2000-08-21 17:06:46 +00:00
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# Begin of automatic generation
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2002-09-04 23:40:45 +00:00
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# Maximal error of functions:
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2015-04-24 11:36:23 +00:00
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Function: "acos":
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2021-03-03 11:22:08 +00:00
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double: 1
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2015-04-24 11:36:23 +00:00
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float: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 1
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2015-04-24 11:36:23 +00:00
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2012-05-04 08:05:41 +00:00
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Function: "acos_downward":
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2016-01-19 09:00:52 +00:00
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double: 1
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2012-05-04 08:05:41 +00:00
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float: 1
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ldouble: 1
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Function: "acos_towardzero":
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2015-04-24 11:36:23 +00:00
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double: 1
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2012-05-04 08:05:41 +00:00
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float: 1
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ldouble: 1
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2012-06-25 08:28:03 +00:00
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Function: "acos_upward":
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2014-01-15 08:49:54 +00:00
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double: 1
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2015-04-24 11:36:23 +00:00
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float: 1
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ldouble: 1
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2014-01-15 08:49:54 +00:00
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Function: "acosh":
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2016-01-19 09:00:52 +00:00
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double: 2
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2015-06-19 11:47:59 +00:00
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float: 2
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2021-03-03 11:22:08 +00:00
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ldouble: 4
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2014-01-15 08:49:54 +00:00
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2014-06-03 15:27:13 +00:00
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Function: "acosh_downward":
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2018-02-22 08:13:22 +00:00
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double: 2
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2016-01-19 09:00:52 +00:00
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float: 2
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ldouble: 3
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2014-06-03 15:27:13 +00:00
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Function: "acosh_towardzero":
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2015-06-19 11:47:59 +00:00
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double: 2
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2016-01-19 09:00:52 +00:00
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float: 2
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ldouble: 2
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2014-06-03 15:27:13 +00:00
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Function: "acosh_upward":
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2015-06-19 11:47:59 +00:00
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double: 2
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2016-01-19 09:00:52 +00:00
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float: 2
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2021-03-03 11:22:08 +00:00
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ldouble: 3
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2014-06-03 15:27:13 +00:00
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2014-01-15 08:49:54 +00:00
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Function: "asin":
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2021-03-03 11:22:08 +00:00
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double: 1
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2015-04-24 11:36:23 +00:00
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float: 1
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2012-06-25 08:28:03 +00:00
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ldouble: 1
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2012-05-04 08:05:41 +00:00
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Function: "asin_downward":
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double: 1
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float: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2012-05-04 08:05:41 +00:00
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Function: "asin_towardzero":
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2016-01-19 09:00:52 +00:00
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double: 1
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2012-05-04 08:05:41 +00:00
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float: 1
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2014-01-15 08:49:54 +00:00
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ldouble: 1
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2012-05-04 08:05:41 +00:00
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Function: "asin_upward":
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2021-03-12 13:31:49 +00:00
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double: 2
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2014-01-15 08:49:54 +00:00
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float: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2014-01-15 08:49:54 +00:00
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Function: "asinh":
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2020-12-22 18:20:56 +00:00
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double: 2
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2020-04-03 07:38:02 +00:00
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float: 2
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2021-03-03 11:22:08 +00:00
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ldouble: 4
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2012-05-04 08:05:41 +00:00
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2014-04-16 11:00:29 +00:00
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Function: "asinh_downward":
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2015-04-24 11:36:23 +00:00
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double: 3
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float: 3
