boost/math
2
0
Fork 0
mirror of https://github.com/boostorg/math.git synced 2026-01-19 04:22:09 +00:00
Code Issues Projects Releases Wiki Activity

Add new tables to old docs. Tweak table formatting slightly.

Browse Source
This commit is contained in:
jzmaddock
2015-07-03 18:40:09 +01:00
parent ed25ba9494
commit 6db20ce240
38 changed files with 1551 additions and 15712 deletions
Download Patch File Download Diff File Expand all files Collapse all files

17
doc/distributions/nc_beta.qbk
View File

@@ -96,23 +96,14 @@ The domain of the random variable is \[0, 1\].
The following table shows the peak errors
(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon])
found on various platforms with various floating point types.
No comparison to the [@http://www.r-project.org/ R-2.5.1 Math library],
or to the FORTRAN implementations of AS226 or AS310 are given since these appear
to only guarantee absolute error: this would causes our test harness
to assign an /"infinite"/ error to these libraries for some of our
test values when measuring /relative error/.
The failures in the comparison to the [@http://www.r-project.org/ R Math library],
seem to be mostly in the corner cases when the probablity would be very small.
Unless otherwise specified any floating-point type that is narrower
than the one shown will have __zero_error.
[table Errors In CDF of the Noncentral Beta
[[Significand Size] [Platform and Compiler] [[alpha], [beta],[lambda] < 200] [[alpha],[beta],[lambda] > 200]]
[[53] [Win32, Visual C++ 8] [Peak=620 Mean=22] [Peak=8670 Mean=1040]]
[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=825 Mean=50] [Peak=2.5x10[super 4] Mean=4000]]
[table_non_central_beta_CDF]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=825 Mean=30] [Peak=1.7x10[super 4] Mean=2500]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=420 Mean=50] [Peak=9200 Mean=1200]]
]
[table_non_central_beta_CDF_complement]
Error rates for the PDF, the complement of the CDF and for the quantile
functions are broadly similar.

26
doc/distributions/nc_chi_squared.qbk
View File

@@ -129,28 +129,18 @@ for the noncentral chi-squared distribution.
[h4 Accuracy]
The following table shows the peak errors
(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon])
found on various platforms with various floating-point types,
along with comparisons to the [@http://www.r-project.org/ R-2.5.1 Math library].
Unless otherwise specified, any floating-point type that is narrower
(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon])
found on various platforms with various floating point types.
The failures in the comparison to the [@http://www.r-project.org/ R Math library],
seem to be mostly in the corner cases when the probablity would be very small.
Unless otherwise specified any floating-point type that is narrower
than the one shown will have __zero_error.
[table Errors In CDF of the Noncentral Chi-Squared
[[Significand Size] [Platform and Compiler] [[nu],[lambda] < 200] [[nu],[lambda] > 200]]
[[53] [Win32, Visual C++ 8] [Peak=50 Mean=9.9
[table_non_central_chi_squared_CDF]
R Peak=685 Mean=109
] [Peak=9780 Mean=718
[table_non_central_chi_squared_CDF_complement]
R Peak=3x10[super 8] Mean=2x10[super 7] ] ]
[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=270 Mean=27] [Peak=7900 Mean=900]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=107 Mean=17] [Peak=5000 Mean=630]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=270 Mean=20] [Peak=4600 Mean=560]]
]
Error rates for the complement of the CDF and for the quantile
Error rates for the quantile
functions are broadly similar. Special mention should go to
the `mode` function: there is no closed form for this function,
so it is evaluated numerically by finding the maxima of the PDF:

10
doc/distributions/nc_t.qbk
View File

@@ -82,13 +82,9 @@ found on various platforms with various floating-point types.
Unless otherwise specified, any floating-point type that is narrower
than the one shown will have __zero_error.
[table Errors In CDF of the Noncentral T Distribution
[[Significand Size (bits)] [Platform and Compiler] [[nu], [delta] < 600]]
[[53] [Win32, Visual C++ 8] [Peak=120 Mean=26 ] ]
[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=121 Mean=26] ]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=122 Mean=25] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=115 Mean=24] ]
]
[table_non_central_t_CDF]
[table_non_central_t_CDF_complement]
[caution The complexity of the current algorithm is dependent upon
[delta][super 2]: consequently the time taken to evaluate the CDF

19
doc/math.qbk
View File

@@ -40,6 +40,8 @@
[import ../../../tools/auto_index/include/auto_index_helpers.qbk]
[/ Must be first included file!]
[import ../reporting/accuracy/doc/accuracy_tables.qbk]
[import html4_symbols.qbk]
[import overview/common_overviews.qbk] [/ overviews that appear in more than one place!]
@@ -647,6 +649,23 @@ and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22.
[include background/lanczos.qbk]
[include background/remez.qbk]
[include background/references.qbk]
[section:logs_and_tables Error logs and tables]
[section:all_table Tables of Error Rates for all Functions]
[all_tables]
[endsect]
[section:logs Error Logs For Error Rate Tables]
[all_errors]
[endsect]
[endsect]
[endmathpart] [/section:backgrounders Backgrounders]
[mathpart status Library Status]

27
doc/sf/bessel_ik.qbk
View File

@@ -63,29 +63,20 @@ 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 comparison to other libraries.
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.
are relative errors in units of epsilon. Note that our test suite
includes some fairly extreme inputs which results in most of the worst
problem cases in other libraries:
[table Errors Rates in cyl_bessel_i
[[Significand Size] [Platform and Compiler] [I[sub v]] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=10 Mean=3.4
GSL Peak=6000] ]
[[64] [Red Hat Linux IA64 / G++ 3.4] [Peak=11 Mean=3] ]
[[64] [SUSE Linux AMD64 / G++ 4.1] [Peak=11 Mean=4] ]
[[113] [HP-UX / HP aCC 6] [Peak=15 Mean=4] ]
]
[table_cyl_bessel_i_integer_orders_]
[table Errors Rates in cyl_bessel_k
[[Significand Size] [Platform and Compiler] [K[sub v]] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=9 Mean=2
[table_cyl_bessel_i]
GSL Peak=9] ]
[[64] [Red Hat Linux IA64 / G++ 3.4] [Peak=10 Mean=2] ]
[[64] [SUSE Linux AMD64 / G++ 4.1] [Peak=10 Mean=2] ]
[[113] [HP-UX / HP aCC 6] [Peak=12 Mean=5] ]
]
[table_cyl_bessel_k_integer_orders_]
[table_cyl_bessel_k]
[h4 Implementation]

