Updated docs with error rates and links to GSL/GLIBC etc.

[SVN r38676]
2026-01-27 07:02:08 +00:00 · 2007-08-15 14:15:53 +00:00
parent e16e81bf10
commit a8fd036dfb
10 changed files with 81 additions and 72 deletions
--- a/doc/bessel_ik.qbk
+++ b/doc/bessel_ik.qbk
@@ -61,7 +61,7 @@ a simplified version of this implementation
 [h4 Accuracy]

 The following tables show how the accuracy of these functions
-varies on various platforms, along with a comparison to the GSL library.  
+varies on various platforms, along with a comparison to the __gsl library.  
 Note that only results for the widest floating-point type on the 
 system are given, as narrower types have __zero_error.  All values
 are relative errors in units of epsilon.
--- a/doc/bessel_jy.qbk
+++ b/doc/bessel_jy.qbk
@@ -62,7 +62,7 @@ a simplified version of this implementation
 [h4 Accuracy]

 The following tables show how the accuracy of these functions
-varies on various platforms, along with comparisons to the GSL and
+varies on various platforms, along with comparisons to the __gsl and
 Cephes libraries.  Note that the cyclic nature of these
 functions means that they have an infinite number of irrational
 roots: in general these functions have arbitrarily large /relative/
@@ -110,7 +110,7 @@ GSL Peak=500 Mean=54
 Cephes Peak=923 Mean=83] 
      [Peak=561 Mean=36 

-GSL Peak=2x10[super 6][space] Mean\=1x10[super 5][space] 
+GSL Peak=1.4x10[super 6][space] Mean\=7x10[super 4][space] 

 Cephes Peak=+INF]]
 [[64] [Red Hat Linux IA64 / G++ 3.4] [Peak=470 Mean=56] [Peak=843 Mean=51] [Peak=741 Mean=51] ]
--- a/doc/beta.qbk
+++ b/doc/beta.qbk
@@ -40,7 +40,7 @@ when T1 and T2 are different types.
 [h4 Accuracy]

 The following table shows peak errors for various domains of input arguments,
-plus comparisons to other open source implementations where available.  Note that
+along with comparisons to the __gsl and Cephes libraries.  Note that
 only results for the widest floating point type on the system are given as
 narrower types have __zero_error.

--- a/doc/erf.qbk
+++ b/doc/erf.qbk
@@ -57,7 +57,8 @@ Returns the complement of the [@http://functions.wolfram.com/GammaBetaErf/Erfc/
 [h4 Accuracy]

 The following table shows the peak errors (in units of epsilon) 
-found on various platforms with various floating point types.
+found on various platforms with various floating point types, 
+along with comparisons to the __gsl, __glibc, __hpc and Cephes libraries.
 Unless otherwise specified any floating point type that is narrower
 than the one shown will have __zero_error.

@@ -78,25 +79,25 @@ GSL Peak=0 Mean=0
 Cephes Peak=0 Mean=0]]
 [[64] [RedHat Linux IA32, gcc-3.3] [Peak=0.7 Mean=0.07

-Native Peak=0.9 Mean=0.2]  [Peak=0.9 Mean=0.2
+__glibc Peak=0.9 Mean=0.2]  [Peak=0.9 Mean=0.2

-Native Peak=0.9 Mean=0.07] [Peak=0 Mean=0
+__glibc Peak=0.9 Mean=0.07] [Peak=0 Mean=0

-Native Peak=0 Mean=0]]
+__glibc Peak=0 Mean=0]]
 [[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=0.7 Mean=0.07

-Native Peak=0 Mean=0]  [Peak=0.9 Mean=0.1
+__glibc Peak=0 Mean=0]  [Peak=0.9 Mean=0.1

-Native Peak=0.5 Mean=0.03] [Peak=0 Mean=0
+__glibc Peak=0.5 Mean=0.03] [Peak=0 Mean=0