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2016-01-19 09:00:52 +00:00
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ldouble: 4
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2014-04-16 11:00:29 +00:00
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Function: "asinh_towardzero":
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2015-03-12 10:04:13 +00:00
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double: 2
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 2
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Function: "asinh_upward":
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2015-04-24 11:36:23 +00:00
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double: 3
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float: 3
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2016-01-19 09:00:52 +00:00
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ldouble: 4
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2014-04-16 11:00:29 +00:00
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2014-01-15 08:49:54 +00:00
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Function: "atan":
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2021-03-12 13:31:49 +00:00
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double: 1
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2015-04-24 11:36:23 +00:00
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float: 1
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ldouble: 1
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2014-01-15 08:49:54 +00:00
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2002-09-04 23:40:45 +00:00
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Function: "atan2":
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2005-07-20 18:20:48 +00:00
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float: 1
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2021-03-03 11:22:08 +00:00
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ldouble: 2
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2000-08-21 17:06:46 +00:00
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2014-04-16 11:00:29 +00:00
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Function: "atan2_downward":
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double: 1
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float: 2
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2014-04-16 11:00:29 +00:00
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Function: "atan2_towardzero":
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double: 1
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float: 2
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2016-01-19 09:00:52 +00:00
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ldouble: 3
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2014-04-16 11:00:29 +00:00
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Function: "atan2_upward":
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double: 1
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float: 1
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ldouble: 2
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Function: "atan_downward":
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double: 1
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2015-06-19 11:47:59 +00:00
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float: 2
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2015-04-24 11:36:23 +00:00
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ldouble: 2
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2014-04-16 11:00:29 +00:00
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Function: "atan_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "atan_upward":
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double: 1
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2015-04-24 11:36:23 +00:00
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float: 2
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2014-04-16 11:00:29 +00:00
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2002-09-04 23:40:45 +00:00
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Function: "atanh":
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2016-01-19 09:00:52 +00:00
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double: 2
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2015-06-19 11:47:59 +00:00
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float: 2
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2021-03-03 11:22:08 +00:00
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ldouble: 4
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2000-08-21 17:06:46 +00:00
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2014-04-16 11:00:29 +00:00
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Function: "atanh_downward":
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2015-06-19 11:47:59 +00:00
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double: 3
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2016-01-19 09:00:52 +00:00
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float: 3
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ldouble: 4
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2015-04-24 11:36:23 +00:00
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Function: "atanh_towardzero":
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double: 2
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float: 2
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ldouble: 2
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Function: "atanh_upward":
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2016-01-19 09:00:52 +00:00
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double: 3
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2015-04-24 11:36:23 +00:00
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float: 3
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2016-01-19 09:00:52 +00:00
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ldouble: 4
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2015-04-24 11:36:23 +00:00
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Function: "cabs":
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2014-04-16 11:00:29 +00:00
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double: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 1
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2014-04-16 11:00:29 +00:00
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2015-04-24 11:36:23 +00:00
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Function: "cabs_downward":
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2015-03-12 10:04:13 +00:00
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double: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 1
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2014-04-16 11:00:29 +00:00
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2015-04-24 11:36:23 +00:00
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Function: "cabs_towardzero":
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double: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 1
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2015-04-24 11:36:23 +00:00
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Function: "cabs_upward":
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2014-04-16 11:00:29 +00:00