55
doc/sf/bessel_jy.qbk
View File

@@ -64,61 +64,26 @@ 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
__cephes libraries. Note that the cyclic nature of these
varies on various platforms, along with comparisons to other
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/
errors when the arguments are sufficiently close to a root. Of
course the absolute error in such cases is always small.
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.
are relative errors in units of epsilon. Most of the gross errors
exhibited by other libraries occur for very large arguments - you will
need to drill down into the actual program output if you need more
information on this.
[table Errors Rates in cyl_bessel_j
[[Significand Size] [Platform and Compiler] [J[sub 0][space] and J[sub 1]] [J[sub v]] [J[sub v][space] (large values of x > 1000)] ]
[[53] [Win32 / Visual C++ 8.0]
[Peak=2.5 Mean=1.1
[table_cyl_bessel_j_integer_orders_]
GSL Peak=6.6
[table_cyl_bessel_j]
__cephes Peak=2.5 Mean=1.1]
[Peak=11 Mean=2.2
[table_cyl_neumann_integer_orders_]
GSL Peak=11
__cephes Peak=17 Mean=2.5]
[Peak=59 Mean=10
GSL Peak=6x10[super 11]
__cephes Peak=2x10[super 5] ] ]
[[64] [Red Hat Linux IA64 / G++ 3.4] [Peak=7 Mean=3] [Peak=117 Mean=10] [Peak=2x10[super 4][space] Mean=6x10[super 3]] ]
[[64] [SUSE Linux AMD64 / G++ 4.1] [Peak=7 Mean=3] [Peak=400 Mean=40] [Peak=2x10[super 4][space] Mean=1x10[super 4]] ]
[[113] [HP-UX / HP aCC 6] [Peak=14 Mean=6] [Peak=29 Mean=3] [Peak=2700 Mean=450] ]
]
[table Errors Rates in cyl_neumann
[[Significand Size] [Platform and Compiler] [Y[sub 0][space] and Y[sub 1]] [Y[sub n] (integer orders)] [Y[sub v] (fractional orders)] ]
[[53] [Win32 / Visual C++ 8.0]
[Peak=4.7 Mean=1.7
GSL Peak=34 Mean=9
__cephes Peak=330 Mean=54]
[Peak=117 Mean=10
GSL Peak=500 Mean=54
__cephes Peak=923 Mean=83]
[Peak=800 Mean=40
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] ]
[[64] [SUSE Linux AMD64 / G++ 4.1] [Peak=1300 Mean=424] [Peak=2x10[super 4][space] Mean=8x10[super 3]] [Peak=1x10[super 5][space] Mean=6x10[super 3]] ]
[[113] [HP-UX / HP aCC 6] [Peak=180 Mean=63] [Peak=340 Mean=150] [Peak=2x10[super 4][space] Mean=1200] ]
]
[table_cyl_neumann]
Note that for large /x/ these functions are largely dependent on
the accuracy of the `std::sin` and `std::cos` functions.

20
doc/sf/bessel_prime.qbk
View File

@@ -65,8 +65,24 @@ does not use.
[h4 Accuracy]
The accuracy of these functions is broadly similar to the underlying Bessel functions. Refer to those functions
for more information.
The accuracy of these functions is broadly similar to the underlying Bessel functions.
[table_cyl_bessel_i_prime_integer_orders_]
[table_cyl_bessel_i_prime]
[table_cyl_bessel_j_prime_integer_orders_]
[table_cyl_bessel_j_prime]
[table_cyl_bessel_k_prime_integer_orders_]
[table_cyl_bessel_k_prime]
[table_sph_bessel_prime]
[table_sph_neumann_prime]
[h4 Implementation]

5
doc/sf/bessel_spherical.qbk
View File

@@ -58,8 +58,9 @@ a simplified version of this implementation
[h4 Accuracy]
Other than for some special cases, these functions are computed in terms of
__cyl_bessel_j and __cyl_neumann: refer to these functions for accuracy data.
[table_sph_bessel]
[table_sph_neumann]
[h4 Implementation]

20
doc/sf/beta.qbk
View File

@@ -44,25 +44,7 @@ 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.
[table Peak Errors In the Beta Function
[[Significand Size] [Platform and Compiler] [Errors in range
0.4 < a,b < 100] [Errors in range
1e-6 < a,b < 36]]
[[53] [Win32, Visual C++ 8] [Peak=99 Mean=22
(GSL Peak=1178 Mean=238)
(__cephes=1612)] [Peak=10.7 Mean=2.6
(GSL Peak=12 Mean=2.0)
(__cephes=174)]]
[[64] [Red Hat Linux IA32, g++ 3.4.4] [Peak=112.1 Mean=26.9] [Peak=15.8 Mean=3.6]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=61.4 Mean=19.5] [Peak=12.2 Mean=3.6]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=42.03 Mean=13.94] [Peak=9.8 Mean=3.1]]
]
[table_beta]
Note that the worst errors occur when a or b are large, and that
when this is the case the result is very close to zero, so absolute

8
doc/sf/digamma.qbk
View File

@@ -37,13 +37,7 @@ found on various platforms with various floating point types.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table
[[Significand Size] [Platform and Compiler] [Random Positive Values] [Values Near The Positive Root] [Values Near Zero] [Negative Values]]
[[53] [Win32 Visual C++ 8] [Peak=0.98 Mean=0.36] [Peak=0.99 Mean=0.5] [Peak=0.95 Mean=0.5] [Peak=214 Mean=16] ]
[[64] [Linux IA32 / GCC] [Peak=1.4 Mean=0.4] [Peak=1.3 Mean=0.45] [Peak=0.98 Mean=0.35] [Peak=180 Mean=13] ]
[[64] [Linux IA64 / GCC] [Peak=0.92 Mean=0.4] [Peak=1.3 Mean=0.45] [Peak=0.98 Mean=0.4] [Peak=180 Mean=13] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=0.9 Mean=0.4] [Peak=1.1 Mean=0.5] [Peak=0.99 Mean=0.4] [Peak=64 Mean=6] ]
]
[table_digamma]
As shown above, error rates for positive arguments are generally very low.
For negative arguments there are an infinite number of irrational roots:

