changed the computation methods

Author: vivekmaurya001

lib/node_modules/@stdlib/math/base/special/expf/lib/expmulti.js

@@ -18,46 +18,17 @@
 *
 * ## Notice
 *
-* The following copyrights, licenses, and long comment were part of the original implementation available as part of [Go]{@link https://github.com/golang/go/blob/cb07765045aed5104a3df31507564ac99e6ddce8/src/math/exp.go}, which in turn was based on an implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_exp.c}. The implementation follows the original, but has been modified for JavaScript.
-*
-* ```text
-* Copyright (c) 2009 The Go Authors. All rights reserved.
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions are
-* met:
-*
-*    * Redistributions of source code must retain the above copyright
-* notice, this list of conditions and the following disclaimer.
-*    * Redistributions in binary form must reproduce the above
-* copyright notice, this list of conditions and the following disclaimer
-* in the documentation and/or other materials provided with the
-* distribution.
-*    * Neither the name of Google Inc. nor the names of its
-* contributors may be used to endorse or promote products derived from
-* this software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-* ```
-*
-* ```text
-* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+* The following copyrights, licenses, and long comment were part of the original implementation available as part of{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_expf.c?view=markup}, The implementation follows the original, but has been modified for JavaScript.
 *
+* e_expf.c -- float version of e_exp.c.
+* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
+* ====================================================
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
-* ```
+* ====================================================
 */
 
 'use strict';

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

@@ -18,46 +18,17 @@
 *
 * ## Notice
 *
-* The following copyrights, licenses, and long comment were part of the original implementation available as part of [Go]{@link https://github.com/golang/go/blob/cb07765045aed5104a3df31507564ac99e6ddce8/src/math/exp.go}, which in turn was based on an implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_exp.c}. The implementation follows the original, but has been modified for JavaScript.
-*
-* ```text
-* Copyright (c) 2009 The Go Authors. All rights reserved.
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions are
-* met:
-*
-*    * Redistributions of source code must retain the above copyright
-* notice, this list of conditions and the following disclaimer.
-*    * Redistributions in binary form must reproduce the above
-* copyright notice, this list of conditions and the following disclaimer
-* in the documentation and/or other materials provided with the
-* distribution.
-*    * Neither the name of Google Inc. nor the names of its
-* contributors may be used to endorse or promote products derived from
-* this software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-* ```
-*
-* ```text
-* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+* The following copyrights, licenses, and long comment were part of the original implementation available as part of{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_expf.c?view=markup}, The implementation follows the original, but has been modified for JavaScript.
 *
+* e_expf.c -- float version of e_exp.c.
+* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
+* ====================================================
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
-* ```
+* ====================================================
 */
 
 'use strict';
@@ -74,8 +45,8 @@ var expmulti = require( './expmulti.js' );
 
 // VARIABLES //
 
-var LN2_HI = [6.9314575195e-01, -6.9314575195e-01]; 
-var LN2_LO = [1.4286067653e-06, -1.4286067653e-06]; 
+var LN2_HI = 6.9314575195e-01; 
+var LN2_LO = 1.4286067653e-06; 
 var halF = [0.5, -0.5]; 
 var INVLN2 = 1.4426950216e+00;
 var OVERFLOW = 8.8721679688e+01; 
@@ -218,8 +189,8 @@ function expf( x ) {
 	// Argument reduction
 
     k = truncf(INVLN2 * x + halF[xsb]);
-    hi = x - k * LN2_HI[0];
-    lo = k * LN2_LO[0];
+    hi = x - k * LN2_HI;
+    lo = k * LN2_LO;
 