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double: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 1
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2014-04-16 11:00:29 +00:00
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2012-05-04 08:05:41 +00:00
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Function: Real part of "cacos":
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double: 1
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2013-07-22 07:51:52 +00:00
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float: 2
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ldouble: 2
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2006-02-01 03:02:06 +00:00
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2012-05-04 08:05:41 +00:00
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Function: Imaginary part of "cacos":
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2017-03-08 07:34:58 +00:00
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double: 2
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2013-07-22 07:51:52 +00:00
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float: 2
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ldouble: 2
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2012-05-04 08:05:41 +00:00
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2014-06-03 15:27:13 +00:00
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Function: Real part of "cacos_downward":
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2017-03-08 07:34:58 +00:00
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double: 3
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2014-06-03 15:27:13 +00:00
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float: 2
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2017-03-08 07:34:58 +00:00
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ldouble: 3
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2014-06-03 15:27:13 +00:00
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Function: Imaginary part of "cacos_downward":
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double: 5
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float: 3
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2017-03-08 07:34:58 +00:00
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ldouble: 6
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2014-06-03 15:27:13 +00:00
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Function: Real part of "cacos_towardzero":
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2017-03-08 07:34:58 +00:00
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double: 3
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2014-06-03 15:27:13 +00:00
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float: 2
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2017-03-08 07:34:58 +00:00
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ldouble: 3
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2014-06-03 15:27:13 +00:00
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Function: Imaginary part of "cacos_towardzero":
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2017-03-08 07:34:58 +00:00
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double: 4
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float: 2
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2014-06-03 15:27:13 +00:00
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ldouble: 5
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Function: Real part of "cacos_upward":
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double: 2
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float: 2
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ldouble: 3
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Function: Imaginary part of "cacos_upward":
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2017-03-08 07:34:58 +00:00
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double: 5
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float: 5
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ldouble: 7
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2014-06-03 15:27:13 +00:00
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2000-08-21 17:06:46 +00:00
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Function: Real part of "cacosh":
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2017-03-08 07:34:58 +00:00
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double: 2
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2013-07-22 07:51:52 +00:00
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float: 2
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ldouble: 2
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2000-08-21 17:06:46 +00:00
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Function: Imaginary part of "cacosh":
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double: 1
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2013-07-22 07:51:52 +00:00
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float: 2
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ldouble: 2
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2000-08-21 17:06:46 +00:00
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2014-04-16 11:00:29 +00:00
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Function: Real part of "cacosh_downward":
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2017-03-08 07:34:58 +00:00
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double: 4
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 5
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Function: Imaginary part of "cacosh_downward":
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2017-03-08 07:34:58 +00:00
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double: 3
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2014-04-16 11:00:29 +00:00
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float: 3
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2017-03-08 07:34:58 +00:00
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ldouble: 4
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Function: Real part of "cacosh_towardzero":
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double: 4
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 5
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Function: Imaginary part of "cacosh_towardzero":
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2017-03-08 07:34:58 +00:00
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double: 3
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2014-04-16 11:00:29 +00:00
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float: 2
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2017-03-08 07:34:58 +00:00
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ldouble: 3
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2014-04-16 11:00:29 +00:00
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Function: Real part of "cacosh_upward":
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double: 4
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2017-03-08 07:34:58 +00:00
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float: 3
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ldouble: 6
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2014-04-16 11:00:29 +00:00
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Function: Imaginary part of "cacosh_upward":
