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Boost-Commit : |
From: john_at_[hidden]
Date: 2008-08-22 07:04:11
Author: johnmaddock
Date: 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
New Revision: 48291
URL: http://svn.boost.org/trac/boost/changeset/48291
Log:
Update inverse hypergeometric docs with accuracy, testing and implementation notes.
Added:
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.svg (contents, props changed)
Text files modified:
sandbox/math_toolkit/libs/math/doc/sf_and_dist/inv_hyper.qbk | 116 +++++++++++++++++++++++++++++++++++++--
1 files changed, 110 insertions(+), 6 deletions(-)
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,39 @@
+<?xml version='1.0'?>
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+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>acosh1</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>acosh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mi>ln</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>+</mo>
+ <msqrt>
+ <mrow>
+ <msup>
+ <mi>x</mi>
+ <mn>2</mn>
+ </msup>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msqrt>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.png
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh1.svg
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,40 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>acosh2</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>acosh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>≈</mo>
+ <mi>ln</mi>
+ <mfenced>
+ <mrow>
+ <mn>2</mn>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>x</mi>
+ <mo>></mo>
+ <mfrac>
+ <mn>1</mn>
+ <msqrt>
+ <mi>ε</mi>
+ </msqrt>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.png
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh2.svg
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,48 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>acosh3</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>acosh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mtext>log1p</mtext>
+ <mfenced>
+ <mrow>
+ <mi>y</mi>
+ <mo>+</mo>
+ <msqrt>
+ <mrow>
+ <msup>
+ <mi>y</mi>
+ <mn>2</mn>
+ </msup>
+ <mo>+</mo>
+ <mn>2</mn>
+ <mi>y</mi>
+ </mrow>
+ </msqrt>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>y</mi>
+ <mo>=</mo>
+ <mi>x</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.png
==============================================================================
Binary file. No diff available.
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh3.svg
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,65 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>acosh4</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>acosh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>≈</mo>
+ <msqrt>
+ <mrow>
+ <mn>2</mn>
+ <mi>y</mi>
+ </mrow>
+ </msqrt>
+ <mfenced>
+ <mrow>
+ <mn>1</mn>
+ <mo>+</mo>
+ <mfrac>
+ <mi>y</mi>
+ <mn>12</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mfrac>
+ <mrow>
+ <mn>3</mn>
+ <msup>
+ <mi>y</mi>
+ <mn>2</mn>
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+ </mfenced>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>y</mi>
+ <mo>=</mo>
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+ <mspace width="1em"/>
+ <mo>∧</mo>
+ <mspace width="1em"/>
+ <mi>y</mi>
+ <mo><</mo>
+ <msqrt>
+ <mi>ε</mi>
+ </msqrt>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.png
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/acosh4.svg
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,39 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>asinh1</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>asinh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mi>ln</mi>
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+ <mo>+</mo>
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+ <mo>+</mo>
+ <mn>1</mn>
+ </mrow>
+ </msqrt>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.png
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh1.svg
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.mml
==============================================================================
--- (empty file)
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@@ -0,0 +1,51 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>asinh2</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>asinh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>≈</mo>
+ <mi>ln</mi>
+ <mfenced>
+ <mrow>
+ <mn>2</mn>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>+</mo>
+ <mfrac>
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+ <mrow>
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+ <msup>
+ <mi>x</mi>
+ <mn>2</mn>
+ </msup>
+ </mrow>
+ </mfrac>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>x</mi>
+ <mo>></mo>
+ <mfrac>
+ <mn>1</mn>
+ <msqrt>
+ <mi>ε</mi>
+ </msqrt>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.png
==============================================================================
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh2.svg
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,41 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>asinh3</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>asinh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>≈</mo>
+ <mi>x</mi>
+ <mo>−</mo>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mi>x</mi>
+ <mn>3</mn>
+ </msup>
+ </mrow>
+ <mn>6</mn>
+ </mfrac>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>x</mi>
+ <mo><</mo>
+ <msqrt>
+ <mi>ε</mi>
+ </msqrt>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.png
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh3.svg
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,38 @@
+<?xml version='1.0'?>
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+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>asinh4</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>asinh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mtext>log1p</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>+</mo>
+ <mtext>sqrtp1m1</mtext>
+ <mfenced>
+ <mrow>
+ <msup>
+ <mi>x</mi>
+ <mn>2</mn>
+ </msup>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.png
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/asinh4.svg
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.mml
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@@ -0,0 +1,44 @@
+<?xml version='1.0'?>
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+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>atanh1</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>atanh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mfrac>
