chore: refactor implementation

Author: Neerajpathak07

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

@@ -40,20 +40,7 @@
 #include "stdlib/constants/float64/ninf.h"
 #include <stdint.h>
 
-static const double one = 1.0;
-
-static const double zero = 0.0;
-
-static const double huge = 1e300;
-
-// 0x3ff00000 = 1072693248 => 0 01111111111 00000000000000000000 => biased exponent: 1023 = 0+1023 => 2^0 = 1
-static const int32_t HIGH_BIASED_EXP_0 = 0x3ff00000;
-
-// 0x3e300000 = 1040187392 => 0 01111100011 00000000000000000000 => biased exponent: 100 = -23+127
-static const int32_t HIGH_BIASED_EXP_NEG_7 = 0x3e300000;
-
-// 0x3fe00000 = 1071644672 => 0 01111111110 00000000000000000000 => biased exponent: 1022 = -1+1023 => 2^-1
-static const int32_t HIGH_BIASED_EXP_NEG_1 = 0x3fe00000;
+static const double NEAR_ZERO = 1.0 / (1 << 28); // 2**-28
 
 /**
 * Computes the hyperbolic arctangent of a double-precision floating-point number.
@@ -95,37 +82,42 @@ static const int32_t HIGH_BIASED_EXP_NEG_1 = 0x3fe00000;
 * // returns ~1.472
 */
 double stdlib_base_atanh( const double x ) {
+	uint32_t ahx;
 	uint32_t lx;
 	uint32_t hx;
-	uint32_t ahx;
 	double ax;
 	double t;
+
 	if ( stdlib_base_is_nan( x ) || x < -1.0 || x > 1.0 ) {
 		return 0.0 / 0.0; // NaN
 	}
+
 	// Split `x` into high and low words:
 	stdlib_base_float64_to_words( x, &hx, &lx );
 
+	ax = x;
 	ahx = hx & STDLIB_CONSTANT_FLOAT64_HIGH_WORD_ABS_MASK;
 
-	if( ( ahx | ( ( lx | (-lx) )>>31 ))> HIGH_BIASED_EXP_0 ) {
-		return ( x - x ) / ( x - x ); // |x|>1
+	// special cases
+	if ( ax == 1.0 ) {
+		return STDLIB_CONSTANT_FLOAT64_PINF;
 	}
-	if( ahx == HIGH_BIASED_EXP_0 ) {
-		return x / zero;
+	if ( ax == -1.0 ) {
+		return STDLIB_CONSTANT_FLOAT64_NINF;
 	}
-	if( ahx < HIGH_BIASED_EXP_NEG_7 && ( huge+x ) > zero) {
-		return x; // x<2**-28
+
+	// Case: |x| < 2**-28
+	if ( ax < NEAR_ZERO ) {
+		return ( hx == 1 ) ? -ax : ax;
 	}
 
-	ax = x;
 	stdlib_base_float64_set_high_word( ahx, &ax );
 
-	if( ahx < HIGH_BIASED_EXP_NEG_1 ) {
+	if( ahx < 0.5 ) {
 		t = ax + ax;
-		t = 0.5 * stdlib_base_log1p( t + ( t * ax / ( one - ax ) ) );
+		t = 0.5 * stdlib_base_log1p( t + ( t * ax / ( 1.0 - ax ) ) );
 	} else {
-		t = 0.5 * stdlib_base_log1p( ( ax + ax ) / ( one - ax ) );
+		t = 0.5 * stdlib_base_log1p( ( ax + ax ) / ( 1.0 - ax ) );
 	}
 	return ( hx == 1 ) ? -t : t;
 }

lib/node_modules/@stdlib/math/base/special/atanh/test/test.native.js

@@ -74,7 +74,7 @@ tape( 'the function computes the hyperbolic arctangent (negative values)', opts,
 			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
 		} else {
 			delta = abs( y - expected[i] );
-			tol = 10.0 * EPS * abs( expected[i] );
+			tol = 1.0 * EPS * abs( expected[i] );
 			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
 		}
 	}