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fix: correct C implementation and tests
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‎lib/node_modules/@stdlib/math/base/special/expf/LICENSE

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@@ -190,33 +190,3 @@ Developed at SunPro, a Sun Microsystems, Inc. business.
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Permission to use, copy, modify, and distribute this
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software is freely granted, provided that this notice
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is preserved.
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* Go <https://raw.githubusercontent.com/golang/go/master/LICENSE>
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Copyright (c) 2009 The Go Authors. All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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* Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above
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copyright notice, this list of conditions and the following disclaimer
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in the documentation and/or other materials provided with the
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distribution.
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* Neither the name of Google Inc. nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

‎lib/node_modules/@stdlib/math/base/special/expf/include/stdlib/math/base/special/expf.h

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@@ -26,7 +26,7 @@ extern "C" {
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#endif
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/**
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* Evaluates the natural exponential function (single-precision).
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* Evaluates the natural exponential function for a single-precision floating-point number.
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*/
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float stdlib_base_expf( const float x );
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‎lib/node_modules/@stdlib/math/base/special/expf/lib/main.js

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@@ -86,21 +86,21 @@ var ONE = f32( 1.0 );
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* \end{align*}
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* ```
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*
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* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(5\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-59}\\). In other words,
89+
* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(2\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-27.74}\\). In other words,
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*
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* ```tex
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* R(z) \sim 2 + P_1 z + P_2 z^2 + P_3 z^3 + P_4 z^4 + P_5 z^5
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* R(z) \sim 2 + P_1 z + P_2 z^2
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* ```
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*
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* where \\( z = r^2 \\) and
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*
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* ```tex
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* \left| 2 + P_1 z + \ldots + P_5 z^5 - R(z) \right| \leq 2^{-59}
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* \left| 2 + P_1 z + P_2 z^2 - R(z) \right| \leq 2^{-27.74}
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* ```
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*
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* <!-- <note> -->
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*
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* The values of \\( P_1 \\) to \\( P_5 \\) are listed in the source code.
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* The values of \\( P_1 \\) to \\( P_2 \\) are listed in the source code.
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*
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* <!-- </note> -->
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*
@@ -116,7 +116,7 @@ var ONE = f32( 1.0 );
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* where
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*
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* ```tex
119-
* R_1(r) = r - P_1\ r^2 + P_2\ r^4 + \ldots + P_5\ r^{10}
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* R_1(r) = r - P_1\ r^2 + P_2\ r^4
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* ```
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*
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* 3. We scale back to obtain \\( e^{x} \\). From step 1, we have

‎lib/node_modules/@stdlib/math/base/special/expf/manifest.json

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@@ -39,11 +39,10 @@
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"libpath": [],
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"dependencies": [
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"@stdlib/math/base/napi/unary",
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"@stdlib/math/base/assert/is-nan",
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"@stdlib/math/base/assert/is-nanf",
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"@stdlib/math/base/special/ldexpf",
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"@stdlib/constants/float32/ninf",
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"@stdlib/constants/float32/pinf",
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"@stdlib/math/base/special/truncf",
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"@stdlib/math/base/special/ldexpf"
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"@stdlib/constants/float32/pinf"
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]
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},
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{
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"libraries": [],
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"libpath": [],
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"dependencies": [
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"@stdlib/math/base/assert/is-nan",
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"@stdlib/math/base/assert/is-nanf",
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"@stdlib/math/base/special/ldexpf",
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"@stdlib/constants/float32/ninf",
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"@stdlib/constants/float32/pinf",
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"@stdlib/math/base/special/truncf",
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"@stdlib/math/base/special/ldexpf"
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"@stdlib/constants/float32/pinf"
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]
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},
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{
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"libraries": [],
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"libpath": [],
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"dependencies": [
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"@stdlib/math/base/assert/is-nan",
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"@stdlib/math/base/assert/is-nanf",
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"@stdlib/math/base/special/ldexpf",
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"@stdlib/constants/float32/ninf",
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"@stdlib/constants/float32/pinf",
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"@stdlib/math/base/special/truncf",
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"@stdlib/math/base/special/ldexpf"
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"@stdlib/constants/float32/pinf"
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]
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},
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{
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"libraries": [],
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"libpath": [],
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"dependencies": [
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"@stdlib/math/base/assert/is-nan",
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"@stdlib/math/base/assert/is-nanf",
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"@stdlib/math/base/special/ldexpf",
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"@stdlib/constants/float32/ninf",
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"@stdlib/constants/float32/pinf",
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"@stdlib/math/base/special/truncf",
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"@stdlib/math/base/special/ldexpf"
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"@stdlib/constants/float32/pinf"
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]
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}
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]

