refactor: add support for ratios evaluating as infinity in `math/base…

…/tools/evalrational-compile-c`

PR-URL: 	#1970
Ref: #1834 (comment)
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com> 
Signed-off-by: Athan Reines <kgryte@gmail.com>

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/lib/main.js

@@ -25,6 +25,8 @@ var readFile = require( '@stdlib/fs/read-file' ).sync;
 var replace = require( '@stdlib/string/replace' );
 var isInteger = require( '@stdlib/assert/is-integer' ).isPrimitive;
 var uppercase = require( '@stdlib/string/base/uppercase' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
 
 
 // VARIABLES //
@@ -51,7 +53,14 @@ var NAN_TEMPLATE = readFile( join( dir, 'nan.c.txt' ), opts );
 * @returns {string} serialized value
 */
 function value2string( x ) {
-	var str = x.toString();
+	var str;
+	if ( x === PINF ) {
+		return '1.0{{dtype_suffix}} / 0.0{{dtype_suffix}}';
+	}
+	if ( x === NINF ) {
+		return '-1.0{{dtype_suffix}} / 0.0{{dtype_suffix}}';
+	}
+	str = x.toString();
 	if ( isInteger( x ) ) {
 		str += '.0';
 	}
@@ -224,7 +233,7 @@ function compile( P, Q, options ) {
 	if ( n > 500 ) {
 		str = replace( LOOP_TEMPLATE, '{{P}}', array2list( P ) );
 		str = replace( str, '{{Q}}', array2list( Q ) );
-		str = replace( str, '{{ratio}}', value2string( P[0]/Q[0] ) );
+		str = replace( str, '{{ratio}}', value2string( P[0] / Q[0] ) );
 		str = replace( str, '{{num_coefficients}}', n.toString() );
 		str = replace( str, '{{dtype}}', opts.dtype );
 		str = replace( str, '{{dtype_suffix}}', opts.suffix );
@@ -236,7 +245,7 @@ function compile( P, Q, options ) {
 	str = replace( str, '{{Q_ASCENDING}}', hornerAscending( Q ) );
 	str = replace( str, '{{P_DESCENDING}}', hornerDescending( P ) );
 	str = replace( str, '{{Q_DESCENDING}}', hornerDescending( Q ) );
-	str = replace( str, '{{ratio}}', value2string( P[0]/Q[0] ) );
+	str = replace( str, '{{ratio}}', value2string( P[0] / Q[0] ) );
 	str = replace( str, '{{dtype}}', opts.dtype );
 	str = replace( str, '{{dtype_suffix}}', opts.suffix );
 	return replace( str, '{{fname}}', opts.name );

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/test/fixtures/coefficient_ratio_negative_infinity.c.txt

@@ -0,0 +1,9 @@
+/**
+* Evaluates a rational function.
+*
+* @param x    value at which to evaluate the rational function
+* @return     evaluated rational function
+*/
+static double evalrational() {
+	return -1.0 / 0.0;
+}

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/test/fixtures/coefficient_ratio_negative_infinity_custom.c.txt

@@ -0,0 +1,9 @@
+/**
+* Evaluates a rational function.
+*
+* @param x    value at which to evaluate the rational function
+* @return     evaluated rational function
+*/
+static float rational123() {
+	return -1.0f / 0.0f;
+}

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/test/fixtures/coefficient_ratio_positive_infinity.c.txt

@@ -0,0 +1,9 @@
+/**
+* Evaluates a rational function.
+*
+* @param x    value at which to evaluate the rational function
+* @return     evaluated rational function
+*/
+static double evalrational() {
+	return 1.0 / 0.0;
+}

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/test/fixtures/coefficient_ratio_positive_infinity_custom.c.txt

@@ -0,0 +1,9 @@
+/**
+* Evaluates a rational function.
+*
+* @param x    value at which to evaluate the rational function
+* @return     evaluated rational function
+*/
+static float rational123() {
+	return 1.0f / 0.0f;
+}

lib/node_modules/@stdlib/math/base/tools/evalrational-compile-c/test/fixtures/evalrational4.c.txt

@@ -0,0 +1,36 @@
+/**
+* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)).
+*
+* ## Notes
+*
+* -   Coefficients should be sorted in ascending degree.
+* -   The implementation uses [Horner's rule][horners-method] for efficient computation.
+*
+* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
+*
+* @param x    value at which to evaluate the rational function
+* @return     evaluated rational function
+*/
+static double evalrational( const double x ) {
+	double ax;
+	double ix;
+	double s1;
+	double s2;
+	if ( x == 0.0 ) {
+		return -1.0 / 0.0;
+	}
+	if ( x < 0.0 ) {
+		ax = -x;
+	} else {
+		ax = x;
+	}
+	if ( ax <= 1.0 ) {
+		s1 = -1.0 + (x * (2.5 + (x * (3.14 + (x * -1.0)))));
+		s2 = 0.0 + (x * (-3.5 + (x * (2.2 + (x * 1.25)))));
+	} else {
+		ix = 1.0 / x;
+		s1 = -1.0 + (ix * (3.14 + (ix * (2.5 + (ix * -1.0)))));
+		s2 = 1.25 + (ix * (2.2 + (ix * (-3.5 + (ix * 0.0)))));
+	}
+	return s1 / s2;
+}