fix: use correct inverse coversed cosine formula

Author: anandkaranubc

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

@@ -26,17 +26,12 @@ limitations under the License.
 
 The [inverse coversed cosine][inverse-coversed-cosine] is defined as
 
-<!-- <equation class="equation" label="eq:arccovercosine" align="center" raw="\operatorname{acovercos}(\theta) = \arcsin(1+\theta)" alt="Inverse coversed cosine."> -->
+<!-- <equation class="equation" label="eq:arccovercosine" align="center" raw="\operatorname{acovercos}(\theta) = \arcsin(\theta-1)" alt="Inverse coversed cosine."> -->
 
 ```math
-\mathop{\mathrm{acovercos}}(\theta) = \arcsin(1+\theta)
+\mathop{\mathrm{acovercos}}(\theta) = \arcsin(\theta-1)
 ```
 
-<!-- <div class="equation" align="center" data-raw-text="\operatorname{acovercos}(\theta) = \arcsin(1+\theta)" data-equation="eq:arccovercosine">
-    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/acovercos/docs/img/equation_arccovercosine.svg" alt="Inverse coversed cosine.">
-    <br>
-</div> -->
-
 <!-- </equation> -->
 
 </section>
@@ -57,22 +52,22 @@ Computes the [inverse coversed cosine][inverse-coversed-cosine].
 
 ```javascript
 var v = acovercos( 0.0 );
-// returns ~1.5708
+// returns ~-1.5708
 
-v = acovercos( -3.141592653589793/2.0 );
-// returns ~-0.6075
+v = acovercos( 3.141592653589793/2.0 );
+// returns ~0.6075
 
-v = acovercos( -3.141592653589793/6.0 );
-// returns ~0.4966
+v = acovercos( 3.141592653589793/6.0 );
+// returns ~-0.4966
 ```
 
