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27 <a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error
28 Rates for all Functions</a>
29 </h3></div></div></div>
31 <a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table 17.3. Error rates for beta</b></p>
32 <div class="table-contents"><table class="table" summary="Error rates for beta">
45 Microsoft Visual C++ version 12.0<br> Win32<br> double
50 GNU C++ version 5.1.0<br> linux<br> long double
55 GNU C++ version 5.1.0<br> linux<br> double
60 Sun compiler version 0x5130<br> Sun Solaris<br> long double
68 Beta Function: Small Values
73 <span class="blue">Max = 1.75ε (Mean = 0.828ε)</span>
78 <span class="blue">Max = 2.65ε (Mean = 1.22ε)</span><br> <br>
79 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 11.9ε (Mean = 7.03ε))
84 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
85 1.16:</em></span> Max = 3.94ε (Mean = 1.44ε))<br> (<span class="emphasis"><em>Rmath
86 3.0.2:</em></span> Max = 1.14ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
87 Max = 1.97ε (Mean = 0.934ε))
92 <span class="blue">Max = 2.86ε (Mean = 1.31ε)</span>
99 Beta Function: Medium Values
104 <span class="blue">Max = 99.1ε (Mean = 22.4ε)</span>
109 <span class="blue">Max = 60.4ε (Mean = 19.4ε)</span><br> <br>
110 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.07e+03ε (Mean =
116 <span class="blue">Max = 0.978ε (Mean = 0.0578ε)</span><br>
117 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
118 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.09e+03ε (Mean = 265ε))<br>
119 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.5e+03ε (Mean = 329ε))
124 <span class="blue">Max = 107ε (Mean = 24.5ε)</span>
131 Beta Function: Divergent Values
136 <span class="blue">Max = 10.7ε (Mean = 2.22ε)</span>
141 <span class="blue">Max = 10.3ε (Mean = 2.41ε)</span><br> <br>
142 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
147 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
148 1.16:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath
149 3.0.2:</em></span> Max = 176ε (Mean = 28ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
150 Max = 175ε (Mean = 22ε))
155 <span class="blue">Max = 19.7ε (Mean = 2.75ε)</span>
162 <br class="table-break"><div class="table">
163 <a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table 17.4. Error rates for beta (incomplete)</b></p>
164 <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
177 Microsoft Visual C++ version 12.0<br> Win32<br> double
182 GNU C++ version 5.1.0<br> linux<br> double
187 GNU C++ version 5.1.0<br> linux<br> long double
192 Sun compiler version 0x5130<br> Sun Solaris<br> long double
200 Incomplete Beta Function: Small Values
205 <span class="blue">Max = 11.1ε (Mean = 2.28ε)</span>
210 <span class="blue">Max = 0ε (Mean = 0ε)</span>
215 <span class="blue">Max = 12.5ε (Mean = 2.01ε)</span>
220 <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
227 Incomplete Beta Function: Medium Values
232 <span class="blue">Max = 91.1ε (Mean = 12.7ε)</span>
237 <span class="blue">Max = 0.568ε (Mean = 0.0342ε)</span>
242 <span class="blue">Max = 67.1ε (Mean = 13.3ε)</span>
247 <span class="blue">Max = 174ε (Mean = 25ε)</span>
254 Incomplete Beta Function: Large and Diverse Values
259 <span class="blue">Max = 635ε (Mean = 29.5ε)</span>
264 <span class="blue">Max = 0.999ε (Mean = 0.0399ε)</span>
269 <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
274 <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
281 Incomplete Beta Function: Small Integer Values
286 <span class="blue">Max = 26.8ε (Mean = 6.61ε)</span>
291 <span class="blue">Max = 0.786ε (Mean = 0.0248ε)</span>
296 <span class="blue">Max = 10.2ε (Mean = 3.49ε)</span>
301 <span class="blue">Max = 51.8ε (Mean = 11ε)</span>
308 <br class="table-break"><div class="table">
309 <a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table 17.5. Error rates for betac</b></p>
310 <div class="table-contents"><table class="table" summary="Error rates for betac">
323 Microsoft Visual C++ version 12.0<br> Win32<br> double
328 GNU C++ version 5.1.0<br> linux<br> double
333 GNU C++ version 5.1.0<br> linux<br> long double
338 Sun compiler version 0x5130<br> Sun Solaris<br> long double
346 Incomplete Beta Function: Small Values
351 <span class="blue">Max = 12ε (Mean = 2.43ε)</span>
356 <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
361 <span class="blue">Max = 7.75ε (Mean = 1.91ε)</span>
366 <span class="blue">Max = 12.6ε (Mean = 3.02ε)</span>
373 Incomplete Beta Function: Medium Values
378 <span class="blue">Max = 91.3ε (Mean = 14.8ε)</span>
383 <span class="blue">Max = 0.949ε (Mean = 0.0944ε)</span>
388 <span class="blue">Max = 63.5ε (Mean = 13.4ε)</span>
393 <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
400 Incomplete Beta Function: Large and Diverse Values
405 <span class="blue">Max = 3.72e+003ε (Mean = 113ε)</span>
410 <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
415 <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
420 <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
427 Incomplete Beta Function: Small Integer Values
432 <span class="blue">Max = 26.7ε (Mean = 6.67ε)</span>
437 <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
442 <span class="blue">Max = 10.4ε (Mean = 3.54ε)</span>
447 <span class="blue">Max = 103ε (Mean = 17.4ε)</span>
454 <br class="table-break"><div class="table">
455 <a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table 17.6. Error rates for binomial_coefficient</b></p>
456 <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
469 Microsoft Visual C++ version 12.0<br> Win32<br> double
474 GNU C++ version 5.1.0<br> linux<br> double
479 GNU C++ version 5.1.0<br> linux<br> long double
484 Sun compiler version 0x5130<br> Sun Solaris<br> long double
492 Binomials: small arguments
497 <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
502 <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
507 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
512 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
519 Binomials: large arguments
524 <span class="blue">Max = 24.3ε (Mean = 6.3ε)</span>
529 <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
534 <span class="blue">Max = 26ε (Mean = 6.09ε)</span>
539 <span class="blue">Max = 54.1ε (Mean = 10.9ε)</span>
546 <br class="table-break"><div class="table">
547 <a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table 17.7. Error rates for cbrt</b></p>
548 <div class="table-contents"><table class="table" summary="Error rates for cbrt">
561 Microsoft Visual C++ version 12.0<br> Win32<br> double
566 GNU C++ version 5.1.0<br> linux<br> double
571 GNU C++ version 5.1.0<br> linux<br> long double
576 Sun compiler version 0x5130<br> Sun Solaris<br> long double
588 <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
589 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
594 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span>
595 Max = 0ε (Mean = 0ε))
600 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
601 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
602 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
607 <span class="blue">Max = 1.11ε (Mean = 0.424ε)</span><br> <br>
608 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.11ε (Mean = 0.424ε))
614 <br class="table-break"><div class="table">
615 <a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table 17.8. Error rates for cos_pi</b></p>
616 <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
629 Microsoft Visual C++ version 12.0<br> Win32<br> double
634 GNU C++ version 5.1.0<br> linux<br> double
639 GNU C++ version 5.1.0<br> linux<br> long double
644 Sun compiler version 0x5130<br> Sun Solaris<br> long double
657 <span class="blue">Max = 0.996ε (Mean = 0.281ε)</span>
662 <span class="blue">Max = 0ε (Mean = 0ε)</span>
667 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
672 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
679 sin_pi and cos_pi near integers and half integers
684 <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
689 <span class="blue">Max = 0ε (Mean = 0ε)</span>
694 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
699 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
706 <br class="table-break"><div class="table">
707 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table 17.9. Error rates for cyl_bessel_i</b></p>
708 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
721 Microsoft Visual C++ version 12.0<br> Win32<br> double
726 GNU C++ version 5.1.0<br> linux<br> long double
731 GNU C++ version 5.1.0<br> linux<br> double
736 Sun compiler version 0x5130<br> Sun Solaris<br> long double
744 Bessel I0: Mathworld Data
749 <span class="blue">Max = 0.877ε (Mean = 0.549ε)</span>
754 <span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br>
755 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε)
756 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I0_Mathworld_Data">And
762 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
763 1.16:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I0_Mathworld_Data">And
764 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
765 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I0_Mathworld_Data">And
766 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
767 <span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I0_Mathworld_Data">And
768 other failures.</a>)</span>
773 <span class="blue">Max = 4.54ε (Mean = 2.11ε)</span>
780 Bessel I1: Mathworld Data
785 <span class="blue">Max = 0.885ε (Mean = 0.55ε)</span>
790 <span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br>
791 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε)
792 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I1_Mathworld_Data">And
798 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
799 1.16:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I1_Mathworld_Data">And
800 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
801 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I1_Mathworld_Data">And
802 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
803 <span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I1_Mathworld_Data">And
804 other failures.</a>)</span>
809 <span class="blue">Max = 6.52ε (Mean = 2.25ε)</span>
816 Bessel In: Mathworld Data
821 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
826 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
827 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε)
828 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_In_Mathworld_Data">And
834 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
835 1.16:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Mathworld_Data">And
836 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
837 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_In_Mathworld_Data">And
838 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
839 <span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_In_Mathworld_Data">And
840 other failures.</a>)</span>
845 <span class="blue">Max = 463ε (Mean = 140ε)</span>
852 Bessel Iv: Mathworld Data
857 <span class="blue">Max = 2.97ε (Mean = 1.33ε)</span>
862 <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
863 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 616ε (Mean = 221ε)
864 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data">And
870 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
871 1.16:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data">And
872 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
873 Max = 1e+04ε (Mean = 3.18e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
874 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Mathworld_Data">And
875 other failures.</a>)</span>
880 <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
887 Bessel In: Random Data
892 <span class="blue">Max = 9.67ε (Mean = 1.89ε)</span>
897 <span class="blue">Max = 6.79ε (Mean = 1.15ε)</span><br> <br>
898 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 645ε (Mean = 132ε))
903 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
904 1.16:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Random_Data">And
905 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
906 Max = 7.37ε (Mean = 2.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
907 = 4.22e+06ε (Mean = 2.26e+05ε))
912 <span class="blue">Max = 176ε (Mean = 39.2ε)</span>
919 Bessel Iv: Random Data
924 <span class="blue">Max = 7.46ε (Mean = 1.54ε)</span>
929 <span class="blue">Max = 8.35ε (Mean = 1.49ε)</span><br> <br>
930 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.05e+03ε (Mean =
931 224ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Random_Data">And
937 <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br>
938 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε)
939 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Random_Data">And
940 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
941 <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span><br>
942 (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 6e+30ε (Mean
943 = 4e+29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Random_Data">And
944 other failures.</a>)</span>
949 <span class="blue">Max = 283ε (Mean = 88.4ε)</span>
956 Bessel Iv: Mathworld Data (large values)
961 <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
966 <span class="blue">Max = 14.7ε (Mean = 6.57ε)</span><br> <br>
967 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 118ε (Mean = 57.2ε)
968 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data_large_values_">And
974 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
975 1.16:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data_large_values_">And
976 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
977 <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_Iv_Mathworld_Data_large_values_">And
978 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
979 Max = 73.7ε (Mean = 58.5ε))
984 <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
991 <br class="table-break"><div class="table">
992 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 17.10. Error rates for cyl_bessel_i (integer orders)</b></p>
993 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
1006 Microsoft Visual C++ version 12.0<br> Win32<br> double
1011 GNU C++ version 5.1.0<br> linux<br> long double
1016 GNU C++ version 5.1.0<br> linux<br> double
1021 Sun compiler version 0x5130<br> Sun Solaris<br> long double
1029 Bessel I0: Mathworld Data (Integer Version)
1034 <span class="blue">Max = 0.877ε (Mean = 0.549ε)</span>
1039 <span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br>
1040 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε)
1041 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
1042 other failures.</a>)
1047 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1048 1.16:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
1049 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I0_Mathworld_Data_Integer_Version_">And
1050 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1051 <span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I0_Mathworld_Data_Integer_Version_">And
1052 other failures.</a>)</span>
1057 <span class="blue">Max = 4.54ε (Mean = 2.11ε)</span>
1064 Bessel I1: Mathworld Data (Integer Version)
1069 <span class="blue">Max = 0.885ε (Mean = 0.55ε)</span>
1074 <span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br>
1075 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε)
1076 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
1077 other failures.</a>)
1082 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1083 1.16:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
1084 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I1_Mathworld_Data_Integer_Version_">And
1085 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1086 <span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I1_Mathworld_Data_Integer_Version_">And
1087 other failures.</a>)</span>
1092 <span class="blue">Max = 6.52ε (Mean = 2.25ε)</span>
1099 Bessel In: Mathworld Data (Integer Version)
1104 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
1109 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
1110 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε)
1111 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
1112 other failures.</a>)
1117 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1118 1.16:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_1_16_Bessel_In_Mathworld_Data_Integer_Version_">And
1119 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1120 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_In_Mathworld_Data_Integer_Version_">And
1121 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1122 <span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_In_Mathworld_Data_Integer_Version_">And
1123 other failures.</a>)</span>
1128 <span class="blue">Max = 463ε (Mean = 140ε)</span>
1135 <br class="table-break"><div class="table">
1136 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 17.11. Error rates for cyl_bessel_i_prime</b></p>
1137 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
1150 Microsoft Visual C++ version 12.0<br> Win32<br> double
1155 GNU C++ version 5.1.0<br> linux<br> double
1160 GNU C++ version 5.1.0<br> linux<br> long double
1165 Sun compiler version 0x5130<br> Sun Solaris<br> long double
1173 Bessel I'0: Mathworld Data
1178 <span class="blue">Max = 0.885ε (Mean = 0.567ε)</span>
1183 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1188 <span class="blue">Max = 7.83ε (Mean = 2.84ε)</span>
1193 <span class="blue">Max = 6.52ε (Mean = 2.26ε)</span>
1200 Bessel I'1: Mathworld Data
1205 <span class="blue">Max = 1.61ε (Mean = 0.786ε)</span>
1210 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1215 <span class="blue">Max = 2.3ε (Mean = 1.28ε)</span>
1220 <span class="blue">Max = 2.3ε (Mean = 1.29ε)</span>
1227 Bessel I'n: Mathworld Data
1232 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
1237 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1242 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
1247 <span class="blue">Max = 701ε (Mean = 212ε)</span>
1254 Bessel I'v: Mathworld Data
1259 <span class="blue">Max = 3.76e+003ε (Mean = 1.19e+003ε)</span>
1264 <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
1269 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
1274 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
1281 Bessel I'n: Random Data
1286 <span class="blue">Max = 9.85ε (Mean = 1.83ε)</span>
1291 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1296 <span class="blue">Max = 6.79ε (Mean = 1.13ε)</span>
1301 <span class="blue">Max = 195ε (Mean = 37.1ε)</span>
1308 Bessel I'v: Random Data
1313 <span class="blue">Max = 14ε (Mean = 2.46ε)</span>
1318 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1323 <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
1328 <span class="blue">Max = 336ε (Mean = 68.5ε)</span>
1335 Bessel I'v: Mathworld Data (large values)
1340 <span class="blue">Max = 59.5ε (Mean = 26.8ε)</span>
1345 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1350 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
1355 <span class="blue">Max = 43.9ε (Mean = 20.7ε)</span>
1362 <br class="table-break"><div class="table">
1363 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 17.12. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
1364 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
1377 Microsoft Visual C++ version 12.0<br> Win32<br> double
1382 GNU C++ version 5.1.0<br> linux<br> double
1387 GNU C++ version 5.1.0<br> linux<br> long double
1392 Sun compiler version 0x5130<br> Sun Solaris<br> long double
1400 Bessel I'0: Mathworld Data (Integer Version)
1405 <span class="blue">Max = 0.885ε (Mean = 0.567ε)</span>
1410 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1415 <span class="blue">Max = 7.83ε (Mean = 2.84ε)</span>
1420 <span class="blue">Max = 6.52ε (Mean = 2.26ε)</span>
1427 Bessel I'1: Mathworld Data (Integer Version)
1432 <span class="blue">Max = 1.61ε (Mean = 0.786ε)</span>
1437 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1442 <span class="blue">Max = 2.3ε (Mean = 1.28ε)</span>
1447 <span class="blue">Max = 2.3ε (Mean = 1.29ε)</span>
1454 Bessel I'n: Mathworld Data (Integer Version)
1459 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
1464 <span class="blue">Max = 0ε (Mean = 0ε)</span>
1469 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