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2017-03-08 07:34:58 +00:00
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double: 3
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2014-04-16 11:00:29 +00:00
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float: 2
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2017-03-08 07:34:58 +00:00
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ldouble: 4
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2014-04-16 11:00:29 +00:00
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2015-04-24 11:36:23 +00:00
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Function: "carg":
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float: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2015-04-24 11:36:23 +00:00
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2014-04-16 11:00:29 +00:00
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Function: "carg_downward":
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double: 1
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2016-01-19 09:00:52 +00:00
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float: 2
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ldouble: 2
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2014-04-16 11:00:29 +00:00
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Function: "carg_towardzero":
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2015-04-24 11:36:23 +00:00
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double: 1
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float: 2
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2016-01-19 09:00:52 +00:00
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ldouble: 3
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2014-04-16 11:00:29 +00:00
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Function: "carg_upward":
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double: 1
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float: 1
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2016-01-19 09:00:52 +00:00
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ldouble: 2
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2014-04-16 11:00:29 +00:00
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2000-08-21 17:06:46 +00:00
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Function: Real part of "casin":
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2002-09-04 23:40:45 +00:00
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double: 1
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2000-08-21 17:06:46 +00:00
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float: 1
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2013-07-22 07:51:52 +00:00
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ldouble: 2
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2000-08-21 17:06:46 +00:00
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2006-02-01 03:02:06 +00:00
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Function: Imaginary part of "casin":
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2017-03-08 07:34:58 +00:00
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double: 2
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2013-07-22 07:51:52 +00:00
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float: 2
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ldouble: 2
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2006-02-01 03:02:06 +00:00
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2014-04-16 11:00:29 +00:00
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Function: Real part of "casin_downward":
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2015-04-24 11:36:23 +00:00
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double: 3
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2017-03-08 07:34:58 +00:00
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 3
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Function: Imaginary part of "casin_downward":
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double: 5
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float: 3
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2017-03-08 07:34:58 +00:00
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ldouble: 6
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2014-04-16 11:00:29 +00:00
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Function: Real part of "casin_towardzero":
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2015-04-24 11:36:23 +00:00
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double: 3
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2014-04-16 11:00:29 +00:00
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float: 1
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ldouble: 3
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Function: Imaginary part of "casin_towardzero":
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2017-03-08 07:34:58 +00:00
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double: 4
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 5
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Function: Real part of "casin_upward":
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2017-03-08 07:34:58 +00:00
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double: 3
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float: 2
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2014-04-16 11:00:29 +00:00
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ldouble: 3
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Function: Imaginary part of "casin_upward":
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2017-03-08 07:34:58 +00:00
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double: 5
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float: 5
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ldouble: 7
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2014-04-16 11:00:29 +00:00
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|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "casinh":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 2
|
2013-07-22 07:51:52 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "casinh":
|
2013-01-09 15:33:06 +00:00
|
|
|
double: 1
|
|
|
|
float: 1
|
2013-07-22 07:51:52 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "casinh_downward":
|
|
|
|
double: 5
|
|
|
|
float: 3
|
2017-03-08 07:34:58 +00:00
|
|
|
ldouble: 6
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "casinh_downward":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 3
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "casinh_towardzero":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 4
|
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: Imaginary part of "casinh_towardzero":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "casinh_upward":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 5
|
|
|
|
float: 5
|
|
|
|
ldouble: 7
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "casinh_upward":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
2013-07-22 07:51:52 +00:00
|
|
|
Function: Real part of "catan":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 1
|
2013-07-22 07:51:52 +00:00
|
|
|
float: 1
|
2013-01-09 15:33:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catan":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "catan_downward":
|
|
|
|
double: 1
