diff options
| -rw-r--r-- | ChangeLog | 15 | ||||
| -rw-r--r-- | math/libm-test.inc | 256 | ||||
| -rw-r--r-- | math/s_catan.c | 22 | ||||
| -rw-r--r-- | math/s_catanf.c | 22 | ||||
| -rw-r--r-- | math/s_catanh.c | 20 | ||||
| -rw-r--r-- | math/s_catanhf.c | 20 | ||||
| -rw-r--r-- | math/s_catanhl.c | 20 | ||||
| -rw-r--r-- | math/s_catanl.c | 22 | ||||
| -rw-r--r-- | sysdeps/i386/fpu/libm-test-ulps | 104 | ||||
| -rw-r--r-- | sysdeps/x86_64/fpu/libm-test-ulps | 422 |
10 files changed, 909 insertions, 14 deletions
diff --git a/ChangeLog b/ChangeLog index 9a9be01a16..0da24720f4 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,18 @@ +2013-04-30 Joseph Myers <joseph@codesourcery.com> + + [BZ #15416] + * math/s_catan.c (__catan): Compute expressions 1 - x^2 - y^2 more + accurately for denominator in atan2. + * math/s_catanf.c (__catanf): Likewise. + * math/s_catanh.c (__catanh): Likewise. + * math/s_catanhf.c (__catanhf): Likewise. + * math/s_catanhl.c (__catanhl): Likewise. + * math/s_catanl.c (__catanl): Likewise. + * math/libm-test.inc (catan_test): Add more tests. + (catanh_test): Likewise. + * sysdeps/i386/fpu/libm-test-ulps: Update. + * sysdeps/x86_64/fpu/libm-test-ulps: Likewise. + 2013-04-30 Siddhesh Poyarekar <siddhesh@redhat.com> * sysdeps/ieee754/dbl-64/s_sin.c: Format code. diff --git a/math/libm-test.inc b/math/libm-test.inc index b82c592da4..d131ffa6f6 100644 --- a/math/libm-test.inc +++ b/math/libm-test.inc @@ -4483,6 +4483,134 @@ catan_test (void) TEST_c_c (catan, -0x1.fp16383L, 0x1.fp16383L, -1.570796326794896619231321691639751442099L, 4.338197604015604524209906861060325938836e-4933L, UNDERFLOW_EXCEPTION); TEST_c_c (catan, -0x1.fp16383L, -0x1.fp16383L, -1.570796326794896619231321691639751442099L, -4.338197604015604524209906861060325938836e-4933L, UNDERFLOW_EXCEPTION); #endif + TEST_c_c (catan, 0x1p-13L, 1.0L, 7.854286809755354140031716771044626356262e-1L, 4.852030264850939738801379894163661227127L); + TEST_c_c (catan, 0x1p-13L, -1.0L, 7.854286809755354140031716771044626356262e-1L, -4.852030264850939738801379894163661227127L); + TEST_c_c (catan, -0x1p-13L, 1.0L, -7.854286809755354140031716771044626356262e-1L, 4.852030264850939738801379894163661227127L); + TEST_c_c (catan, -0x1p-13L, -1.0L, -7.854286809755354140031716771044626356262e-1L, -4.852030264850939738801379894163661227127L); + TEST_c_c (catan, 1.0L, 0x1p-13L, 7.853981671227386080775748393881580082970e-1L, 6.103515609841754902688560615027452023669e-5L); + TEST_c_c (catan, -1.0L, 0x1p-13L, -7.853981671227386080775748393881580082970e-1L, 6.103515609841754902688560615027452023669e-5L); + TEST_c_c (catan, 1.0L, -0x1p-13L, 7.853981671227386080775748393881580082970e-1L, -6.103515609841754902688560615027452023669e-5L); + TEST_c_c (catan, -1.0L, -0x1p-13L, -7.853981671227386080775748393881580082970e-1L, -6.103515609841754902688560615027452023669e-5L); + TEST_c_c (catan, 0x1p-27L, 1.0L, 7.853981652600934588466178684534110069553e-1L, 9.704060527839234335310696652368086117807L); + TEST_c_c (catan, 0x1p-27L, -1.0L, 7.853981652600934588466178684534110069553e-1L, -9.704060527839234335310696652368086117807L); + TEST_c_c (catan, -0x1p-27L, 1.0L, -7.853981652600934588466178684534110069553e-1L, 9.704060527839234335310696652368086117807L); + TEST_c_c (catan, -0x1p-27L, -1.0L, -7.853981652600934588466178684534110069553e-1L, -9.704060527839234335310696652368086117807L); + TEST_c_c (catan, 1.0L, 0x1p-27L, 7.853981633974483234934486536343324763447e-1L, 3.725290298461914028034141143623846306386e-9L); + TEST_c_c (catan, -1.0L, 0x1p-27L, -7.853981633974483234934486536343324763447e-1L, 3.725290298461914028034141143623846306386e-9L); + TEST_c_c (catan, 1.0L, -0x1p-27L, 7.853981633974483234934486536343324763447e-1L, -3.725290298461914028034141143623846306386e-9L); + TEST_c_c (catan, -1.0L, -0x1p-27L, -7.853981633974483234934486536343324763447e-1L, -3.725290298461914028034141143623846306386e-9L); + TEST_c_c (catan, 0x1p-33L, 1.0L, 7.853981634265521400723945494331241018449e-1L, 1.178350206951907026009379309773625595762e1L); + TEST_c_c (catan, 0x1p-33L, -1.0L, 7.853981634265521400723945494331241018449e-1L, -1.178350206951907026009379309773625595762e1L); + TEST_c_c (catan, -0x1p-33L, 1.0L, -7.853981634265521400723945494331241018449e-1L, 1.178350206951907026009379309773625595762e1L); + TEST_c_c (catan, -0x1p-33L, -1.0L, -7.853981634265521400723945494331241018449e-1L, -1.178350206951907026009379309773625595762e1L); + TEST_c_c (catan, 1.0L, 0x1p-33L, 7.853981633974483096190489776088929224056e-1L, 5.820766091346740722643102318246316469910e-11L); + TEST_c_c (catan, -1.0L, 0x1p-33L, -7.853981633974483096190489776088929224056e-1L, 5.820766091346740722643102318246316469910e-11L); + TEST_c_c (catan, 1.0L, -0x1p-33L, 7.853981633974483096190489776088929224056e-1L, -5.820766091346740722643102318246316469910e-11L); + TEST_c_c (catan, -1.0L, -0x1p-33L, -7.853981633974483096190489776088929224056e-1L, -5.820766091346740722643102318246316469910e-11L); + TEST_c_c (catan, 0x1p-54L, 1.0L, 7.853981633974483234934486536343324763447e-1L, 1.906154746539849600897388334009985581467e1L); + TEST_c_c (catan, 0x1p-54L, -1.0L, 7.853981633974483234934486536343324763447e-1L, -1.906154746539849600897388334009985581467e1L); + TEST_c_c (catan, -0x1p-54L, 1.0L, -7.853981633974483234934486536343324763447e-1L, 1.906154746539849600897388334009985581467e1L); + TEST_c_c (catan, -0x1p-54L, -1.0L, -7.853981633974483234934486536343324763447e-1L, -1.906154746539849600897388334009985581467e1L); + TEST_c_c (catan, 1.0L, 0x1p-54L, 7.853981633974483096156608458198764914213e-1L, 2.775557561562891351059079170227049355775e-17L); + TEST_c_c (catan, -1.0L, 0x1p-54L, -7.853981633974483096156608458198764914213e-1L, 2.775557561562891351059079170227049355775e-17L); + TEST_c_c (catan, 1.0L, -0x1p-54L, 7.853981633974483096156608458198764914213e-1L, -2.775557561562891351059079170227049355775e-17L); + TEST_c_c (catan, -1.0L, -0x1p-54L, -7.853981633974483096156608458198764914213e-1L, -2.775557561562891351059079170227049355775e-17L); + TEST_c_c (catan, 0x1p-57L, 1.0L, 7.853981633974483113503843217966828154612e-1L, 2.010126823623841397309973152228712047720e1L); + TEST_c_c (catan, 0x1p-57L, -1.0L, 7.853981633974483113503843217966828154612e-1L, -2.010126823623841397309973152228712047720e1L); + TEST_c_c (catan, -0x1p-57L, 1.0L, -7.853981633974483113503843217966828154612e-1L, 2.010126823623841397309973152228712047720e1L); + TEST_c_c (catan, -0x1p-57L, -1.0L, -7.853981633974483113503843217966828154612e-1L, -2.010126823623841397309973152228712047720e1L); + TEST_c_c (catan, 1.0L, 0x1p-57L, 7.853981633974483096156608458198757330864e-1L, 3.469446951953614188823848962783813448721e-18L); + TEST_c_c (catan, -1.0L, 0x1p-57L, -7.853981633974483096156608458198757330864e-1L, 3.469446951953614188823848962783813448721e-18L); + TEST_c_c (catan, 1.0L, -0x1p-57L, 7.853981633974483096156608458198757330864e-1L, -3.469446951953614188823848962783813448721e-18L); + TEST_c_c (catan, -1.0L, -0x1p-57L, -7.853981633974483096156608458198757330864e-1L, -3.469446951953614188823848962783813448721e-18L); + TEST_c_c (catan, 0x1p-13L, 0x1.000002p0L, 7.859169620684960844300240092596908675974e-1L, 4.852030056234795712498957387213592193975L); + TEST_c_c (catan, 0x1p-13L, -0x1.000002p0L, 7.859169620684960844300240092596908675974e-1L, -4.852030056234795712498957387213592193975L); + TEST_c_c (catan, -0x1p-13L, 0x1.000002p0L, -7.859169620684960844300240092596908675974e-1L, 4.852030056234795712498957387213592193975L); + TEST_c_c (catan, -0x1p-13L, -0x1.000002p0L, -7.859169620684960844300240092596908675974e-1L, -4.852030056234795712498957387213592193975L); + TEST_c_c (catan, 0x1.000002p0L, 0x1p-13L, 7.853982267273793866654490522673596014524e-1L, 6.103514882246036852433556327261700380577e-5L); + TEST_c_c (catan, -0x1.000002p0L, 0x1p-13L, -7.853982267273793866654490522673596014524e-1L, 6.103514882246036852433556327261700380577e-5L); + TEST_c_c (catan, 0x1.000002p0L, -0x1p-13L, 7.853982267273793866654490522673596014524e-1L, -6.103514882246036852433556327261700380577e-5L); + TEST_c_c (catan, -0x1.000002p0L, -0x1p-13L, -7.853982267273793866654490522673596014524e-1L, -6.103514882246036852433556327261700380577e-5L); + TEST_c_c (catan, 0x1p-13L, 0x0.ffffffp0L, 7.851845403708474595909269086711426246675e-1L, 4.852030190345140708455871037447717761868L); + TEST_c_c (catan, 0x1p-13L, -0x0.ffffffp0L, 7.851845403708474595909269086711426246675e-1L, -4.852030190345140708455871037447717761868L); + TEST_c_c (catan, -0x1p-13L, 0x0.ffffffp0L, -7.851845403708474595909269086711426246675e-1L, 4.852030190345140708455871037447717761868L); + TEST_c_c (catan, -0x1p-13L, -0x0.ffffffp0L, -7.851845403708474595909269086711426246675e-1L, -4.852030190345140708455871037447717761868L); + TEST_c_c (catan, 0x0.ffffffp0L, 0x1p-13L, 7.853981373204155542484315721351697277336e-1L, 6.103515973639646453881721999956617260502e-5L); + TEST_c_c (catan, -0x0.ffffffp0L, 0x1p-13L, -7.853981373204155542484315721351697277336e-1L, 6.103515973639646453881721999956617260502e-5L); + TEST_c_c (catan, 0x0.ffffffp0L, -0x1p-13L, 7.853981373204155542484315721351697277336e-1L, -6.103515973639646453881721999956617260502e-5L); + TEST_c_c (catan, -0x0.ffffffp0L, -0x1p-13L, -7.853981373204155542484315721351697277336e-1L, -6.103515973639646453881721999956617260502e-5L); +#ifndef TEST_FLOAT + TEST_c_c (catan, 0x1p-27L, 0x1.0000000000001p0L, 7.853981801612546526942695000283242525531e-1L, 9.704060527839234168777242958594699810015L); + TEST_c_c (catan, 0x1p-27L, -0x1.0000000000001p0L, 7.853981801612546526942695000283242525531e-1L, -9.704060527839234168777242958594699810015L); + TEST_c_c (catan, -0x1p-27L, 0x1.0000000000001p0L, -7.853981801612546526942695000283242525531e-1L, 9.704060527839234168777242958594699810015L); + TEST_c_c (catan, -0x1p-27L, -0x1.0000000000001p0L, -7.853981801612546526942695000283242525531e-1L, -9.704060527839234168777242958594699810015L); + TEST_c_c (catan, 0x1.0000000000001p0L, 0x1p-27L, 7.853981633974484345157511161499711112683e-1L, 3.725290298461913200853528590596263270474e-9L); + TEST_c_c (catan, -0x1.0000000000001p0L, 0x1p-27L, -7.853981633974484345157511161499711112683e-1L, 3.725290298461913200853528590596263270474e-9L); + TEST_c_c (catan, 0x1.0000000000001p0L, -0x1p-27L, 7.853981633974484345157511161499711112683e-1L, -3.725290298461913200853528590596263270474e-9L); + TEST_c_c (catan, -0x1.0000000000001p0L, -0x1p-27L, -7.853981633974484345157511161499711112683e-1L, -3.725290298461913200853528590596263270474e-9L); + TEST_c_c (catan, 0x1p-27L, 0x0.fffffffffffff8p0L, 7.853981578095128619227903983047292781021e-1L, 9.704060527839234252043969805481351363824L); + TEST_c_c (catan, 0x1p-27L, -0x0.fffffffffffff8p0L, 7.853981578095128619227903983047292781021e-1L, -9.704060527839234252043969805481351363824L); + TEST_c_c (catan, -0x1p-27L, 0x0.fffffffffffff8p0L, -7.853981578095128619227903983047292781021e-1L, 9.704060527839234252043969805481351363824L); + TEST_c_c (catan, -0x1p-27L, -0x0.fffffffffffff8p0L, -7.853981578095128619227903983047292781021e-1L, -9.704060527839234252043969805481351363824L); + TEST_c_c (catan, 0x0.fffffffffffff8p0L, 0x1p-27L, 7.853981633974482679822974223765039144191e-1L, 3.725290298461914441624447420137706700965e-9L); + TEST_c_c (catan, -0x0.fffffffffffff8p0L, 0x1p-27L, -7.853981633974482679822974223765039144191e-1L, 3.725290298461914441624447420137706700965e-9L); + TEST_c_c (catan, 0x0.fffffffffffff8p0L, -0x1p-27L, 7.853981633974482679822974223765039144191e-1L, -3.725290298461914441624447420137706700965e-9L); + TEST_c_c (catan, -0x0.fffffffffffff8p0L, -0x1p-27L, -7.853981633974482679822974223765039144191e-1L, -3.725290298461914441624447420137706700965e-9L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 64 + TEST_c_c (catan, 0x1p-33L, 0x1.0000000000000002p0L, 7.853981638922134273801338071094141188767e-1L, 1.178350206951907025990405771755129268176e1L); + TEST_c_c (catan, 0x1p-33L, -0x1.0000000000000002p0L, 7.853981638922134273801338071094141188767e-1L, -1.178350206951907025990405771755129268176e1L); + TEST_c_c (catan, -0x1p-33L, 0x1.0000000000000002p0L, -7.853981638922134273801338071094141188767e-1L, 1.178350206951907025990405771755129268176e1L); + TEST_c_c (catan, -0x1p-33L, -0x1.0000000000000002p0L, -7.853981638922134273801338071094141188767e-1L, -1.178350206951907025990405771755129268176e1L); + TEST_c_c (catan, 0x1.0000000000000002p0L, 0x1p-33L, 7.853981633974483096732590862331681441026e-1L, 5.820766091346740722012013594069507025615e-11L); + TEST_c_c (catan, -0x1.0000000000000002p0L, 0x1p-33L, -7.853981633974483096732590862331681441026e-1L, 5.820766091346740722012013594069507025615e-11L); + TEST_c_c (catan, 0x1.0000000000000002p0L, -0x1p-33L, 7.853981633974483096732590862331681441026e-1L, -5.820766091346740722012013594069507025615e-11L); + TEST_c_c (catan, -0x1.0000000000000002p0L, -0x1p-33L, -7.853981633974483096732590862331681441026e-1L, -5.820766091346740722012013594069507025615e-11L); + TEST_c_c (catan, 0x1p-33L, 0x0.ffffffffffffffffp0L, 7.853981631937214964185249205444919953948e-1L, 1.178350206951907026002603046195591193050e1L); + TEST_c_c (catan, 0x1p-33L, -0x0.ffffffffffffffffp0L, 7.853981631937214964185249205444919953948e-1L, -1.178350206951907026002603046195591193050e1L); + TEST_c_c (catan, -0x1p-33L, 0x0.ffffffffffffffffp0L, -7.853981631937214964185249205444919953948e-1L, 1.178350206951907026002603046195591193050e1L); + TEST_c_c (catan, -0x1p-33L, -0x0.ffffffffffffffffp0L, -7.853981631937214964185249205444919953948e-1L, -1.178350206951907026002603046195591193050e1L); + TEST_c_c (catan, 0x0.ffffffffffffffffp0L, 0x1p-33L, 7.853981633974483095919439232967553115548e-1L, 5.820766091346740722958646680334721192083e-11L); + TEST_c_c (catan, -0x0.ffffffffffffffffp0L, 0x1p-33L, -7.853981633974483095919439232967553115548e-1L, 5.820766091346740722958646680334721192083e-11L); + TEST_c_c (catan, 0x0.ffffffffffffffffp0L, -0x1p-33L, 7.853981633974483095919439232967553115548e-1L, -5.820766091346740722958646680334721192083e-11L); + TEST_c_c (catan, -0x0.ffffffffffffffffp0L, -0x1p-33L, -7.853981633974483095919439232967553115548e-1L, -5.820766091346740722958646680334721192083e-11L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106 + TEST_c_c (catan, 0x1p-54L, 0x1.000000000000000000000000008p0L, 7.853981633974485455380535786656405610710e-1L, 1.906154746539849600897388334009981267384e1L); + TEST_c_c (catan, 0x1p-54L, -0x1.000000000000000000000000008p0L, 7.853981633974485455380535786656405610710e-1L, -1.906154746539849600897388334009981267384e1L); + TEST_c_c (catan, -0x1p-54L, 0x1.000000000000000000000000008p0L, -7.853981633974485455380535786656405610710e-1L, 1.906154746539849600897388334009981267384e1L); + TEST_c_c (catan, -0x1p-54L, -0x1.000000000000000000000000008p0L, -7.853981633974485455380535786656405610710e-1L, -1.906154746539849600897388334009981267384e1L); + TEST_c_c (catan, 0x1.000000000000000000000000008p0L, 0x1p-54L, 7.853981633974483096156608458198888173729e-1L, 2.775557561562891351059079170226980932999e-17L); + TEST_c_c (catan, -0x1.000000000000000000000000008p0L, 0x1p-54L, -7.853981633974483096156608458198888173729e-1L, 2.775557561562891351059079170226980932999e-17L); + TEST_c_c (catan, 0x1.000000000000000000000000008p0L, -0x1p-54L, 7.853981633974483096156608458198888173729e-1L, -2.775557561562891351059079170226980932999e-17L); + TEST_c_c (catan, -0x1.000000000000000000000000008p0L, -0x1p-54L, -7.853981633974483096156608458198888173729e-1L, -2.775557561562891351059079170226980932999e-17L); + TEST_c_c (catan, 0x1p-54L, 0x0.ffffffffffffffffffffffffffcp0L, 7.853981633974482124711461911186784339815e-1L, 1.906154746539849600897388334009984040723e1L); + TEST_c_c (catan, 0x1p-54L, -0x0.ffffffffffffffffffffffffffcp0L, 7.853981633974482124711461911186784339815e-1L, -1.906154746539849600897388334009984040723e1L); + TEST_c_c (catan, -0x1p-54L, 0x0.ffffffffffffffffffffffffffcp0L, -7.853981633974482124711461911186784339815e-1L, 1.906154746539849600897388334009984040723e1L); + TEST_c_c (catan, -0x1p-54L, -0x0.ffffffffffffffffffffffffffcp0L, -7.853981633974482124711461911186784339815e-1L, -1.906154746539849600897388334009984040723e1L); + TEST_c_c (catan, 0x0.ffffffffffffffffffffffffffcp0L, 0x1p-54L, 7.853981633974483096156608458198703284454e-1L, 2.775557561562891351059079170227083567164e-17L); + TEST_c_c (catan, -0x0.ffffffffffffffffffffffffffcp0L, 0x1p-54L, -7.853981633974483096156608458198703284454e-1L, 2.775557561562891351059079170227083567164e-17L); + TEST_c_c (catan, 0x0.ffffffffffffffffffffffffffcp0L, -0x1p-54L, 7.853981633974483096156608458198703284454e-1L, -2.775557561562891351059079170227083567164e-17L); + TEST_c_c (catan, -0x0.ffffffffffffffffffffffffffcp0L, -0x1p-54L, -7.853981633974483096156608458198703284454e-1L, -2.775557561562891351059079170227083567164e-17L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 113 + TEST_c_c (catan, 0x1p-57L, 0x1.0000000000000000000000000001p0L, 7.853981633974483252281721296111395707566e-1L, 2.010126823623841397309973152228712033275e1L); + TEST_c_c (catan, 0x1p-57L, -0x1.0000000000000000000000000001p0L, 7.853981633974483252281721296111395707566e-1L, -2.010126823623841397309973152228712033275e1L); + TEST_c_c (catan, -0x1p-57L, 0x1.0000000000000000000000000001p0L, -7.853981633974483252281721296111395707566e-1L, 2.010126823623841397309973152228712033275e1L); + TEST_c_c (catan, -0x1p-57L, -0x1.0000000000000000000000000001p0L, -7.853981633974483252281721296111395707566e-1L, -2.010126823623841397309973152228712033275e1L); + TEST_c_c (catan, 0x1.0000000000000000000000000001p0L, 0x1p-57L, 7.853981633974483096156608458198758293829e-1L, 3.469446951953614188823848962783812780530e-18L); + TEST_c_c (catan, -0x1.0000000000000000000000000001p0L, 0x1p-57L, -7.853981633974483096156608458198758293829e-1L, 3.469446951953614188823848962783812780530e-18L); + TEST_c_c (catan, 0x1.0000000000000000000000000001p0L, -0x1p-57L, 7.853981633974483096156608458198758293829e-1L, -3.469446951953614188823848962783812780530e-18L); + TEST_c_c (catan, -0x1.0000000000000000000000000001p0L, -0x1p-57L, -7.853981633974483096156608458198758293829e-1L, -3.469446951953614188823848962783812780530e-18L); + TEST_c_c (catan, 0x1p-57L, 0x0.ffffffffffffffffffffffffffff8p0L, 7.853981633974483044114904178894544378135e-1L, 2.010126823623841397309973152228712040498e1L); + TEST_c_c (catan, 0x1p-57L, -0x0.ffffffffffffffffffffffffffff8p0L, 7.853981633974483044114904178894544378135e-1L, -2.010126823623841397309973152228712040498e1L); + TEST_c_c (catan, -0x1p-57L, 0x0.ffffffffffffffffffffffffffff8p0L, -7.853981633974483044114904178894544378135e-1L, 2.010126823623841397309973152228712040498e1L); + TEST_c_c (catan, -0x1p-57L, -0x0.ffffffffffffffffffffffffffff8p0L, -7.853981633974483044114904178894544378135e-1L, -2.010126823623841397309973152228712040498e1L); + TEST_c_c (catan, 0x0.ffffffffffffffffffffffffffff8p0L, 0x1p-57L, 7.853981633974483096156608458198756849381e-1L, 3.469446951953614188823848962783813782817e-18L); + TEST_c_c (catan, -0x0.ffffffffffffffffffffffffffff8p0L, 0x1p-57L, -7.853981633974483096156608458198756849381e-1L, 3.469446951953614188823848962783813782817e-18L); + TEST_c_c (catan, 0x0.ffffffffffffffffffffffffffff8p0L, -0x1p-57L, 7.853981633974483096156608458198756849381e-1L, -3.469446951953614188823848962783813782817e-18L); + TEST_c_c (catan, -0x0.ffffffffffffffffffffffffffff8p0L, -0x1p-57L, -7.853981633974483096156608458198756849381e-1L, -3.469446951953614188823848962783813782817e-18L); +#endif TEST_c_c (catan, 0.75L, 1.25L, 1.10714871779409050301706546017853704L, 0.549306144334054845697622618461262852L); TEST_c_c (catan, -2, -3, -1.4099210495965755225306193844604208L, -0.22907268296853876629588180294200276L); @@ -4679,6 +4807,134 @@ catanh_test (void) TEST_c_c (catanh, -0x1.fp16383L, 0x1.fp16383L, -4.338197604015604524209906861060325938836e-4933L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION); TEST_c_c (catanh, -0x1.fp16383L, -0x1.fp16383L, -4.338197604015604524209906861060325938836e-4933L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION); #endif + TEST_c_c (catanh, 0x1p-13L, 1.0L, 6.103515609841754902688560615027452023669e-5L, 7.853981671227386080775748393881580082970e-1L); + TEST_c_c (catanh, 0x1p-13L, -1.0L, 6.103515609841754902688560615027452023669e-5L, -7.853981671227386080775748393881580082970e-1L); + TEST_c_c (catanh, -0x1p-13L, 1.0L, -6.103515609841754902688560615027452023669e-5L, 7.853981671227386080775748393881580082970e-1L); + TEST_c_c (catanh, -0x1p-13L, -1.0L, -6.103515609841754902688560615027452023669e-5L, -7.853981671227386080775748393881580082970e-1L); + TEST_c_c (catanh, 1.0L, 0x1p-13L, 4.852030264850939738801379894163661227127L, 7.854286809755354140031716771044626356262e-1L); + TEST_c_c (catanh, -1.0L, 0x1p-13L, -4.852030264850939738801379894163661227127L, 7.854286809755354140031716771044626356262e-1L); + TEST_c_c (catanh, 1.0L, -0x1p-13L, 4.852030264850939738801379894163661227127L, -7.854286809755354140031716771044626356262e-1L); + TEST_c_c (catanh, -1.0L, -0x1p-13L, -4.852030264850939738801379894163661227127L, -7.854286809755354140031716771044626356262e-1L); + TEST_c_c (catanh, 0x1p-27L, 1.0L, 3.725290298461914028034141143623846306386e-9L, 7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, 0x1p-27L, -1.0L, 3.725290298461914028034141143623846306386e-9L, -7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, -0x1p-27L, 1.0L, -3.725290298461914028034141143623846306386e-9L, 7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, -0x1p-27L, -1.0L, -3.725290298461914028034141143623846306386e-9L, -7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, 1.0L, 0x1p-27L, 9.704060527839234335310696652368086117807L, 7.853981652600934588466178684534110069553e-1L); + TEST_c_c (catanh, -1.0L, 0x1p-27L, -9.704060527839234335310696652368086117807L, 7.853981652600934588466178684534110069553e-1L); + TEST_c_c (catanh, 1.0L, -0x1p-27L, 9.704060527839234335310696652368086117807L, -7.853981652600934588466178684534110069553e-1L); + TEST_c_c (catanh, -1.0L, -0x1p-27L, -9.704060527839234335310696652368086117807L, -7.853981652600934588466178684534110069553e-1L); + TEST_c_c (catanh, 0x1p-33L, 1.0L, 5.820766091346740722643102318246316469910e-11L, 7.853981633974483096190489776088929224056e-1L); + TEST_c_c (catanh, 0x1p-33L, -1.0L, 5.820766091346740722643102318246316469910e-11L, -7.853981633974483096190489776088929224056e-1L); + TEST_c_c (catanh, -0x1p-33L, 1.0L, -5.820766091346740722643102318246316469910e-11L, 7.853981633974483096190489776088929224056e-1L); + TEST_c_c (catanh, -0x1p-33L, -1.0L, -5.820766091346740722643102318246316469910e-11L, -7.853981633974483096190489776088929224056e-1L); + TEST_c_c (catanh, 1.0L, 0x1p-33L, 1.178350206951907026009379309773625595762e1L, 7.853981634265521400723945494331241018449e-1L); + TEST_c_c (catanh, -1.0L, 0x1p-33L, -1.178350206951907026009379309773625595762e1L, 7.853981634265521400723945494331241018449e-1L); + TEST_c_c (catanh, 1.0L, -0x1p-33L, 1.178350206951907026009379309773625595762e1L, -7.853981634265521400723945494331241018449e-1L); + TEST_c_c (catanh, -1.0L, -0x1p-33L, -1.178350206951907026009379309773625595762e1L, -7.853981634265521400723945494331241018449e-1L); + TEST_c_c (catanh, 0x1p-54L, 1.0L, 2.775557561562891351059079170227049355775e-17L, 7.853981633974483096156608458198764914213e-1L); + TEST_c_c (catanh, 0x1p-54L, -1.0L, 2.775557561562891351059079170227049355775e-17L, -7.853981633974483096156608458198764914213e-1L); + TEST_c_c (catanh, -0x1p-54L, 1.0L, -2.775557561562891351059079170227049355775e-17L, 7.853981633974483096156608458198764914213e-1L); + TEST_c_c (catanh, -0x1p-54L, -1.0L, -2.775557561562891351059079170227049355775e-17L, -7.853981633974483096156608458198764914213e-1L); + TEST_c_c (catanh, 1.0L, 0x1p-54L, 1.906154746539849600897388334009985581467e1L, 7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, -1.0L, 0x1p-54L, -1.906154746539849600897388334009985581467e1L, 7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, 1.0L, -0x1p-54L, 1.906154746539849600897388334009985581467e1L, -7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, -1.0L, -0x1p-54L, -1.906154746539849600897388334009985581467e1L, -7.853981633974483234934486536343324763447e-1L); + TEST_c_c (catanh, 0x1p-57L, 1.0L, 3.469446951953614188823848962783813448721e-18L, 7.853981633974483096156608458198757330864e-1L); + TEST_c_c (catanh, 0x1p-57L, -1.0L, 3.469446951953614188823848962783813448721e-18L, -7.853981633974483096156608458198757330864e-1L); + TEST_c_c (catanh, -0x1p-57L, 1.0L, -3.469446951953614188823848962783813448721e-18L, 7.853981633974483096156608458198757330864e-1L); + TEST_c_c (catanh, -0x1p-57L, -1.0L, -3.469446951953614188823848962783813448721e-18L, -7.853981633974483096156608458198757330864e-1L); + TEST_c_c (catanh, 1.0L, 0x1p-57L, 2.010126823623841397309973152228712047720e1L, 7.853981633974483113503843217966828154612e-1L); + TEST_c_c (catanh, -1.0L, 0x1p-57L, -2.010126823623841397309973152228712047720e1L, 7.853981633974483113503843217966828154612e-1L); + TEST_c_c (catanh, 1.0L, -0x1p-57L, 2.010126823623841397309973152228712047720e1L, -7.853981633974483113503843217966828154612e-1L); + TEST_c_c (catanh, -1.0L, -0x1p-57L, -2.010126823623841397309973152228712047720e1L, -7.853981633974483113503843217966828154612e-1L); + TEST_c_c (catanh, 0x1p-13L, 0x1.000002p0L, 6.103514882246036852433556327261700380577e-5L, 7.853982267273793866654490522673596014524e-1L); + TEST_c_c (catanh, 0x1p-13L, -0x1.000002p0L, 6.103514882246036852433556327261700380577e-5L, -7.853982267273793866654490522673596014524e-1L); + TEST_c_c (catanh, -0x1p-13L, 0x1.000002p0L, -6.103514882246036852433556327261700380577e-5L, 7.853982267273793866654490522673596014524e-1L); + TEST_c_c (catanh, -0x1p-13L, -0x1.000002p0L, -6.103514882246036852433556327261700380577e-5L, -7.853982267273793866654490522673596014524e-1L); + TEST_c_c (catanh, 0x1.000002p0L, 0x1p-13L, 4.852030056234795712498957387213592193975L, 7.859169620684960844300240092596908675974e-1L); + TEST_c_c (catanh, -0x1.000002p0L, 0x1p-13L, -4.852030056234795712498957387213592193975L, 7.859169620684960844300240092596908675974e-1L); + TEST_c_c (catanh, 0x1.000002p0L, -0x1p-13L, 4.852030056234795712498957387213592193975L, -7.859169620684960844300240092596908675974e-1L); + TEST_c_c (catanh, -0x1.000002p0L, -0x1p-13L, -4.852030056234795712498957387213592193975L, -7.859169620684960844300240092596908675974e-1L); + TEST_c_c (catanh, 0x1p-13L, 0x0.ffffffp0L, 6.103515973639646453881721999956617260502e-5L, 7.853981373204155542484315721351697277336e-1L); + TEST_c_c (catanh, 0x1p-13L, -0x0.ffffffp0L, 6.103515973639646453881721999956617260502e-5L, -7.853981373204155542484315721351697277336e-1L); + TEST_c_c (catanh, -0x1p-13L, 0x0.ffffffp0L, -6.103515973639646453881721999956617260502e-5L, 7.853981373204155542484315721351697277336e-1L); + TEST_c_c (catanh, -0x1p-13L, -0x0.ffffffp0L, -6.103515973639646453881721999956617260502e-5L, -7.853981373204155542484315721351697277336e-1L); + TEST_c_c (catanh, 0x0.ffffffp0L, 0x1p-13L, 4.852030190345140708455871037447717761868L, 7.851845403708474595909269086711426246675e-1L); + TEST_c_c (catanh, -0x0.ffffffp0L, 0x1p-13L, -4.852030190345140708455871037447717761868L, 7.851845403708474595909269086711426246675e-1L); + TEST_c_c (catanh, 0x0.ffffffp0L, -0x1p-13L, 4.852030190345140708455871037447717761868L, -7.851845403708474595909269086711426246675e-1L); + TEST_c_c (catanh, -0x0.ffffffp0L, -0x1p-13L, -4.852030190345140708455871037447717761868L, -7.851845403708474595909269086711426246675e-1L); +#ifndef