-Native Peak=0 Mean=0]]
+__glibc Peak=0 Mean=0]]
 [[113] [HPUX IA64, aCC A.06.06] [Peak=0.8 Mean=0.1

-Native Peak=0.9 Mean=0.2]  [Peak=0.9 Mean=0.1
+__hpc Lib Peak=0.9 Mean=0.2]  [Peak=0.9 Mean=0.1

-Native Peak=0.5 Mean=0.02] [Peak=0 Mean=0
+__hpc Lib Peak=0.5 Mean=0.02] [Peak=0 Mean=0

-Native Peak=0 Mean=0]]
+__hpc Lib Peak=0 Mean=0]]
 ]

 [table Errors In the Function erfc(z)
@@ -116,25 +117,25 @@ GSL Peak=3.9 Mean=0.4
 Cephes Peak=2.7 Mean=0.4]]
 [[64] [RedHat Linux IA32, gcc-3.3] [Peak=0 Mean=0

-Native Peak=0 Mean=0]  [Peak=1.4 Mean=0.3
+__glibc Peak=0 Mean=0]  [Peak=1.4 Mean=0.3

-Native Peak=1.3 Mean=0.3] [Peak=1.6 Mean=0.4
+__glibc Peak=1.3 Mean=0.3] [Peak=1.6 Mean=0.4

-Native Peak=1.3 Mean=0.4]]
+__glibc Peak=1.3 Mean=0.4]]
 [[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=0 Mean=0

-Native Peak=0 Mean=0]  [Peak=1.4 Mean=0.3
+__glibc Peak=0 Mean=0]  [Peak=1.4 Mean=0.3

-Native Peak=0 Mean=0] [Peak=1.5 Mean=0.4
+__glibc Peak=0 Mean=0] [Peak=1.5 Mean=0.4

-Native Peak=0 Mean=0] ]
+__glibc Peak=0 Mean=0] ]
 [[113] [HPUX IA64, aCC A.06.06] [Peak=0 Mean=0

-Native Peak=0 Mean=0]  [Peak=1.5 Mean=0.3
+__hpc Peak=0 Mean=0]  [Peak=1.5 Mean=0.3

-Native Peak=0.9 Mean=0.08] [Peak=1.6 Mean=0.4
+__hpc Peak=0.9 Mean=0.08] [Peak=1.6 Mean=0.4

-Native Peak=0.9 Mean=0.1]]
+__hpc Peak=0.9 Mean=0.1]]
 ]

 [h4 Testing]
--- a/doc/ibeta.qbk
+++ b/doc/ibeta.qbk
@@ -96,7 +96,7 @@ Returns the full (non-normalised) complement of the incomplete beta function of
 [h4 Accuracy]

 The following tables give peak and mean relative errors in over various domains of
-a, b and x, along with comparisons to other open source implementations where available.  
+a, b and x, along with comparisons to the __gsl and Cephes libraries.  
 Note that only results for the widest floating-point type on the system are given as
 narrower types have __zero_error.

--- a/doc/igamma.qbk
+++ b/doc/igamma.qbk
@@ -103,7 +103,7 @@ Returns the full (non-normalised) upper incomplete gamma function of a and z:
 [h4 Accuracy]

 The following tables give peak and mean relative errors in over various domains of
-a and z, along with comparisons to other open source implementations where available.  
+a and z, along with comparisons to the __gsl and Cephes libraries.
 Note that only results for the widest floating point type on the system are given as
 narrower types have __zero_error.

@@ -119,37 +119,37 @@ All values are in units of epsilon.