16
doc/sf/ellint_carlson.qbk
View File

@@ -207,12 +207,16 @@ 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.
[table Errors Rates in the Carlson Elliptic Integrals
[[Significand Size] [Platform and Compiler] [R[sub F]] [R[sub D]] [R[sub J]] [R[sub C]]]
[[53] [Win32 / Visual C++ 8.0] [Peak=2.9 Mean=0.75] [Peak=2.6 Mean=0.9] [Peak=108 Mean=6.9] [Peak=2.4 Mean=0.6] ]
[[64] [Red Hat Linux / G++ 3.4] [Peak=2.5 Mean=0.75] [Peak=2.7 Mean=0.9] [Peak=105 Mean=8] [Peak=1.9 Mean=0.7] ]
[[113] [HP-UX / HP aCC 6] [Peak=5.3 Mean=1.6] [Peak=2.9 Mean=0.99] [Peak=180 Mean=12] [Peak=1.8 Mean=0.7] ]
]
[table_ellint_rc]
[table_ellint_rd]
[table_ellint_rg]
[table_ellint_rf]
[table_ellint_rj]
[heading Implementation]

32
doc/sf/ellint_legendre.qbk
View File

@@ -77,13 +77,7 @@ 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.
[table Errors Rates in the Elliptic Integrals of the First Kind
[[Significand Size] [Platform and Compiler] [F([phi], k)] [K(k)] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=3 Mean=0.8] [Peak=1.8 Mean=0.7] ]
[[64] [Red Hat Linux / G++ 3.4] [Peak=2.6 Mean=1.7] [Peak=2.2 Mean=1.8] ]
[[113] [HP-UX / HP aCC 6] [Peak=4.6 Mean=1.5] [Peak=3.7 Mean=1.5] ]
]
[table_ellint_1]
[heading Testing]
@@ -177,13 +171,7 @@ 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.
[table Errors Rates in the Elliptic Integrals of the Second Kind
[[Significand Size] [Platform and Compiler] [F([phi], k)] [K(k)] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=4.6 Mean=1.2] [Peak=3.5 Mean=1.0] ]
[[64] [Red Hat Linux / G++ 3.4] [Peak=4.3 Mean=1.1] [Peak=4.6 Mean=1.2] ]
[[113] [HP-UX / HP aCC 6] [Peak=5.8 Mean=2.2] [Peak=10.8 Mean=2.3] ]
]
[table_ellint_2]
[heading Testing]
@@ -280,13 +268,7 @@ 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.
[table Errors Rates in the Elliptic Integrals of the Third Kind
[[Significand Size] [Platform and Compiler] [[Pi](n, [phi], k)] [[Pi](n, k)] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=29 Mean=2.2] [Peak=3 Mean=0.8] ]
[[64] [Red Hat Linux / G++ 3.4] [Peak=14 Mean=1.3] [Peak=2.3 Mean=0.8] ]
[[113] [HP-UX / HP aCC 6] [Peak=10 Mean=1.4] [Peak=4.2 Mean=1.1] ]
]
[table_ellint_3]
[heading Testing]
@@ -406,6 +388,10 @@ These functions are trivially computed in terms of other elliptic integrals
and generally have very low error rates (a few epsilon) unless parameter [phi]
is very large, in which case the usual trigonometric function argument-reduction issues apply.
[table_ellint_d_complete_]
[table_ellint_d]
[heading Testing]
The tests use a mixture of spot test values calculated using
@@ -475,6 +461,8 @@ These functions are trivially computed in terms of other elliptic integrals
and generally have very low error rates (a few epsilon) unless parameter [phi]
is very large, in which case the usual trigonometric function argument-reduction issues apply.
[table_jacobi_zeta]
[heading Testing]
The tests use a mixture of spot test values calculated using
@@ -543,6 +531,8 @@ These functions are trivially computed in terms of other elliptic integrals
and generally have very low error rates (a few epsilon) unless parameter [phi]
is very large, in which case the usual trigonometric function argument-reduction issues apply.
[table_heuman_lambda]
[heading Testing]
The tests use a mixture of spot test values calculated using

76
doc/sf/erf.qbk
View File

@@ -62,81 +62,9 @@ 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.
[table Errors In the Function erf(z)
[[Significand Size] [Platform and Compiler] [z < 0.5] [0.5 < z < 8] [z > 8]]
[[53] [Win32, Visual C++ 8] [Peak=0 Mean=0
[table_erf]
GSL Peak=2.0 Mean=0.3
__cephes Peak=1.1 Mean=0.7] [Peak=0.9 Mean=0.09
GSL Peak=2.3 Mean=0.3
__cephes Peak=1.3 Mean=0.2] [Peak=0 Mean=0
GSL Peak=0 Mean=0
__cephes Peak=0 Mean=0]]
[[64] [RedHat Linux IA32, gcc-3.3] [Peak=0.7 Mean=0.07
__glibc Peak=0.9 Mean=0.2] [Peak=0.9 Mean=0.2
__glibc Peak=0.9 Mean=0.07] [Peak=0 Mean=0
__glibc Peak=0 Mean=0]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=0.7 Mean=0.07
__glibc Peak=0 Mean=0] [Peak=0.9 Mean=0.1
__glibc Peak=0.5 Mean=0.03] [Peak=0 Mean=0
__glibc Peak=0 Mean=0]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=0.8 Mean=0.1
__hpc Lib Peak=0.9 Mean=0.2] [Peak=0.9 Mean=0.1
__hpc Lib Peak=0.5 Mean=0.02] [Peak=0 Mean=0
__hpc Lib Peak=0 Mean=0]]
]
[table Errors In the Function erfc(z)
[[Significand Size] [Platform and Compiler] [z < 0.5] [0.5 < z < 8] [z > 8]]
[[53] [Win32, Visual C++ 8] [Peak=0.7 Mean=0.06
GSL Peak=1.0 Mean=0.4
__cephes Peak=0.7 Mean=0.06] [Peak=0.99 Mean=0.3
GSL Peak=2.6 Mean=0.6
__cephes Peak=3.6 Mean=0.7] [Peak=1.0 Mean=0.2
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
__glibc Peak=0 Mean=0] [Peak=1.4 Mean=0.3
__glibc Peak=1.3 Mean=0.3] [Peak=1.6 Mean=0.4
__glibc Peak=1.3 Mean=0.4]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=0 Mean=0
__glibc Peak=0 Mean=0] [Peak=1.4 Mean=0.3
__glibc Peak=0 Mean=0] [Peak=1.5 Mean=0.4
__glibc Peak=0 Mean=0] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=0 Mean=0
__hpc Peak=0 Mean=0] [Peak=1.5 Mean=0.3
__hpc Peak=0.9 Mean=0.08] [Peak=1.6 Mean=0.4
__hpc Peak=0.9 Mean=0.1]]
]
[table_erfc]
[h4 Testing]