TEST_FLOAT + TEST_c_c (catanh, 0x1p-27L, 0x1.0000000000001p0L, 3.725290298461913200853528590596263270474e-9L, 7.853981633974484345157511161499711112683e-1L); + TEST_c_c (catanh, 0x1p-27L, -0x1.0000000000001p0L, 3.725290298461913200853528590596263270474e-9L, -7.853981633974484345157511161499711112683e-1L); + TEST_c_c (catanh, -0x1p-27L, 0x1.0000000000001p0L, -3.725290298461913200853528590596263270474e-9L, 7.853981633974484345157511161499711112683e-1L); + TEST_c_c (catanh, -0x1p-27L, -0x1.0000000000001p0L, -3.725290298461913200853528590596263270474e-9L, -7.853981633974484345157511161499711112683e-1L); + TEST_c_c (catanh, 0x1.0000000000001p0L, 0x1p-27L, 9.704060527839234168777242958594699810015L, 7.853981801612546526942695000283242525531e-1L); + TEST_c_c (catanh, -0x1.0000000000001p0L, 0x1p-27L, -9.704060527839234168777242958594699810015L, 7.853981801612546526942695000283242525531e-1L); + TEST_c_c (catanh, 0x1.0000000000001p0L, -0x1p-27L, 9.704060527839234168777242958594699810015L, -7.853981801612546526942695000283242525531e-1L); + TEST_c_c (catanh, -0x1.0000000000001p0L, -0x1p-27L, -9.704060527839234168777242958594699810015L, -7.853981801612546526942695000283242525531e-1L); + TEST_c_c (catanh, 0x1p-27L, 0x0.fffffffffffff8p0L, 3.725290298461914441624447420137706700965e-9L, 7.853981633974482679822974223765039144191e-1L); + TEST_c_c (catanh, 0x1p-27L, -0x0.fffffffffffff8p0L, 3.725290298461914441624447420137706700965e-9L, -7.853981633974482679822974223765039144191e-1L); + TEST_c_c (catanh, -0x1p-27L, 0x0.fffffffffffff8p0L, -3.725290298461914441624447420137706700965e-9L, 7.853981633974482679822974223765039144191e-1L); + TEST_c_c (catanh, -0x1p-27L, -0x0.fffffffffffff8p0L, -3.725290298461914441624447420137706700965e-9L, -7.853981633974482679822974223765039144191e-1L); + TEST_c_c (catanh, 0x0.fffffffffffff8p0L, 0x1p-27L, 9.704060527839234252043969805481351363824L, 7.853981578095128619227903983047292781021e-1L); + TEST_c_c (catanh, -0x0.fffffffffffff8p0L, 0x1p-27L, -9.704060527839234252043969805481351363824L, 7.853981578095128619227903983047292781021e-1L); + TEST_c_c (catanh, 0x0.fffffffffffff8p0L, -0x1p-27L, 9.704060527839234252043969805481351363824L, -7.853981578095128619227903983047292781021e-1L); + TEST_c_c (catanh, -0x0.fffffffffffff8p0L, -0x1p-27L, -9.704060527839234252043969805481351363824L, -7.853981578095128619227903983047292781021e-1L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 64 + TEST_c_c (catanh, 0x1p-33L, 0x1.0000000000000002p0L, 5.820766091346740722012013594069507025615e-11L, 7.853981633974483096732590862331681441026e-1L); + TEST_c_c (catanh, 0x1p-33L, -0x1.0000000000000002p0L, 5.820766091346740722012013594069507025615e-11L, -7.853981633974483096732590862331681441026e-1L); + TEST_c_c (catanh, -0x1p-33L, 0x1.0000000000000002p0L, -5.820766091346740722012013594069507025615e-11L, 7.853981633974483096732590862331681441026e-1L); + TEST_c_c (catanh, -0x1p-33L, -0x1.0000000000000002p0L, -5.820766091346740722012013594069507025615e-11L, -7.853981633974483096732590862331681441026e-1L); + TEST_c_c (catanh, 0x1.0000000000000002p0L, 0x1p-33L, 1.178350206951907025990405771755129268176e1L, 7.853981638922134273801338071094141188767e-1L); + TEST_c_c (catanh, -0x1.0000000000000002p0L, 0x1p-33L, -1.178350206951907025990405771755129268176e1L, 7.853981638922134273801338071094141188767e-1L); + TEST_c_c (catanh, 0x1.0000000000000002p0L, -0x1p-33L, 1.178350206951907025990405771755129268176e1L, -7.853981638922134273801338071094141188767e-1L); + TEST_c_c (catanh, -0x1.0000000000000002p0L, -0x1p-33L, -1.178350206951907025990405771755129268176e1L, -7.853981638922134273801338071094141188767e-1L); + TEST_c_c (catanh, 0x1p-33L, 0x0.ffffffffffffffffp0L, 5.820766091346740722958646680334721192083e-11L, 7.853981633974483095919439232967553115548e-1L); + TEST_c_c (catanh, 0x1p-33L, -0x0.ffffffffffffffffp0L, 5.820766091346740722958646680334721192083e-11L, -7.853981633974483095919439232967553115548e-1L); + TEST_c_c (catanh, -0x1p-33L, 0x0.ffffffffffffffffp0L, -5.820766091346740722958646680334721192083e-11L, 7.853981633974483095919439232967553115548e-1L); + TEST_c_c (catanh, -0x1p-33L, -0x0.ffffffffffffffffp0L, -5.820766091346740722958646680334721192083e-11L, -7.853981633974483095919439232967553115548e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffp0L, 0x1p-33L, 1.178350206951907026002603046195591193050e1L, 7.853981631937214964185249205444919953948e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffp0L, 0x1p-33L, -1.178350206951907026002603046195591193050e1L, 7.853981631937214964185249205444919953948e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffp0L, -0x1p-33L, 1.178350206951907026002603046195591193050e1L, -7.853981631937214964185249205444919953948e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffp0L, -0x1p-33L, -1.178350206951907026002603046195591193050e1L, -7.853981631937214964185249205444919953948e-1L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106 + TEST_c_c (catanh, 0x1p-54L, 0x1.000000000000000000000000008p0L, 2.775557561562891351059079170226980932999e-17L, 7.853981633974483096156608458198888173729e-1L); + TEST_c_c (catanh, 0x1p-54L, -0x1.000000000000000000000000008p0L, 2.775557561562891351059079170226980932999e-17L, -7.853981633974483096156608458198888173729e-1L); + TEST_c_c (catanh, -0x1p-54L, 0x1.000000000000000000000000008p0L, -2.775557561562891351059079170226980932999e-17L, 7.853981633974483096156608458198888173729e-1L); + TEST_c_c (catanh, -0x1p-54L, -0x1.000000000000000000000000008p0L, -2.775557561562891351059079170226980932999e-17L, -7.853981633974483096156608458198888173729e-1L); + TEST_c_c (catanh, 0x1.000000000000000000000000008p0L, 0x1p-54L, 1.906154746539849600897388334009981267384e1L, 7.853981633974485455380535786656405610710e-1L); + TEST_c_c (catanh, -0x1.000000000000000000000000008p0L, 0x1p-54L, -1.906154746539849600897388334009981267384e1L, 7.853981633974485455380535786656405610710e-1L); + TEST_c_c (catanh, 0x1.000000000000000000000000008p0L, -0x1p-54L, 1.906154746539849600897388334009981267384e1L, -7.853981633974485455380535786656405610710e-1L); + TEST_c_c (catanh, -0x1.000000000000000000000000008p0L, -0x1p-54L, -1.906154746539849600897388334009981267384e1L, -7.853981633974485455380535786656405610710e-1L); + TEST_c_c (catanh, 0x1p-54L, 0x0.ffffffffffffffffffffffffffcp0L, 2.775557561562891351059079170227083567164e-17L, 7.853981633974483096156608458198703284454e-1L); + TEST_c_c (catanh, 0x1p-54L, -0x0.ffffffffffffffffffffffffffcp0L, 2.775557561562891351059079170227083567164e-17L, -7.853981633974483096156608458198703284454e-1L); + TEST_c_c (catanh, -0x1p-54L, 0x0.ffffffffffffffffffffffffffcp0L, -2.775557561562891351059079170227083567164e-17L, 7.853981633974483096156608458198703284454e-1L); + TEST_c_c (catanh, -0x1p-54L, -0x0.ffffffffffffffffffffffffffcp0L, -2.775557561562891351059079170227083567164e-17L, -7.853981633974483096156608458198703284454e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffffffffffffcp0L, 0x1p-54L, 1.906154746539849600897388334009984040723e1L, 7.853981633974482124711461911186784339815e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffffffffffffcp0L, 0x1p-54L, -1.906154746539849600897388334009984040723e1L, 7.853981633974482124711461911186784339815e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffffffffffffcp0L, -0x1p-54L, 1.906154746539849600897388334009984040723e1L, -7.853981633974482124711461911186784339815e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffffffffffffcp0L, -0x1p-54L, -1.906154746539849600897388334009984040723e1L, -7.853981633974482124711461911186784339815e-1L); +#endif +#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 113 + TEST_c_c (catanh, 0x1p-57L, 0x1.0000000000000000000000000001p0L, 3.469446951953614188823848962783812780530e-18L, 7.853981633974483096156608458198758293829e-1L); + TEST_c_c (catanh, 0x1p-57L, -0x1.0000000000000000000000000001p0L, 3.469446951953614188823848962783812780530e-18L, -7.853981633974483096156608458198758293829e-1L); + TEST_c_c (catanh, -0x1p-57L, 0x1.0000000000000000000000000001p0L, -3.469446951953614188823848962783812780530e-18L, 7.853981633974483096156608458198758293829e-1L); + TEST_c_c (catanh, -0x1p-57L, -0x1.0000000000000000000000000001p0L, -3.469446951953614188823848962783812780530e-18L, -7.853981633974483096156608458198758293829e-1L); + TEST_c_c (catanh, 0x1.0000000000000000000000000001p0L, 0x1p-57L, 2.010126823623841397309973152228712033275e1L, 7.853981633974483252281721296111395707566e-1L); + TEST_c_c (catanh, -0x1.0000000000000000000000000001p0L, 0x1p-57L, -2.010126823623841397309973152228712033275e1L, 7.853981633974483252281721296111395707566e-1L); + TEST_c_c (catanh, 0x1.0000000000000000000000000001p0L, -0x1p-57L, 2.010126823623841397309973152228712033275e1L, -7.853981633974483252281721296111395707566e-1L); + TEST_c_c (catanh, -0x1.0000000000000000000000000001p0L, -0x1p-57L, -2.010126823623841397309973152228712033275e1L, -7.853981633974483252281721296111395707566e-1L); + TEST_c_c (catanh, 0x1p-57L, 0x0.ffffffffffffffffffffffffffff8p0L, 3.469446951953614188823848962783813782817e-18L, 7.853981633974483096156608458198756849381e-1L); + TEST_c_c (catanh, 0x1p-57L, -0x0.ffffffffffffffffffffffffffff8p0L, 3.469446951953614188823848962783813782817e-18L, -7.853981633974483096156608458198756849381e-1L); + TEST_c_c (catanh, -0x1p-57L, 0x0.ffffffffffffffffffffffffffff8p0L, -3.469446951953614188823848962783813782817e-18L, 7.853981633974483096156608458198756849381e-1L); + TEST_c_c (catanh, -0x1p-57L, -0x0.ffffffffffffffffffffffffffff8p0L, -3.469446951953614188823848962783813782817e-18L, -7.853981633974483096156608458198756849381e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffffffffffffff8p0L, 0x1p-57L, 2.010126823623841397309973152228712040498e1L, 7.853981633974483044114904178894544378135e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffffffffffffff8p0L, 0x1p-57L, -2.010126823623841397309973152228712040498e1L, 7.853981633974483044114904178894544378135e-1L); + TEST_c_c (catanh, 0x0.ffffffffffffffffffffffffffff8p0L, -0x1p-57L, 2.010126823623841397309973152228712040498e1L, -7.853981633974483044114904178894544378135e-1L); + TEST_c_c (catanh, -0x0.ffffffffffffffffffffffffffff8p0L, -0x1p-57L, -2.010126823623841397309973152228712040498e1L, -7.853981633974483044114904178894544378135e-1L); +#endif TEST_c_c (catanh, 0.75L, 1.25L, 0.261492138795671927078652057366532140L, 0.996825126463918666098902241310446708L); TEST_c_c (catanh, -2, -3, -0.14694666622552975204743278515471595L, -1.3389725222944935611241935759091443L); diff --git a/math/s_catan.c b/math/s_catan.c index 4b7fbad30a..3a041f2245 100644 --- a/math/s_catan.c +++ b/math/s_catan.c @@ -77,14 +77,30 @@ __catan (__complex__ double x) } else { - double r2, num, den, f; + double r2, num, den, f, absx, absy; - r2 = __real__ x * __real__ x; + absx = fabs (__real__ x); + absy = fabs (__imag__ x); + if (absx < absy) + { + double t = absx; + absx = absy; + absy = t; + } - den = 1 - r2 - __imag__ x * __imag__ x; + if (absx >= 1.0) + den = (1.0 - absx) * (1.0 + absx) - absy * absy; + else if (absx >= 0.75 && absy < DBL_EPSILON / 2.0) + den = (1.0 - absx) * (1.0 + absx); + else if (absx >= 0.75 || absy >= 0.5) + den = -__x2y2m1 (absx, absy); + else + den = (1.0 - absx) * (1.0 + absx) - absy * absy; __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den); + r2 = __real__ x * __real__ x; + num = __imag__ x + 1.0; num = r2 + num * num; diff --git a/math/s_catanf.c b/math/s_catanf.c index aa71e5e63a..698e2af461 100644 --- a/math/s_catanf.c +++ b/math/s_catanf.c @@ -78,14 +78,30 @@ __catanf (__complex__ float x) } else { - float r2, num, den, f; + float r2, num, den, f, absx, absy; - r2 = __real__ x * __real__ x; + absx = fabsf (__real__ x); + absy = fabsf (__imag__ x); + if (absx < absy) + { + float t = absx; + absx = absy; + absy = t; + } - den = 1 - r2 - __imag__ x * __imag__ x; + if (absx >= 1.0f) + den = (1.0f - absx) * (1.0f + absx) - absy * absy; + else if (absx >= 0.75f && absy < FLT_EPSILON / 2.0f) + den = (1.0f - absx) * (1.0f + absx); + else if (absx >= 0.75f || absy >= 0.5f) + den = -__x2y2m1f (absx, absy); + else + den = (1.0f - absx) * (1.0f + absx) - absy * absy; __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den); + r2 = __real__ x * __real__ x; + num = __imag__ x + 1.0f; num = r2 + num * num; diff --git a/math/s_catanh.c b/math/s_catanh.c index 55c56283b3..5248cbc0c8 100644 --- a/math/s_catanh.c +++ b/math/s_catanh.c @@ -89,7 +89,25 @@ __catanh (__complex__ double x) __real__ res = 0.25 * __log1p (num / den); } - den = 1 - __real__ x * __real__ x - i2; + double absx, absy; + + absx = fabs (__real__ x); + absy = fabs (__imag__ x); + if (absx < absy) + { + double t = absx; + absx = absy; + absy = t; + } + + if (absx >= 1.0) + den = (1.0 - absx) * (1.0 + absx) - absy * absy; + else if (absx >= 0.75 && absy < DBL_EPSILON / 2.0) + den = (1.0 - absx) * (1.0 + absx); + else if (absx >= 0.75 || absy >= 0.5) + den = -__x2y2m1 (absx, absy); + else + den = (1.0 - absx) * (1.0 + absx) - absy * absy; __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den); } diff --git a/math/s_catanhf.c b/math/s_catanhf.c index 3e87942369..249deb5669 100644 --- a/math/s_catanhf.c +++ b/math/s_catanhf.c @@ -90,7 +90,25 @@ __catanhf (__complex__ float x) __real__ res = 0.25f * __log1pf (num / den); } - den = 1 - __real__ x * __real__ x - i2; + float absx, absy; + + absx = fabsf (__real__ x); + absy = fabsf (__imag__ x); + if (absx < absy) + { + float t = absx; + absx = absy; + absy = t; + } + + if (absx >= 1.0f) + den = (1.0f - absx) * (1.0f + absx) - absy * absy; + else if (absx >= 0.75f && absy < FLT_EPSILON / 2.0f) + den = (1.0f - absx) * (1.0f + absx); + else if (absx >= 0.75f || absy >= 0.5f) + den = -__x2y2m1f (absx, absy); + else + den = (1.0f - absx) * (1.0f + absx) - absy * absy; __imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den); } diff --git a/math/s_catanhl.c b/math/s_catanhl.c index 64c30b5573..ab75b807e0 100644 --- a/math/s_catanhl.c +++ b/math/s_catanhl.c @@ -97,7 +97,25 @@ __catanhl (__complex__ long double x) __real__ res = 0.25L * __log1pl (num / den); } - den = 1 - __real__ x * __real__ x - i2; + long double absx, absy; + + absx = fabsl (__real__ x); + absy = fabsl (__imag__ x); + if (absx < absy) + { + long double t = absx; + absx = absy; + absy = t; + } + + if (absx >= 1.0L) + den = (1.0L - absx) * (1.0L + absx) - absy * absy; + else if (absx >= 0.75 && absy < LDBL_EPSILON / 2.0L) + den = (1.0L - absx) * (1.0L + absx); + else if (absx >= 0.75L || absy >= 0.5L) + den = -__x2y2m1l (absx, absy); + else + den = (1.0L - absx) * (1.0L + absx) - absy * absy; __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den); } diff --git a/math/s_catanl.c b/math/s_catanl.c index 17ab62d340..1a815ad776 100644 --- a/math/s_catanl.c +++ b/math/s_catanl.c @@ -85,14 +85,30 @@ __catanl (__complex__ long double x) } else { - long double r2, num, den, f; + long double r2, num, den, f, absx, absy; - r2 = __real__ x * __real__ x; + absx = fabsl (__real__ x); + absy = fabsl (__imag__ x); + if (absx < absy) + { + long double t = absx; + absx = absy; + absy = t; + } - den = 1 - r2 - __imag__ x * __imag__ x; + if (absx >= 1.0L) + den = (1.0L - absx) * (1.0L + absx) - absy * absy; + else if (absx >= 0.75L && absy < LDBL_EPSILON / 2.0L) + den = (1.0L - absx) * (1.0L + absx); + else if (absx >= 0.75L || absy >= 0.5L) + den = -__x2y2m1l (absx, absy); + else + den = (1.0L - absx) * (1.0L + absx) - absy * absy; __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den); + r2 = __real__ x * __real__ x; + num = __imag__ x + 1.0L; num = r2 + num * num; diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index e36d0c374d..a3f58447d9 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -3480,6 +3480,23 @@ double: 1 idouble: 1 # catan +Test "Imaginary part of: catan (-0x0.fffffffffffff8p0 + 0x1p-27 i) == -7.853981633974482679822974223765039144191e-1 + 3.725290298461914441624447420137706700965e-9 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catan (-0x0.ffffffffffffffffp0 + 0x1p-33 i) == -7.853981633974483095919439232967553115548e-1 + 5.820766091346740722958646680334721192083e-11 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-0x0.ffffffp0 + 0x1p-13 i) == -7.853981373204155542484315721351697277336e-1 + 6.103515973639646453881721999956617260502e-5 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1.0000000000001p0 + 0x1p-27 i) == -7.853981633974484345157511161499711112683e-1 + 3.725290298461913200853528590596263270474e-9 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-0x1.000002p0 - 0x1p-13 i) == -7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +double: 1 +idouble: 1 Test "Imaginary part of: catan (-0x1.fp1023 + 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i": ildouble: 1 ldouble: 1 @@ -3492,11 +3509,37 @@ ldouble: 1 Test "Imaginary part of: catan (-0x1.fp127 - 0x1.fp127 i) == -1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 i": ildouble: 1 ldouble: 1 +Test "Imaginary part of: catan (-0x1p-33 + 0x0.ffffffffffffffffp0 i) == -7.853981631937214964185249205444919953948e-1 + 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-0x1p-33 - 0x0.ffffffffffffffffp0 i) == -7.853981631937214964185249205444919953948e-1 - 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-1.0 - 0x1p-13 i) == -7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +ildouble: 1 +ldouble: 1 Test "Imaginary part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i": double: 1 float: 1 idouble: 1 ifloat: 1 +Test "Imaginary part of: catan (0x0.fffffffffffff8p0 + 0x1p-27 i) == 7.853981633974482679822974223765039144191e-1 + 3.725290298461914441624447420137706700965e-9 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catan (0x0.ffffffffffffffffp0 + 0x1p-33 i) == 7.853981633974483095919439232967553115548e-1 + 5.820766091346740722958646680334721192083e-11 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (0x0.ffffffp0 + 0x1p-13 i) == 7.853981373204155542484315721351697277336e-1 + 6.103515973639646453881721999956617260502e-5 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1.0000000000001p0 + 0x1p-27 i) == 7.853981633974484345157511161499711112683e-1 + 3.725290298461913200853528590596263270474e-9 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (0x1.000002p0 - 0x1p-13 i) == 