@stdlib/math/base/assert/is-nonnegative-integer",
-        "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/assert/is-odd",
         "@stdlib/constants/float64/ninf",
         "@stdlib/constants/float64/pinf"
@@ -55,8 +53,6 @@
       "libraries": [],
       "libpath": [],
       "dependencies": [
-        "@stdlib/math/base/assert/is-nonnegative-integer",
-        "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/assert/is-odd",
         "@stdlib/constants/float64/ninf",
         "@stdlib/constants/float64/pinf"
@@ -73,8 +69,6 @@
       "libraries": [],
       "libpath": [],
       "dependencies": [
-        "@stdlib/math/base/assert/is-nonnegative-integer",
-        "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/assert/is-odd",
         "@stdlib/constants/float64/ninf",
         "@stdlib/constants/float64/pinf"