1474 <span class="blue">Max = 701ε (Mean = 212ε)</span>
1481 <br class="table-break"><div class="table">
1482 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table 17.13. Error rates for cyl_bessel_j</b></p>
1483 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
1496 Microsoft Visual C++ version 12.0<br> Win32<br> double
1501 GNU C++ version 5.1.0<br> linux<br> long double
1506 GNU C++ version 5.1.0<br> linux<br> double
1511 Sun compiler version 0x5130<br> Sun Solaris<br> long double
1519 Bessel J0: Mathworld Data
1524 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
1529 <span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br>
1530 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε)
1531 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J0_Mathworld_Data">And
1532 other failures.</a>)
1537 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1538 1.16:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J0_Mathworld_Data">And
1539 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1540 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J0_Mathworld_Data">And
1541 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1542 Max = 1.12ε (Mean = 0.568ε))
1547 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
1554 Bessel J0: Mathworld Data (Tricky cases)
1559 <span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span>
1564 <span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br>
1565 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean
1571 <span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br>
1572 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
1573 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br>
1574 (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean
1575 = 1.04e+08ε))</span>
1580 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
1587 Bessel J1: Mathworld Data
1592 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
1597 <span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br>
1598 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε)
1599 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J1_Mathworld_Data">And
1600 other failures.</a>)
1605 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1606 1.16:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J1_Mathworld_Data">And
1607 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1608 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J1_Mathworld_Data">And
1609 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1610 Max = 2.88ε (Mean = 1.12ε))
1615 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
1622 Bessel J1: Mathworld Data (tricky cases)
1627 <span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span>
1632 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
1633 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean
1639 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
1640 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
1641 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br>
1642 (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε))
1647 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
1654 Bessel JN: Mathworld Data
1659 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
1664 <span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br>
1665 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
1666 = 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_JN_Mathworld_Data">And
1667 other failures.</a>)</span>
1672 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1673 1.16:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_JN_Mathworld_Data">And
1674 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1675 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_JN_Mathworld_Data">And
1676 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1677 Max = 5.53e+05ε (Mean = 1.9e+05ε))
1682 <span class="blue">Max = 463ε (Mean = 112ε)</span>
1689 Bessel J: Mathworld Data
1694 <span class="blue">Max = 14.9ε (Mean = 3.82ε)</span>
1699 <span class="blue">Max = 14.7ε (Mean = 4.05ε)</span><br> <br>
1700 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.49e+05ε (Mean =
1701 7.89e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data">And
1702 other failures.</a>)
1707 <span class="blue">Max = 10ε (Mean = 2.19ε)</span><br> <br>
1708 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.39e+05ε (Mean = 5.24e+04ε)
1709 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data">And
1710 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1711 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J_Mathworld_Data">And
1712 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1713 Max = 5.47e+05ε (Mean = 1.3e+05ε))
1718 <span class="blue">Max = 14.7ε (Mean = 4.12ε)</span>
1725 Bessel J: Mathworld Data (large values)
1730 <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
1735 <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br>
1736 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 34.9ε (Mean = 17.4ε)
1737 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data_large_values_">And
1738 other failures.</a>)
1743 <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
1744 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε)
1745 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data_large_values_">And
1746 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1747 Max = 35.9ε (Mean = 18.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Cephes_Bessel_J_Mathworld_Data_large_values_">And
1748 other failures.</a>)</span>
1753 <span class="blue">Max = 607ε (Mean = 305ε)</span>
1760 Bessel JN: Random Data
1765 <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
1770 <span class="blue">Max = 50.8ε (Mean = 4.15ε)</span><br> <br>
1771 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.12e+03ε (Mean =
1777 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1778 1.16:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath
1779 3.0.2:</em></span> Max = 3.93ε (Mean = 1.22ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
1780 Max = 91.4ε (Mean = 6.47ε))
1785 <span class="blue">Max = 99.6ε (Mean = 22ε)</span>
1792 Bessel J: Random Data
1797 <span class="blue">Max = 9.24ε (Mean = 1.36ε)</span>
1802 <span class="blue">Max = 9.81ε (Mean = 1.59ε)</span><br> <br>
1803 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
1808 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1809 1.16:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Random_Data">And
1810 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1811 Max = 6.74ε (Mean = 1.3ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
1812 = 16.7ε (Mean = 2.5ε))
1817 <span class="blue">Max = 260ε (Mean = 34ε)</span>
1824 Bessel J: Random Data (Tricky large values)
1829 <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
1834 <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
1835 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
1836 = 5.01e+17ε (Mean = 6.23e+16ε))</span>
1841 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1842 1.16:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
1843 3.0.2:</em></span> Max = 71.6ε (Mean = 11.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
1844 Max = 2.48e+05ε (Mean = 3.02e+04ε))
1849 <span class="blue">Max = 785ε (Mean = 97.4ε)</span>
1856 <br class="table-break"><div class="table">
1857 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 17.14. Error rates for cyl_bessel_j (integer orders)</b></p>
1858 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
1871 Microsoft Visual C++ version 12.0<br> Win32<br> double
1876 GNU C++ version 5.1.0<br> linux<br> long double
1881 GNU C++ version 5.1.0<br> linux<br> double
1886 Sun compiler version 0x5130<br> Sun Solaris<br> long double
1894 Bessel J0: Mathworld Data (Integer Version)
1899 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
1900 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
1905 <span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br>
1906 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε)
1907 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
1908 other failures.</a>)
1913 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1914 1.16:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
1915 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J0_Mathworld_Data_Integer_Version_">And
1916 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1917 Max = 1.12ε (Mean = 0.568ε))
1922 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
1929 Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
1934 <span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span><br>
1935 <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
1936 = 2.54e+008ε (Mean = 1.04e+008ε))</span>
1941 <span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br>
1942 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean
1948 <span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br>
1949 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
1950 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br>
1951 (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean
1952 = 1.04e+08ε))</span>
1957 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
1964 Bessel J1: Mathworld Data (Integer Version)
1969 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
1970 (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
1975 <span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br>
1976 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε)
1977 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
1978 other failures.</a>)
1983 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
1984 1.16:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
1985 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J1_Mathworld_Data_Integer_Version_">And
1986 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1987 Max = 2.88ε (Mean = 1.12ε))
1992 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
1999 Bessel J1: Mathworld Data (tricky cases) (Integer Version)
2004 <span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span><br>
2005 <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+007ε (Mean
2011 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
2012 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean
2018 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
2019 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
2020 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br>
2021 (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε))
2026 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
2033 Bessel JN: Mathworld Data (Integer Version)
2038 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
2039 (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max =
2040 +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
2041 other failures.</a>)</span>
2046 <span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br>
2047 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
2048 = 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
2049 other failures.</a>)</span>
2054 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2055 1.16:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_1_16_Bessel_JN_Mathworld_Data_Integer_Version_">And
2056 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2057 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_JN_Mathworld_Data_Integer_Version_">And
2058 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
2059 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Cephes_Bessel_JN_Mathworld_Data_Integer_Version_">And
2060 other failures.</a>)</span>
2065 <span class="blue">Max = 463ε (Mean = 112ε)</span>
2072 <br class="table-break"><div class="table">
2073 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 17.15. Error rates for cyl_bessel_j_prime</b></p>
2074 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
2087 Microsoft Visual C++ version 12.0<br> Win32<br> double
2092 GNU C++ version 5.1.0<br> linux<br> double
2097 GNU C++ version 5.1.0<br> linux<br> long double
2102 Sun compiler version 0x5130<br> Sun Solaris<br> long double
2110 Bessel J0': Mathworld Data
2115 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
2120 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2125 <span class="blue">Max = 18.9ε (Mean = 6.81ε)</span>
2130 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
2137 Bessel J0': Mathworld Data (Tricky cases)
2142 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
2147 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2152 <span class="blue">Max = 8.08ε (Mean = 4.57ε)</span>
2157 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
2164 Bessel J1': Mathworld Data
2169 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
2174 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2179 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
2184 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
2191 Bessel J1': Mathworld Data (tricky cases)
2196 <span class="blue">Max = 288ε (Mean = 129ε)</span>
2201 <span class="blue">Max = 287ε (Mean = 129ε)</span>
2206 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
2211 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
2218 Bessel JN': Mathworld Data
2223 <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
2228 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
2233 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
2238 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
2245 Bessel J': Mathworld Data
2250 <span class="blue">Max = 23.7ε (Mean = 8.01ε)</span>
2255 <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
2260 <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
2265 <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
2272 Bessel J': Mathworld Data (large values)
2277 <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
2282 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2287 <span class="blue">Max = 989ε (Mean = 495ε)</span>
2292 <span class="blue">Max = 989ε (Mean = 495ε)</span>
2299 Bessel JN': Random Data
2304 <span class="blue">Max = 6.34ε (Mean = 0.997ε)</span>
2309 <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
2314 <span class="blue">Max = 17.3ε (Mean = 2.47ε)</span>
2319 <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
2326 Bessel J': Random Data
2331 <span class="blue">Max = 176ε (Mean = 9.76ε)</span>
2336 <span class="blue">Max = 0.885ε (Mean = 0.0457ε)</span>
2341 <span class="blue">Max = 139ε (Mean = 6.47ε)</span>
2346 <span class="blue">Max = 279ε (Mean = 27.2ε)</span>
2353 Bessel J': Random Data (Tricky large values)
2358 <span class="blue">Max = 379ε (Mean = 45.4ε)</span>
2363 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2368 <span class="blue">Max = 474ε (Mean = 62.2ε)</span>
2373 <span class="blue">Max = 474ε (Mean = 64.5ε)</span>
2380 <br class="table-break"><div class="table">
2381 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 17.16. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
2382 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
2395 Microsoft Visual C++ version 12.0<br> Win32<br> double
2400 GNU C++ version 5.1.0<br> linux<br> double
2405 GNU C++ version 5.1.0<br> linux<br> long double
2410 Sun compiler version 0x5130<br> Sun Solaris<br> long double
2418 Bessel J0': Mathworld Data (Integer Version)
2423 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
2428 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2433 <span class="blue">Max = 18.9ε (Mean = 6.81ε)</span>
2438 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
2445 Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
2450 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
2455 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2460 <span class="blue">Max = 8.08ε (Mean = 4.57ε)</span>
2465 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
2472 Bessel J1': Mathworld Data (Integer Version)
2477 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
2482 <span class="blue">Max = 0ε (Mean = 0ε)</span>
2487 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
2492 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
2499 Bessel J1': Mathworld Data (tricky cases) (Integer Version)
2504 <span class="blue">Max = 288ε (Mean = 129ε)</span>
2509 <span class="blue">Max = 287ε (Mean = 129ε)</span>
2514 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
2519 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
2526 Bessel JN': Mathworld Data (Integer Version)
2531 <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
2536 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
2541 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
2546 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
2553 <br class="table-break"><div class="table">
2554 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table 17.17. Error rates for cyl_bessel_k</b></p>
2555 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
2568 Microsoft Visual C++ version 12.0<br> Win32<br> double
2573 GNU C++ version 5.1.0<br> linux<br> long double
2578 GNU C++ version 5.1.0<br> linux<br> double
2583 Sun compiler version 0x5130<br> Sun Solaris<br> long double
2591 Bessel K0: Mathworld Data
2596 <span class="blue">Max = 1.55ε (Mean = 0.837ε)</span>
2601 <span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br>
2602 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
2607 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2608 1.16:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath
2609 3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε))
2614 <span class="blue">Max = 4.16ε (Mean = 1.49ε)</span>
2621 Bessel K1: Mathworld Data
2626 <span class="blue">Max = 1ε (Mean = 0.573ε)</span>
2631 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br>
2632 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
2637 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2638 1.16:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath
2639 3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε))
2644 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
2651 Bessel Kn: Mathworld Data
2656 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
2661 <span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br>
2662 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε)
2663 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kn_Mathworld_Data">And
2664 other failures.</a>)
2669 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2670 1.16:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Mathworld_Data">And
2671 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2672 Max = 8.48ε (Mean = 2.98ε))
2677 <span class="blue">Max = 4.48ε (Mean = 1.98ε)</span>
2684 Bessel Kv: Mathworld Data
2689 <span class="blue">Max = 4.78ε (Mean = 2.2ε)</span>
2694 <span class="blue">Max = 3.58ε (Mean = 2.44ε)</span><br> <br>
2695 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13ε (Mean = 4.81ε)
2696 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data">And
2697 other failures.</a>)
2702 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2703 1.16:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data">And
2704 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2705 Max = 3.15ε (Mean = 1.35ε))
2710 <span class="blue">Max = 3.58ε (Mean = 2.29ε)</span>
2717 Bessel Kv: Mathworld Data (large values)
2722 <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
2727 <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br>
2728 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 42.3ε (Mean = 19.8ε)
2729 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data_large_values_">And
2730 other failures.</a>)
2735 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2736 1.16:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data_large_values_">And
2737 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2738 Max = 84.6ε (Mean = 37.8ε))
2743 <span class="blue">Max = 43.1ε (Mean = 21.3ε)</span>
2750 Bessel Kn: Random Data
2755 <span class="blue">Max = 7.47ε (Mean = 1.4ε)</span>
2760 <span class="blue">Max = 4.55ε (Mean = 1.09ε)</span><br> <br>
2761 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
2766 <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br>
2767 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.71ε (Mean = 1.76ε)
2768 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Random_Data">And
2769 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2770 Max = 7.47ε (Mean = 1.34ε))
2775 <span class="blue">Max = 4.55ε (Mean = 1.21ε)</span>
2782 Bessel Kv: Random Data