4
doc/sf/erf_inv.qbk
View File

@@ -62,6 +62,10 @@ are accurate to less than ~ 2 epsilon. For higher precision types these
functions have the same accuracy as the
[link math_toolkit.sf_erf.error_function forward error functions].
[table_erf_inv]
[table_erfc_inv]
[h4 Testing]
There are two sets of tests:

29
doc/sf/expint.qbk
View File

@@ -42,23 +42,11 @@ of z:
The following table shows the peak errors (in units of epsilon)
found on various platforms with various floating point types,
along with comparisons to the __cephes library.
along with comparisons to other libraries.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table Errors In the Function expint(n, z)
[[Significand Size] [Platform and Compiler] [En][E1]]
[[53] [Win32, Visual C++ 8] [Peak=7.1 Mean=1.8
__cephes Peak=5.1 Mean=1.3
]
[Peak=0.99 Mean=0.5
__cephes Peak=3.1 Mean=1.1]]
[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=9.9 Mean=2.1] [Peak=0.97 Mean=0.4]]
[[64] [Redhat Linux IA64, gcc-4.1] [Peak=9.9 Mean=2.1] [Peak=0.97 Mean=0.4]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=23.3 Mean=3.7] [Peak=1.6 Mean=0.5]]
]
[table_expint_En_]
[h4 Testing]
@@ -147,18 +135,7 @@ along with comparisons to Cody's SPECFUN implementation and the __gsl library.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table Errors In the Function expint(z)
[[Significand Size] [Platform and Compiler] [Error]]
[[53] [Win32, Visual C++ 8] [Peak=2.4 Mean=0.6
GSL Peak=8.9 Mean=0.7
SPECFUN (Cody) Peak=2.5 Mean=0.6
]]
[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=5.1 Mean=0.8]]
[[64] [Redhat Linux IA64, gcc-4.1] [Peak=5.0 Mean=0.8] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=1.9 Mean=0.63]]
]
[table_expint_Ei_]
It should be noted that all three libraries tested above
offer sub-epsilon precision over most of their range.

20
doc/sf/gamma_ratios.qbk
View File

@@ -64,25 +64,9 @@ found on various platforms with various floating point types.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table Errors In the Function tgamma_delta_ratio(a, delta)
[[Significand Size] [Platform and Compiler] [20 < a < 80
[table_tgamma_delta_ratio]
and
delta < 1]]
[[53] [Win32, Visual C++ 8] [Peak=16.9 Mean=1.7] ]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=24 Mean=2.7]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=12.8 Mean=1.8]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=21.4 Mean=2.3] ]
]
[table Errors In the Function tgamma_ratio(a, b)
[[Significand Size] [Platform and Compiler] [6 < a,b < 50]]
[[53] [Win32, Visual C++ 8] [Peak=34 Mean=9] ]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=91 Mean=23]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=35.6 Mean=9.3]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=43.9 Mean=13.2] ]
]
[table_tgamma_ratio]
[h4 Testing]

10
doc/sf/hermite.qbk
View File

@@ -76,15 +76,7 @@ for various domains of input arguments.
Note that only results for the widest floating point type on the system are
given as narrower types have __zero_error.
[table Peak Errors In the Hermite Polynomial
[[Significand Size] [Platform and Compiler] [Errors in range
0 < l < 20] ]
[[53] [Win32, Visual C++ 8] [Peak=4.5 Mean=1.5] ]
[[64] [Red Hat Linux IA32, g++ 4.1] [Peak=6 Mean=2]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=6 Mean=2] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=6 Mean=4]]
]
[table_hermite]
Note that the worst errors occur when the degree increases, values greater than
~120 are very unlikely to produce sensible results, especially in the associated