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "catan_downward":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "catan_towardzero":
|
|
|
|
double: 1
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "catan_towardzero":
|
|
|
|
double: 2
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 2
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "catan_upward":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
2017-03-08 07:34:58 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catan_upward":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "catanh":
|
2013-07-22 07:51:52 +00:00
|
|
|
double: 1
|
|
|
|
float: 1
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catanh":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 1
|
2013-07-22 07:51:52 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "catanh_downward":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catanh_downward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "catanh_towardzero":
|
|
|
|
double: 2
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 2
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catanh_towardzero":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "catanh_upward":
|
|
|
|
double: 4
|
2017-03-08 07:34:58 +00:00
|
|
|
float: 4
|
2017-03-10 07:45:29 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "catanh_upward":
|
2017-03-08 07:34:58 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
2017-03-08 07:34:58 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "cbrt":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 4
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "cbrt_downward":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "cbrt_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "cbrt_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 5
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "ccos":
|
|
|
|
double: 1
|
2002-09-04 23:40:45 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "ccos":
|
2012-06-25 08:28:03 +00:00
|
|
|
double: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "ccos_downward":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccos_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "ccos_towardzero":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccos_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "ccos_upward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccos_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "ccosh":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccosh":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: Real part of "ccosh_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccosh_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "ccosh_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Imaginary part of "ccosh_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "ccosh_upward":
|
2012-06-25 08:28:03 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Imaginary part of "ccosh_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Real part of "cexp":
|
2012-05-04 08:05:41 +00:00
|
|
|
double: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "cexp":
|
2012-05-04 08:05:41 +00:00
|
|
|
double: 1
|
|
|
|
float: 2
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2015-07-07 14:11:14 +00:00
|
|
|
Function: Real part of "cexp_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2015-07-07 14:11:14 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "cexp_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2015-07-07 14:11:14 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "cexp_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2015-07-07 14:11:14 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "cexp_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2015-07-07 14:11:14 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "cexp_upward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Imaginary part of "cexp_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2015-07-07 14:11:14 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
2002-09-04 23:40:45 +00:00
|
|
|
Function: Real part of "clog":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2002-09-04 23:40:45 +00:00
|
|
|
|
2012-06-25 08:28:03 +00:00
|
|
|
Function: Imaginary part of "clog":
|
2021-03-12 13:31:49 +00:00
|
|
|
double: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2012-12-21 02:25:54 +00:00
|
|
|
Function: Real part of "clog10":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
float: 4
|
|
|
|
ldouble: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Imaginary part of "clog10":
|
2016-10-04 13:27:40 +00:00
|
|
|
double: 2
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "clog10_downward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 5
|
2017-10-05 10:50:49 +00:00
|
|
|
float: 5
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog10_downward":
|
|
|
|
double: 2
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "clog10_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 5
|
2016-01-19 09:00:52 +00:00
|
|
|
float: 5
|
|
|
|
ldouble: 4
|
2015-04-24 11:36:23 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog10_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 4
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "clog10_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 6
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 5
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog10_upward":
|
|
|
|
double: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
float: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "clog_downward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
|
|
|
float: 3
|
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog_downward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "clog_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
|
|
|
float: 4
|
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog_towardzero":
|
|
|
|
double: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
float: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "clog_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
|
|
|
float: 3
|
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "clog_upward":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 1
|
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "cos":
|
2018-04-05 14:20:03 +00:00
|
|
|
double: 1
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "cos_downward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "cos_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "cos_upward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "cosh":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 2
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 2
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "cosh_downward":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "cosh_towardzero":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "cosh_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "cpow":
|
2002-09-04 23:40:45 +00:00
|
|
|
double: 2
|
2012-06-25 08:28:03 +00:00
|
|
|
float: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 4
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "cpow":
|
|
|
|
float: 2
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
2014-07-01 14:04:58 +00:00
|
|
|
Function: Real part of "cpow_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 5
|
2014-07-01 14:04:58 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 6
|
|
|
|
|
|
|
|
Function: Imaginary part of "cpow_downward":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 1
|