2787 <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
2792 <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
2793 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε)
2794 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Random_Data">And
2795 other failures.</a>)
2800 <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br>
2801 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 9.71ε (Mean = 1.47ε)
2802 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Random_Data">And
2803 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2804 Max = 7.37ε (Mean = 1.49ε))
2809 <span class="blue">Max = 7.88ε (Mean = 1.49ε)</span>
2816 <br class="table-break"><div class="table">
2817 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17.18. Error rates for cyl_bessel_k (integer orders)</b></p>
2818 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
2831 Microsoft Visual C++ version 12.0<br> Win32<br> double
2836 GNU C++ version 5.1.0<br> linux<br> long double
2841 GNU C++ version 5.1.0<br> linux<br> double
2846 Sun compiler version 0x5130<br> Sun Solaris<br> long double
2854 Bessel K0: Mathworld Data (Integer Version)
2859 <span class="blue">Max = 1.55ε (Mean = 0.837ε)</span>
2864 <span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br>
2865 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
2870 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2871 1.16:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath
2872 3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
2873 Max = 1.1e+06ε (Mean = 3.68e+05ε))
2878 <span class="blue">Max = 4.16ε (Mean = 1.49ε)</span>
2885 Bessel K1: Mathworld Data (Integer Version)
2890 <span class="blue">Max = 1ε (Mean = 0.573ε)</span>
2895 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br>
2896 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
2901 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2902 1.16:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
2903 3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
2904 Max = 5.38e+05ε (Mean = 1.79e+05ε))
2909 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
2916 Bessel Kn: Mathworld Data (Integer Version)
2921 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
2926 <span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br>
2927 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε)
2928 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k_integer_orders___tr1_cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
2929 other failures.</a>)
2934 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
2935 1.16:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath
2936 3.0.2:</em></span> Max = 8.48ε (Mean = 2.98ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
2937 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_integer_orders__Cephes_Bessel_Kn_Mathworld_Data_Integer_Version_">And
2938 other failures.</a>)</span>
2943 <span class="blue">Max = 4.48ε (Mean = 1.98ε)</span>
2950 <br class="table-break"><div class="table">
2951 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 17.19. Error rates for cyl_bessel_k_prime</b></p>
2952 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
2965 Microsoft Visual C++ version 12.0<br> Win32<br> double
2970 GNU C++ version 5.1.0<br> linux<br> double
2975 GNU C++ version 5.1.0<br> linux<br> long double
2980 Sun compiler version 0x5130<br> Sun Solaris<br> long double
2988 Bessel K'0: Mathworld Data
2993 <span class="blue">Max = 1ε (Mean = 0.573ε)</span>
2998 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3003 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
3008 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
3015 Bessel K'1: Mathworld Data
3020 <span class="blue">Max = 1.09ε (Mean = 0.607ε)</span>
3025 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3030 <span class="blue">Max = 1.96ε (Mean = 1ε)</span>
3035 <span class="blue">Max = 1.96ε (Mean = 1.04ε)</span>
3042 Bessel K'n: Mathworld Data
3047 <span class="blue">Max = 4.17ε (Mean = 1.74ε)</span>
3052 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3057 <span class="blue">Max = 4.47ε (Mean = 2.05ε)</span>
3062 <span class="blue">Max = 4.47ε (Mean = 1.93ε)</span>
3069 Bessel K'v: Mathworld Data
3074 <span class="blue">Max = 3.94ε (Mean = 1.43ε)</span>
3079 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3084 <span class="blue">Max = 3.94ε (Mean = 2.49ε)</span>
3089 <span class="blue">Max = 3.94ε (Mean = 2.35ε)</span>
3096 Bessel K'v: Mathworld Data (large values)
3101 <span class="blue">Max = 18.6ε (Mean = 12.1ε)</span>
3106 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3111 <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
3116 <span class="blue">Max = 59.8ε (Mean = 43.4ε)</span>
3123 Bessel K'n: Random Data
3128 <span class="blue">Max = 8.18ε (Mean = 1.45ε)</span>
3133 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3138 <span class="blue">Max = 4.53ε (Mean = 1.12ε)</span>
3143 <span class="blue">Max = 4.45ε (Mean = 1.23ε)</span>
3150 Bessel K'v: Random Data
3155 <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
3160 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3165 <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
3170 <span class="blue">Max = 7.95ε (Mean = 1.55ε)</span>
3177 <br class="table-break"><div class="table">
3178 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 17.20. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
3179 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
3192 Microsoft Visual C++ version 12.0<br> Win32<br> double
3197 GNU C++ version 5.1.0<br> linux<br> double
3202 GNU C++ version 5.1.0<br> linux<br> long double
3207 Sun compiler version 0x5130<br> Sun Solaris<br> long double
3215 Bessel K'0: Mathworld Data (Integer Version)
3220 <span class="blue">Max = 1ε (Mean = 0.573ε)</span>
3225 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3230 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
3235 <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
3242 Bessel K'1: Mathworld Data (Integer Version)
3247 <span class="blue">Max = 1.09ε (Mean = 0.607ε)</span>
3252 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3257 <span class="blue">Max = 1.96ε (Mean = 1ε)</span>
3262 <span class="blue">Max = 1.96ε (Mean = 1.04ε)</span>
3269 Bessel K'n: Mathworld Data (Integer Version)
3274 <span class="blue">Max = 4.17ε (Mean = 1.74ε)</span>
3279 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3284 <span class="blue">Max = 4.47ε (Mean = 2.05ε)</span>
3289 <span class="blue">Max = 4.47ε (Mean = 1.93ε)</span>
3296 <br class="table-break"><div class="table">
3297 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table 17.21. Error rates for cyl_neumann</b></p>
3298 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
3311 Microsoft Visual C++ version 12.0<br> Win32<br> double
3316 GNU C++ version 5.1.0<br> linux<br> double
3321 GNU C++ version 5.1.0<br> linux<br> long double
3326 Sun compiler version 0x5130<br> Sun Solaris<br> long double
3339 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
3344 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3345 1.16:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath
3346 3.0.2:</em></span> Max = 167ε (Mean = 56.5ε))
3351 <span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br>
3352 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean =
3358 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
3370 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
3375 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3376 1.16:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath
3377 3.0.2:</em></span> Max = 193ε (Mean = 64.4ε))
3382 <span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br>
3383 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean =
3389 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
3401 <span class="blue">Max = 35ε (Mean = 11.8ε)</span>
3406 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
3407 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε)
3408 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yn_Mathworld_Data">And
3409 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3410 Max = 1.24e+04ε (Mean = 4e+03ε))
3415 <span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br>
3416 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
3417 = 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yn_Mathworld_Data">And
3418 other failures.</a>)</span>
3423 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
3435 <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
3440 <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br>
3441 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε)
3442 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data">And
3443 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3444 Max = 1.05e+03ε (Mean = 326ε))
3449 <span class="blue">Max = 10.7ε (Mean = 4.92ε)</span><br> <br>
3450 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
3451 = 3.49e+15ε (Mean = 1.05e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data">And
3452 other failures.</a>)</span>
3457 <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
3464 Yv: Mathworld Data (large values)
3469 <span class="blue">Max = 0.682ε (Mean = 0.35ε)</span>
3474 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3475 1.16:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data_large_values_">And
3476 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3477 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_Rmath_3_0_2_Yv_Mathworld_Data_large_values_">And
3478 other failures.</a>)</span>
3483 <span class="blue">Max = 1.57ε (Mean = 1.17ε)</span><br> <br>
3484 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε)
3485 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data_large_values_">And
3486 other failures.</a>)
3491 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
3498 Y0 and Y1: Random Data
3503 <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
3508 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3509 1.16:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath
3510 3.0.2:</em></span> Max = 83ε (Mean = 14.2ε))
3515 <span class="blue">Max = 11.8ε (Mean = 3.28ε)</span><br> <br>
3516 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.59e+03ε (Mean =
3522 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
3534 <span class="blue">Max = 117ε (Mean = 10.2ε)</span>
3539 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3540 1.16:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath
3541 3.0.2:</em></span> Max = 691ε (Mean = 67.9ε))
3546 <span class="blue">Max = 338ε (Mean = 28.2ε)</span><br> <br>
3547 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.01e+03ε (Mean =
3553 <span class="blue">Max = 338ε (Mean = 27.5ε)</span>
3565 <span class="blue">Max = 1.23e+003ε (Mean = 69.9ε)</span>
3570 <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
3571 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
3572 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
3577 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br>
3578 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
3579 = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Random_Data">And
3580 other failures.</a>)</span>
3585 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
3592 <br class="table-break"><div class="table">
3593 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 17.22. Error rates for cyl_neumann (integer orders)</b></p>
3594 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
3607 Microsoft Visual C++ version 12.0<br> Win32<br> double
3612 GNU C++ version 5.1.0<br> linux<br> double
3617 GNU C++ version 5.1.0<br> linux<br> long double
3622 Sun compiler version 0x5130<br> Sun Solaris<br> long double
3630 Y0: Mathworld Data (Integer Version)
3635 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
3636 (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+003ε (Mean = 1.81e+003ε))
3641 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3642 1.16:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath
3643 3.0.2:</em></span> Max = 167ε (Mean = 56.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
3644 Max = 5.37e+03ε (Mean = 1.81e+03ε))
3649 <span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br>
3650 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean =
3656 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
3663 Y1: Mathworld Data (Integer Version)
3668 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
3669 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+004ε (Mean = 6.2e+003ε))
3674 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
3675 1.16:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
3676 3.0.2:</em></span> Max = 193ε (Mean = 64.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
3677 Max = 1.86e+04ε (Mean = 6.2e+03ε))
3682 <span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br>
3683 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean =
3689 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
3696 Yn: Mathworld Data (Integer Version)
3701 <span class="blue">Max = 35ε (Mean = 11.8ε)</span><br> <br>
3702 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.49e+005ε (Mean = 8.14e+004ε))
3707 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
3708 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
3709 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))<br>
3710 (<span class="emphasis"><em>Cephes:</em></span> Max = 2.49e+05ε (Mean = 8.14e+04ε))
3715 <span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br>
3716 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
3717 = 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann_integer_orders___tr1_cmath__Yn_Mathworld_Data_Integer_Version_">And
3718 other failures.</a>)</span>
3723 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
3730 <br class="table-break"><div class="table">
3731 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table 17.23. Error rates for cyl_neumann_prime</b></p>
3732 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
3745 Microsoft Visual C++ version 12.0<br> Win32<br> double
3750 GNU C++ version 5.1.0<br> linux<br> double
3755 GNU C++ version 5.1.0<br> linux<br> long double
3760 Sun compiler version 0x5130<br> Sun Solaris<br> long double
3773 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
3778 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3783 <span class="blue">Max = 12.7ε (Mean = 4.85ε)</span>
3788 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
3800 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
3805 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
3810 <span class="blue">Max = 36.6ε (Mean = 12.7ε)</span>
3815 <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
3827 <span class="blue">Max = 563ε (Mean = 178ε)</span>
3832 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
3837 <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
3842 <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
3854 <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
3859 <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
3864 <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
3869 <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
3876 Y'v: Mathworld Data (large values)
3881 <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
3886 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3891 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
3896 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
3903 Y'0 and Y'1: Random Data
3908 <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
3913 <span class="blue">Max = 0ε (Mean = 0ε)</span>
3918 <span class="blue">Max = 23.8ε (Mean = 3.84ε)</span>
3923 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
3935 <span class="blue">Max = 621ε (Mean = 36ε)</span>
3940 <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
3945 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
3950 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
3962 <span class="blue">Max = 3.23e+004ε (Mean = 1.13e+003ε)</span>
3967 <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
3972 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
3977 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
3984 <br class="table-break"><div class="table">
3985 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 17.24. Error rates for cyl_neumann_prime (integer orders)</b></p>
3986 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
3999 Microsoft Visual C++ version 12.0<br> Win32<br> double
4004 GNU C++ version 5.1.0<br> linux<br> double
4009 GNU C++ version 5.1.0<br> linux<br> long double
4014 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4022 Y'0: Mathworld Data (Integer Version)
4027 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
4032 <span class="blue">Max = 0ε (Mean = 0ε)</span>
4037 <span class="blue">Max = 12.7ε (Mean = 4.85ε)</span>
4042 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
4049 Y'1: Mathworld Data (Integer Version)
4054 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
4059 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
4064 <span class="blue">Max = 36.6ε (Mean = 12.7ε)</span>
4069 <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
4076 Y'n: Mathworld Data (Integer Version)
4081 <span class="blue">Max = 563ε (Mean = 178ε)</span>
4086 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
4091 <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
4096 <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
4103 <br class="table-break"><div class="table">
4104 <a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table 17.25. Error rates for digamma</b></p>
4105 <div class="table-contents"><table class="table" summary="Error rates for digamma">
4118 Microsoft Visual C++ version 12.0<br> Win32<br> double
4123 GNU C++ version 5.1.0<br> linux<br> double
4128 GNU C++ version 5.1.0<br> linux<br> long double
4133 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4141 Digamma Function: Large Values
4146 <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
4151 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4152 1.16:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath
4153 3.0.2:</em></span> Max = 1.18ε (Mean = 0.331ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4154 Max = 0.919ε (Mean = 0.394ε))
4159 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
4164 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
4171 Digamma Function: Near the Positive Root
4176 <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
4181 <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br>
4182 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 135ε (Mean = 11.9ε))<br>
4183 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.02e+03ε (Mean = 256ε))<br>
4184 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.42e+04ε (Mean = 1.14e+03ε))
4189 <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
4194 <span class="blue">Max = 1.31ε (Mean = 0.451ε)</span>
4201 Digamma Function: Near Zero
4206 <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
4211 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4212 1.16:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
4213 3.0.2:</em></span> Max = 1.17ε (Mean = 0.564ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4214 Max = 3.5ε (Mean = 1.04ε))
4219 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
4224 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
4231 Digamma Function: Negative Values
4236 <span class="blue">Max = 214ε (Mean = 16.1ε)</span>
4241 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4242 1.16:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
4243 3.0.2:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4244 Max = 214ε (Mean = 16.4ε))
4249 <span class="blue">Max = 180ε (Mean = 13ε)</span>
4254 <span class="blue">Max = 180ε (Mean = 13ε)</span>
4261 Digamma Function: Values near 0
4266 <span class="blue">Max = 0ε (Mean = 0ε)</span>
4271 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4272 1.16:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
4273 3.0.2:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4274 Max = 0.5ε (Mean = 0.224ε))
4279 <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
4284 <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
4291 Digamma Function: Integer arguments
4296 <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
4301 <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