105
doc/sf/ibeta.qbk
View File

@@ -111,110 +111,13 @@ more extreme test cases to be tested. For example expected results that
are zero at double precision, may be finite but exceptionally small with
the wider exponent range of the long double types.
[table Errors In the Function ibeta(a,b,x)
[[Significand Size] [Platform and Compiler] [0 < a,b < 10
[table_ibeta]
and
[table_ibetac]
0 < x < 1] [0 < a,b < 100
[table_beta_incomplete_]
and
0 < x < 1][1x10[super -5] < a,b < 1x10[super 5]
and
0 < x < 1]]
[[53] [Win32, Visual C++ 8]
[Peak=42.3 Mean=2.9
(GSL Peak=682 Mean=32.5)
(__cephes Peak=42.7 Mean=7.0)]
[Peak=108 Mean=16.6
(GSL Peak=690 Mean=151)
(__cephes Peak=1545 Mean=218)]
[Peak=4x10[super 3][space] Mean=203
(GSL Peak~3x10[super 5][space] Mean~2x10[super 4][space])
(__cephes Peak~5x10[super 5][space] Mean~2x10[super 4][space])]]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=21.9 Mean=3.1]
[Peak=270.7 Mean=26.8] [Peak~5x10[super 4][space] Mean=3x10[super 3][space] ]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=15.4 Mean=3.0] [Peak=112.9 Mean=14.3]
[Peak~5x10[super 4][space] Mean=3x10[super 3][space]]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=20.9 Mean=2.6] [Peak=88.1 Mean=14.3]
[Peak~2x10[super 4][space] Mean=1x10[super 3][space] ]]
]
[table Errors In the Function ibetac(a,b,x)
[[Significand Size] [Platform and Compiler] [0 < a,b < 10
and
0 < x < 1] [0 < a,b < 100
and
0 < x < 1][1x10[super -5] < a,b < 1x10[super 5]
and
0 < x < 1]]
[[53] [Win32, Visual C++ 8] [Peak=13.9 Mean=2.0]
[Peak=56.2 Mean=14] [Peak=3x10[super 3][space] Mean=159]]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=21.1 Mean=3.6]
[Peak=221.7 Mean=25.8]
[Peak~9x10[super 4][space] Mean=3x10[super 3][space] ]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=10.6 Mean=2.2]
[Peak=73.9 Mean=11.9]
[Peak~9x10[super 4][space] Mean=3x10[super 3][space] ]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=9.9 Mean=2.6]
[Peak=117.7 Mean=15.1]
[Peak~3x10[super 4][space] Mean=1x10[super 3][space] ]]
]
[table Errors In the Function beta(a, b, x)
[[Significand Size] [Platform and Compiler] [0 < a,b < 10
and
0 < x < 1] [0 < a,b < 100
and
0 < x < 1][1x10[super -5] < a,b < 1x10[super 5]
and
0 < x < 1]]
[[53] [Win32, Visual C++ 8] [Peak=39 Mean=2.9] [Peak=91 Mean=12.7] [Peak=635 Mean=25]]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=26 Mean=3.6] [Peak=180.7 Mean=30.1] [Peak~7x10[super 4][space] Mean=3x10[super 3][space] ]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=13 Mean=2.4] [Peak=67.1 Mean=13.4] [Peak~7x10[super 4][space] Mean=3x10[super 3][space] ]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=27.3 Mean=3.6] [Peak=49.8 Mean=9.1] [Peak~6x10[super 4][space] Mean=3x10[super 3][space] ]]
]
[table Errors In the Function betac(a,b,x)
[[Significand Size] [Platform and Compiler] [0 < a,b < 10
and
0 < x < 1] [0 < a,b < 100
and
0 < x < 1][1x10[super -5] < a,b < 1x10[super 5]
and
0 < x < 1]]
[[53] [Win32, Visual C++ 8] [Peak=12.0 Mean=2.4] [Peak=91 Mean=15] [Peak=4x10[super 3][space] Mean=113]]
[[64] [Redhat Linux IA32, gcc-3.4.4] [Peak=19.8 Mean=3.8] [Peak=295.1 Mean=33.9] [Peak~1x10[super 5][space] Mean=5x10[super 3][space] ]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=11.2 Mean=2.4] [Peak=63.5 Mean=13.6] [Peak~1x10[super 5][space] Mean=5x10[super 3][space] ]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=15.6 Mean=3.5] [Peak=39.8 Mean=8.9] [Peak~9x10[super 4][space] Mean=5x10[super 3][space] ]]
]
[table_betac]
[h4 Testing]

16
doc/sf/ibeta_inv.qbk
View File

@@ -182,6 +182,22 @@ note that in some parts of their domain, these functions can
be extremely sensitive to changes in input, particularly when
the argument /p/ (or it's complement /q/) is very close to `0` or `1`.
Comparisons to other libraries are shown below, note that our test data
exercises some rather extreme cases in the incomplete beta function
which many other libraries fail to handle:
[table_ibeta_inv]
[table_ibetac_inv]
[table_ibeta_inva]
[table_ibetac_inva]
[table_ibeta_invb]
[table_ibetac_invb]
[h4 Testing]
There are two sets of tests:

104
doc/sf/igamma.qbk
View File

@@ -117,109 +117,13 @@ reflect the more extreme nature of the tests conducted for these types.
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
[table_gamma_p]
and
[table_gamma_q]
0.01*a < z < 100*a]
[1x10[super -12] < a < 5x10[super -2]
[table_tgamma_lower]
and
0.01*a < z < 100*a]
[1e-6 < a < 1.7x10[super 6]
and
1 < z < 100*a]]
[[53] [Win32, Visual C++ 8]
[Peak=36 Mean=9.1
(GSL Peak=342 Mean=46)
(__cephes Peak=491 Mean=102)]
[Peak=4.5 Mean=1.4
(GSL Peak=4.8 Mean=0.76)
(__cephes Peak=21 Mean=5.6)]
[Peak=244 Mean=21
(GSL Peak=1022 Mean=1054)
(__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]]
]
[table Errors In the Function gamma_q(a,z)
[[Significand Size] [Platform and Compiler]
[0.5 < a < 100
and
0.01*a < z < 100*a]
[1x10[super -12] < a < 5x10[super -2]
and
0.01*a < z < 100*a] [1x10[super -6] < a < 1.7x10[super 6]
and
1 < z < 100*a]]
[[53] [Win32, Visual C++ 8] [Peak=28.3 Mean=7.2
(GSL Peak=201 Mean=13)
(__cephes Peak=556 Mean=97)] [Peak=4.8 Mean=1.6
(GSL Peak~1.3x10[super 10] Mean=1x10[super +9])
(__cephes Peak~3x10[super 11] Mean=4x10[super 10])] [Peak=469 Mean=33
(GSL Peak=27,050 Mean=2159)
(__cephes Peak~8x10[super 6] Mean~7x10[super 5])]]
[[64] [RedHat Linux IA32, gcc-3.3] [Peak=280 Mean=33] [Peak=4.1 Mean=1.6] [Peak=11,490 Mean=732]]
[[64] [Redhat Linux IA64, gcc-3.4] [Peak=32 Mean=9.4] [Peak=4.7 Mean=1.5] [Peak=6815 Mean=414]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=37 Mean=10] [Peak=11.2 Mean=2.0] [Peak=4,999 Mean=298]]
]
[table Errors In the Function tgamma_lower(a,z)
[[Significand Size] [Platform and Compiler] [0.5 < a < 100
and
0.01*a < z < 100*a] [1x10[super -12] < a < 5x10[super -2]
and
0.01*a < z < 100*a]]
[[53] [Win32, Visual C++ 8] [Peak=5.5 Mean=1.4] [Peak=3.6 Mean=0.78]]
[[64] [RedHat Linux IA32, gcc-3.3] [Peak=402 Mean=79] [Peak=3.4 Mean=0.8]]
[[64] [Redhat Linux IA64, gcc-3.4] [Peak=6.8 Mean=1.4] [Peak=3.4 Mean=0.78]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=6.1 Mean=1.8] [Peak=3.7 Mean=0.89]]
]
[table Errors In the Function tgamma(a,z)
[[Significand Size] [Platform and Compiler] [0.5 < a < 100
and
0.01*a < z < 100*a] [1x10[super -12] < a < 5x10[super -2]
and
0.01*a < z < 100*a]]
[[53] [Win32, Visual C++ 8] [Peak=5.9 Mean=1.5] [Peak=1.8 Mean=0.6]]
[[64] [RedHat Linux IA32, gcc-3.3] [Peak=596 Mean=116] [Peak=3.2 Mean=0.84]]
[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=40.2 Mean=2.5] [Peak=3.2 Mean=0.8]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=364 Mean=17.6] [Peak=12.7 Mean=1.8]]
]
[table_tgamma_incomplete_]
[h4 Testing]