7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +double: 1 +idouble: 1 Test "Imaginary part of: catan (0x1.fp1023 + 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i": ildouble: 1 ldouble: 1 @@ -3509,8 +3552,23 @@ ldouble: 1 Test "Imaginary part of: catan (0x1.fp127 - 0x1.fp127 i) == 1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 i": ildouble: 1 ldouble: 1 +Test "Imaginary part of: catan (0x1p-33 + 0x0.ffffffffffffffffp0 i) == 7.853981631937214964185249205444919953948e-1 + 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (0x1p-33 - 0x0.ffffffffffffffffp0 i) == 7.853981631937214964185249205444919953948e-1 - 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (1.0 - 0x1p-13 i) == 7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +ildouble: 1 +ldouble: 1 # catanh +Test "Real part of: catanh (-0x0.ffffffffffffffffp0 + 0x1p-33 i) == -1.178350206951907026002603046195591193050e1 + 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (-0x0.ffffffffffffffffp0 - 0x1p-33 i) == -1.178350206951907026002603046195591193050e1 - 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 Test "Real part of: catanh (-0x1.fp1023 + 0x1.fp1023 i) == -2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i": ildouble: 1 ldouble: 1 @@ -3523,6 +3581,18 @@ ldouble: 1 Test "Real part of: catanh (-0x1.fp127 - 0x1.fp127 i) == -1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i": ildouble: 1 ldouble: 1 +Test "Real part of: catanh (-0x1p-13 + 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 + 7.853982267273793866654490522673596014524e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (-0x1p-13 + 1.0 i) == -6.103515609841754902688560615027452023669e-5 + 7.853981671227386080775748393881580082970e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (-0x1p-13 - 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 - 7.853982267273793866654490522673596014524e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (-0x1p-13 - 1.0 i) == -6.103515609841754902688560615027452023669e-5 - 7.853981671227386080775748393881580082970e-1 i": +ildouble: 1 +ldouble: 1 Test "Real part of: catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i": double: 2 float: 1 @@ -3535,6 +3605,12 @@ double: 1 idouble: 1 ildouble: 1 ldouble: 1 +Test "Real part of: catanh (0x0.ffffffffffffffffp0 + 0x1p-33 i) == 1.178350206951907026002603046195591193050e1 + 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (0x0.ffffffffffffffffp0 - 0x1p-33 i) == 1.178350206951907026002603046195591193050e1 - 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 Test "Real part of: catanh (0x1.fp1023 + 0x1.fp1023 i) == 2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i": ildouble: 1 ldouble: 1 @@ -3547,6 +3623,34 @@ ldouble: 1 Test "Real part of: catanh (0x1.fp127 - 0x1.fp127 i) == 1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i": ildouble: 1 ldouble: 1 +Test "Real part of: catanh (0x1p-13 + 0x0.ffffffp0 i) == 6.103515973639646453881721999956617260502e-5 + 7.853981373204155542484315721351697277336e-1 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-13 - 0x0.ffffffp0 i) == 6.103515973639646453881721999956617260502e-5 - 7.853981373204155542484315721351697277336e-1 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-27 + 0x0.fffffffffffff8p0 i) == 3.725290298461914441624447420137706700965e-9 + 7.853981633974482679822974223765039144191e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (0x1p-27 + 0x1.0000000000001p0 i) == 3.725290298461913200853528590596263270474e-9 + 7.853981633974484345157511161499711112683e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (0x1p-27 - 0x0.fffffffffffff8p0 i) == 3.725290298461914441624447420137706700965e-9 - 7.853981633974482679822974223765039144191e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (0x1p-27 - 0x1.0000000000001p0 i) == 3.725290298461913200853528590596263270474e-9 - 7.853981633974484345157511161499711112683e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (0x1p-33 + 0x0.ffffffffffffffffp0 i) == 5.820766091346740722958646680334721192083e-11 + 7.853981633974483095919439232967553115548e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (0x1p-33 - 0x0.ffffffffffffffffp0 i) == 5.820766091346740722958646680334721192083e-11 - 7.853981633974483095919439232967553115548e-1 i": +ildouble: 1 +ldouble: 1 # cbrt Test "cbrt (-27.0) == -3.0": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index 43b5595c5a..7ef2832190 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -4205,6 +4205,32 @@ double: 1 idouble: 1 # catan +Test "Imaginary part of: catan (-0x0.fffffffffffff8p0 + 0x1p-27 i) == -7.853981633974482679822974223765039144191e-1 + 3.725290298461914441624447420137706700965e-9 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catan (-0x0.ffffffffffffffffp0 + 0x1p-33 i) == -7.853981633974483095919439232967553115548e-1 + 5.820766091346740722958646680334721192083e-11 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-0x0.ffffffp0 + 0x1p-13 i) == -7.853981373204155542484315721351697277336e-1 + 6.103515973639646453881721999956617260502e-5 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1.0000000000001p0 + 0x1p-27 i) == -7.853981633974484345157511161499711112683e-1 + 3.725290298461913200853528590596263270474e-9 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (-0x1.0000000000001p0 - 0x1p-27 i) == -7.853981633974484345157511161499711112683e-1 - 3.725290298461913200853528590596263270474e-9 i": +double: 1 +idouble: 1 +Test "Real part of: catan (-0x1.000002p0 + 0x1p-13 i) == -7.853982267273793866654490522673596014524e-1 + 6.103514882246036852433556327261700380577e-5 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1.000002p0 - 0x1p-13 i) == -7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1.000002p0 - 0x1p-13 i) == -7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +double: 1 +idouble: 1 Test "Imaginary part of: catan (-0x1.fp1023 + 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i": double: 1 idouble: 1 @@ -4225,6 +4251,84 @@ double: 1 idouble: 1 ildouble: 1 ldouble: 1 +Test "Real part of: catan (-0x1p-13 + 0x1.000002p0 i) == -7.859169620684960844300240092596908675974e-1 + 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-13 + 1.0 i) == -7.854286809755354140031716771044626356262e-1 + 4.852030264850939738801379894163661227127 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-13 - 0x1.000002p0 i) == -7.859169620684960844300240092596908675974e-1 - 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1p-13 - 0x1.000002p0 i) == -7.859169620684960844300240092596908675974e-1 - 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-13 - 1.0 i) == -7.854286809755354140031716771044626356262e-1 - 4.852030264850939738801379894163661227127 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-27 + 1.0 i) == -7.853981652600934588466178684534110069553e-1 + 9.704060527839234335310696652368086117807 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-27 - 1.0 i) == -7.853981652600934588466178684534110069553e-1 - 9.704060527839234335310696652368086117807 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1p-33 + 0x0.ffffffffffffffffp0 i) == -7.853981631937214964185249205444919953948e-1 + 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (-0x1p-33 + 1.0 i) == -7.853981634265521400723945494331241018449e-1 + 1.178350206951907026009379309773625595762e1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (-0x1p-33 - 0x0.ffffffffffffffffp0 i) == -7.853981631937214964185249205444919953948e-1 - 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (-0x1p-33 - 1.0 i) == -7.853981634265521400723945494331241018449e-1 - 1.178350206951907026009379309773625595762e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-54 + 1.0 i) == -7.853981633974483234934486536343324763447e-1 + 1.906154746539849600897388334009985581467e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-54 - 1.0 i) == -7.853981633974483234934486536343324763447e-1 - 1.906154746539849600897388334009985581467e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-57 + 1.0 i) == -7.853981633974483113503843217966828154612e-1 + 2.010126823623841397309973152228712047720e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-0x1p-57 - 1.0 i) == -7.853981633974483113503843217966828154612e-1 - 2.010126823623841397309973152228712047720e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 + 0x1p-13 i) == -7.853981671227386080775748393881580082970e-1 + 6.103515609841754902688560615027452023669e-5 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 + 0x1p-27 i) == -7.853981633974483234934486536343324763447e-1 + 3.725290298461914028034141143623846306386e-9 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 + 0x1p-33 i) == -7.853981633974483096190489776088929224056e-1 + 5.820766091346740722643102318246316469910e-11 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 + 0x1p-54 i) == -7.853981633974483096156608458198764914213e-1 + 2.775557561562891351059079170227049355775e-17 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 + 0x1p-57 i) == -7.853981633974483096156608458198757330864e-1 + 3.469446951953614188823848962783813448721e-18 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 - 0x1p-13 