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

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#include "stdlib/math/base/napi/unary.h"
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#include "stdlib/math/base/special/expf.h"
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23-
// cppcheck-suppress shadowFunction
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STDLIB_MATH_BASE_NAPI_MODULE_F_F( stdlib_base_expf )

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

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* ```
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*/
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33-
#include "stdlib/constants/float32/ninf.h"
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#include "stdlib/constants/float32/pinf.h"
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#include "stdlib/math/base/assert/is_nan.h"
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#include "stdlib/math/base/special/expf.h"
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#include "stdlib/math/base/assert/is_nanf.h"
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#include "stdlib/math/base/special/ldexpf.h"
38-
#include "stdlib/math/base/special/truncf.h"
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#include "stdlib/constants/float32/ninf.h"
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#include "stdlib/constants/float32/pinf.h"
3938
#include <stdint.h>
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41-
static const float LN2_HI = 6.9314575195e-01;
42-
static const float LN2_LO = 1.4286067653e-06;
43-
static const float LOG2_E = 1.4426950216e+00;
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static const float half[ 2 ] = { 0.5, -0.5 };
45-
static const float EXP_OVERFLOW = 8.8721679688e+01;
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static const float EXP_UNDERFLOW = -1.0397208405e+02;
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static const float NEARZERO = 1.0 / ( 1 << 14 );
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static const float NEG_NEARZERO = -1.0 / ( 1 << 14 );
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static const float LN2_HI = 6.9314575195e-01; // 0x3F317200
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static const float LN2_LO = 1.4286067653e-06; // 0x35BFBE8E
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static const float INVLN2 = 1.4426950216e+00; // 0x3FB8AA3B
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static const float EXP_OVERFLOW = 8.8721679688e+01; // 0x42B17180
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static const float EXP_UNDERFLOW = -1.0397208405e+02; // 0xC2CFF1B5
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static const float NEARZERO = 1.0f / (1 << 14); // 0x39000000
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static const float NEG_NEARZERO = -NEARZERO; // 0xB9000000
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/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */
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@@ -72,30 +70,25 @@ static float polyval_p( const float x ) {
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/* End auto-generated functions. */
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7472
/**
75-
* Computes \\(e^{r} 2^k\\) where \\(r = \mathrm{hi} - \mathrm{lo}\\) and \\(|r| \leq \ln(2)/2\\).
73+
* Computes \\(e^{r} 2^k\\) for a single-precision floating-point number, where \\(r = \mathrm{hi} - \mathrm{lo}\\) and \\(|r| \leq \ln(2)/2\\).
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*
7775
* @param hi upper bound
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* @param lo lower bound
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* @param k power of 2
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* @return function value
8179
*/
82-
static float expmulti( const float hi, const float lo, const int32_t k ) {
80+
static float expmultif( const float hi, const float lo, const int32_t k ) {
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float r;
8482
float t;
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float c;
8684
float y;
87-
float twom100;
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89-
twom100 = 7.8886090522e-31;
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r = hi - lo;
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t = r * r;
9288
c = r - ( t * polyval_p( t ) );
93-
y = 1.0 - ( lo - ( ( r * c ) / ( 2.0 - c ) ) - hi );
94-
if ( k >= -125 ) {
95-
return stdlib_base_ldexpf( y, k );
96-
} else {
97-
return stdlib_base_ldexpf( y, k + 100 ) * twom100 * twom100;
98-
}
89+
y = 1.0f - ( lo - ( ( r*c )/( 2.0f-c ) ) - hi );
90+
91+
return stdlib_base_ldexpf( y, k );
9992
}
10093