+ <mrow>
+ <mi>ln</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
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+ <mo>+</mo>
+ <mi>x</mi>
+ </mrow>
+ <mrow>
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+ <mo>−</mo>
+ <mi>x</mi>
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+ </mfrac>
+ </mrow>
+ </mfenced>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.png
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh1.svg
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.mml
==============================================================================
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+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,40 @@
+<?xml version='1.0'?>
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+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>atanh2</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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+ <mtext>atanh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>≈</mo>
+ <mi>x</mi>
+ <mo>+</mo>
+ <mfrac>
+ <msup>
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+ </msup>
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+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <mi>x</mi>
+ <mo><</mo>
+ <mroot>
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+ <mi/>
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+ </mrow>
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+</body>
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.png
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh2.svg
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.mml 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -0,0 +1,41 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>atanh3</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtext>atanh</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>=</mo>
+ <mfrac>
+ <mrow>
+ <mtext>log1p</mtext>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mo>−</mo>
+ <mtext>log1p</mtext>
+ <mfenced>
+ <mrow>
+ <mo>−</mo>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.png
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Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/atanh3.svg
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Modified: sandbox/math_toolkit/libs/math/doc/sf_and_dist/inv_hyper.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/sf_and_dist/inv_hyper.qbk (original)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/inv_hyper.qbk 2008-08-22 07:04:10 EDT (Fri, 22 Aug 2008)
@@ -85,9 +85,7 @@
Computes the reciprocal of (the restriction to the range of __form1)
[link math_toolkit.special.inv_hyper.inv_hyper_over
-the hyperbolic cosine function], at x. Values returned are positive. Generalised
-Taylor series are used near 1 and Laurent series are used near the
-infinity to ensure accuracy.
+the hyperbolic cosine function], at x. Values returned are positive.
If x is in the range __form2 then returns the result of __domain_error.
@@ -98,6 +96,45 @@
[graph acosh]
+[h4 Accuracy]
+
+Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+
+[h4 Testing]
+
+This function is tested using a combination of random test values designed to give
+full function coverage computed at high precision using the "naive" formula:
+
+[equation acosh1]
+
+along with a selection of sanity check values
+computed using functions.wolfram.com to at least 50 decimal digits.
+
+[h4 Implementation]
+
+For sufficiently large x, we can use the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
+approximation]:
+
+[equation acosh2]
+
+For x sufficiently close to 1 we can use the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
+approximation]:
+
+[equation acosh4]
+
+Otherwise for x close to 1 we can use the following rearrangement of the
+primary definition to preserve accuracy:
+
+[equation acosh3]
+
+Otherwise the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
+primary definition] is used:
+
+[equation acosh1]
+
[endsect]
[section:asinh asinh]
@@ -115,8 +152,6 @@
Computes the reciprocal of
[link math_toolkit.special.inv_hyper.inv_hyper_over
the hyperbolic sine function].
-Taylor series are used at the origin and Laurent series are used near the
-infinity to ensure accuracy.
The return type of this function is computed using the __arg_pomotion_rules:
the return type is `double` when T is an integer type, and T otherwise.
@@ -125,6 +160,44 @@
[optional_policy]
+[h4 Accuracy]
+
+Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+
+[h4 Testing]
+
+This function is tested using a combination of random test values designed to give
+full function coverage computed at high precision using the "naive" formula:
+
+[equation asinh1]
+
+along with a selection of sanity check values
+computed using functions.wolfram.com to at least 50 decimal digits.
+
+[h4 Implementation]
+
+For sufficiently large x we can use the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
+approximation]:
+
+[equation asinh2]
+
+While for very small x we can use the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
+approximation]:
+
+[equation asinh3]
+
+For 0.5 > x > [epsilon] the following rearrangement of the primary definition is used:
+
+[equation asinh4]
+
+Otherwise evalution is via the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
+primary definition]:
+
+[equation asinh4]
+
[endsect]
[section:atanh atanh]
@@ -142,7 +215,6 @@
Computes the reciprocal of
[link math_toolkit.special.inv_hyper.inv_hyper_over
the hyperbolic tangent function], at x.
-Taylor series are used at the origin to ensure accuracy.
[optional_policy]
@@ -170,6 +242,38 @@
[graph atanh]
+[h4 Accuracy]
+
+Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+
+[h4 Testing]
+
+This function is tested using a combination of random test values designed to give
+full function coverage computed at high precision using the "naive" formula:
+
+[equation atanh1]
+
+along with a selection of sanity check values
+computed using functions.wolfram.com to at least 50 decimal digits.
+
+[h4 Implementation]
+
+For sufficiently small x we can use the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/ approximation]:
+
+[equation atanh2]
+
+Otherwise the
+[@http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/ primary definition]:
+
+[equation atanh1]
+
+or it's equivalent form:
+
+[equation atanh3]
+
+is used.
+
[endsect]
[endsect]
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