10
doc/sf/igamma_inv.qbk
View File

@@ -105,7 +105,15 @@ they are deliberately "detuned" so as not to be too accurate: it is in
any case impossible for these function to be more accurate than the
regular forward incomplete gamma functions. In practice, the accuracy
of these functions is very similar to that of __gamma_p and __gamma_q
functions.
functions:
[table_gamma_p_inv]
[table_gamma_q_inv]
[table_gamma_p_inva]
[table_gamma_q_inva]
[h4 Testing]

9
doc/sf/jacobi_elliptic.qbk
View File

@@ -132,12 +132,11 @@ 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.
[table Errors Rates in the Jacobi Elliptic Functions
[[Significand Size] [Platform and Compiler] [u < 1] [Large u] ]
[[53] [Win32 / Visual C++ 8.0] [Peak=2 Mean=0.5] [Peak=44000 Mean=2500] ]
[[64] [Ubuntu Linux / G++ 4.7] [Peak=2.0 Mean=0.5] [Peak=25000 Mean=1500] ]
]
[table_jacobi_cn]
[table_jacobi_dn]
[table_jacobi_sn]
[heading Testing]

20
doc/sf/laguerre.qbk
View File

@@ -126,25 +126,9 @@ for various domains of input arguments.
Note that only results for the widest floating point type on the system are
given as narrower types have __zero_error.
[table Peak Errors In the Laguerre Polynomial
[[Significand Size] [Platform and Compiler] [Errors in range
[table_laguerre_n_x_]
0 < l < 20] ]
[[53] [Win32, Visual C++ 8] [Peak=3000 Mean=185] ]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=1x10[super 4] Mean=828]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=1x10[super 4] Mean=828] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=680 Mean=40]]
]
[table Peak Errors In the Associated Laguerre Polynomial
[[Significand Size] [Platform and Compiler] [Errors in range
0 < l < 20] ]
[[53] [Win32, Visual C++ 8] [Peak=433 Mean=11]]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=61.4 Mean=19.5]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=61.4 Mean=19.5] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=540 Mean=13.94] ]
]
[table_laguerre_n_m_x_]
Note that the worst errors occur when the degree increases, values greater than
~120 are very unlikely to produce sensible results, especially in the associated

38
doc/sf/legendre.qbk
View File

@@ -193,49 +193,17 @@ for various domains of input arguments.
Note that only results for the widest floating point type on the system are
given as narrower types have __zero_error.
[table Peak Errors In the Legendre P Function
[[Significand Size] [Platform and Compiler] [Errors in range
[table_legendre_p]
0 < l < 20] [Errors in range
[table_legendre_q]
20 < l < 120]]
[[53] [Win32, Visual C++ 8] [Peak=211 Mean=20] [Peak=300 Mean=33]]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=70 Mean=10] [Peak=700 Mean=60]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=70 Mean=10] [Peak=700 Mean=60]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=35 Mean=6] [Peak=292 Mean=41]]
]
[table Peak Errors In the Associated Legendre P Function
[[Significand Size] [Platform and Compiler] [Errors in range
0 < l < 20] ]
[[53] [Win32, Visual C++ 8] [Peak=1200 Mean=7]]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=80 Mean=5]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=80 Mean=5] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=42 Mean=4] ]
]
[table Peak Errors In the Legendre Q Function
[[Significand Size] [Platform and Compiler] [Errors in range
0 < l < 20] [Errors in range
20 < l < 120]]
[[53] [Win32, Visual C++ 8] [Peak=50 Mean=7] [Peak=4600 Mean=370]]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=51 Mean=8] [Peak=6000 Mean=480]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=51 Mean=8] [Peak=6000 Mean=480]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=90 Mean=10] [Peak=1700 Mean=140]]
]
[table_legendre_p_associated_]
Note that the worst errors occur when the order increases, values greater than
~120 are very unlikely to produce sensible results, especially in the associated
polynomial case when the degree is also large. Further the relative errors
are likely to grow arbitrarily large when the function is very close to a root.
No comparisons to other libraries are shown here: there appears to be only one
viable implementation method for these functions, the comparisons to other
libraries that have been run show identical error rates to those given here.
[h4 Testing]
A mixture of spot tests of values calculated using functions.wolfram.com,