 	return expmulti( hi, lo, k );
 }

lib/node_modules/@stdlib/math/base/special/expf/scripts/fixtures/julia/REQUIRE

@@ -0,0 +1,2 @@
+julia 1.5
+JSON 0.21

lib/node_modules/@stdlib/math/base/special/expf/scripts/fixtures/julia/data.json

@@ -0,0 +1,63 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2018 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import JSON
+
+"""
+    gen( x, filepath )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `x`: domain
+* `filepath::AbstractString`: filepath of the output file
+
+# Examples
+
+``` julia
+julia> x = range( -1000, stop = 1000, length = 2001 );
+julia> gen( x, \"./data.json\" );
+```
+"""
+function gen( x, filepath )
+	y = Array{Float32}( undef, length(x) );
+	for i in eachindex(x)
+		y[i] = exp( Float32.(x[i]) );
+	end
+
+	data = Dict([
+		("x", x),
+		("expected", y)
+	]);
+
+	outfile = open( filepath, "w" );
+	write( outfile, JSON.json(data) );
+	write( outfile, "\n" );
+	close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+x = range( -300, stop = 300, length = 10000 );
+out = joinpath( dir, "data.json" );
+gen( x, out );

lib/node_modules/@stdlib/math/base/special/expf/scripts/fixtures/julia/runner.jl

@@ -17,8 +17,8 @@
 * limitations under the License.
 */
 
-#include "stdlib/math/base/special/expf.h"
 #include "stdlib/math/base/napi/unary.h"
+#include "stdlib/math/base/special/expf.h"
 
 // cppcheck-suppress shadowFunction
 STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_expf )

lib/node_modules/@stdlib/math/base/special/expf/src/addon.c

@@ -18,63 +18,35 @@
 *
 * ## Notice
 *
-* * The following copyrights, licenses, and long comment were part of the original implementation available as part of [Go]{@link https://github.com/golang/go/blob/cb07765045aed5104a3df31507564ac99e6ddce8/src/math/exp.go}, which in turn was based on an implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_exp.c}. The implementation follows the original, but has been modified according to project conventions.
-*
-* ```text
-* Copyright (c) 2009 The Go Authors. All rights reserved.
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions are
-* met:
-*
-*    * Redistributions of source code must retain the above copyright
-* notice, this list of conditions and the following disclaimer.
-*    * Redistributions in binary form must reproduce the above
-* copyright notice, this list of conditions and the following disclaimer
-* in the documentation and/or other materials provided with the
-* distribution.
-*    * Neither the name of Google Inc. nor the names of its
-* contributors may be used to endorse or promote products derived from
-* this software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-* ```
-*
-* ```text
-* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+* The following copyrights, licenses, and long comment were part of the original implementation available as part of{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_expf.c?view=markup}, The implementation follows the original, but has been modified for JavaScript.
 *
+* e_expf.c -- float version of e_exp.c.
+* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
+* ====================================================
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
-* ```
+* ====================================================
 */
 
-#include "stdlib/math/base/special/expf.h"
-#include "stdlib/math/base/assert/is_nan.h"
-#include "stdlib/math/base/special/truncf.h"
 #include "stdlib/constants/float32/ninf.h"
 #include "stdlib/constants/float32/pinf.h"
+#include "stdlib/math/base/assert/is_nan.h"
+#include "stdlib/math/base/special/expf.h"
 #include "stdlib/math/base/special/ldexpf.h"
+#include "stdlib/math/base/special/truncf.h"
 #include <stdint.h>
 
-static const float LN2_HI = 0.69314718f;
-static const float LN2_LO = 1.90821484e-10f;
-static const float LOG2_E = 1.44269504f;
-static const float EXP_OVERFLOW = 88.722839f; 
-static const float EXP_UNDERFLOW = -103.97208f; 
-static const float NEARZERO = 1.0f / (1 << 14); 
-static const float NEG_NEARZERO = -NEARZERO;
+static const float LN2_HI = 0.69314718;
+static const float LN2_LO = 1.4286067653e-06;
+static const float LOG2_E = 1.4426950216;
+static const float half[ 2 ] = { 0.5, -0.5 };
+static const float EXP_OVERFLOW = 88.721679688;
+static const float EXP_UNDERFLOW = -103.97208405;
+static const float NEARZERO = 1.0 / ( 1 << 14 );
+static const float NEG_NEARZERO = -1.0 / ( 1 << 14 );
 