10194
/**
@@ -127,21 +120,21 @@ static float expmulti( const float hi, const float lo, const int32_t k ) {
127120
* \end{align*}
128121
* ```
129122
*
130-
* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(5\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-59}\\). In other words,
123+
* We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(2\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-27.74}\\). In other words,
131124
*
132125
* ```tex
133-
* R(z) \sim 2 + P_1 z + P_2 z^2 + P_3 z^3 + P_4 z^4 + P_5 z^5
126+
* R(z) \sim 2 + P_1 z + P_2 z^2
134127
* ```
135128
*
136129
* where \\( z = r^2 \\) and
137130
*
138131
* ```tex
139-
* \left| 2 + P_1 z + \ldots + P_5 z^5 - R(z) \right| \leq 2^{-59}
132+
* \left| 2 + P_1 z + P_2 z^2 - R(z) \right| \leq 2^{-27.74}
140133
* ```
141134
*
142135
* <!-- <note> -->
143136
*
144-
* The values of \\( P_1 \\) to \\( P_5 \\) are listed in the source code.
137+
* The values of \\( P_1 \\) to \\( P_2 \\) are listed in the source code.
145138
*
146139
* <!-- </note> -->
147140
*
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157150
* where
158151
*
159152
* ```tex
160-
* R_1(r) = r - P_1\ r^2 + P_2\ r^4 + \ldots + P_5\ r^{10}
153+
* R_1(r) = r - P_1\ r^2 + P_2\ r^4
161154
* ```
162155
*
163156
* 3. We scale back to obtain \\( e^{x} \\). From step 1, we have
@@ -166,7 +159,6 @@ static float expmulti( const float hi, const float lo, const int32_t k ) {
166159
* e^{x} = 2^k e^{r}
167160
* ```
168161
*
169-
*
170162
* ## Special Cases
171163
*
172164
* ```tex
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186178
* @return output value
187179
*
188180
* @example
189-
* double out = stdlib_base_expf( 0.0f );
181+
* float out = stdlib_base_expf( 0.0f );
190182
* // returns 1.0f
191183
*/
192184
float stdlib_base_expf( const float x ) {
185+
int32_t k;
193186
float hi;
194187
float lo;
195-
int32_t k;
196-
int xsb;
197188

198-
xsb = ( x < 0.0 ) ? 1 : 0;
199-
if ( stdlib_base_is_nan( x ) || x == STDLIB_CONSTANT_FLOAT32_PINF ) {
189+
if ( stdlib_base_is_nanf( x ) || x == STDLIB_CONSTANT_FLOAT32_PINF ) {
200190
return x;
201191
}
202192
if ( x == STDLIB_CONSTANT_FLOAT32_NINF ) {
203-
return 0.0;
193+
return 0.0f;
204194
}
205195
if ( x > EXP_OVERFLOW ) {
206196
return STDLIB_CONSTANT_FLOAT32_PINF;
207197
}
208198
if ( x < EXP_UNDERFLOW ) {
209-
return 0.0;
199+
return 0.0f;
210200
}
211201
if ( x > NEG_NEARZERO && x < NEARZERO ) {
212-
return 1.0 + x;
202+
return 1.0f + x;
213203
}
214204
// Reduce and compute `r = hi - lo` for extra precision...
215-
k = stdlib_base_truncf( ( LOG2_E * x ) + half[ xsb ] );
205+
if ( x < 0.0f ) {
206+
k = (int32_t)( ( INVLN2 * x ) - 0.5f );
207+
} else {
208+
k = (int32_t)( ( INVLN2 * x ) + 0.5f );
209+
}
216210
hi = x - ( k * LN2_HI );
217211
lo = k * LN2_LO;
218212

219-
return expmulti( hi, lo, k );
213+
return expmultif( hi, lo, k );
220214
}

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