4302 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18ε (Mean = 0.607ε))<br>
4303 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.33ε (Mean = 0.982ε))<br>
4304 (<span class="emphasis"><em>Cephes:</em></span> Max = 0.992ε (Mean = 0.383ε))
4309 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
4314 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
4321 Digamma Function: Half integer arguments
4326 <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
4331 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4332 1.16:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
4333 3.0.2:</em></span> Max = 46.2ε (Mean = 7.24ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4334 Max = 8.56ε (Mean = 1.44ε))
4339 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
4344 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
4351 <br class="table-break"><div class="table">
4352 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table 17.26. Error rates for ellint_1</b></p>
4353 <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
4366 Microsoft Visual C++ version 12.0<br> Win32<br> double
4371 GNU C++ version 5.1.0<br> linux<br> long double
4376 GNU C++ version 5.1.0<br> linux<br> double
4381 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4389 Elliptic Integral F: Mathworld Data
4394 <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
4399 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
4400 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4401 = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_1__tr1_cmath__Elliptic_Integral_F_Mathworld_Data">And
4402 other failures.</a>)</span>
4407 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4408 1.16:</em></span> Max = 0.919ε (Mean = 0.544ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4409 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_1_Cephes_Elliptic_Integral_F_Mathworld_Data">And
4410 other failures.</a>)</span>
4415 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
4422 Elliptic Integral F: Random Data
4427 <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
4432 <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
4433 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
4438 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4439 1.16:</em></span> Max = 2.99ε (Mean = 0.797ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4440 Max = 2.18ε (Mean = 0.535ε))
4445 <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
4452 <br class="table-break"><div class="table">
4453 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table 17.27. Error rates for ellint_1 (complete)</b></p>
4454 <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
4467 Microsoft Visual C++ version 12.0<br> Win32<br> double
4472 GNU C++ version 5.1.0<br> linux<br> long double
4477 GNU C++ version 5.1.0<br> linux<br> double
4482 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4490 Elliptic Integral K: Mathworld Data
4495 <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
4500 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
4501 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
4506 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4507 1.16:</em></span> Max = 0.623ε (Mean = 0.393ε))
4512 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
4519 Elliptic Integral K: Random Data
4524 <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
4529 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
4530 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
4535 <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br>
4536 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.32ε (Mean = 0.688ε))
4541 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
4548 <br class="table-break"><div class="table">
4549 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table 17.28. Error rates for ellint_2</b></p>
4550 <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
4563 Microsoft Visual C++ version 12.0<br> Win32<br> double
4568 GNU C++ version 5.1.0<br> linux<br> long double
4573 GNU C++ version 5.1.0<br> linux<br> double
4578 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4586 Elliptic Integral E: Mathworld Data
4591 <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
4596 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
4597 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4598 = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_2__tr1_cmath__Elliptic_Integral_E_Mathworld_Data">And
4599 other failures.</a>)</span>
4604 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4605 1.16:</em></span> Max = 0.63ε (Mean = 0.325ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4606 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_Cephes_Elliptic_Integral_E_Mathworld_Data">And
4607 other failures.</a>)</span>
4612 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
4619 Elliptic Integral E: Random Data
4624 <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
4629 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
4630 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.08e+04ε (Mean =
4636 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4637 1.16:</em></span> Max = 4.4ε (Mean = 1.16ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
4638 Max = 8.92ε (Mean = 1.48ε))
4643 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
4650 <br class="table-break"><div class="table">
4651 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table 17.29. Error rates for ellint_2 (complete)</b></p>
4652 <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
4665 Microsoft Visual C++ version 12.0<br> Win32<br> double
4670 GNU C++ version 5.1.0<br> linux<br> long double
4675 GNU C++ version 5.1.0<br> linux<br> double
4680 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4688 Elliptic Integral E: Mathworld Data
4693 <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
4698 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
4699 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
4704 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4705 1.16:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_complete__GSL_1_16_Elliptic_Integral_E_Mathworld_Data">And
4706 other failures.</a>)
4711 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
4718 Elliptic Integral E: Random Data
4723 <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
4728 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
4729 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.49e+04ε (Mean =
4735 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4736 1.16:</em></span> Max = 4.34ε (Mean = 1.18ε))
4741 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
4748 <br class="table-break"><div class="table">
4749 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table 17.30. Error rates for ellint_3</b></p>
4750 <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
4763 Microsoft Visual C++ version 12.0<br> Win32<br> double
4768 GNU C++ version 5.1.0<br> linux<br> long double
4773 GNU C++ version 5.1.0<br> linux<br> double
4778 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4786 Elliptic Integral PI: Mathworld Data
4791 <span class="blue">Max = 565ε (Mean = 102ε)</span>
4796 <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
4797 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4798 = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Mathworld_Data">And
4799 other failures.</a>)</span>
4804 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4805 1.16:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_GSL_1_16_Elliptic_Integral_PI_Mathworld_Data">And
4806 other failures.</a>)
4811 <span class="blue">Max = 475ε (Mean = 86.3ε)</span>
4818 Elliptic Integral PI: Random Data
4823 <span class="blue">Max = 9.08ε (Mean = 0.99ε)</span>
4828 <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
4829 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4830 = 3.37e+20ε (Mean = 3.47e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Random_Data">And
4831 other failures.</a>)</span>
4836 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4837 1.16:</em></span> Max = 633ε (Mean = 50.1ε))
4842 <span class="blue">Max = 4.49ε (Mean = 0.891ε)</span>
4849 Elliptic Integral PI: Large Random Data
4854 <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
4859 <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
4860 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4861 = 2.52e+18ε (Mean = 4.83e+17ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Large_Random_Data">And
4862 other failures.</a>)</span>
4867 <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br>
4868 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 40.1ε (Mean = 7.77ε))
4873 <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
4880 <br class="table-break"><div class="table">
4881 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table 17.31. Error rates for ellint_3 (complete)</b></p>
4882 <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
4895 Microsoft Visual C++ version 12.0<br> Win32<br> double
4900 GNU C++ version 5.1.0<br> linux<br> long double
4905 GNU C++ version 5.1.0<br> linux<br> double
4910 Sun compiler version 0x5130<br> Sun Solaris<br> long double
4918 Complete Elliptic Integral PI: Mathworld Data
4923 <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
4928 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
4929 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4930 = 6.31e+20ε (Mean = 1.53e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
4931 other failures.</a>)</span>
4936 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4937 1.16:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_complete__GSL_1_16_Complete_Elliptic_Integral_PI_Mathworld_Data">And
4938 other failures.</a>)
4943 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
4950 Complete Elliptic Integral PI: Random Data
4955 <span class="blue">Max = 2.46ε (Mean = 0.654ε)</span>
4960 <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
4961 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
4962 = 8.78e+20ε (Mean = 1.02e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Random_Data">And
4963 other failures.</a>)</span>
4968 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
4969 1.16:</em></span> Max = 24ε (Mean = 2.99ε))
4974 <span class="blue">Max = 2.4ε (Mean = 0.681ε)</span>
4981 <br class="table-break"><div class="table">
4982 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table 17.32. Error rates for ellint_d</b></p>
4983 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
4996 Microsoft Visual C++ version 12.0<br> Win32<br> double
5001 GNU C++ version 5.1.0<br> linux<br> double
5006 GNU C++ version 5.1.0<br> linux<br> long double
5011 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5019 Elliptic Integral E: Mathworld Data
5024 <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
5029 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5030 1.16:</em></span> Max = 0.862ε (Mean = 0.568ε))
5035 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
5040 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
5047 Elliptic Integral D: Random Data
5052 <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
5057 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5058 1.16:</em></span> Max = 3.01ε (Mean = 0.928ε))
5063 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
5068 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
5075 <br class="table-break"><div class="table">
5076 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table 17.33. Error rates for ellint_d (complete)</b></p>
5077 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
5090 Microsoft Visual C++ version 12.0<br> Win32<br> double
5095 GNU C++ version 5.1.0<br> linux<br> double
5100 GNU C++ version 5.1.0<br> linux<br> long double
5105 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5113 Elliptic Integral E: Mathworld Data
5118 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
5123 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
5128 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
5133 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
5140 Elliptic Integral D: Random Data
5145 <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
5150 <span class="blue">Max = 0ε (Mean = 0ε)</span>
5155 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
5160 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
5167 <br class="table-break"><div class="table">
5168 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table 17.34. Error rates for ellint_rc</b></p>
5169 <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
5182 Microsoft Visual C++ version 12.0<br> Win32<br> double
5187 GNU C++ version 5.1.0<br> linux<br> double
5192 GNU C++ version 5.1.0<br> linux<br> long double
5197 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5209 <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
5214 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5215 1.16:</em></span> Max = 2.4ε (Mean = 0.624ε))
5220 <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
5225 <span class="blue">Max = 0.995ε (Mean = 0.438ε)</span>
5231 <br class="table-break"><div class="table">
5232 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table 17.35. Error rates for ellint_rd</b></p>
5233 <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
5246 Microsoft Visual C++ version 12.0<br> Win32<br> double
5251 GNU C++ version 5.1.0<br> linux<br> double
5256 GNU C++ version 5.1.0<br> linux<br> long double
5261 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5274 <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
5279 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5280 1.16:</em></span> Max = 2.59ε (Mean = 0.878ε))
5285 <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
5290 <span class="blue">Max = 2.73ε (Mean = 0.829ε)</span>
5302 <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
5307 <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
5308 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.88ε (Mean = 0.839ε))
5313 <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
5318 <span class="blue">Max = 2.65ε (Mean = 0.819ε)</span>
5330 <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
5335 <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br>
5336 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.74ε (Mean = 0.84ε))
5341 <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
5346 <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
5358 <span class="blue">Max = 1.16ε (Mean = 0.493ε)</span>
5363 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5364 1.16:</em></span> Max = 2ε (Mean = 0.656ε))
5369 <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
5374 <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
5386 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
5391 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5392 1.16:</em></span> Max = 1.03ε (Mean = 0.418ε))
5397 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
5402 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
5414 <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
5419 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5420 1.16:</em></span> Max = 2.85ε (Mean = 0.781ε))
5425 <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
5430 <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
5437 <br class="table-break"><div class="table">
5438 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table 17.36. Error rates for ellint_rf</b></p>
5439 <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
5452 Microsoft Visual C++ version 12.0<br> Win32<br> double
5457 GNU C++ version 5.1.0<br> linux<br> double
5462 GNU C++ version 5.1.0<br> linux<br> long double
5467 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5480 <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
5485 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5486 1.16:</em></span> Max = 2.73ε (Mean = 0.804ε))
5491 <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
5496 <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
5508 <span class="blue">Max = 0.999ε (Mean = 0.335ε)</span>
5513 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5514 1.16:</em></span> Max = 0.999ε (Mean = 0.34ε))
5519 <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
5524 <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
5531 RF: x = y or y = z or x = z
5536 <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
5541 <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br>
5542 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.89ε (Mean = 0.749ε))
5547 <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
5552 <span class="blue">Max = 1.57ε (Mean = 0.418ε)</span>
5564 <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
5569 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5570 1.16:</em></span> Max = 1.29ε (Mean = 0.527ε))
5575 <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
5580 <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
5592 <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
5597 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5598 1.16:</em></span> Max = 2.54ε (Mean = 0.781ε))
5603 <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
5608 <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
5615 <br class="table-break"><div class="table">
5616 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table 17.37. Error rates for ellint_rg</b></p>
5617 <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
5630 Microsoft Visual C++ version 12.0<br> Win32<br> double
5635 GNU C++ version 5.1.0<br> linux<br> double
5640 GNU C++ version 5.1.0<br> linux<br> long double
5645 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5658 <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
5663 <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br>
5664 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.983ε (Mean = 0.0172ε))
5669 <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
5674 <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
5686 <span class="blue">Max = 0ε (Mean = 0ε)</span>
5691 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5692 1.16:</em></span> Max = 0ε (Mean = 0ε))
5697 <span class="blue">Max = 0ε (Mean = 0ε)</span>
5702 <span class="blue">Max = 0ε (Mean = 0ε)</span>
5709 RG: All values the same or zero
5714 <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
5719 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5720 1.16:</em></span> Max = 0ε (Mean = 0ε))
5725 <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
5730 <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
5737 RG: two values the same
5742 <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
5747 <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br>
5748 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.594ε (Mean = 0.0103ε))
5753 <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
5758 <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
5770 <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
5775 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5776 1.16:</em></span> Max = 0ε (Mean = 0ε))
5781 <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
5786 <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
5793 <br class="table-break"><div class="table">
5794 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table 17.38. Error rates for ellint_rj</b></p>
5795 <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
5808 Microsoft Visual C++ version 12.0<br> Win32<br> double
5813 GNU C++ version 5.1.0<br> linux<br> double
5818 GNU C++ version 5.1.0<br> linux<br> long double
5823 Sun compiler version 0x5130<br> Sun Solaris<br> long double
5836 <span class="blue">Max = 119ε (Mean = 4.32ε)</span>
5841 <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
5842 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_rj_GSL_1_16_RJ_Random_data">And
5843 other failures.</a>)
5848 <span class="blue">Max = 186ε (Mean = 6.67ε)</span>
5853 <span class="blue">Max = 186ε (Mean = 6.7ε)</span>
5865 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
5870 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5871 1.16:</em></span> Max = 1.03ε (Mean = 0.418ε))
5876 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
5881 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
5893 <span class="blue">Max = 39.9ε (Mean = 1.12ε)</span>
5898 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
5899 1.16:</em></span> Max = 3.96ε (Mean = 1.06ε))