 /* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */
 
@@ -93,7 +65,12 @@ static const float NEG_NEARZERO = -NEARZERO;
 * @return     evaluated polynomial
 */
 static float polyval_p( const float x ) {
-    return 0.16666667f + (x * (-0.0027777778f + (x * (0.000066137566f + (x * (-0.000001653439f + (x * 4.1381369e-8f)))))));
+	static const float P1 = 1.6666625440e-1;
+	static const float P2 = -2.7667332906e-3;
+	if ( x == 0.0 ) {
+		return P1;
+	}
+	return P1 + x * P2;
 }
 
 // END: polyval_p
@@ -109,17 +86,19 @@ static float polyval_p( const float x ) {
 * @return      function value
 */
 static float expmulti( const float hi, const float lo, const int32_t k ) {
-    float r;
-    float t;
-    float c;
-    float y;
+	float r;
+	float t;
+	float c;
+	float y;
+	float twom100;
 
-    r = hi - lo;
-    t = r * r;
-    c = r - (t * polyval_p( t ));
-    y = 1.0f - (lo - ((r * c) / (2.0f - c)) - hi);
+	twom100 = 7.8886090522e-31;
+	r = hi - lo;
+	t = r * r;
+	c = r - ( t * polyval_p( t ) );
+	y = 1.0 - ( lo - ( ( r * c ) / ( 2.0 - c ) ) - hi );
 
-    return stdlib_base_ldexpf( y, k );
+	return stdlib_base_ldexpf( y, k + 100 ) * twom100 * twom100;
 }
 
 /**
@@ -221,33 +200,31 @@ static float expmulti( const float hi, const float lo, const int32_t k ) {
 * // returns 1.0f
 */
 float stdlib_base_expf( const float x ) {
-    float hi;
-    float lo;
-    int32_t k;
+	float hi;
+	float lo;
+	int32_t k;
+	int xsb;
 
+	xsb = ( x < 0.0 ) ? 1 : 0;
 	if ( stdlib_base_is_nan( x ) || x == STDLIB_CONSTANT_FLOAT32_PINF ) {
-        return x;
-    }
-    if ( x == STDLIB_CONSTANT_FLOAT32_NINF ) {
-        return 0.0f;
-    }
-    if ( x > EXP_OVERFLOW ) {
-        return STDLIB_CONSTANT_FLOAT32_PINF;
-    }
-    if ( x < EXP_UNDERFLOW ) {
-        return 0.0f;
-    }
-    if ( x > NEG_NEARZERO && x < NEARZERO ) {
-        return 1.0f + x;
-    }
-	// Reduce and compute `r = hi - lo` for extra precision...
-	if ( x < 0.0f ) {
-        k = stdlib_base_truncf( (LOG2_E * x) - 0.5f );
-    } else {
-        k = stdlib_base_truncf( (LOG2_E * x) + 0.5f );
-    }
-    hi = x - (k * LN2_HI);
-    lo = k * LN2_LO;
+		return x;
+	}
+	if ( x == STDLIB_CONSTANT_FLOAT32_NINF ) {
+		return 0.0;
+	}
+	if ( x > EXP_OVERFLOW ) {
+		return STDLIB_CONSTANT_FLOAT32_PINF;
+	}
+	if ( x < EXP_UNDERFLOW ) {
+		return 0.0;
+	}
+	if ( x > NEG_NEARZERO && x < NEARZERO ) {
+		return 1.0 + x;
+	}
+ // Reduce and compute `r = hi - lo` for extra precision...
+	k = stdlib_base_truncf( ( LOG2_E * x ) + half[ xsb ] );
+	hi = x - ( k * LN2_HI );
+	lo = k * LN2_LO;
 
-    return expmulti( hi, lo, k );
+	return expmulti( hi, lo, k );
 }