i) == -7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (-1.0 - 0x1p-13 i) == -7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (-1.0 - 0x1p-27 i) == -7.853981633974483234934486536343324763447e-1 - 3.725290298461914028034141143623846306386e-9 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 - 0x1p-33 i) == -7.853981633974483096190489776088929224056e-1 - 5.820766091346740722643102318246316469910e-11 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 - 0x1p-54 i) == -7.853981633974483096156608458198764914213e-1 - 2.775557561562891351059079170227049355775e-17 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (-1.0 - 0x1p-57 i) == -7.853981633974483096156608458198757330864e-1 - 3.469446951953614188823848962783813448721e-18 i": +float: 1 +ifloat: 1 Test "Real part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i": float: 3 ifloat: 3 @@ -4236,6 +4340,32 @@ ifloat: 1 Test "Real part of: catan (0.75 + 1.25 i) == 1.10714871779409050301706546017853704 + 0.549306144334054845697622618461262852 i": float: 4 ifloat: 4 +Test "Imaginary part of: catan (0x0.fffffffffffff8p0 + 0x1p-27 i) == 7.853981633974482679822974223765039144191e-1 + 3.725290298461914441624447420137706700965e-9 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catan (0x0.ffffffffffffffffp0 + 0x1p-33 i) == 7.853981633974483095919439232967553115548e-1 + 5.820766091346740722958646680334721192083e-11 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (0x0.ffffffp0 + 0x1p-13 i) == 7.853981373204155542484315721351697277336e-1 + 6.103515973639646453881721999956617260502e-5 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1.0000000000001p0 + 0x1p-27 i) == 7.853981633974484345157511161499711112683e-1 + 3.725290298461913200853528590596263270474e-9 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catan (0x1.0000000000001p0 - 0x1p-27 i) == 7.853981633974484345157511161499711112683e-1 - 3.725290298461913200853528590596263270474e-9 i": +double: 1 +idouble: 1 +Test "Real part of: catan (0x1.000002p0 + 0x1p-13 i) == 7.853982267273793866654490522673596014524e-1 + 6.103514882246036852433556327261700380577e-5 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1.000002p0 - 0x1p-13 i) == 7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1.000002p0 - 0x1p-13 i) == 7.853982267273793866654490522673596014524e-1 - 6.103514882246036852433556327261700380577e-5 i": +double: 1 +idouble: 1 Test "Imaginary part of: catan (0x1.fp1023 + 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i": double: 1 idouble: 1 @@ -4256,8 +4386,104 @@ double: 1 idouble: 1 ildouble: 1 ldouble: 1 +Test "Real part of: catan (0x1p-13 + 0x1.000002p0 i) == 7.859169620684960844300240092596908675974e-1 + 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-13 + 1.0 i) == 7.854286809755354140031716771044626356262e-1 + 4.852030264850939738801379894163661227127 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-13 - 0x1.000002p0 i) == 7.859169620684960844300240092596908675974e-1 - 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1p-13 - 0x1.000002p0 i) == 7.859169620684960844300240092596908675974e-1 - 4.852030056234795712498957387213592193975 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-13 - 1.0 i) == 7.854286809755354140031716771044626356262e-1 - 4.852030264850939738801379894163661227127 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-27 + 1.0 i) == 7.853981652600934588466178684534110069553e-1 + 9.704060527839234335310696652368086117807 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-27 - 1.0 i) == 7.853981652600934588466178684534110069553e-1 - 9.704060527839234335310696652368086117807 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1p-33 + 0x0.ffffffffffffffffp0 i) == 7.853981631937214964185249205444919953948e-1 + 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (0x1p-33 + 1.0 i) == 7.853981634265521400723945494331241018449e-1 + 1.178350206951907026009379309773625595762e1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (0x1p-33 - 0x0.ffffffffffffffffp0 i) == 7.853981631937214964185249205444919953948e-1 - 1.178350206951907026002603046195591193050e1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (0x1p-33 - 1.0 i) == 7.853981634265521400723945494331241018449e-1 - 1.178350206951907026009379309773625595762e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-54 + 1.0 i) == 7.853981633974483234934486536343324763447e-1 + 1.906154746539849600897388334009985581467e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-54 - 1.0 i) == 7.853981633974483234934486536343324763447e-1 - 1.906154746539849600897388334009985581467e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-57 + 1.0 i) == 7.853981633974483113503843217966828154612e-1 + 2.010126823623841397309973152228712047720e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (0x1p-57 - 1.0 i) == 7.853981633974483113503843217966828154612e-1 - 2.010126823623841397309973152228712047720e1 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 + 0x1p-13 i) == 7.853981671227386080775748393881580082970e-1 + 6.103515609841754902688560615027452023669e-5 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 + 0x1p-27 i) == 7.853981633974483234934486536343324763447e-1 + 3.725290298461914028034141143623846306386e-9 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 + 0x1p-33 i) == 7.853981633974483096190489776088929224056e-1 + 5.820766091346740722643102318246316469910e-11 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 + 0x1p-54 i) == 7.853981633974483096156608458198764914213e-1 + 2.775557561562891351059079170227049355775e-17 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 + 0x1p-57 i) == 7.853981633974483096156608458198757330864e-1 + 3.469446951953614188823848962783813448721e-18 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 - 0x1p-13 i) == 7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catan (1.0 - 0x1p-13 i) == 7.853981671227386080775748393881580082970e-1 - 6.103515609841754902688560615027452023669e-5 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catan (1.0 - 0x1p-27 i) == 7.853981633974483234934486536343324763447e-1 - 3.725290298461914028034141143623846306386e-9 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 - 0x1p-33 i) == 7.853981633974483096190489776088929224056e-1 - 5.820766091346740722643102318246316469910e-11 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 - 0x1p-54 i) == 7.853981633974483096156608458198764914213e-1 - 2.775557561562891351059079170227049355775e-17 i": +float: 1 +ifloat: 1 +Test "Real part of: catan (1.0 - 0x1p-57 i) == 7.853981633974483096156608458198757330864e-1 - 3.469446951953614188823848962783813448721e-18 i": +float: 1 +ifloat: 1 # catanh +Test "Real part of: catanh (-0x0.ffffffffffffffffp0 + 0x1p-33 i) == -1.178350206951907026002603046195591193050e1 + 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (-0x0.ffffffffffffffffp0 - 0x1p-33 i) == -1.178350206951907026002603046195591193050e1 - 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (-0x1.000002p0 + 0x1p-13 i) == -4.852030056234795712498957387213592193975 + 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1.000002p0 + 0x1p-13 i) == -4.852030056234795712498957387213592193975 + 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1.000002p0 - 0x1p-13 i) == -4.852030056234795712498957387213592193975 - 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1.000002p0 - 0x1p-13 i) == -4.852030056234795712498957387213592193975 - 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 Test "Real part of: catanh (-0x1.fp1023 + 0x1.fp1023 i) == -2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i": double: 1 idouble: 1 @@ -4278,6 +4504,90 @@ double: 1 idouble: 1 ildouble: 1 ldouble: 1 +Test "Real part of: catanh (-0x1p-13 + 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 + 7.853982267273793866654490522673596014524e-1 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catanh (-0x1p-13 + 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 + 7.853982267273793866654490522673596014524e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1p-13 + 1.0 i) == -6.103515609841754902688560615027452023669e-5 + 7.853981671227386080775748393881580082970e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (-0x1p-13 + 1.0 i) == -6.103515609841754902688560615027452023669e-5 + 7.853981671227386080775748393881580082970e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1p-13 - 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 - 7.853982267273793866654490522673596014524e-1 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catanh (-0x1p-13 - 0x1.000002p0 i) == -6.103514882246036852433556327261700380577e-5 - 7.853982267273793866654490522673596014524e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1p-13 - 1.0 i) == -6.103515609841754902688560615027452023669e-5 - 7.853981671227386080775748393881580082970e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (-0x1p-13 - 1.0 i) == -6.103515609841754902688560615027452023669e-5 - 7.853981671227386080775748393881580082970e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1p-27 + 0x1.0000000000001p0 i) == -3.725290298461913200853528590596263270474e-9 + 7.853981633974484345157511161499711112683e-1 