2014-07-01 14:04:58 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "cpow_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 5
|
2014-07-01 14:04:58 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 6
|
|
|
|
|
|
|
|
Function: Imaginary part of "cpow_towardzero":
|
2015-04-24 11:36:23 +00:00
|
|
|
double: 1
|
2014-07-01 14:04:58 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "cpow_upward":
|
|
|
|
double: 4
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Imaginary part of "cpow_upward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
2006-02-01 03:02:06 +00:00
|
|
|
Function: Real part of "csin":
|
2012-06-25 08:28:03 +00:00
|
|
|
double: 1
|
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: Imaginary part of "csin":
|
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "csin_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "csin_downward":
|
|
|
|
double: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "csin_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "csin_towardzero":
|
2015-07-15 07:33:14 +00:00
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "csin_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Imaginary part of "csin_upward":
|
|
|
|
double: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "csinh":
|
|
|
|
float: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csinh":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
2012-06-25 08:28:03 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "csinh_downward":
|
2015-07-07 14:11:14 +00:00
|
|
|
double: 2
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csinh_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: Real part of "csinh_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
2015-07-15 07:33:14 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csinh_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
2015-07-15 07:33:14 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "csinh_upward":
|
|
|
|
double: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Imaginary part of "csinh_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 1
|
2015-07-15 07:33:14 +00:00
|
|
|
float: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "csqrt":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2006-02-01 03:02:06 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csqrt":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: Real part of "csqrt_downward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 5
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 4
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csqrt_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 4
|
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "csqrt_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csqrt_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 4
|
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Real part of "csqrt_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 5
|
|
|
|
float: 4
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "csqrt_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: Real part of "ctan":
|
2000-08-21 17:06:46 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: Imaginary part of "ctan":
|
2012-12-21 02:25:54 +00:00
|
|
|
double: 2
|
2018-02-22 08:13:22 +00:00
|
|
|
float: 2
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: Real part of "ctan_downward":
|
|
|
|
double: 6
|
|
|
|
float: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 4
|
|
|
|
|
|
|
|
Function: Imaginary part of "ctan_downward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 2
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: Real part of "ctan_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 5
|
2018-11-28 14:20:18 +00:00
|
|
|
float: 3
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 4
|
2012-12-21 02:25:54 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "ctan_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: Real part of "ctan_upward":
|
|
|
|
double: 2
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 4
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "ctan_upward":
|
2018-11-28 14:20:18 +00:00
|
|
|
double: 2
|
2018-02-22 08:13:22 +00:00
|
|
|
float: 2
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: Real part of "ctanh":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
float: 2
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: Imaginary part of "ctanh":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2012-12-21 02:25:54 +00:00
|
|
|
Function: Real part of "ctanh_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 2
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: Imaginary part of "ctanh_downward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 6
|
|
|
|
float: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 4
|
|
|
|
|
|
|
|
Function: Real part of "ctanh_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2012-12-21 02:25:54 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: Imaginary part of "ctanh_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: Real part of "ctanh_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 1
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 2
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 5
|
2014-01-15 08:49:54 +00:00
|
|
|
|
2012-12-21 02:25:54 +00:00
|
|
|
Function: Imaginary part of "ctanh_upward":
|
|
|
|
double: 2
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 3
|
|
|
|
ldouble: 5
|
2012-12-21 02:25:54 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "erf":
|
|
|
|
double: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "erf_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "erf_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 1
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "erf_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 1
|
2004-07-01 01:43:38 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "erfc":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 4
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "erfc_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 4
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 4
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "erfc_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "erfc_upward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 4
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 4
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "exp":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 1
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
|
|
|
|
Function: "exp10":
|
2014-04-16 11:00:29 +00:00
|
|
|
double: 2
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2015-06-19 11:47:59 +00:00
|
|
|
|
|
|
|
Function: "exp10_downward":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2020-06-24 12:51:06 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "exp10_towardzero":
|
2018-09-06 12:29:01 +00:00
|
|
|
double: 3
|
2020-06-24 12:51:06 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "exp10_upward":
|
|
|
|
double: 2
|
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2024-06-19 06:42:30 +00:00
|
|
|
Function: "exp10m1":
|
|
|
|
double: 2
|
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "exp10m1_downward":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "exp10m1_towardzero":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "exp10m1_upward":
|
|
|
|
double: 3
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
2015-06-19 11:47:59 +00:00
|
|
|
Function: "exp2":
|
2012-12-21 02:25:54 +00:00
|
|
|