63
doc/sf/lgamma.qbk
View File

@@ -50,9 +50,8 @@ 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, along with comparisons to the
__gsl, __glibc, __hpc and
__cephes libraries. Unless otherwise specified any
with various floating point types, along with comparisons to
various other libraries. Unless otherwise specified any
floating point type that is narrower than the one shown will have
__zero_error.
@@ -61,63 +60,7 @@ are very low, the lgamma function has an infinite number of irrational
roots for negative arguments: very close to these negative roots only
a low absolute error can be guaranteed.
[table
[[Significand Size] [Platform and Compiler] [Factorials and Half factorials] [Values Near Zero] [Values Near 1 or 2] [Values Near a Negative Pole]]
[[53] [Win32 Visual C++ 8]
[Peak=0.88 Mean=0.14
(GSL=33) (__cephes=1.5)]
[Peak=0.96 Mean=0.46
(GSL=5.2) (__cephes=1.1)]
[Peak=0.86 Mean=0.46
(GSL=1168) (__cephes~500000)]
[Peak=4.2 Mean=1.3
(GSL=25) (__cephes=1.6)] ]
[[64] [Linux IA32 / GCC]
[Peak=1.9 Mean=0.43
(__glibc Peak=1.7 Mean=0.49)]
[Peak=1.4 Mean=0.57
(__glibc Peak= 0.96 Mean=0.54)]
[Peak=0.86 Mean=0.35
(__glibc Peak=0.74 Mean=0.26)]
[Peak=6.0 Mean=1.8
(__glibc Peak=3.0 Mean=0.86)] ]
[[64] [Linux IA64 / GCC]
[Peak=0.99 Mean=0.12
(__glibc Peak 0)]
[Pek=1.2 Mean=0.6
(__glibc Peak 0)]
[Peak=0.86 Mean=0.16
(__glibc Peak 0)]
[Peak=2.3 Mean=0.69
(__glibc Peak 0)] ]
[[113] [HPUX IA64, aCC A.06.06]
[Peak=0.96 Mean=0.13
(__hpc Peak 0)]
[Peak=0.99 Mean=0.53
(__hpc Peak 0)]
[Peak=0.9 Mean=0.4
(__hpc Peak 0)]
[Peak=3.0 Mean=0.9
(__hpc Peak 0)] ]
]
[table_lgamma]
[h4 Testing]

2
doc/sf/owens_t.qbk
View File

@@ -68,6 +68,8 @@ where G(h) is the univariate normal with zero mean and unit variance integral fr
Over the built-in types and range tested,
errors are less than 10 * std::numeric_limits<RealType>::epsilon().
[table_owens_t]
[h4 Testing]
Test data was generated by Patefield and Tandy algorithms T1 and T4,

7
doc/sf/polygamma.qbk
View File

@@ -40,12 +40,7 @@ found on various platforms with various floating point types.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table
[[Significand Size] [Platform and Compiler] [Small-medium positive arguments] [Small-medium negative x] ]
[[53] [Win32 Visual C++ 12] [Peak=5.0 Mean=1] [Peak=1200 Mean=65]]
[[64] [Win64 Mingw GCC] [Peak=16 Mean=3] [Peak=33 Mean=3] ]
[[113] [Win64 Mingw GCC __float128] [Peak=6.5 Mean=1][Peak=30 Mean=4] ]
]
[table_polygamma]
As shown above, error rates are generally very acceptable for moderately sized
arguments. Error rates should stay low for exact inputs, however, please note that the

14
doc/sf/powers.qbk
View File

@@ -25,6 +25,8 @@ the return is `double` when /x/ is an integer type and T otherwise.
This function performs exact all-integer arithmetic argument reduction before computing the sine of ['[pi]x].
[table_sin_pi]
[endsect]
[section:cos_pi cos_pi]
@@ -52,6 +54,8 @@ the return is `double` when /x/ is an integer type and T otherwise.
This function performs exact all-integer arithmetic argument reduction before computing the cosine of ['[pi]x].
[table_cos_pi]
[endsect]
[section:log1p log1p]
@@ -107,6 +111,8 @@ The following graph illustrates the behaviour of log1p:
For built in floating point types `log1p`
should have approximately 1 epsilon accuracy.
[table_log1p]
[h4 Testing]
A mixture of spot test sanity checks, and random high precision test values
@@ -155,6 +161,8 @@ The following graph illustrates the behaviour of expm1:
For built in floating point types `expm1`
should have approximately 1 epsilon accuracy.
[table_expm1]
[h4 Testing]
A mixture of spot test sanity checks, and random high precision test values
@@ -196,6 +204,8 @@ The following graph illustrates the behaviour of cbrt:
For built in floating-point types `cbrt`
should have approximately 2 epsilon accuracy.
[table_cbrt]
[h4 Testing]
A mixture of spot test sanity checks, and random high precision test values
@@ -240,6 +250,8 @@ The following graph illustrates the behaviour of sqrt1pm1:
For built in floating-point types `sqrt1pm1`
should have approximately 3 epsilon accuracy.
[table_sqrt1pm1]
[h4 Testing]
A selection of random high precision test values
@@ -283,6 +295,8 @@ The following graph illustrates the behaviour of powm1:
Should have approximately 2-3 epsilon accuracy.
[table_powm1]
[h4 Testing]
A selection of random high precision test values

10
doc/sf/spherical_harmonic.qbk
View File

@@ -107,15 +107,9 @@ roots of the associated Legendre function.
All values are in units of epsilon.
[table Peak Errors In the Sperical Harmonic Functions
[[Significand Size] [Platform and Compiler] [Errors in range
[table_spherical_harmonic_r]
0 < l < 20] ]
[[53] [Win32, Visual C++ 8] [Peak=2x10[super 4] Mean=700] ]
[[64] [SUSE Linux IA32, g++ 4.1] [Peak=2900 Mean=100]]
[[64] [Red Hat Linux IA64, g++ 3.4.4] [Peak=2900 Mean=100] ]
[[113] [HPUX IA64, aCC A.06.06] [Peak=6700 Mean=230]]
]
[table_spherical_harmonic_i]
Note that the worst errors occur when the degree increases, values greater than
~120 are very unlikely to produce sensible results, especially

