From 47cca3f1297563a8a3d05911c72f93a5c26f212c Mon Sep 17 00:00:00 2001
From: stdlib-bot <82920195+stdlib-bot@users.noreply.github.com>
Date: Tue, 16 Apr 2024 05:31:31 +0000
Subject: [PATCH] Update artifacts

---
 math/base/special/log2/coverage.ndjson |   1 +
 math/base/special/log2/index.html      |  67 ++---------
 math/base/special/log2/index.js.html   |   2 +-
 math/base/special/log2/main.js.html    | 150 ++++++++++++++++++++-----
 math/base/special/log2/native.js.html  |   8 +-
 5 files changed, 137 insertions(+), 91 deletions(-)

diff --git a/math/base/special/log2/coverage.ndjson b/math/base/special/log2/coverage.ndjson
index cae9246c3..3756cc0b1 100644
--- a/math/base/special/log2/coverage.ndjson
+++ b/math/base/special/log2/coverage.ndjson
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+[290,290,100,16,16,100,2,2,100,290,290,100,"be5ece8057f8f4ce6895df69a71abffd9b80733d","2024-04-15 22:29:10 -0700"]
diff --git a/math/base/special/log2/index.html b/math/base/special/log2/index.html
index 088202519..c824a54c6 100644
--- a/math/base/special/log2/index.html
+++ b/math/base/special/log2/index.html
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 *
 * ## Notice
 *
-* The following copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_log2.c}. The implementation follows the original, but has been modified for JavaScript.
+* The following copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_log2.c}. The implementation follows the original, but has been modified for JavaScript.
 *
 * ```text
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@@ -402,7 +462,7 @@ <h1><a href="../../../../../index.html">All files</a> / <a href="index.html">mat
 var HIGH_SIGNIFICAND_MASK = require( '@stdlib/constants/float64/high-word-significand-mask' );
 var BIAS = require( '@stdlib/constants/float64/exponent-bias' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var klog = require( './klog.js' );
+var kernelLog1p = require( '@stdlib/math/base/special/kernel-log1p' );
 &nbsp;
 &nbsp;
 // VARIABLES //
@@ -457,11 +517,17 @@ <h1><a href="../../../../../index.html">All files</a> / <a href="index.html">mat
 * // returns NaN
 */
 function log2( x ) {
-	var hi;
-	var lo;
+	var valHi;
+	var valLo;
+	var hfsq;
 	var hx;
 	var lx;
+	var hi;
+	var lo;
 	var f;
+	var R;
+	var w;
+	var y;
 	var i;
 	var k;
 &nbsp;
@@ -486,18 +552,42 @@ <h1><a href="../../../../../index.html">All files</a> / <a href="index.html">mat
 	if ( hx &gt;= HIGH_MAX_NORMAL_EXP ) {
 		return x + x;
 	}
+	// Case: log(1) = +0
+	if ( hx === HIGH_BIASED_EXP_0 &amp;&amp; lx === 0 ) {
+		return 0.0;
+	}
 	k += ( (hx&gt;&gt;20) - BIAS )|0; // asm type annotation
 	hx &amp;= HIGH_SIGNIFICAND_MASK;
-	i = ( ( hx+0x95f64 ) &amp; 0x100000 )|0; // asm type annotation
+	i = ( ( hx+0x95f64 ) &amp; HIGH_MIN_NORMAL_EXP )|0; // asm type annotation
 &nbsp;
 	// Normalize x or x/2...
 	x = setHighWord( x, hx|(i^HIGH_BIASED_EXP_0) );
 	k += (i&gt;&gt;20)|0; // asm type annotation
-	f = klog( x );
-	x -= 1;
-	hi = setLowWord( x, 0 );
-	lo = x - hi;
-	return ( (x+f)*IVLN2LO ) + ( (lo+f)*IVLN2HI ) + ( hi*IVLN2HI ) + k;
+	y = k;
+	f = x - 1.0;
+	hfsq = 0.5 * f * f;
+	R = kernelLog1p( f );
+&nbsp;
+	/*
+	* Notes:
+	*
+	* -   `f-hfsq` must (for args near `1`) be evaluated in extra precision to avoid a large cancellation when `x` is near `sqrt(2)` or `1/sqrt(2)`.This is fairly efficient since `f-hfsq` only depends on `f`, so can be evaluated in parallel with `R`. Not combining `hfsq` with `R` also keeps `R` small (though not as small as a true `lo` term would be), so that extra precision is not needed for terms involving `R`.
+	* -   When implemented in C, compiler bugs involving extra precision used to break Dekker's theorem for spitting `f-hfsq` as `hi+lo`. These problems are now automatically avoided as a side effect of the optimization of combining the Dekker splitting step with the clear-low-bits step.
+	* -   `y` must (for args near `sqrt(2)` and `1/sqrt(2)`) be added in extra precision to avoid a very large cancellation when `x` is very near these values.  Unlike the above cancellations, this problem is specific to base `2`.  It is strange that adding `+-1` is so much harder than adding `+-ln2` or `+-log10_2`.
+	* -   This implementation uses Dekker's theorem to normalize `y+val_hi`, so, when implemented in C, compiler bugs may reappear in some configurations.
+	* -   The multi-precision calculations for the multiplications are routine.
+	*/
+	hi = f - hfsq;
+	hi = setLowWord( hi, 0 );
+	lo = ( f - hi ) - hfsq + R;
+	valHi = hi * IVLN2HI;
+	valLo = ( ( lo + hi ) * IVLN2LO ) + ( lo * IVLN2HI );
+&nbsp;
+	w = y + valHi;
+	valLo += ( y - w ) + valHi;
+	valHi = w;
+&nbsp;
+	return valLo + valHi;
 }
 &nbsp;
 &nbsp;
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             <div class='footer quiet pad2 space-top1 center small'>
                 Code coverage generated by
                 <a href="https://istanbul.js.org/" target="_blank" rel="noopener noreferrer">istanbul</a>
-                at 2024-03-12T01:12:38.723Z
+                at 2024-04-16T05:31:22.395Z
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         <script>
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+                at 2024-04-16T05:31:22.395Z
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