 [table Errors In the Function gamma_p(a,z)
 [[Significand Size] [Platform and Compiler] 
-[0.5 < a < 100
+   [0.5 < a < 100

-and
+   and

-0.01*a < z < 100*a]  
-[1x10[super -12] < a < 5x10[super -2]
+   0.01*a < z < 100*a]  
+      [1x10[super -12] < a < 5x10[super -2]

-and
+      and

-0.01*a < z < 100*a] 
-[1e-6 < a < 1.7x10[super 6]
+      0.01*a < z < 100*a] 
+         [1e-6 < a < 1.7x10[super 6]

-and
+         and

-1 < z < 100*a]]
+         1 < z < 100*a]]
 [[53] [Win32, Visual C++ 8] 
-[Peak=36 Mean=9.1
+   [Peak=36 Mean=9.1

-(GSL Peak=342 Mean=46)
+   (GSL Peak=342 Mean=46)

-(Cephes Peak=491 Mean=102)]  
-[Peak=4.5 Mean=1.4
+   (Cephes Peak=491 Mean=102)]  
+      [Peak=4.5 Mean=1.4

-(GSL Peak=4.8 Mean=0.76)
+      (GSL Peak=4.8 Mean=0.76)

-(Cephes Peak=21 Mean=5.6)] 
-[Peak=244 Mean=21
+      (Cephes Peak=21 Mean=5.6)] 
+         [Peak=244 Mean=21

-(GSL Peak=1022 Mean=1054)
+         (GSL Peak=1022 Mean=1054)

-(Cephes Peak~8x10[super 6] Mean~7x10[super 4])]]
+         (Cephes Peak~8x10[super 6] Mean~7x10[super 4])]]
 [[64] [RedHat Linux IA32, gcc-3.3] [Peak=241 Mean=36]  [Peak=4.7 Mean=1.5] [Peak~30,220 Mean=1929]]
 [[64] [Redhat Linux IA64, gcc-3.4] [Peak=41 Mean=10]  [Peak=4.7 Mean=1.4] [Peak~30,790 Mean=1864]]
 [[113] [HPUX IA64, aCC A.06.06] [Peak=40.2 Mean=10.2]  [Peak=5 Mean=1.6] [Peak=5,476 Mean=440]]
--- a/doc/lgamma.qbk
+++ b/doc/lgamma.qbk
@@ -50,7 +50,9 @@ the result is of type `double` if T is an integer type, or type T otherwise.

 The following table shows the peak errors (in units of epsilon) 
 found on various platforms
-with various floating point types. Unless otherwise specified any
+with various floating point types, along with comparisons to the 
+__gsl, __glibc, __hpc and
+Cephes libraries. Unless otherwise specified any
 floating point type that is narrower than the one shown will have
 __zero_error.

@@ -77,44 +79,44 @@ a low absolute error can be guaranteed.
 [[64]            [Linux IA32 / GCC]  
 [Peak=1.9 Mean=0.43

-(Native Peak=1.7 Mean=0.49)]           
+(__glibc Peak=1.7 Mean=0.49)]           
 [Peak=1.4 Mean=0.57

-(Native Peak= 0.96 Mean=0.54)]    
+(__glibc Peak= 0.96 Mean=0.54)]    
 [Peak=0.86 Mean=0.35

-(Native Peak=0.74 Mean=0.26)]       
+(__glibc Peak=0.74 Mean=0.26)]       

 [Peak=6.0 Mean=1.8

-(Native Peak=3.0 Mean=0.86)]           ]
+(__glibc Peak=3.0 Mean=0.86)]           ]
 [[64]            [Linux IA64 / GCC]  
 [Peak=0.99 Mean=0.12 

-(Native=0)]           
+(__glibc Peak 0)]           

 [Pek=1.2 Mean=0.6 

-(Native=0)]    
+(__glibc Peak 0)]    
 [Peak=0.86 Mean=0.16 

-(Native=0)]       
+(__glibc Peak 0)]       
 [Peak=2.3 Mean=0.69 

-(Native 0)]           ]
+(__glibc Peak 0)]           ]
 [[113]           [HPUX IA64, aCC A.06.06]    
 [Peak=0.96 Mean=0.13 

-(Native=0)] 
+(__hpc Peak 0)] 
 [Peak=0.99 Mean=0.53 

-(Native=0)]    
+(__hpc Peak 0)]    
 [Peak=0.9 Mean=0.4 

-(Native=0)] 
+(__hpc Peak 0)] 
 [Peak=3.0 Mean=0.9 

-(Native=0)]  ]
+(__hpc Peak 0)]  ]
 ]