5904 <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
5909 <span class="blue">Max = 18.2ε (Mean = 0.917ε)</span>
5921 <span class="blue">Max = 214ε (Mean = 5.05ε)</span>
5926 <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
5927 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.57ε (Mean = 0.754ε))
5932 <span class="blue">Max = 220ε (Mean = 6.64ε)</span>
5937 <span class="blue">Max = 135ε (Mean = 5.3ε)</span>
5949 <span class="blue">Max = 15.4ε (Mean = 1.05ε)</span>
5954 <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br>
5955 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.62ε (Mean = 0.699ε))
5960 <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
5965 <span class="blue">Max = 16.6ε (Mean = 1.15ε)</span>
5972 <br class="table-break"><div class="table">
5973 <a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table 17.39. Error rates for erf</b></p>
5974 <div class="table-contents"><table class="table" summary="Error rates for erf">
5987 Microsoft Visual C++ version 12.0<br> Win32<br> double
5992 GNU C++ version 5.1.0<br> linux<br> long double
5997 GNU C++ version 5.1.0<br> linux<br> double
6002 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6010 Erf Function: Small Values
6015 <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
6016 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
6021 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
6022 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
6023 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
6028 <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br>
6029 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.06ε (Mean = 0.319ε))<br>
6030 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.13ε (Mean = 0.442ε))
6035 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
6036 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
6043 Erf Function: Medium Values
6048 <span class="blue">Max = 1ε (Mean = 0.169ε)</span><br> <br>
6049 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.19ε (Mean = 0.244ε))
6054 <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
6055 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
6056 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
6061 <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br>
6062 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.31ε (Mean = 0.368ε))<br>
6063 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.34ε (Mean = 0.279ε))
6068 <span class="blue">Max = 1.5ε (Mean = 0.202ε)</span><br> <br>
6069 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
6076 Erf Function: Large Values
6081 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
6082 Max = 0ε (Mean = 0ε))
6087 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span>
6088 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
6089 Max = 0ε (Mean = 0ε))
6094 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
6095 1.16:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
6096 Max = 0ε (Mean = 0ε))
6101 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
6102 Max = 0ε (Mean = 0ε))
6109 <br class="table-break"><div class="table">
6110 <a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table 17.40. Error rates for erf_inv</b></p>
6111 <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
6124 Microsoft Visual C++ version 12.0<br> Win32<br> double
6129 GNU C++ version 5.1.0<br> linux<br> double
6134 GNU C++ version 5.1.0<br> linux<br> long double
6139 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6146 Inverse Erf Function
6151 <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
6156 <span class="blue">Max = 0ε (Mean = 0ε)</span>
6161 <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
6166 <span class="blue">Max = 0.996ε (Mean = 0.385ε)</span>
6172 <br class="table-break"><div class="table">
6173 <a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table 17.41. Error rates for erfc</b></p>
6174 <div class="table-contents"><table class="table" summary="Error rates for erfc">
6187 Microsoft Visual C++ version 12.0<br> Win32<br> double
6192 GNU C++ version 5.1.0<br> linux<br> long double
6197 GNU C++ version 5.1.0<br> linux<br> double
6202 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6210 Erf Function: Small Values
6215 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
6216 Max = 0ε (Mean = 0ε))
6221 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span>
6222 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
6223 Max = 0ε (Mean = 0ε))
6228 <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br>
6229 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.01ε (Mean = 0.485ε))<br>
6230 (<span class="emphasis"><em>Cephes:</em></span> Max = 0.786ε (Mean = 0.0642ε))
6235 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
6236 Max = 0ε (Mean = 0ε))
6243 Erf Function: Medium Values
6248 <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
6249 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
6254 <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
6255 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
6256 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
6261 <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
6262 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.64ε (Mean = 0.662ε))<br>
6263 (<span class="emphasis"><em>Cephes:</em></span> Max = 3.59ε (Mean = 0.779ε))
6268 <span class="blue">Max = 1.76ε (Mean = 0.383ε)</span><br> <br>
6269 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
6276 Erf Function: Large Values
6281 <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
6282 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
6287 <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
6288 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
6289 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
6294 <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
6295 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9ε (Mean = 0.472ε))<br>
6296 (<span class="emphasis"><em>Cephes:</em></span> Max = 2.74ε (Mean = 0.413ε))
6301 <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
6302 (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
6309 <br class="table-break"><div class="table">
6310 <a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table 17.42. Error rates for erfc_inv</b></p>
6311 <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
6324 Microsoft Visual C++ version 12.0<br> Win32<br> double
6329 GNU C++ version 5.1.0<br> linux<br> double
6334 GNU C++ version 5.1.0<br> linux<br> long double
6339 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6347 Inverse Erfc Function
6352 <span class="blue">Max = 1ε (Mean = 0.491ε)</span>
6357 <span class="blue">Max = 0ε (Mean = 0ε)</span>
6362 <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
6367 <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
6374 Inverse Erfc Function: extreme values
6383 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
6388 <span class="blue">Max = 1.62ε (Mean = 0.385ε)</span>
6395 <br class="table-break"><div class="table">
6396 <a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table 17.43. Error rates for expint (Ei)</b></p>
6397 <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
6410 Microsoft Visual C++ version 12.0<br> Win32<br> double
6415 GNU C++ version 5.1.0<br> linux<br> long double
6420 GNU C++ version 5.1.0<br> linux<br> double
6425 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6433 Exponential Integral Ei
6438 <span class="blue">Max = 1.43ε (Mean = 0.541ε)</span>
6443 <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
6444 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε)
6445 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expint_Ei___tr1_cmath__Exponential_Integral_Ei">And
6446 other failures.</a>)
6451 <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
6452 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.96ε (Mean = 0.703ε))<br>
6453 (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean
6454 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_expint_Ei__Cephes_Exponential_Integral_Ei">And
6455 other failures.</a>)</span>
6460 <span class="blue">Max = 3.34ε (Mean = 0.631ε)</span>
6467 Exponential Integral Ei: double exponent range
6472 <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
6477 <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
6478 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
6483 <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
6484 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.612ε))<br>
6485 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.77ε (Mean = 0.644ε))
6490 <span class="blue">Max = 1.72ε (Mean = 0.618ε)</span>
6497 Exponential Integral Ei: long exponent range
6504 <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
6505 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
6512 <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
6519 <br class="table-break"><div class="table">
6520 <a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table 17.44. Error rates for expint (En)</b></p>
6521 <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
6534 Microsoft Visual C++ version 12.0<br> Win32<br> double
6539 GNU C++ version 5.1.0<br> linux<br> double
6544 GNU C++ version 5.1.0<br> linux<br> long double
6549 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6557 Exponential Integral En
6562 <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
6567 <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br>
6568 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 58.5ε (Mean = 17.1ε))
6573 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
6578 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
6585 Exponential Integral En: small z values
6590 <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
6595 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
6596 1.16:</em></span> Max = 115ε (Mean = 23.6ε))
6601 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
6606 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
6613 Exponential Integral E1
6618 <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
6623 <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br>
6624 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.988ε (Mean = 0.469ε))
6629 <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
6634 <span class="blue">Max = 0.965ε (Mean = 0.409ε)</span>
6641 <br class="table-break"><div class="table">
6642 <a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table 17.45. Error rates for expm1</b></p>
6643 <div class="table-contents"><table class="table" summary="Error rates for expm1">
6656 Microsoft Visual C++ version 12.0<br> Win32<br> double
6661 GNU C++ version 5.1.0<br> linux<br> double
6666 GNU C++ version 5.1.0<br> linux<br> long double
6671 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6683 <span class="blue">Max = 0.996ε (Mean = 0.283ε)</span><br> <br>
6684 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
6689 <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
6690 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.793ε (Mean = 0.126ε))<br>
6691 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.53ε (Mean = 0.535ε))
6696 <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
6697 (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
6698 = 1.26e+19ε (Mean = 4.89e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expm1__tr1_cmath__Random_test_data">And
6699 other failures.</a>)</span><br> (<span class="emphasis"><em><math.h>:</em></span>
6700 Max = 0.992ε (Mean = 0.402ε))
6705 <span class="blue">Max = 1.31ε (Mean = 0.406ε)</span><br> <br>
6706 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
6712 <br class="table-break"><div class="table">
6713 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table 17.46. Error rates for gamma_p</b></p>
6714 <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
6727 Microsoft Visual C++ version 12.0<br> Win32<br> double
6732 GNU C++ version 5.1.0<br> linux<br> double
6737 GNU C++ version 5.1.0<br> linux<br> long double
6742 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6750 tgamma(a, z) medium values
6755 <span class="blue">Max = 35.1ε (Mean = 6.97ε)</span>
6760 <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
6761 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
6762 3.0.2:</em></span> Max = 389ε (Mean = 44ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
6763 Max = 492ε (Mean = 101ε))
6768 <span class="blue">Max = 41ε (Mean = 8.09ε)</span>
6773 <span class="blue">Max = 239ε (Mean = 30.2ε)</span>
6780 tgamma(a, z) small values
6785 <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
6790 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
6791 1.16:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
6792 3.0.2:</em></span> Max = 1.01ε (Mean = 0.306ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
6793 Max = 21ε (Mean = 5.65ε))
6798 <span class="blue">Max = 2ε (Mean = 0.461ε)</span>
6803 <span class="blue">Max = 2ε (Mean = 0.472ε)</span>
6810 tgamma(a, z) large values
6815 <span class="blue">Max = 244ε (Mean = 20.2ε)</span>
6820 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
6821 1.16:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
6822 3.0.2:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
6823 Max = 8.18e+06ε (Mean = 7.69e+05ε))
6828 <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
6833 <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
6840 tgamma(a, z) integer and half integer values
6845 <span class="blue">Max = 13ε (Mean = 2.93ε)</span>
6850 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
6851 1.16:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath
6852 3.0.2:</em></span> Max = 66.2ε (Mean = 12.2ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
6853 Max = 83.6ε (Mean = 22.2ε))
6858 <span class="blue">Max = 11.8ε (Mean = 2.65ε)</span>
6863 <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
6870 <br class="table-break"><div class="table">
6871 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table 17.47. Error rates for gamma_p_inv</b></p>
6872 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
6885 Microsoft Visual C++ version 12.0<br> Win32<br> double
6890 GNU C++ version 5.1.0<br> linux<br> double
6895 GNU C++ version 5.1.0<br> linux<br> long double
6900 Sun compiler version 0x5130<br> Sun Solaris<br> long double
6908 incomplete gamma inverse(a, z) medium values
6913 <span class="blue">Max = 1.01ε (Mean = 0.307ε)</span>
6918 <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
6919 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.88ε (Mean = 0.868ε))
6924 <span class="blue">Max = 1.62ε (Mean = 0.365ε)</span>
6929 <span class="blue">Max = 1.86ε (Mean = 0.405ε)</span>
6936 incomplete gamma inverse(a, z) large values
6941 <span class="blue">Max = 0.924ε (Mean = 0.118ε)</span>
6946 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
6947 3.0.2:</em></span> Max = 0.816ε (Mean = 0.0874ε))
6952 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
6957 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
6964 incomplete gamma inverse(a, z) small values
6969 <span class="blue">Max = 1.1e+003ε (Mean = 108ε)</span>
6974 <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
6975 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 547ε (Mean = 61.6ε))
6980 <span class="blue">Max = 9.17e+03ε (Mean = 1.32e+03ε)</span>
6985 <span class="blue">Max = 1.09e+04ε (Mean = 1.46e+03ε)</span>
6992 <br class="table-break"><div class="table">
6993 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table 17.48. Error rates for gamma_p_inva</b></p>
6994 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
7007 Microsoft Visual C++ version 12.0<br> Win32<br> double
7012 GNU C++ version 5.1.0<br> linux<br> double
7017 GNU C++ version 5.1.0<br> linux<br> long double
7022 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7029 Incomplete gamma inverses.
7034 <span class="blue">Max = 3.52ε (Mean = 0.997ε)</span>
7039 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7044 <span class="blue">Max = 6.44ε (Mean = 1.1ε)</span>
7049 <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
7055 <br class="table-break"><div class="table">
7056 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table 17.49. Error rates for gamma_q</b></p>
7057 <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
7070 Microsoft Visual C++ version 12.0<br> Win32<br> double
7075 GNU C++ version 5.1.0<br> linux<br> double
7080 GNU C++ version 5.1.0<br> linux<br> long double
7085 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7093 tgamma(a, z) medium values
7098 <span class="blue">Max = 23.7ε (Mean = 4.03ε)</span>
7103 <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
7104 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
7105 3.0.2:</em></span> Max = 131ε (Mean = 12.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7106 Max = 388ε (Mean = 93.8ε))
7111 <span class="blue">Max = 31.3ε (Mean = 6.56ε)</span>
7116 <span class="blue">Max = 199ε (Mean = 26.6ε)</span>
7123 tgamma(a, z) small values
7128 <span class="blue">Max = 2.26ε (Mean = 0.732ε)</span>
7133 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7134 1.16:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
7135 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 65.6ε (Mean = 11ε))<br>
7136 (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 3.42e+11ε (Mean
7137 = 4.1e+10ε))</span>
7142 <span class="blue">Max = 2.45ε (Mean = 0.832ε)</span>
7147 <span class="blue">Max = 2.25ε (Mean = 0.81ε)</span>
7154 tgamma(a, z) large values
7159 <span class="blue">Max = 470ε (Mean = 31.5ε)</span>
7164 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7165 1.16:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
7166 3.0.2:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7167 Max = 8.17e+06ε (Mean = 7.7e+05ε))
7172 <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
7177 <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
7184 tgamma(a, z) integer and half integer values
7189 <span class="blue">Max = 8.48ε (Mean = 1.42ε)</span>
7194 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7195 1.16:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath
7196 3.0.2:</em></span> Max = 138ε (Mean = 16.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7197 Max = 129ε (Mean = 26.5ε))
7202 <span class="blue">Max = 11.1ε (Mean = 2.09ε)</span>
7207 <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
7214 <br class="table-break"><div class="table">
7215 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table 17.50. Error rates for gamma_q_inv</b></p>
7216 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
7229 Microsoft Visual C++ version 12.0<br> Win32<br> double
7234 GNU C++ version 5.1.0<br> linux<br> double
7239 GNU C++ version 5.1.0<br> linux<br> long double
7244 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7252 incomplete gamma inverse(a, z) medium values
7257 <span class="blue">Max = 3.46ε (Mean = 0.475ε)</span>
7262 <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
7263 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.66ε (Mean = 0.792ε))
7268 <span class="blue">Max = 6.2ε (Mean = 0.659ε)</span>
7273 <span class="blue">Max = 6.2ε (Mean = 0.661ε)</span>
7280 incomplete gamma inverse(a, z) large values
7285 <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
7290 <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br>
7291 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.894ε (Mean = 0.106ε))
7296 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7301 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7308 incomplete gamma inverse(a, z) small values
7313 <span class="blue">Max = 451ε (Mean = 65ε)</span>
7318 <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
7319 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 415ε (Mean = 48.7ε))
7324 <span class="blue">Max = 8.28e+03ε (Mean = 963ε)</span>
7329 <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
7336 <br class="table-break"><div class="table">
7337 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table 17.51. Error rates for gamma_q_inva</b></p>
7338 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
7351 Microsoft Visual C++ version 12.0<br> Win32<br> double
7356 GNU C++ version 5.1.0<br> linux<br> double
7361 GNU C++ version 5.1.0<br> linux<br> long double
7366 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7373 Incomplete gamma inverses.
