chore: add test for small negative values

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---

Author: officiallyanee

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

@@ -140,17 +140,20 @@ function digammaf( x ) {
 		// Argument reduction for tan:
 		rem = f32( xx - floorf( xx ) );
 
-		// Reflect:
-		xx = f32( 1.0 - xx );
-
 		// Check for singularity (negative integer or zero)...
 		if ( rem === 0.0 ) {
 			return NaN;
 		}
-		if ( rem > 0.5 ) {
-			rem = f32(rem - 1.0);
+		if ( rem === 0.5 ) {
+			tmp = 0.0;
+		} else {
+			if ( rem > 0.5 ) {
+				rem = f32( xx - f32( floorf( xx ) + 1.0 ) );
+			}
+			tmp = f32( FLOAT32_PI / tanf( f32( FLOAT32_PI * rem ) ) );
 		}
-		tmp = f32( FLOAT32_PI / tanf( f32( FLOAT32_PI * rem ) ) );
+		// Reflect:
+		xx = f32( 1.0 - xx );
 	} else {
 		tmp = 0.0;
 	}

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

@@ -133,18 +133,22 @@ float stdlib_base_digammaf( const float x ) {
 		// Argument reduction for tan:
 		rem = xx - stdlib_base_floorf( xx );
 
-		// Reflect:
-		xx = 1.0f - xx;
-
 		// Check for evaluation at a negative pole:
 		if ( rem == 0.0f ) {
 			return 0.0f / 0.0f; // NaN
 		}
 
-		if ( rem > 0.5f ) {
-			rem -= 1.0f;
+		if ( rem == 0.5f ) {
+			tmp = 0.0f;
+		} else {
+			if ( rem > 0.5f ) {
+				rem = xx - ( stdlib_base_floorf( xx ) + 1.0f );
+			}
+			tmp = STDLIB_CONSTANT_FLOAT32_PI / stdlib_base_tanf( STDLIB_CONSTANT_FLOAT32_PI * rem );
 		}
-		tmp = STDLIB_CONSTANT_FLOAT32_PI / stdlib_base_tanf( STDLIB_CONSTANT_FLOAT32_PI * rem );
+
+		// Reflect:
+		xx = 1.0f - xx;
 	} else {
 		tmp = 0.0f;
 	}

lib/node_modules/@stdlib/math/base/special/digammaf/test/fixtures/julia/runner.jl

@@ -70,6 +70,10 @@ gen( x, "positive.json" );
 x = range( 0.01f0, stop = 0.5f0, length = 200 );
 gen( x, "small_positive.json" );
 
+# Generate fixture data for very small negative values:
+x = Float32[ -1.0e-10, -1.0e-15, -1.0e-21, -1.0e-25 ];
+gen( x, "small_negative.json" );
+
 # Generate fixture data for large positive values:
 x = range( 10.0f0, stop = 100.0f0, length = 200 );
 gen( x, "large_positive.json" );

lib/node_modules/@stdlib/math/base/special/digammaf/test/fixtures/julia/small_negative.json

@@ -0,0 +1 @@
+{"expected":[1.0e10,1.0e15,1.0e21,1.0e25],"x":[-1.0e-10,-1.0e-15,-1.0e-21,-1.0e-25]}

lib/node_modules/@stdlib/math/base/special/digammaf/test/test.js

@@ -34,6 +34,7 @@ var positive = require( './fixtures/julia/positive.json' );
 var smallPositive = require( './fixtures/julia/small_positive.json' );
 var largePositive = require( './fixtures/julia/large_positive.json' );
 var negative = require( './fixtures/julia/negative.json' );
+var smallNegative = require( './fixtures/julia/small_negative.json' );
 var nearIntegers = require( './fixtures/julia/near_integers.json' );
 var halfIntegers = require( './fixtures/julia/half_integers.json' );
 var veryLargePositive = require( './fixtures/julia/very_large_positive.json' );
@@ -174,6 +175,32 @@ tape( 'the function computes the digamma function (large positive values)', func
 	t.end();
 });
 
+tape( 'the function evaluates the digamma function (small negative values)', function test( t ) {
+	var expected;
+	var delta;
+	var tol;
+	var x;
+	var y;
+	var i;
+	var e;
+
+	x = smallNegative.x;
+	expected = smallNegative.expected;
+
+	for ( i = 0; i < x.length; i++ ) {
+		y = digammaf( x[ i ] );
+		e = f32( expected[ i ] );
+		if ( y === e ) {
+			t.strictEqual( y, e, 'x: ' + x[ i ] + '. E: ' + e );
+		} else {
+			delta = absf( y - e );
+			tol = 150.0 * EPS * absf( e );
+			t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. y: ' + y + '. E: ' + e + '. tol: ' + tol + '. Δ: ' + delta + '.' );
+		}
+	}
+	t.end();
+});
+
 tape( 'the function computes the digamma function (negative values)', function test( t ) {
 	var expected;
 	var delta;