double: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
2015-06-19 11:47:59 +00:00
|
|
|
Function: "exp2_downward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
|
2015-06-19 11:47:59 +00:00
|
|
|
Function: "exp2_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
|
2015-06-19 11:47:59 +00:00
|
|
|
Function: "exp2_upward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2024-06-19 06:42:30 +00:00
|
|
|
Function: "exp2m1":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "exp2m1_downward":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "exp2m1_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "exp2m1_upward":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "exp_downward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2017-10-05 10:50:49 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
|
|
|
|
Function: "exp_towardzero":
|
|
|
|
double: 1
|
2017-10-05 10:50:49 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
|
|
|
|
Function: "exp_upward":
|
|
|
|
double: 1
|
2017-10-05 10:50:49 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
|
|
|
|
Function: "expm1":
|
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "expm1_downward":
|
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2015-04-24 11:36:23 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "expm1_towardzero":
|
2002-09-04 23:40:45 +00:00
|
|
|
double: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 4
|
2006-02-01 03:02:06 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "expm1_upward":
|
2013-07-22 07:51:52 +00:00
|
|
|
double: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 1
|
2015-04-24 11:36:23 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "gamma":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "gamma_downward":
|
|
|
|
double: 4
|
|
|
|
float: 4
|
|
|
|
ldouble: 8
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "gamma_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "gamma_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
|
|
|
float: 5
|
|
|
|
ldouble: 8
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "hypot":
|
|
|
|
double: 1
|
2023-02-28 09:38:25 +00:00
|
|
|
float: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "hypot_downward":
|
|
|
|
double: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "hypot_towardzero":
|
|
|
|
double: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "hypot_upward":
|
|
|
|
double: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "j0":
|
2021-04-15 09:05:43 +00:00
|
|
|
double: 4
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 9
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "j0_downward":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 6
|
|
|
|
float: 9
|
|
|
|
ldouble: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "j0_towardzero":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 7
|
|
|
|
float: 9
|
|
|
|
ldouble: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "j0_upward":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 9
|
2021-10-06 14:34:40 +00:00
|
|
|
float: 9
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
ldouble: 7
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "j1":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 4
|
|
|
|
float: 9
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 4
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "j1_downward":
|
2021-04-15 09:05:43 +00:00
|
|
|
double: 9
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 6
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "j1_towardzero":
|
2021-04-15 09:05:43 +00:00
|
|
|
double: 5
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "j1_upward":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 9
|
|
|
|
float: 9
|
|
|
|
ldouble: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "jn":
|
2002-09-04 23:40:45 +00:00
|
|
|
double: 4
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 4
|
|
|
|
ldouble: 7
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2015-07-07 14:11:14 +00:00
|
|
|
Function: "jn_downward":
|
|
|
|
double: 4
|
|
|
|
float: 5
|
|
|
|
ldouble: 8
|
|
|
|
|
|
|
|
Function: "jn_towardzero":
|
|
|
|
double: 4
|
|
|
|
float: 5
|
|
|
|
ldouble: 8
|
|
|
|
|
|
|
|
Function: "jn_upward":
|
|
|
|
double: 5
|
|
|
|
float: 4
|
|
|
|
ldouble: 7
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "lgamma":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "lgamma_downward":
|
|
|
|
double: 4
|
|
|
|
float: 4
|
|
|
|
ldouble: 8
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "lgamma_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 5
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "lgamma_upward":
|
2016-01-19 09:00:52 +00:00
|
|
|
double: 4
|
|
|
|
float: 5
|
|
|
|
ldouble: 8
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "log":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
|
|
|
Function: "log10":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
2002-09-04 23:40:45 +00:00
|
|
|
float: 2
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 2
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-06-03 15:27:13 +00:00
|
|
|
Function: "log10_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 3
|
2014-06-03 15:27:13 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "log10_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
2018-02-15 08:06:18 +00:00
|
|
|
float: 1
|
2014-06-03 15:27:13 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "log10_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2014-06-03 15:27:13 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
2024-06-19 06:42:30 +00:00
|
|
|
Function: "log10p1":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "log10p1_downward":
|
|
|
|
double: 2
|
|
|
|
float: 1
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "log10p1_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "log10p1_upward":
|
|
|
|
double: 2
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "log1p":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 3
|
2006-02-01 03:02:06 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "log1p_downward":
|
|
|
|
double: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "log1p_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "log1p_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2006-02-01 03:02:06 +00:00
|
|
|
Function: "log2":
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-07-01 14:04:58 +00:00
|
|
|
Function: "log2_downward":
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-07-01 14:04:58 +00:00
|
|
|
|
|
|
|
Function: "log2_towardzero":
|
2018-11-28 14:20:18 +00:00
|
|
|
double: 1
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "log2_upward":
|
2018-11-28 14:20:18 +00:00
|
|
|
double: 1
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
2024-05-24 07:53:49 +00:00
|
|
|
Function: "log2p1":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "log2p1_downward":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "log2p1_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "log2p1_upward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "log_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "log_towardzero":
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "log_upward":
|
|
|
|
ldouble: 1
|
|
|
|
|
Implement C23 logp1
C23 adds various <math.h> function families originally defined in TS
18661-4. Add the logp1 functions (aliases for log1p functions - the
name is intended to be more consistent with the new log2p1 and
log10p1, where clearly it would have been very confusing to name those