7378 <span class="blue">Max = 5.64ε (Mean = 1.09ε)</span>
7383 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7388 <span class="blue">Max = 6.91ε (Mean = 1.17ε)</span>
7393 <span class="blue">Max = 7.86ε (Mean = 1.25ε)</span>
7399 <br class="table-break"><div class="table">
7400 <a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table 17.52. Error rates for hermite</b></p>
7401 <div class="table-contents"><table class="table" summary="Error rates for hermite">
7414 Microsoft Visual C++ version 12.0<br> Win32<br> double
7419 GNU C++ version 5.1.0<br> linux<br> double
7424 GNU C++ version 5.1.0<br> linux<br> long double
7429 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7441 <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
7446 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7451 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
7456 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
7462 <br class="table-break"><div class="table">
7463 <a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table 17.53. Error rates for heuman_lambda</b></p>
7464 <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
7477 Microsoft Visual C++ version 12.0<br> Win32<br> double
7482 GNU C++ version 5.1.0<br> linux<br> double
7487 GNU C++ version 5.1.0<br> linux<br> long double
7492 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7500 Elliptic Integral Jacobi Zeta: Mathworld Data
7505 <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
7510 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7515 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
7520 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
7527 Elliptic Integral Heuman Lambda: Random Data
7532 <span class="blue">Max = 2.12ε (Mean = 0.59ε)</span>
7537 <span class="blue">Max = 0ε (Mean = 0ε)</span>
7542 <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
7547 <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
7554 <br class="table-break"><div class="table">
7555 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table 17.54. Error rates for ibeta</b></p>
7556 <div class="table-contents"><table class="table" summary="Error rates for ibeta">
7569 Microsoft Visual C++ version 12.0<br> Win32<br> double
7574 GNU C++ version 5.1.0<br> linux<br> double
7579 GNU C++ version 5.1.0<br> linux<br> long double
7584 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7592 Incomplete Beta Function: Small Values
7597 <span class="blue">Max = 9.42ε (Mean = 2.24ε)</span>
7602 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7603 1.16:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath
7604 3.0.2:</em></span> Max = 22.9ε (Mean = 3.35ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7605 Max = 22.7ε (Mean = 1.69ε))
7610 <span class="blue">Max = 6.27ε (Mean = 1.7ε)</span>
7615 <span class="blue">Max = 21.3ε (Mean = 2.74ε)</span>
7622 Incomplete Beta Function: Medium Values
7627 <span class="blue">Max = 108ε (Mean = 16.3ε)</span>
7632 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7633 1.16:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath
7634 3.0.2:</em></span> Max = 232ε (Mean = 27.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7635 Max = 1.55e+03ε (Mean = 121ε))
7640 <span class="blue">Max = 51.4ε (Mean = 12ε)</span>
7645 <span class="blue">Max = 124ε (Mean = 18.4ε)</span>
7652 Incomplete Beta Function: Large and Diverse Values
7657 <span class="blue">Max = 1.19e+003ε (Mean = 59.5ε)</span>
7662 <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
7663 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε)
7664 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_GSL_1_16_Incomplete_Beta_Function_Large_and_Diverse_Values">And
7665 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
7666 Max = 574ε (Mean = 49.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
7667 = 5.92e+05ε (Mean = 2.17e+04ε))
7672 <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
7677 <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
7684 Incomplete Beta Function: Small Integer Values
7689 <span class="blue">Max = 3.69ε (Mean = 0.765ε)</span>
7694 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
7695 1.16:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath
7696 3.0.2:</em></span> Max = 62.2ε (Mean = 8.95ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
7697 Max = 7.96ε (Mean = 1.3ε))
7702 <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
7707 <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
7714 <br class="table-break"><div class="table">
7715 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table 17.55. Error rates for ibeta_inv</b></p>
7716 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
7729 Microsoft Visual C++ version 12.0<br> Win32<br> double
7734 GNU C++ version 5.1.0<br> linux<br> double
7739 GNU C++ version 5.1.0<br> linux<br> long double
7744 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7751 Inverse incomplete beta
7756 <span class="blue">Max = 7.08e+003ε (Mean = 244ε)</span>
7761 <span class="blue">Max = 3.21ε (Mean = 0.158ε)</span><br> <br>
7762 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
7763 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
7764 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
7765 <span class="red">Max = 1.28e+10ε (Mean = 5.17e+08ε))</span>
7770 <span class="blue">Max = 4.53e+04ε (Mean = 2.93e+03ε)</span>
7775 <span class="blue">Max = 4.22e+04ε (Mean = 2.8e+03ε)</span>
7781 <br class="table-break"><div class="table">
7782 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table 17.56. Error rates for ibeta_inva</b></p>
7783 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
7796 Microsoft Visual C++ version 12.0<br> Win32<br> double
7801 GNU C++ version 5.1.0<br> linux<br> double
7806 GNU C++ version 5.1.0<br> linux<br> long double
7811 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7818 Inverse incomplete beta
7823 <span class="blue">Max = 395ε (Mean = 24.7ε)</span>
7828 <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
7833 <span class="blue">Max = 377ε (Mean = 25.1ε)</span>
7838 <span class="blue">Max = 438ε (Mean = 31.6ε)</span>
7844 <br class="table-break"><div class="table">
7845 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table 17.57. Error rates for ibeta_invb</b></p>
7846 <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
7859 Microsoft Visual C++ version 12.0<br> Win32<br> double
7864 GNU C++ version 5.1.0<br> linux<br> double
7869 GNU C++ version 5.1.0<br> linux<br> long double
7874 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7881 Inverse incomplete beta
7886 <span class="blue">Max = 409ε (Mean = 17.9ε)</span>
7891 <span class="blue">Max = 0.836ε (Mean = 0.0491ε)</span>
7896 <span class="blue">Max = 407ε (Mean = 27.2ε)</span>
7901 <span class="blue">Max = 407ε (Mean = 24.4ε)</span>
7907 <br class="table-break"><div class="table">
7908 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table 17.58. Error rates for ibetac</b></p>
7909 <div class="table-contents"><table class="table" summary="Error rates for ibetac">
7922 Microsoft Visual C++ version 12.0<br> Win32<br> double
7927 GNU C++ version 5.1.0<br> linux<br> double
7932 GNU C++ version 5.1.0<br> linux<br> long double
7937 Sun compiler version 0x5130<br> Sun Solaris<br> long double
7945 Incomplete Beta Function: Small Values
7950 <span class="blue">Max = 6.56ε (Mean = 1.88ε)</span>
7955 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
7956 3.0.2:</em></span> Max = 22.4ε (Mean = 3.67ε))
7961 <span class="blue">Max = 8.47ε (Mean = 1.68ε)</span>
7966 <span class="blue">Max = 13.8ε (Mean = 2.69ε)</span>
7973 Incomplete Beta Function: Medium Values
7978 <span class="blue">Max = 56.2ε (Mean = 14.1ε)</span>
7983 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
7984 3.0.2:</em></span> Max = 204ε (Mean = 25.8ε))
7989 <span class="blue">Max = 75.3ε (Mean = 11.3ε)</span>
7994 <span class="blue">Max = 132ε (Mean = 19.8ε)</span>
8001 Incomplete Beta Function: Large and Diverse Values
8006 <span class="blue">Max = 1.87e+003ε (Mean = 93.8ε)</span>
8011 <span class="blue">Max = 0.981ε (Mean = 0.0638ε)</span><br>
8012 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 889ε (Mean = 68.4ε))
8017 <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
8022 <span class="blue">Max = 4.26e+04ε (Mean = 1.54e+03ε)</span>
8029 Incomplete Beta Function: Small Integer Values
8034 <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
8039 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
8040 3.0.2:</em></span> Max = 84.6ε (Mean = 18ε))
8045 <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
8050 <span class="blue">Max = 107ε (Mean = 17.1ε)</span>
8057 <br class="table-break"><div class="table">
8058 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table 17.59. Error rates for ibetac_inv</b></p>
8059 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
8072 Microsoft Visual C++ version 12.0<br> Win32<br> double
8077 GNU C++ version 5.1.0<br> linux<br> double
8082 GNU C++ version 5.1.0<br> linux<br> long double
8087 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8094 Inverse incomplete beta
8099 <span class="blue">Max = 5.53e+003ε (Mean = 220ε)</span>
8104 <span class="blue">Max = 1.71ε (Mean = 0.108ε)</span><br> <br>
8105 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
8106 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibetac_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
8107 other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
8108 Max = 1.71ε (Mean = 0.108ε))
8113 <span class="blue">Max = 6.17e+04ε (Mean = 3.77e+03ε)</span>
8118 <span class="blue">Max = 5.15e+04ε (Mean = 3.51e+03ε)</span>
8124 <br class="table-break"><div class="table">
8125 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table 17.60. Error rates for ibetac_inva</b></p>
8126 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
8139 Microsoft Visual C++ version 12.0<br> Win32<br> double
8144 GNU C++ version 5.1.0<br> linux<br> double
8149 GNU C++ version 5.1.0<br> linux<br> long double
8154 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8161 Inverse incomplete beta
8166 <span class="blue">Max = 408ε (Mean = 27.8ε)</span>
8171 <span class="blue">Max = 0.683ε (Mean = 0.0271ε)</span>
8176 <span class="blue">Max = 382ε (Mean = 22.2ε)</span>
8181 <span class="blue">Max = 315ε (Mean = 23.7ε)</span>
8187 <br class="table-break"><div class="table">
8188 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table 17.61. Error rates for ibetac_invb</b></p>
8189 <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
8202 Microsoft Visual C++ version 12.0<br> Win32<br> double
8207 GNU C++ version 5.1.0<br> linux<br> double
8212 GNU C++ version 5.1.0<br> linux<br> long double
8217 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8224 Inverse incomplete beta
8229 <span class="blue">Max = 329ε (Mean = 18.2ε)</span>
8234 <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
8239 <span class="blue">Max = 317ε (Mean = 19.7ε)</span>
8244 <span class="blue">Max = 369ε (Mean = 21.7ε)</span>
8250 <br class="table-break"><div class="table">
8251 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table 17.62. Error rates for jacobi_cn</b></p>
8252 <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
8265 Microsoft Visual C++ version 12.0<br> Win32<br> double
8270 GNU C++ version 5.1.0<br> linux<br> double
8275 GNU C++ version 5.1.0<br> linux<br> long double
8280 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8288 Jacobi Elliptic: Mathworld Data
8293 <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
8298 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8299 1.16:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8300 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8301 other failures.</a>)</span>
8306 <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
8311 <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
8318 Jacobi Elliptic: Random Data
8323 <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
8328 <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br>
8329 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43ε (Mean = 0.803ε))<br>
8330 (<span class="emphasis"><em>Cephes:</em></span> Max = 1.83ε (Mean = 0.437ε))
8335 <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
8340 <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
8347 Jacobi Elliptic: Random Small Values
8352 <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
8357 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8358 1.16:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8359 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8360 other failures.</a>)</span>
8365 <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
8370 <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
8377 Jacobi Elliptic: Modulus near 1
8382 <span class="blue">Max = 513ε (Mean = 126ε)</span>
8387 <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
8388 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8389 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8390 other failures.</a>)</span>
8395 <span class="blue">Max = 675ε (Mean = 87.1ε)</span>
8400 <span class="blue">Max = 675ε (Mean = 86.8ε)</span>
8407 Jacobi Elliptic: Large Phi
8412 <span class="blue">Max = 3.27e+004ε (Mean = 1.93e+003ε)</span>
8417 <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
8418 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03ε (Mean = 477ε))<br>
8419 (<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04ε (Mean = 1.93e+03ε))
8424 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
8429 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
8436 <br class="table-break"><div class="table">
8437 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table 17.63. Error rates for jacobi_dn</b></p>
8438 <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
8451 Microsoft Visual C++ version 12.0<br> Win32<br> double
8456 GNU C++ version 5.1.0<br> linux<br> double
8461 GNU C++ version 5.1.0<br> linux<br> long double
8466 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8474 Jacobi Elliptic: Mathworld Data
8479 <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
8484 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8485 1.16:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8486 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8487 other failures.</a>)</span>
8492 <span class="blue">Max = 49ε (Mean = 14ε)</span>
8497 <span class="blue">Max = 49ε (Mean = 14ε)</span>
8504 Jacobi Elliptic: Random Data
8509 <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
8514 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8515 1.16:</em></span> Max = 3ε (Mean = 0.61ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
8516 Max = 1.49ε (Mean = 0.321ε))
8521 <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
8526 <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
8533 Jacobi Elliptic: Random Small Values
8538 <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
8543 <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
8544 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8545 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8546 other failures.</a>)</span>
8551 <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
8556 <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
8563 Jacobi Elliptic: Modulus near 1
8568 <span class="blue">Max = 6.24e+003ε (Mean = 482ε)</span>
8573 <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
8574 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8575 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8576 other failures.</a>)</span>
8581 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
8586 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
8593 Jacobi Elliptic: Large Phi
8598 <span class="blue">Max = 1.67e+004ε (Mean = 1e+003ε)</span>
8603 <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
8604 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 22ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
8605 Max = 196ε (Mean = 30.2ε))
8610 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
8615 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
8622 <br class="table-break"><div class="table">
8623 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table 17.64. Error rates for jacobi_sn</b></p>
8624 <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
8637 Microsoft Visual C++ version 12.0<br> Win32<br> double
8642 GNU C++ version 5.1.0<br> linux<br> double
8647 GNU C++ version 5.1.0<br> linux<br> long double
8652 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8660 Jacobi Elliptic: Mathworld Data
8665 <span class="blue">Max = 481ε (Mean = 113ε)</span>
8670 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8671 1.16:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8672 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8673 other failures.</a>)</span>
8678 <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
8683 <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
8690 Jacobi Elliptic: Random Data
8695 <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
8700 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8701 1.16:</em></span> Max = 4.02ε (Mean = 1.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
8702 Max = 1.92ε (Mean = 0.567ε))
8707 <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
8712 <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
8719 Jacobi Elliptic: Random Small Values
8724 <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
8729 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8730 1.16:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8731 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8732 other failures.</a>)</span>
8737 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
8742 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
8749 Jacobi Elliptic: Modulus near 1
8754 <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
8759 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
8760 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8761 other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8762 other failures.</a>)</span>
8767 <span class="blue">Max = 109ε (Mean = 7.35ε)</span>
8772 <span class="blue">Max = 109ε (Mean = 7.38ε)</span>
8779 Jacobi Elliptic: Large Phi
8784 <span class="blue">Max = 4.36e+004ε (Mean = 2.54e+003ε)</span>
8789 <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
8790 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))<br>
8791 (<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04ε (Mean = 2.54e+03ε))
8796 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
8801 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
8808 <br class="table-break"><div class="table">
8809 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table 17.65. Error rates for jacobi_zeta</b></p>
8810 <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
8823 Microsoft Visual C++ version 12.0<br> Win32<br> double
8828 GNU C++ version 5.1.0<br> linux<br> double
8833 GNU C++ version 5.1.0<br> linux<br> long double
8838 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8846 Elliptic Integral Jacobi Zeta: Mathworld Data
8851 <span class="blue">Max = 0.505ε (Mean = 0.119ε)</span>
8856 <span class="blue">Max = 0ε (Mean = 0ε)</span>
8861 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
8866 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
8873 Elliptic Integral Jacobi Zeta: Random Data
8878 <span class="blue">Max = 3.89ε (Mean = 0.818ε)</span>
8883 <span class="blue">Max = 0ε (Mean = 0ε)</span>
8888 <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
8893 <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
8900 Elliptic Integral Jacobi Zeta: Large Phi Values
8905 <span class="blue">Max = 2.92ε (Mean = 0.964ε)</span>
8910 <span class="blue">Max = 0ε (Mean = 0ε)</span>
8915 <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
8920 <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
8927 <br class="table-break"><div class="table">
8928 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table 17.66. Error rates for laguerre(n, m, x)</b></p>
8929 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
8942 Microsoft Visual C++ version 12.0<br> Win32<br> double
8947 GNU C++ version 5.1.0<br> linux<br> double
8952 GNU C++ version 5.1.0<br> linux<br> long double
8957 Sun compiler version 0x5130<br> Sun Solaris<br> long double
8964 Associated Laguerre Polynomials
8969 <span class="blue">Max = 434ε (Mean = 11.1ε)</span>
8974 <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
8975 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 434ε (Mean = 10.7ε))
8980 <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
8981 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
8986 <span class="blue">Max = 167ε (Mean = 6.38ε)</span>
8992 <br class="table-break"><div class="table">
8993 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table 17.67. Error rates for laguerre(n, x)</b></p>
8994 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
9007 Microsoft Visual C++ version 12.0<br> Win32<br> double
9012 GNU C++ version 5.1.0<br> linux<br> double
9017 GNU C++ version 5.1.0<br> linux<br> long double
9022 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9029 Laguerre Polynomials
9034 <span class="blue">Max = 3.1e+003ε (Mean = 185ε)</span>
9039 <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
9040 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.1e+03ε (Mean = 185ε))
9045 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br>
9046 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.2e+03ε (Mean
9052 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
9058 <br class="table-break"><div class="table">
9059 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table 17.68. Error rates for legendre_p</b></p>
9060 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
9073 Microsoft Visual C++ version 12.0<br> Win32<br> double
9078 GNU C++ version 5.1.0<br> linux<br> double
9083 GNU C++ version 5.1.0<br> linux<br> long double
9088 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9096 Legendre Polynomials: Small Values
9101 <span class="blue">Max = 211ε (Mean = 20.4ε)</span>
9106 <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br>