-If `x < -2`, `x > 0`, or `x` is `NaN`, the function returns `NaN`.
+If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`.
 
 ```javascript
-var v = acovercos( 1.0 );
+var v = acovercos( -1.0 );
 // returns NaN
 
-v = acovercos( -3.14 );
+v = acovercos( 3.14 );
 // returns NaN
 
 v = acovercos( NaN );
@@ -94,7 +89,7 @@ var uniform = require( '@stdlib/random/array/uniform' );
 var logEachMap = require( '@stdlib/console/log-each-map' );
 var acovercos = require( '@stdlib/math/base/special/acovercos' );
 
-var x = uniform( 100, -2.0, 0.0, {
+var x = uniform( 100, 0.0, 2.0, {
     'dtype': 'float64'
 });
 
@@ -171,7 +166,7 @@ double stdlib_base_acovercos( const double x );
 #include <stdio.h>
 
 int main( void ) {
-    const double x[] = { -2.0, -1.80, -1.78, -1.67, -0.56, -0.27, -1.67, -0.78, -1.89, 0.0 };
+    const double x[] = { 0.0, 0.27, 0.56, 0.78, 1.67, 1.67, 1.78, 1.80, 1.89, 2.0 };
 
     double v;
     int i;

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

@@ -34,7 +34,7 @@ bench( pkg, function benchmark( b ) {
 	var y;
 	var i;
 
-	x = uniform( 100, -2.0, 0.0 );
+	x = uniform( 100, 0.0, 2.0 );
 
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {

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

@@ -43,7 +43,7 @@ bench( pkg+'::native', opts, function benchmark( b ) {
 	var y;
 	var i;
 
-	x = uniform( 100, -2.0, 0.0 );
+	x = uniform( 100, 0.0, 2.0 );
 
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {

lib/node_modules/@stdlib/math/base/special/acovercos/benchmark/c/benchmark.c

@@ -96,12 +96,12 @@ static double benchmark( void ) {
 	int i;
 
 	for ( i = 0; i < 100; i++ ) {
-		x[ i ] = ( -2.0*rand_double() ) + 0.0;
+		x[ i ] = 2.0*rand_double();
 	}
 
 	t = tic();
 	for ( i = 0; i < ITERATIONS; i++ ) {
-		y = asin( 1.0 + x[ i%100 ] );
+		y = asin( x[ i%100 ] - 1.0 );
 		if ( y != y ) {
 			printf( "should not return NaN\n" );
 			break;

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

@@ -97,7 +97,7 @@ static double benchmark( void ) {
 	int i;
 
 	for ( i = 0; i < 100; i++ ) {
-		x[ i ] = ( -2.0*rand_double() );
+		x[ i ] = 2.0*rand_double();
 	}
 
 	t = tic();

lib/node_modules/@stdlib/math/base/special/acovercos/docs/img/equation_arccovercosine.svg

@@ -2,9 +2,9 @@
 {{alias}}( x )
     Computes the inverse coversed cosine.
 
-    The inverse coversed cosine is defined as `asin(1+x)`.
+    The inverse coversed cosine is defined as `asin(x-1)`.
 
-    If `x < -2`, `x > 0`, or `x` is `NaN`, the function returns `NaN`.
+    If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`.
 
     Parameters
     ----------
@@ -18,10 +18,10 @@
 
     Examples
     --------
-    > var y = {{alias}}( -1.5 )
-    ~-0.5236
+    > var y = {{alias}}( 1.5 )
+    ~0.5236
     > y = {{alias}}( -0.0 )
-    ~1.5708
+    ~-1.5708
 
     See Also
     --------

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

@@ -26,15 +26,15 @@
 *
 * @example
 * var v = acovercos( 0.0 );
-* // returns ~1.5708
+* // returns ~-1.5708
 *
 * @example
-* var v = acovercos( -3.141592653589793/2.0 );
-* // returns ~-0.6075
+* var v = acovercos( 3.141592653589793/2.0 );
+* // returns ~0.6075
 *
 * @example
-* var v = acovercos( -3.141592653589793/6.0 );
-* // returns ~0.4966
+* var v = acovercos( 3.141592653589793/6.0 );
+* // returns ~-0.4966
 *
 * @example
 * var v = acovercos( NaN );

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

@@ -23,7 +23,7 @@ import acovercos = require( './index' );
 
 // The function returns a number...
 {
-	acovercos( 8 ); // $ExpectType number
+	acovercos( 1 ); // $ExpectType number
 }
 
 // The compiler throws an error if the function is provided a value other than a number...

lib/node_modules/@stdlib/math/base/special/acovercos/docs/types/test.ts

@@ -20,7 +20,7 @@
 #include <stdio.h>
 
 int main( void ) {
-	const double x[] = { -2.0, -1.80, -1.78, -1.67, -0.56, -0.27, -1.67, -0.78, -1.89, 0.0 };
+	const double x[] = { 0.0, 0.27, 0.56, 0.78, 1.67, 1.67, 1.78, 1.80, 1.89, 2.0 };
 
 	double v;
 	int i;

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

@@ -22,7 +22,7 @@ var uniform = require( '@stdlib/random/array/uniform' );
 var logEachMap = require( '@stdlib/console/log-each-map' );
 var acovercos = require( './../lib' );
 
-var x = uniform( 100, -2.0, 0.0, {
+var x = uniform( 100, 0.0, 2.0, {
 	'dtype': 'float64'
 });
 

lib/node_modules/@stdlib/math/base/special/acovercos/examples/index.js

@@ -27,13 +27,13 @@
 * var acovercos = require( '@stdlib/math/base/special/acovercos' );
 *
 * var v = acovercos( 0.0 );
-* // returns ~1.5708
+* // returns ~-1.5708
 *
-* v = acovercos( -3.141592653589793/2.0 );
-* // returns ~-0.6075
+* v = acovercos( 3.141592653589793/2.0 );
+* // returns ~0.6075
 *
-* v = acovercos( -3.141592653589793/6.0 );
-* // returns ~0.4966
+* v = acovercos( 3.141592653589793/6.0 );
+* // returns ~-0.4966
 *
 * v = acovercos( NaN );
 * // returns NaN

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

@@ -33,22 +33,22 @@ var asin = require( '@stdlib/math/base/special/asin' );
 *
 * @example
 * var v = acovercos( 0.0 );
-* // returns ~1.5708
+* // returns ~-1.5708
 *
 * @example
-* var v = acovercos( -3.141592653589793/2.0 );
-* // returns ~-0.6075
+* var v = acovercos( 3.141592653589793/2.0 );
+* // returns ~0.6075
 *
 * @example
-* var v = acovercos( -3.141592653589793/6.0 );
-* // returns ~0.4966
+* var v = acovercos( 3.141592653589793/6.0 );
+* // returns ~-0.4966
 *
 * @example
 * var v = acovercos( NaN );
 * // returns NaN
 */
 function acovercos( x ) {
-	return asin( 1.0 + x );
+	return asin( x - 1.0 );
 }
 
 

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

@@ -34,15 +34,15 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var v = acovercos( 0.0 );
-* // returns ~1.5708
+* // returns ~-1.5708
 *
 * @example
-* var v = acovercos( -3.141592653589793/2.0 );
-* // returns ~-0.6075
+* var v = acovercos( 3.141592653589793/2.0 );
+* // returns ~0.6075
 *
 * @example
-* var v = acovercos( -3.141592653589793/6.0 );
-* // returns ~0.4966
+* var v = acovercos( 3.141592653589793/6.0 );
+* // returns ~-0.4966
 *
 * @example
 * var v = acovercos( NaN );

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

@@ -27,8 +27,8 @@
 *
 * @example
 * double out = stdlib_base_acovercos( 0.0 );
-* // returns ~1.5708
+* // returns ~-1.5708
 */
 double stdlib_base_acovercos( const double x ) {
-	return stdlib_base_asin( 1.0 + x );
+	return stdlib_base_asin( x - 1.0 );
 }

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

@@ -19,7 +19,7 @@
 import JSON
 
 """
-    gen( domain, name )
+	gen( domain, name )
 
 Generate fixture data and write to file.
 
@@ -37,7 +37,7 @@ julia> gen( x, \"data.json\" );
 """
 function gen( domain, name )
 	x = collect( domain );
-	y = asin.( 1.0 .+ x );
+	y = asin.( x .- 1.0 );
 
 	# Store data to be written to file as a collection:
 	data = Dict([
@@ -62,9 +62,9 @@ file = @__FILE__;
 dir = dirname( file );
 
 # Generate fixture data for decimal values:
-x = range( -2.0, stop = 0.0, length = 2003 );
+x = range( 0.0, stop = 2.0, length = 2003 );
 gen( x, "data.json" );
 
 # Generate fixture data for small negative values:
-x = range( -1e-200, stop = -1e-208, length = 2003 );
-gen( x, "small_negative.json" );
+x = range( 1e-208, stop = 1e-200, length = 2003 );
+gen( x, "small_positive.json" );