functions log21p and log101p). As aliases rather than new functions,
the content of this patch is somewhat different from those actually
adding new functions.
Tests are shared with log1p, so this patch *does* mechanically update
all affected libm-test-ulps files to expect the same errors for both
functions.
The vector versions of log1p on aarch64 and x86_64 are *not* updated
to have logp1 aliases (and thus there are no corresponding header,
tests, abilist or ulps changes for vector functions either). It would
be reasonable for such vector aliases and corresponding changes to
other files to be made separately. For now, the log1p tests instead
avoid testing logp1 in the vector case (a Makefile change is needed to
avoid problems with grep, used in generating the .c files for vector
function tests, matching more than one ALL_RM_TEST line in a file
testing multiple functions with the same inputs, when it assumes that
the .inc file only has a single such line).
Tested for x86_64 and x86, and with build-many-glibcs.py.
2024-06-17 13:47:09 +00:00
|
|
|
Function: "logp1":
|
|
|
|
double: 1
|
|
|
|
float: 1
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "logp1_downward":
|
|
|
|
double: 1
|
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "logp1_towardzero":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "logp1_upward":
|
|
|
|
double: 2
|
|
|
|
float: 2
|
|
|
|
ldouble: 2
|
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "pow":
|
2018-02-15 08:06:18 +00:00
|
|
|
double: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "pow_downward":
|
2014-07-01 14:04:58 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "pow_towardzero":
|
2014-07-01 14:04:58 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "pow_upward":
|
2014-07-01 14:04:58 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "sin":
|
2018-04-05 14:20:03 +00:00
|
|
|
double: 1
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 1
|
2021-03-03 11:22:08 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "sin_downward":
|
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
2014-01-15 08:49:54 +00:00
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "sin_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "sin_upward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "sincos":
|
2018-04-05 14:20:03 +00:00
|
|
|
double: 1
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 1
|
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "sincos_downward":
|
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "sincos_towardzero":
|
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 2
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "sincos_upward":
|
|
|
|
double: 1
|
2018-08-17 14:39:13 +00:00
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2015-04-24 11:36:23 +00:00
|
|
|
Function: "sinh":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2015-04-24 11:36:23 +00:00
|
|
|
Function: "sinh_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "sinh_towardzero":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2012-05-04 08:05:41 +00:00
|
|
|
|
|
|
|
Function: "sinh_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2015-04-24 11:36:23 +00:00
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-01-15 08:49:54 +00:00
|
|
|
|
2015-06-19 11:47:59 +00:00
|
|
|
Function: "tan":
|
|
|
|
float: 1
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 1
|
2015-06-19 11:47:59 +00:00
|
|
|
|
2014-01-15 08:49:54 +00:00
|
|
|
Function: "tan_downward":
|
2002-01-17 00:50:24 +00:00
|
|
|
double: 1
|
2014-01-15 08:49:54 +00:00
|
|
|
float: 2
|
|
|
|
ldouble: 1
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2012-05-04 08:05:41 +00:00
|
|
|
Function: "tan_towardzero":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
|
|
|
ldouble: 1
|
|
|
|
|
|
|
|
Function: "tan_upward":
|
2014-01-15 08:49:54 +00:00
|
|
|
double: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
float: 1
|
2015-04-24 11:36:23 +00:00
|
|
|
ldouble: 1
|
2012-05-04 08:05:41 +00:00
|
|
|
|
2006-02-01 03:02:06 +00:00
|
|
|
Function: "tanh":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 2
|
2006-02-01 03:02:06 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "tanh_downward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
|
|
|
float: 3
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "tanh_towardzero":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 2
|
|
|
|
float: 2
|
2016-01-19 09:00:52 +00:00
|
|
|
ldouble: 3
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "tanh_upward":
|
2015-06-19 11:47:59 +00:00
|
|
|
double: 3
|
2013-07-22 07:51:52 +00:00
|
|
|
float: 3
|
2015-06-19 11:47:59 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "tgamma":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 9
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 8
|
2013-07-22 07:51:52 +00:00
|
|
|
ldouble: 4
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2015-07-07 14:11:14 +00:00
|
|
|
Function: "tgamma_downward":
|
2021-04-13 14:51:07 +00:00
|
|
|
double: 9
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 7
|
2015-07-07 14:11:14 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "tgamma_towardzero":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 9
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 7
|
2015-07-07 14:11:14 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "tgamma_upward":
|
2020-12-22 18:20:56 +00:00
|
|
|
double: 9
|
2020-04-03 07:38:02 +00:00
|
|
|
float: 8
|
2015-07-07 14:11:14 +00:00
|
|
|
ldouble: 4
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "y0":
|
|
|
|
double: 2
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
2006-02-01 03:02:06 +00:00
|
|
|
ldouble: 3
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "y0_downward":
|
|
|
|
double: 3
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 7
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "y0_towardzero":
|
|
|
|
double: 3
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 3
|
|
|
|
|
|
|
|
Function: "y0_upward":
|
2019-06-25 13:14:17 +00:00
|
|
|
double: 3
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 8
|
|
|
|
ldouble: 4
|
2014-04-16 11:00:29 +00:00
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "y1":
|
|
|
|
double: 3
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 9
|
|
|
|
ldouble: 5
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-04-16 11:00:29 +00:00
|
|
|
Function: "y1_downward":
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
double: 6
|
|
|
|
float: 8
|
|
|
|
ldouble: 5
|
2014-04-16 11:00:29 +00:00
|
|
|
|
|
|
|
Function: "y1_towardzero":
|
|
|
|
double: 3
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 2
|
|
|
|
|
|
|
|
Function: "y1_upward":
|
2019-06-25 13:14:17 +00:00
|
|
|
double: 7
|
Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
2021-04-01 06:14:10 +00:00
|
|
|
float: 9
|
2014-04-16 11:00:29 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
Function: "yn":
|
|
|
|
double: 3
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 3
|
2014-02-25 08:36:18 +00:00
|
|
|
ldouble: 5
|
2000-08-21 17:06:46 +00:00
|
|
|
|
2014-07-01 14:04:58 +00:00
|
|
|
Function: "yn_downward":
|
|
|
|
double: 3
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 4
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "yn_towardzero":
|
|
|
|
double: 3
|
|
|
|
float: 3
|
|
|
|
ldouble: 5
|
|
|
|
|
|
|
|
Function: "yn_upward":
|
|
|
|
double: 4
|
2017-12-16 08:41:56 +00:00
|
|
|
float: 5
|
2014-07-01 14:04:58 +00:00
|
|
|
ldouble: 5
|
|
|
|
|
2000-08-21 17:06:46 +00:00
|
|
|
# end of automatic generation
|