9107 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 211ε (Mean = 20.4ε))
9112 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
9113 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
9118 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
9125 Legendre Polynomials: Large Values
9130 <span class="blue">Max = 300ε (Mean = 33.2ε)</span>
9135 <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br>
9136 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 300ε (Mean = 33.2ε))
9141 <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
9142 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
9147 <span class="blue">Max = 699ε (Mean = 59.6ε)</span>
9154 <br class="table-break"><div class="table">
9155 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table 17.69. Error rates for legendre_p (associated)</b></p>
9156 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
9169 Microsoft Visual C++ version 12.0<br> Win32<br> double
9174 GNU C++ version 5.1.0<br> linux<br> double
9179 GNU C++ version 5.1.0<br> linux<br> long double
9184 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9191 Associated Legendre Polynomials: Small Values
9196 <span class="blue">Max = 121ε (Mean = 7.14ε)</span>
9201 <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
9202 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_legendre_p_associated__GSL_1_16_Associated_Legendre_Polynomials_Small_Values">And
9203 other failures.</a>)
9208 <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
9209 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 175ε (Mean = 9.36ε)
9210 <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_legendre_p_associated___tr1_cmath__Associated_Legendre_Polynomials_Small_Values">And
9211 other failures.</a>)
9216 <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
9222 <br class="table-break"><div class="table">
9223 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table 17.70. Error rates for legendre_q</b></p>
9224 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
9237 Microsoft Visual C++ version 12.0<br> Win32<br> double
9242 GNU C++ version 5.1.0<br> linux<br> double
9247 GNU C++ version 5.1.0<br> linux<br> long double
9252 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9260 Legendre Polynomials: Small Values
9265 <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
9270 <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br>
9271 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 46.4ε (Mean = 7.46ε))
9276 <span class="blue">Max = 50.9ε (Mean = 9ε)</span>
9281 <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
9288 Legendre Polynomials: Large Values
9293 <span class="blue">Max = 4.6e+003ε (Mean = 366ε)</span>
9298 <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
9299 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.6e+03ε (Mean = 366ε))
9304 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
9309 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
9316 <br class="table-break"><div class="table">
9317 <a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table 17.71. Error rates for lgamma</b></p>
9318 <div class="table-contents"><table class="table" summary="Error rates for lgamma">
9331 Microsoft Visual C++ version 12.0<br> Win32<br> double
9336 GNU C++ version 5.1.0<br> linux<br> double
9341 GNU C++ version 5.1.0<br> linux<br> long double
9346 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9359 <span class="blue">Max = 0.914ε (Mean = 0.167ε)</span><br> <br>
9360 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
9365 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9366 1.16:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath
9367 3.0.2:</em></span> Max = 1.55ε (Mean = 0.592ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9368 Max = 1.55ε (Mean = 0.512ε))
9373 <span class="blue">Max = 0.991ε (Mean = 0.311ε)</span><br> <br>
9374 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
9375 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
9380 <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
9381 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
9393 <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
9394 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
9399 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9400 1.16:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath
9401 3.0.2:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9402 Max = 1.16ε (Mean = 0.341ε))
9407 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
9408 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
9409 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
9414 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
9415 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
9427 <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
9428 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
9433 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9434 1.16:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath
9435 3.0.2:</em></span> Max = 7.99e+04ε (Mean = 1.68e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9436 Max = 1.14e+05ε (Mean = 2.64e+04ε))
9441 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
9442 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
9443 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
9448 <span class="blue">Max = 0.866ε (Mean = 0.355ε)</span><br> <br>
9449 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
9461 <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
9462 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
9467 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9468 1.16:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
9469 3.0.2:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9470 Max = 5.08e+05ε (Mean = 9.04e+04ε))
9475 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
9476 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
9477 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
9482 <span class="blue">Max = 0.878ε (Mean = 0.241ε)</span><br> <br>
9483 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
9495 <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
9496 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
9501 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9502 1.16:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath
9503 3.0.2:</em></span> Max = 2.41e+05ε (Mean = 4.29e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9504 Max = 0.997ε (Mean = 0.429ε))
9509 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
9510 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.01ε (Mean = 0.86ε))<br>
9511 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.01ε (Mean = 0.86ε))
9516 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
9517 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
9529 <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
9530 (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
9535 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
9536 1.16:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath
9537 3.0.2:</em></span> Max = 4.08e+04ε (Mean = 7.26e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
9538 Max = 1.64ε (Mean = 0.693ε))
9543 <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
9544 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
9545 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
9550 <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
9551 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
9558 <br class="table-break"><div class="table">
9559 <a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table 17.72. Error rates for log1p</b></p>
9560 <div class="table-contents"><table class="table" summary="Error rates for log1p">
9573 Microsoft Visual C++ version 12.0<br> Win32<br> double
9578 GNU C++ version 5.1.0<br> linux<br> double
9583 GNU C++ version 5.1.0<br> linux<br> long double
9588 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9600 <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
9601 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
9606 <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
9607 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.846ε (Mean = 0.153ε))<br>
9608 (<span class="emphasis"><em>Cephes:</em></span> Max = 0.799ε (Mean = 0.122ε))
9613 <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
9614 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
9615 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
9620 <span class="blue">Max = 1.53ε (Mean = 0.627ε)</span><br> <br>
9621 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
9627 <br class="table-break"><div class="table">
9628 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table 17.73. Error rates for non central beta CDF</b></p>
9629 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
9642 Microsoft Visual C++ version 12.0<br> Win32<br> double
9647 GNU C++ version 5.1.0<br> linux<br> double
9652 GNU C++ version 5.1.0<br> linux<br> long double
9657 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9665 Non Central Beta, medium parameters
9670 <span class="blue">Max = 240ε (Mean = 31ε)</span>
9675 <span class="blue">Max = 0.998ε (Mean = 0.0659ε)</span><br>
9676 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
9677 = 1.46e+26ε (Mean = 3.5e+24ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
9678 other failures.</a>)</span>
9683 <span class="blue">Max = 825ε (Mean = 27.4ε)</span>
9688 <span class="blue">Max = 832ε (Mean = 38.1ε)</span>
9695 Non Central Beta, large parameters
9700 <span class="blue">Max = 3.41e+003ε (Mean = 475ε)</span>
9705 <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
9706 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 1.01e+36ε (Mean
9707 = 1.19e+35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
9708 other failures.</a>)</span>
9713 <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
9718 <span class="blue">Max = 2.57e+04ε (Mean = 4.43e+03ε)</span>
9725 <br class="table-break"><div class="table">
9726 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 17.74. Error rates for non central beta CDF complement</b></p>
9727 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
9740 Microsoft Visual C++ version 12.0<br> Win32<br> double
9745 GNU C++ version 5.1.0<br> linux<br> double
9750 GNU C++ version 5.1.0<br> linux<br> long double
9755 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9763 Non Central Beta, medium parameters
9768 <span class="blue">Max = 619ε (Mean = 62.7ε)</span>
9773 <span class="blue">Max = 0.998ε (Mean = 0.0957ε)</span><br>
9774 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
9775 = 7.5e+97ε (Mean = 1.37e+96ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
9776 other failures.</a>)</span>
9781 <span class="blue">Max = 396ε (Mean = 50.7ε)</span>
9786 <span class="blue">Max = 554ε (Mean = 57.3ε)</span>
9793 Non Central Beta, large parameters
9798 <span class="blue">Max = 8.67e+003ε (Mean = 1.04e+003ε)</span>
9803 <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
9804 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
9805 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
9806 other failures.</a>)</span>
9811 <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
9816 <span class="blue">Max = 3.56e+03ε (Mean = 704ε)</span>
9823 <br class="table-break"><div class="table">
9824 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 17.75. Error rates for non central chi squared CDF</b></p>
9825 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
9838 Microsoft Visual C++ version 12.0<br> Win32<br> double
9843 GNU C++ version 5.1.0<br> linux<br> double
9848 GNU C++ version 5.1.0<br> linux<br> long double
9853 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9861 Non Central Chi Squared, medium parameters
9866 <span class="blue">Max = 48.9ε (Mean = 10ε)</span>
9871 <span class="blue">Max = 0.99ε (Mean = 0.0529ε)</span><br> <br>
9872 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 727ε (Mean = 121ε))
9877 <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
9882 <span class="blue">Max = 115ε (Mean = 13.9ε)</span>
9889 Non Central Chi Squared, large parameters
9894 <span class="blue">Max = 9.79e+003ε (Mean = 723ε)</span>
9899 <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
9900 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 3.27e+08ε (Mean
9901 = 2.23e+07ε))</span>
9906 <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
9911 <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
9918 <br class="table-break"><div class="table">
9919 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 17.76. Error rates for non central chi squared CDF complement</b></p>
9920 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
9933 Microsoft Visual C++ version 12.0<br> Win32<br> double
9938 GNU C++ version 5.1.0<br> linux<br> double
9943 GNU C++ version 5.1.0<br> linux<br> long double
9948 Sun compiler version 0x5130<br> Sun Solaris<br> long double
9956 Non Central Chi Squared, medium parameters
9961 <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
9966 <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
9967 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
9968 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_medium_parameters">And
9969 other failures.</a>)</span>
9974 <span class="blue">Max = 107ε (Mean = 17.1ε)</span>
9979 <span class="blue">Max = 171ε (Mean = 22.8ε)</span>
9986 Non Central Chi Squared, large parameters
9991 <span class="blue">Max = 5.43e+003ε (Mean = 705ε)</span>
9996 <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
9997 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
9998 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_large_parameters">And
9999 other failures.</a>)</span>
10004 <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
10009 <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
10016 <br class="table-break"><div class="table">
10017 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table 17.77. Error rates for non central t CDF</b></p>
10018 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
10031 Microsoft Visual C++ version 12.0<br> Win32<br> double
10036 GNU C++ version 5.1.0<br> linux<br> double
10041 GNU C++ version 5.1.0<br> linux<br> long double
10046 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10059 <span class="blue">Max = 138ε (Mean = 31.5ε)</span>
10064 <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br>
10065 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10066 = 5.28e+15ε (Mean = 8.49e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_Rmath_3_0_2_Non_Central_T">And
10067 other failures.</a>)</span>
10072 <span class="blue">Max = 141ε (Mean = 31.1ε)</span>
10077 <span class="blue">Max = 145ε (Mean = 30.2ε)</span>
10084 Non Central T (small non-centrality)
10089 <span class="blue">Max = 3.61ε (Mean = 1.03ε)</span>
10094 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
10095 3.0.2:</em></span> Max = 2.09e+03ε (Mean = 244ε))
10100 <span class="blue">Max = 7.86ε (Mean = 1.69ε)</span>
10105 <span class="blue">Max = 9.15ε (Mean = 2.25ε)</span>
10112 Non Central T (large parameters)
10117 <span class="blue">Max = 286ε (Mean = 62.8ε)</span>
10122 <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
10123 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.46ε (Mean = 0.657ε))
10128 <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
10133 <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
10140 <br class="table-break"><div class="table">
10141 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 17.78. Error rates for non central t CDF complement</b></p>
10142 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
10155 Microsoft Visual C++ version 12.0<br> Win32<br> double
10160 GNU C++ version 5.1.0<br> linux<br> double
10165 GNU C++ version 5.1.0<br> linux<br> long double
10170 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10183 <span class="blue">Max = 150ε (Mean = 32.3ε)</span>
10188 <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br>
10189 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10190 = 6.19e+15ε (Mean = 6.72e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_0_2_Non_Central_T">And
10191 other failures.</a>)</span>
10196 <span class="blue">Max = 203ε (Mean = 31.8ε)</span>
10201 <span class="blue">Max = 340ε (Mean = 43.6ε)</span>
10208 Non Central T (small non-centrality)
10213 <span class="blue">Max = 5.21ε (Mean = 1.43ε)</span>
10218 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
10219 3.0.2:</em></span> Max = 1.87e+03ε (Mean = 263ε))
10224 <span class="blue">Max = 7.48ε (Mean = 1.86ε)</span>
10229 <span class="blue">Max = 10.9ε (Mean = 2.43ε)</span>
10236 Non Central T (large parameters)
10241 <span class="blue">Max = 227ε (Mean = 50.4ε)</span>
10246 <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
10247 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.24ε (Mean = 0.945ε))
10252 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
10257 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
10264 <br class="table-break"><div class="table">
10265 <a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table 17.79. Error rates for owens_t</b></p>
10266 <div class="table-contents"><table class="table" summary="Error rates for owens_t">
10279 Microsoft Visual C++ version 12.0<br> Win32<br> double
10284 GNU C++ version 5.1.0<br> linux<br> double
10289 GNU C++ version 5.1.0<br> linux<br> long double
10294 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10302 Owens T (medium small values)
10307 <span class="blue">Max = 4.37ε (Mean = 0.973ε)</span>
10312 <span class="blue">Max = 0ε (Mean = 0ε)</span>
10317 <span class="blue">Max = 3.34ε (Mean = 0.942ε)</span>
10322 <span class="blue">Max = 3.34ε (Mean = 0.91ε)</span>
10329 Owens T (large and diverse values)
10334 <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
10339 <span class="blue">Max = 0ε (Mean = 0ε)</span>
10344 <span class="blue">Max = 49ε (Mean = 2.16ε)</span>
10349 <span class="blue">Max = 24.5ε (Mean = 1.38ε)</span>
10356 <br class="table-break"><div class="table">
10357 <a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table 17.80. Error rates for polygamma</b></p>
10358 <div class="table-contents"><table class="table" summary="Error rates for polygamma">
10371 Microsoft Visual C++ version 12.0<br> Win32<br> double
10376 GNU C++ version 5.1.0<br> linux<br> double
10381 GNU C++ version 5.1.0<br> linux<br> long double
10386 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10399 <span class="blue">Max = 6.34ε (Mean = 1.53ε)</span>
10404 <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br>
10405 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 108ε (Mean = 15.2ε))<br>
10406 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 62.9ε (Mean = 12.8ε))
10411 <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
10416 <span class="blue">Max = 18.3ε (Mean = 4.16ε)</span>
10423 Mathematica Data - large arguments
10428 <span class="blue">Max = 150ε (Mean = 15.1ε)</span>
10433 <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br>
10434 <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10435 = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_arguments">And
10436 other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10437 Max = 244ε (Mean = 32.8ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_arguments">And
10438 other failures.</a>)
10443 <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
10448 <span class="blue">Max = 2.35ε (Mean = 0.34ε)</span>
10455 Mathematica Data - negative arguments
10460 <span class="blue">Max = 497ε (Mean = 129ε)</span>
10465 <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
10466 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
10467 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_negative_arguments">And
10468 other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10469 Max = 36.6ε (Mean = 3.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_negative_arguments">And
10470 other failures.</a>)
10475 <span class="blue">Max = 269ε (Mean = 87.7ε)</span>
10480 <span class="blue">Max = 269ε (Mean = 87.9ε)</span>
10487 Mathematica Data - large negative arguments
10492 <span class="blue">Max = 162ε (Mean = 101ε)</span>
10497 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
10498 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_negative_arguments">And
10499 other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10500 Max = 1.79ε (Mean = 0.197ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_negative_arguments">And
10501 other failures.</a>)
10506 <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
10511 <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
10518 Mathematica Data - small arguments
10523 <span class="blue">Max = 3ε (Mean = 0.496ε)</span>
10528 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
10529 3.0.2:</em></span> Max = 106ε (Mean = 20ε))<br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10530 Max = 15.2ε (Mean = 5.03ε))
10535 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
10540 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
10547 Mathematica Data - Large orders and other bug cases
10552 <span class="blue">Max = 200ε (Mean = 57.2ε)</span>
10557 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
10558 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_Large_orders_and_other_bug_cases">And
10559 other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10560 Max = 151ε (Mean = 39.3ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_Large_orders_and_other_bug_cases">And
10561 other failures.</a>)
10566 <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
10571 <span class="blue">Max = 90.1ε (Mean = 30.6ε)</span>
10578 <br class="table-break"><div class="table">
10579 <a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table 17.81. Error rates for powm1</b></p>
10580 <div class="table-contents"><table class="table" summary="Error rates for powm1">
10593 Microsoft Visual C++ version 12.0<br> Win32<br> double
10598 GNU C++ version 5.1.0<br> linux<br> double
10603 GNU C++ version 5.1.0<br> linux<br> long double
10608 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10620 <span class="blue">Max = 1.99ε (Mean = 0.461ε)</span>
10625 <span class="blue">Max = 1.26ε (Mean = 0.428ε)</span>