66
doc/sf/tgamma.qbk
View File

@@ -71,73 +71,13 @@ the result is `double` when T is an integer type, and T otherwise.
The following table shows the peak errors (in units of epsilon)
found on various platforms with various floating point types,
along with comparisons to the __gsl, __glibc, __hpc and __cephes libraries.
along with comparisons to other common libraries.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table
[[Significand Size] [Platform and Compiler] [Factorials and Half factorials] [Values Near Zero] [Values Near 1 or 2] [Values Near a Negative Pole]]
[[53] [Win32 Visual C++ 8]
[Peak=1.9 Mean=0.7
[table_tgamma]
(GSL=3.9)
(__cephes=3.0)]
[Peak=2.0 Mean=1.1
(GSL=4.5)
(__cephes=1)]
[Peak=2.0 Mean=1.1
(GSL=7.9)
(__cephes=1.0)]
[Peak=2.6 Mean=1.3
(GSL=2.5)
(__cephes=2.7)] ]
[[64] [Linux IA32 / GCC]
[Peak=300 Mean=49.5
(__glibc Peak=395 Mean=89)]
[Peak=3.0 Mean=1.4
(__glibc Peak=11 Mean=3.3)]
[Peak=5.0 Mean=1.8
(__glibc Peak=0.92 Mean=0.2)]
[Peak=157 Mean=65
(__glibc Peak=205 Mean=108)] ]
[[64] [Linux IA64 / GCC]
[__glibc Peak 2.8 Mean=0.9
(__glibc Peak 0.7)]
[Peak=4.8 Mean=1.5
(__glibc Peak 0)]
[Peak=4.8 Mean=1.5
(__glibc Peak 0)]
[Peak=5.0 Mean=1.7
(__glibc Peak 0)] ]
[[113] [HPUX IA64, aCC A.06.06]
[Peak=2.5 Mean=1.1
(__hpc Peak 0)]
[Peak=3.5 Mean=1.7
(__hpc Peak 0)]
[Peak=3.5 Mean=1.6
(__hpc Peak 0)]
[Peak=5.2 Mean=1.92
(__hpc Peak 0)] ]
]
[table_tgamma1pm1]
[h4 Testing]

7
doc/sf/trigamma.qbk
View File

@@ -37,12 +37,7 @@ found on various platforms with various floating point types.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table
[[Significand Size] [Platform and Compiler] [Random Values] ]
[[53] [Win32 Visual C++ 12] [Peak=1.0 Mean=0.4] ]
[[64] [Win64 Mingw GCC] [Peak=1.4 Mean=0.4] ]
[[113] [Win64 Mingw GCC __float128] [Peak=1.0 Mean=0.5] ]
]
[table_trigamma]
As shown above, error rates are generally very low for built in types.
For multiprecision types, error rates are typically in the order of a

18
doc/sf/zeta.qbk
View File

@@ -46,23 +46,7 @@ along with comparisons to the __gsl and __cephes libraries.
Unless otherwise specified any floating point type that is narrower
than the one shown will have __zero_error.
[table Errors In the Function zeta(z)
[[Significand Size] [Platform and Compiler] [z > 0][z < 0]]
[[53] [Win32, Visual C++ 8] [Peak=0.99 Mean=0.1
GSL Peak=8.7 Mean=1.0
__cephes Peak=2.1 Mean=1.1
] [Peak=7.1 Mean=3.0
GSL Peak=137 Mean=14
__cephes Peak=5084 Mean=470
]]
[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=0.99 Mean=0.5] [Peak=570 Mean=60]]
[[64] [Redhat Linux IA64, gcc-4.1] [Peak=0.99 Mean=0.5] [Peak=559 Mean=56]]
[[113] [HPUX IA64, aCC A.06.06] [Peak=1.0 Mean=0.4] [Peak=1018 Mean=79]]
]
[table_zeta]
[h4 Testing]

3379
reporting/accuracy/doc/accuracy_tables.qbk
View File

File diff suppressed because one or more lines are too long

2
reporting/accuracy/handle_test_result.hpp
View File

@@ -424,7 +424,7 @@ void handle_test_result(const boost::math::tools::test_result<T>& result,
std::stringstream ss;
ss << std::setprecision(3);
if(std::string(TEST_LIBRARY_NAME) != "boost")
ss << "(" << TEST_LIBRARY_NAME << " = ";
ss << "(['" << TEST_LIBRARY_NAME << ":] ";
else
ss << "[role blue ";

12983
reporting/accuracy/html/index.html
View File

File diff suppressed because it is too large Load Diff

4
reporting/accuracy/test_jacobi_zeta.cpp
View File

@@ -5,8 +5,8 @@
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include "bindings.hpp"
#include "../../test/test_jacobi.hpp"
#include <boost/math/special_functions/jacobi_elliptic.hpp>
#include "../../test/test_jacobi_zeta.hpp"
#include <boost/math/special_functions/jacobi_zeta.hpp>
BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
{

10
reporting/accuracy/test_laguerre.cpp
View File

@@ -16,7 +16,7 @@ BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
#ifdef TYPE_TO_TEST
test_spots(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
test_laguerre(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
#else
bool test_float = false;
@@ -46,13 +46,13 @@ BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
#endif
if(test_float)
test_spots(0.0f, "float");
test_laguerre(0.0f, "float");
if(test_double)
test_spots(0.0, "double");
test_laguerre(0.0, "double");
if(test_long_double)
test_spots(0.0L, "long double");
test_laguerre(0.0L, "long double");
#ifdef BOOST_MATH_USE_FLOAT128
//test_spots(0.0Q, "__float128");
//test_laguerre(0.0Q, "__float128");
#endif

2
test/test_ibeta_inv_ab.hpp
View File

@@ -197,6 +197,7 @@ void test_beta(T, const char* name)
test_inverses<T>(ibeta_large_data);
#endif
#endif
#if !defined(TEST_REAL_CONCEPT) || defined(FULL_TEST) || (TEST_DATA == 4)
if(boost::is_floating_point<T>::value){
@@ -211,6 +212,5 @@ void test_beta(T, const char* name)
test_inverses2<T>(ibeta_inva_data, name, "Inverse incomplete beta");
}
#endif
#endif
}