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catanh (-0x1p-27 + 1.0 i) == -3.725290298461914028034141143623846306386e-9 + 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (-0x1p-27 - 0x1.0000000000001p0 i) == -3.725290298461913200853528590596263270474e-9 - 7.853981633974484345157511161499711112683e-1 i": +double: 1 +idouble: 1 +Test "Imaginary part of: catanh (-0x1p-27 - 1.0 i) == -3.725290298461914028034141143623846306386e-9 - 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-33 + 1.0 i) == -5.820766091346740722643102318246316469910e-11 + 7.853981633974483096190489776088929224056e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-33 - 1.0 i) == -5.820766091346740722643102318246316469910e-11 - 7.853981633974483096190489776088929224056e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-54 + 1.0 i) == -2.775557561562891351059079170227049355775e-17 + 7.853981633974483096156608458198764914213e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-54 - 1.0 i) == -2.775557561562891351059079170227049355775e-17 - 7.853981633974483096156608458198764914213e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-57 + 1.0 i) == -3.469446951953614188823848962783813448721e-18 + 7.853981633974483096156608458198757330864e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-0x1p-57 - 1.0 i) == -3.469446951953614188823848962783813448721e-18 - 7.853981633974483096156608458198757330864e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 + 0x1p-13 i) == -4.852030264850939738801379894163661227127 + 7.854286809755354140031716771044626356262e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 + 0x1p-27 i) == -9.704060527839234335310696652368086117807 + 7.853981652600934588466178684534110069553e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 + 0x1p-33 i) == -1.178350206951907026009379309773625595762e1 + 7.853981634265521400723945494331241018449e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 + 0x1p-54 i) == -1.906154746539849600897388334009985581467e1 + 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 + 0x1p-57 i) == -2.010126823623841397309973152228712047720e1 + 7.853981633974483113503843217966828154612e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 - 0x1p-13 i) == -4.852030264850939738801379894163661227127 - 7.854286809755354140031716771044626356262e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 - 0x1p-27 i) == -9.704060527839234335310696652368086117807 - 7.853981652600934588466178684534110069553e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 - 0x1p-33 i) == -1.178350206951907026009379309773625595762e1 - 7.853981634265521400723945494331241018449e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 - 0x1p-54 i) == -1.906154746539849600897388334009985581467e1 - 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (-1.0 - 0x1p-57 i) == -2.010126823623841397309973152228712047720e1 - 7.853981633974483113503843217966828154612e-1 i": +float: 1 +ifloat: 1 Test "Real part of: catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i": double: 4 idouble: 4 @@ -4294,6 +4604,18 @@ ldouble: 1 Test "Imaginary part of: catanh (0.75 + 1.25 i) == 0.261492138795671927078652057366532140 + 0.996825126463918666098902241310446708 i": float: 6 ifloat: 6 +Test "Real part of: catanh (0x0.ffffffffffffffffp0 + 0x1p-33 i) == 1.178350206951907026002603046195591193050e1 + 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: catanh (0x0.ffffffffffffffffp0 - 0x1p-33 i) == 1.178350206951907026002603046195591193050e1 - 7.853981631937214964185249205444919953948e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (0x1.000002p0 + 0x1p-13 i) == 4.852030056234795712498957387213592193975 + 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1.000002p0 - 0x1p-13 i) == 4.852030056234795712498957387213592193975 - 7.859169620684960844300240092596908675974e-1 i": +float: 1 +ifloat: 1 Test "Real part of: catanh (0x1.fp1023 + 0x1.fp1023 i) == 2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i": double: 1 idouble: 1 @@ -4314,6 +4636,100 @@ double: 1 idouble: 1 ildouble: 1 ldouble: 1 +Test "Real part of: catanh (0x1p-13 + 0x0.ffffffp0 i) == 6.103515973639646453881721999956617260502e-5 + 7.853981373204155542484315721351697277336e-1 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-13 + 0x1.000002p0 i) == 6.103514882246036852433556327261700380577e-5 + 7.853982267273793866654490522673596014524e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-13 + 1.0 i) == 6.103515609841754902688560615027452023669e-5 + 7.853981671227386080775748393881580082970e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-13 - 0x0.ffffffp0 i) == 6.103515973639646453881721999956617260502e-5 - 7.853981373204155542484315721351697277336e-1 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-13 - 0x1.000002p0 i) == 6.103514882246036852433556327261700380577e-5 - 7.853982267273793866654490522673596014524e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-13 - 1.0 i) == 6.103515609841754902688560615027452023669e-5 - 7.853981671227386080775748393881580082970e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-27 + 0x0.fffffffffffff8p0 i) == 3.725290298461914441624447420137706700965e-9 + 7.853981633974482679822974223765039144191e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (0x1p-27 + 0x1.0000000000001p0 i) == 3.725290298461913200853528590596263270474e-9 + 7.853981633974484345157511161499711112683e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (0x1p-27 + 1.0 i) == 3.725290298461914028034141143623846306386e-9 + 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-27 - 0x0.fffffffffffff8p0 i) == 3.725290298461914441624447420137706700965e-9 - 7.853981633974482679822974223765039144191e-1 i": +double: 1 +idouble: 1 +Test "Real part of: catanh (0x1p-27 - 0x1.0000000000001p0 i) == 3.725290298461913200853528590596263270474e-9 - 7.853981633974484345157511161499711112683e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (0x1p-27 - 1.0 i) == 3.725290298461914028034141143623846306386e-9 - 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-33 + 0x0.ffffffffffffffffp0 i) == 5.820766091346740722958646680334721192083e-11 + 7.853981633974483095919439232967553115548e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (0x1p-33 + 1.0 i) == 5.820766091346740722643102318246316469910e-11 + 7.853981633974483096190489776088929224056e-1 i": +float: 1 +ifloat: 1 +Test "Real part of: catanh (0x1p-33 - 0x0.ffffffffffffffffp0 i) == 5.820766091346740722958646680334721192083e-11 - 7.853981633974483095919439232967553115548e-1 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: catanh (0x1p-33 - 1.0 i) == 5.820766091346740722643102318246316469910e-11 - 7.853981633974483096190489776088929224056e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-54 + 1.0 i) == 2.775557561562891351059079170227049355775e-17 + 7.853981633974483096156608458198764914213e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-54 - 1.0 i) == 2.775557561562891351059079170227049355775e-17 - 7.853981633974483096156608458198764914213e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-57 + 1.0 i) == 3.469446951953614188823848962783813448721e-18 + 7.853981633974483096156608458198757330864e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (0x1p-57 - 1.0 i) == 3.469446951953614188823848962783813448721e-18 - 7.853981633974483096156608458198757330864e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 + 0x1p-13 i) == 4.852030264850939738801379894163661227127 + 7.854286809755354140031716771044626356262e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 + 0x1p-27 i) == 9.704060527839234335310696652368086117807 + 7.853981652600934588466178684534110069553e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 + 0x1p-33 i) == 1.178350206951907026009379309773625595762e1 + 7.853981634265521400723945494331241018449e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 + 0x1p-54 i) == 1.906154746539849600897388334009985581467e1 + 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 + 0x1p-57 i) == 2.010126823623841397309973152228712047720e1 + 7.853981633974483113503843217966828154612e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 - 0x1p-13 i) == 4.852030264850939738801379894163661227127 - 7.854286809755354140031716771044626356262e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 - 0x1p-27 i) == 9.704060527839234335310696652368086117807 - 7.853981652600934588466178684534110069553e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 - 0x1p-33 i) == 1.178350206951907026009379309773625595762e1 - 7.853981634265521400723945494331241018449e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 - 0x1p-54 i) == 1.906154746539849600897388334009985581467e1 - 7.853981633974483234934486536343324763447e-1 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: catanh (1.0 - 0x1p-57 i) == 2.010126823623841397309973152228712047720e1 - 7.853981633974483113503843217966828154612e-1 i": +float: 1 +ifloat: 1 # cbrt Test "cbrt (-0.001) == -0.1": @@ -6865,13 +7281,15 @@ ldouble: 1 Function: Real part of "catanh": double: 4 +float: 1 idouble: 4 +ifloat: 1 ildouble: 1 ldouble: 1 Function: Imaginary part of "catanh": -float: 6 -ifloat: 6 +float: 1 +ifloat: 1 Function: "cbrt": double: 1 |