10630 <span class="blue">Max = 2.04ε (Mean = 0.521ε)</span>
10635 <span class="blue">Max = 2.14ε (Mean = 0.498ε)</span>
10641 <br class="table-break"><div class="table">
10642 <a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table 17.82. Error rates for sin_pi</b></p>
10643 <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
10656 Microsoft Visual C++ version 12.0<br> Win32<br> double
10661 GNU C++ version 5.1.0<br> linux<br> double
10666 GNU C++ version 5.1.0<br> linux<br> long double
10671 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10684 <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
10689 <span class="blue">Max = 0ε (Mean = 0ε)</span>
10694 <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
10699 <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
10706 sin_pi and cos_pi near integers and half integers
10711 <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
10716 <span class="blue">Max = 0ε (Mean = 0ε)</span>
10721 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
10726 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
10733 <br class="table-break"><div class="table">
10734 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table 17.83. Error rates for sph_bessel</b></p>
10735 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
10748 Microsoft Visual C++ version 12.0<br> Win32<br> double
10753 GNU C++ version 5.1.0<br> linux<br> long double
10758 GNU C++ version 5.1.0<br> linux<br> double
10763 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10770 Bessel j: Random Data
10775 <span class="blue">Max = 245ε (Mean = 16.3ε)</span>
10780 <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
10781 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.91e+06ε (Mean =
10787 <span class="blue">Max = 0.978ε (Mean = 0.0539ε)</span><br>
10788 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.79e+03ε (Mean = 107ε))
10793 <span class="blue">Max = 243ε (Mean = 33.7ε)</span>
10799 <br class="table-break"><div class="table">
10800 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table 17.84. Error rates for sph_bessel_prime</b></p>
10801 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
10814 Microsoft Visual C++ version 12.0<br> Win32<br> double
10819 GNU C++ version 5.1.0<br> linux<br> double
10824 GNU C++ version 5.1.0<br> linux<br> long double
10829 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10836 Bessel j': Random Data
10841 <span class="blue">Max = 307ε (Mean = 25.2ε)</span>
10846 <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
10851 <span class="blue">Max = 167ε (Mean = 12ε)</span>
10856 <span class="blue">Max = 167ε (Mean = 33.2ε)</span>
10862 <br class="table-break"><div class="table">
10863 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table 17.85. Error rates for sph_neumann</b></p>
10864 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
10877 Microsoft Visual C++ version 12.0<br> Win32<br> double
10882 GNU C++ version 5.1.0<br> linux<br> double
10887 GNU C++ version 5.1.0<br> linux<br> long double
10892 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10904 <span class="blue">Max = 281ε (Mean = 31.1ε)</span>
10909 <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br>
10910 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
10915 <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
10916 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
10921 <span class="blue">Max = 234ε (Mean = 19.8ε)</span>
10927 <br class="table-break"><div class="table">
10928 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table 17.86. Error rates for sph_neumann_prime</b></p>
10929 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
10942 Microsoft Visual C++ version 12.0<br> Win32<br> double
10947 GNU C++ version 5.1.0<br> linux<br> double
10952 GNU C++ version 5.1.0<br> linux<br> long double
10957 Sun compiler version 0x5130<br> Sun Solaris<br> long double
10969 <span class="blue">Max = 296ε (Mean = 25.6ε)</span>
10974 <span class="blue">Max = 0.752ε (Mean = 0.062ε)</span>
10979 <span class="blue">Max = 158ε (Mean = 18.8ε)</span>
10984 <span class="blue">Max = 158ε (Mean = 20.2ε)</span>
10990 <br class="table-break"><div class="table">
10991 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table 17.87. Error rates for spherical_harmonic_i</b></p>
10992 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
11005 Microsoft Visual C++ version 12.0<br> Win32<br> double
11010 GNU C++ version 5.1.0<br> linux<br> double
11015 GNU C++ version 5.1.0<br> linux<br> long double
11020 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11027 Spherical Harmonics
11032 <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
11037 <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
11042 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
11047 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
11053 <br class="table-break"><div class="table">
11054 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table 17.88. Error rates for spherical_harmonic_r</b></p>
11055 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
11068 Microsoft Visual C++ version 12.0<br> Win32<br> double
11073 GNU C++ version 5.1.0<br> linux<br> double
11078 GNU C++ version 5.1.0<br> linux<br> long double
11083 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11090 Spherical Harmonics
11095 <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
11100 <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
11105 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
11110 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
11116 <br class="table-break"><div class="table">
11117 <a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table 17.89. Error rates for sqrt1pm1</b></p>
11118 <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
11131 Microsoft Visual C++ version 12.0<br> Win32<br> double
11136 GNU C++ version 5.1.0<br> linux<br> double
11141 GNU C++ version 5.1.0<br> linux<br> long double
11146 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11158 <span class="blue">Max = 1.36ε (Mean = 0.44ε)</span>
11163 <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
11168 <span class="blue">Max = 1.33ε (Mean = 0.409ε)</span>
11173 <span class="blue">Max = 1.54ε (Mean = 0.568ε)</span>
11179 <br class="table-break"><div class="table">
11180 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table 17.90. Error rates for tgamma</b></p>
11181 <div class="table-contents"><table class="table" summary="Error rates for tgamma">
11194 Microsoft Visual C++ version 12.0<br> Win32<br> double
11199 GNU C++ version 5.1.0<br> linux<br> double
11204 GNU C++ version 5.1.0<br> linux<br> long double
11209 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11222 <span class="blue">Max = 1.85ε (Mean = 0.491ε)</span><br> <br>
11223 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
11228 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11229 1.16:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
11230 3.0.2:</em></span> Max = 314ε (Mean = 93.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11231 Max = 3.19ε (Mean = 0.884ε))
11236 <span class="blue">Max = 1.96ε (Mean = 0.483ε)</span><br> <br>
11237 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
11238 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
11243 <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br>
11244 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
11256 <span class="blue">Max = 1.96ε (Mean = 0.684ε)</span><br> <br>
11257 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
11262 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11263 1.16:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath
11264 3.0.2:</em></span> Max = 1ε (Mean = 0.335ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11265 Max = 1ε (Mean = 0.548ε))
11270 <span class="blue">Max = 2ε (Mean = 0.73ε)</span><br> <br>
11271 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1ε (Mean = 0.376ε))<br>
11272 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.376ε))
11277 <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br>
11278 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.5ε (Mean = 0.0791ε))
11290 <span class="blue">Max = 2ε (Mean = 0.865ε)</span><br> <br>
11291 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
11296 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11297 1.16:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath
11298 3.0.2:</em></span> Max = 1ε (Mean = 0.32ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11299 Max = 1ε (Mean = 0.518ε))
11304 <span class="blue">Max = 2ε (Mean = 0.85ε)</span><br> <br>
11305 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
11306 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
11311 <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
11312 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
11324 <span class="blue">Max = 2ε (Mean = 0.995ε)</span><br> <br>
11325 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
11330 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11331 1.16:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath
11332 3.0.2:</em></span> Max = 1ε (Mean = 0.191ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11333 Max = 1.09ε (Mean = 0.502ε))
11338 <span class="blue">Max = 2ε (Mean = 0.913ε)</span><br> <br>
11339 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
11340 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
11345 <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
11346 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
11358 <span class="blue">Max = 1.73ε (Mean = 0.729ε)</span><br> <br>
11359 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
11364 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11365 1.16:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath
11366 3.0.2:</em></span> Max = 6.34e+05ε (Mean = 1.2e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11367 Max = 2.6ε (Mean = 0.956ε))
11372 <span class="blue">Max = 2.6ε (Mean = 0.985ε)</span><br> <br>
11373 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
11374 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
11379 <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
11380 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
11392 <span class="blue">Max = 1.8ε (Mean = 0.817ε)</span><br> <br>
11393 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+004ε (Mean = 6.71e+003ε))
11398 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11399 1.16:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath
11400 3.0.2:</em></span> Max = 6.36e+06ε (Mean = 1.13e+06ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
11401 Max = 2.7ε (Mean = 0.988ε))
11406 <span class="blue">Max = 1.8ε (Mean = 0.847ε)</span><br> <br>
11407 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
11408 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
11413 <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
11414 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
11421 <br class="table-break"><div class="table">
11422 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table 17.91. Error rates for tgamma1pm1</b></p>
11423 <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
11436 Microsoft Visual C++ version 12.0<br> Win32<br> double
11441 GNU C++ version 5.1.0<br> linux<br> double
11446 GNU C++ version 5.1.0<br> linux<br> long double
11451 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11463 <span class="blue">Max = 0.982ε (Mean = 0.399ε)</span>
11468 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11473 <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
11478 <span class="blue">Max = 3.97ε (Mean = 0.713ε)</span>
11484 <br class="table-break"><div class="table">
11485 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table 17.92. Error rates for tgamma_delta_ratio</b></p>
11486 <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
11499 Microsoft Visual C++ version 12.0<br> Win32<br> double
11504 GNU C++ version 5.1.0<br> linux<br> double
11509 GNU C++ version 5.1.0<br> linux<br> long double
11514 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11522 tgamma + small delta ratios
11527 <span class="blue">Max = 10.1ε (Mean = 1.25ε)</span>
11532 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11537 <span class="blue">Max = 5.56ε (Mean = 0.969ε)</span>
11542 <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
11549 tgamma + small delta ratios (negative delta)
11554 <span class="blue">Max = 8.04ε (Mean = 1.31ε)</span>
11559 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11564 <span class="blue">Max = 8.67ε (Mean = 1.29ε)</span>
11569 <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
11576 tgamma + small integer ratios
11581 <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
11586 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11591 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
11596 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
11603 tgamma + small integer ratios (negative delta)
11608 <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
11613 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11618 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
11623 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
11630 integer tgamma ratios
11635 <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
11640 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11645 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
11650 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
11657 integer tgamma ratios (negative delta)
11662 <span class="blue">Max = 0.974ε (Mean = 0.184ε)</span>
11667 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11672 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
11677 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
11684 <br class="table-break"><div class="table">
11685 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table 17.93. Error rates for tgamma (incomplete)</b></p>
11686 <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
11699 Microsoft Visual C++ version 12.0<br> Win32<br> double
11704 GNU C++ version 5.1.0<br> linux<br> double
11709 GNU C++ version 5.1.0<br> linux<br> long double
11714 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11722 tgamma(a, z) medium values
11727 <span class="blue">Max = 8.14ε (Mean = 1.71ε)</span>
11732 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11733 1.16:</em></span> Max = 200ε (Mean = 13.3ε))
11738 <span class="blue">Max = 7.35ε (Mean = 1.69ε)</span>
11743 <span class="blue">Max = 412ε (Mean = 95.5ε)</span>
11750 tgamma(a, z) small values
11755 <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
11760 <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br>
11761 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> <span class="red">Max =
11762 1.38e+10ε (Mean = 1.05e+09ε))</span>
11767 <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
11772 <span class="blue">Max = 2.13ε (Mean = 0.712ε)</span>
11779 tgamma(a, z) integer and half integer values
11784 <span class="blue">Max = 5.16ε (Mean = 1.44ε)</span>
11789 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11790 1.16:</em></span> Max = 117ε (Mean = 12.5ε))
11795 <span class="blue">Max = 5.52ε (Mean = 1.52ε)</span>
11800 <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
11807 <br class="table-break"><div class="table">
11808 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table 17.94. Error rates for tgamma_lower</b></p>
11809 <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
11822 Microsoft Visual C++ version 12.0<br> Win32<br> double
11827 GNU C++ version 5.1.0<br> linux<br> double
11832 GNU C++ version 5.1.0<br> linux<br> long double
11837 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11845 tgamma(a, z) medium values
11850 <span class="blue">Max = 5.62ε (Mean = 1.43ε)</span>
11855 <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br>
11856 <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.833ε (Mean = 0.0315ε))
11861 <span class="blue">Max = 6.79ε (Mean = 1.38ε)</span>
11866 <span class="blue">Max = 363ε (Mean = 63.8ε)</span>
11873 tgamma(a, z) small values
11878 <span class="blue">Max = 1.57ε (Mean = 0.527ε)</span>
11883 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11884 1.16:</em></span> Max = 0ε (Mean = 0ε))
11889 <span class="blue">Max = 1.97ε (Mean = 0.552ε)</span>
11894 <span class="blue">Max = 1.97ε (Mean = 0.567ε)</span>
11901 tgamma(a, z) integer and half integer values
11906 <span class="blue">Max = 2.69ε (Mean = 0.866ε)</span>
11911 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
11912 1.16:</em></span> Max = 0ε (Mean = 0ε))
11917 <span class="blue">Max = 4.83ε (Mean = 1.12ε)</span>
11922 <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
11929 <br class="table-break"><div class="table">
11930 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table 17.95. Error rates for tgamma_ratio</b></p>
11931 <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
11944 Microsoft Visual C++ version 12.0<br> Win32<br> double
11949 GNU C++ version 5.1.0<br> linux<br> double
11954 GNU C++ version 5.1.0<br> linux<br> long double
11959 Sun compiler version 0x5130<br> Sun Solaris<br> long double
11971 <span class="blue">Max = 3.66ε (Mean = 1.27ε)</span>
11976 <span class="blue">Max = 0ε (Mean = 0ε)</span>
11981 <span class="blue">Max = 3.09ε (Mean = 1.15ε)</span>
11986 <span class="blue">Max = 174ε (Mean = 61.2ε)</span>
11992 <br class="table-break"><div class="table">
11993 <a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table 17.96. Error rates for trigamma</b></p>
11994 <div class="table-contents"><table class="table" summary="Error rates for trigamma">
12007 Microsoft Visual C++ version 12.0<br> Win32<br> double
12012 GNU C++ version 5.1.0<br> linux<br> double
12017 GNU C++ version 5.1.0<br> linux<br> long double
12022 Sun compiler version 0x5130<br> Sun Solaris<br> long double
12034 <span class="blue">Max = 1ε (Mean = 0.382ε)</span>
12039 <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
12040 (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))<br>
12041 (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))
12046 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
12051 <span class="blue">Max = 1.28ε (Mean = 0.447ε)</span>
12057 <br class="table-break"><div class="table">
12058 <a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table 17.97. Error rates for zeta</b></p>
12059 <div class="table-contents"><table class="table" summary="Error rates for zeta">
12072 Microsoft Visual C++ version 12.0<br> Win32<br> double
12077 GNU C++ version 5.1.0<br> linux<br> double
12082 GNU C++ version 5.1.0<br> linux<br> long double
12087 Sun compiler version 0x5130<br> Sun Solaris<br> long double
12095 Zeta: Random values greater than 1
12100 <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
12105 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
12106 1.16:</em></span> Max = 8.69ε (Mean = 1.03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
12107 <span class="red">Max = 4.49e+33ε (Mean = 6.85e+32ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_greater_than_1">And
12108 other failures.</a>)</span>
12113 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br>
12114 <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.45ε (Mean
12120 <span class="blue">Max = 0.846ε (Mean = 0.0743ε)</span>
12127 Zeta: Random values less than 1
12132 <span class="blue">Max = 7.03ε (Mean = 2.98ε)</span>
12137 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
12138 1.16:</em></span> Max = 137ε (Mean = 13.8ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
12139 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_less_than_1">And
12140 other failures.</a>)</span>
12145 <span class="blue">Max = 7.03ε (Mean = 2.71ε)</span><br> <br>
12146 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
12151 <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
12158 Zeta: Values close to and greater than 1
12163 <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
12168 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
12169 1.16:</em></span> Max = 7.73ε (Mean = 4.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
12170 <span class="red">Max = 6.77e+15ε (Mean = 1.52e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_greater_than_1">And
12171 other failures.</a>)</span>
12176 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
12177 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
12182 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
12189 Zeta: Values close to and less than 1
12194 <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
12199 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
12200 1.16:</em></span> Max = 0.991ε (Mean = 0.28ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
12201 <span class="red">Max = 8.66e+15ε (Mean = 1.9e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_less_than_1">And
12202 other failures.</a>)</span>
12207 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
12208 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.53e+06ε (Mean =
12214 <span class="blue">Max = 0.998ε (Mean = 0.568ε)</span>
12221 Zeta: Integer arguments
12226 <span class="blue">Max = 6.5ε (Mean = 2.17ε)</span>
12231 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
12232 1.16:</em></span> Max = 3.75ε (Mean = 1.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
12233 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Integer_arguments">And
12234 other failures.</a>)</span>
12239 <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br>
12240 (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 70.3ε (Mean = 17.4ε))
12245 <span class="blue">Max = 21ε (Mean = 7.13ε)</span>
12252 <br class="table-break">
12254 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
12255 <td align="left"></td>
12256 <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
12257 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
12258 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
12259 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
12260 Distributed under the Boost Software License, Version 1.0. (See accompanying
12261 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
12266 <div class="spirit-nav">
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