 [h4 Testing]
--- a/doc/math.qbk
+++ b/doc/math.qbk
@@ -193,6 +193,11 @@ and use the function's name as the link text]
   __chf, __mean, __median, __mode, __variance, __sd, __skewness, 
   __kurtosis, __kurtosis_excess, __range and __support]

+[def __gsl [@http://www.gnu.org/software/gsl/ GSL-1.9]]
+[def __glibc [@http://www.gnu.org/software/libc/ GNU C Lib]]
+[def __hpc [@http://docs.hp.com/en/B9106-90010/index.html HP-UX C Library]]
+
+
 [/ Some composite templates]
 [template super[x]'''<superscript>'''[x]'''</superscript>''']
 [template sub[x]'''<subscript>'''[x]'''</subscript>''']
--- a/doc/powers.qbk
+++ b/doc/powers.qbk
@@ -42,7 +42,7 @@ immune to optimizer-induced errors.

 Finally when BOOST_HAS_LOG1P is defined then the `float/double/long double` 
 specializations of this template simply forward to the platform's 
-native implementation of this function.
+native (POSIX) implementation of this function.

 [h4 Accuracy]

@@ -86,7 +86,7 @@ a series expansion when x is small (giving an accuracy of less than __te).

 Finally when BOOST_HAS_EXPM1 is defined then the `float/double/long double` 
 specializations of this template simply forward to the platform's 
-native implementation of this function.
+native (POSIX) implementation of this function.
   
 [h4 Accuracy]

--- a/doc/tgamma.qbk
+++ b/doc/tgamma.qbk
@@ -70,7 +70,8 @@ the result is `double` when T is an integer type, and T otherwise.
 [h4 Accuracy]

 The following table shows the peak errors (in units of epsilon) 
-found on various platforms with various floating point types.
+found on various platforms with various floating point types, 
+along with comparisons to the __gsl, __glibc, __hpc and Cephes libraries.
 Unless otherwise specified any floating point type that is narrower
 than the one shown will have __zero_error.

@@ -100,42 +101,42 @@ than the one shown will have __zero_error.
 [[64]            [Linux IA32 / GCC]  
 [Peak=300 Mean=49.5

-(Native Peak=395 Mean=89)]           
+(__glibc Peak=395 Mean=89)]           
 [Peak=3.0 Mean=1.4

-(Native Peak=11 Mean=3.3)]    
+(__glibc Peak=11 Mean=3.3)]    
 [Peak=5.0 Mean=1.8

-(Native Peak=0.92 Mean=0.2)]       
+(__glibc Peak=0.92 Mean=0.2)]       
 [Peak=157 Mean=65

-(Native Peak=205 Mean=108)]   ]
+(__glibc Peak=205 Mean=108)]   ]
 [[64]            [Linux IA64 / GCC]  
-[Peak=2.8 Mean=0.9
+[__glibc Peak 2.8 Mean=0.9

-(Native=0.7)]           
+(__glibc Peak 0.7)]           
 [Peak=4.8 Mean=1.5

-(Native=0)]    
+(__glibc Peak 0)]    
 [Peak=4.8 Mean=1.5

-(Native=0)]       
+(__glibc Peak 0)]       

 [Peak=5.0 Mean=1.7
-(Native 0)]           ]
+(__glibc Peak 0)]           ]
 [[113]           [HPUX IA64, aCC A.06.06]    
 [Peak=2.5 Mean=1.1

-(Native=0)] 
+(__hpc Peak 0)] 
 [Peak=3.5 Mean=1.7

-(Native=0)]    
+(__hpc Peak 0)]    
 [Peak=3.5 Mean=1.6

-(Native=0)] 
+(__hpc Peak 0)] 
 [Peak=5.2 Mean=1.92

-(Native=0)]  ]
+(__hpc Peak 0)]  ]
 ]

 [h4 Testing]