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Fix catan, catanh spurious overflows (bug 15409).

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This commit is contained in:
Joseph Myers 2013-04-27 14:56:34 +00:00
parent d5ba74f764
commit 5b4217d71f
11 changed files with 510 additions and 109 deletions
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21
ChangeLog
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@ -1,3 +1,24 @@
2013-04-27 Joseph Myers <joseph@codesourcery.com>
[BZ #15409]
* math/s_catan.c (__catan): Handle arguments with large real or
imaginary part separately without squaring.
* math/s_catanf.c (__catanf): Likewise.
* math/s_catanh.c (__catanh): Likewise.
* math/s_catanhf.c (__catanhf): Likewise.
* math/s_catanhl.c [LDBL_MANT_DIG == 106] (LDBL_EPSILON): Undefine
and redefine.
(__catanhl): Handle arguments with large real or imaginary part
separately without squaring.
* math/s_catanl.c [LDBL_MANT_DIG == 106] (LDBL_EPSILON): Undefine
and redefine.
(__catanl): Handle arguments with large real or imaginary part
separately without squaring.
* 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.
2013-04-27 Andreas Jaeger <aj@suse.de>
[BZ #15007]

2
NEWS
View File

@ -15,7 +15,7 @@ Version 2.18
15006, 15007, 15020, 15023, 15036, 15054, 15055, 15062, 15078, 15160,
15214, 15221, 15232, 15234, 15283, 15285, 15287, 15304, 15305, 15307,
15309, 15327, 15330, 15335, 15336, 15337, 15342, 15346, 15361, 15366,
15394, 15405, 15406.
15394, 15405, 15406, 15409.
* CVE-2013-0242 Buffer overrun in regexp matcher has been fixed (Bugzilla
#15078).

128
math/libm-test.inc
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@ -4364,6 +4364,70 @@ catan_test (void)
TEST_c_c (catan, 0.5L, -0x1p8191L, 1.570796326794896619231321691639751442099L, -1.833603867554847165621412392048483165956e-2466L);
TEST_c_c (catan, -0.5L, -0x1p8191L, -1.570796326794896619231321691639751442099L, -1.833603867554847165621412392048483165956e-2466L);
#endif
TEST_c_c (catan, 0x1p100L, 0.0L, 1.570796326794896619231321691638962581193L, 0.0L);
TEST_c_c (catan, 0x1p100L, -0.0L, 1.570796326794896619231321691638962581193L, -0.0L);
TEST_c_c (catan, -0x1p100L, 0.0L, -1.570796326794896619231321691638962581193L, 0.0L);
TEST_c_c (catan, -0x1p100L, -0.0L, -1.570796326794896619231321691638962581193L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1p100L, 1.570796326794896619231321691639751442099L, 7.888609052210118054117285652827862296732e-31L);
TEST_c_c (catan, -0.0L, 0x1p100L, -1.570796326794896619231321691639751442099L, 7.888609052210118054117285652827862296732e-31L);
TEST_c_c (catan, 0.0L, -0x1p100L, 1.570796326794896619231321691639751442099L, -7.888609052210118054117285652827862296732e-31L);
TEST_c_c (catan, -0.0L, -0x1p100L, -1.570796326794896619231321691639751442099L, -7.888609052210118054117285652827862296732e-31L);
TEST_c_c (catan, 0x1.fp127L, 0.0L, 1.570796326794896619231321691639751442096L, 0.0L);
TEST_c_c (catan, 0x1.fp127L, -0.0L, 1.570796326794896619231321691639751442096L, -0.0L);
TEST_c_c (catan, -0x1.fp127L, 0.0L, -1.570796326794896619231321691639751442096L, 0.0L);
TEST_c_c (catan, -0x1.fp127L, -0.0L, -1.570796326794896619231321691639751442096L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1.fp127L, 1.570796326794896619231321691639751442099L, 3.033533808573645181854803967025150136306e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, -0.0L, 0x1.fp127L, -1.570796326794896619231321691639751442099L, 3.033533808573645181854803967025150136306e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, 0.0L, -0x1.fp127L, 1.570796326794896619231321691639751442099L, -3.033533808573645181854803967025150136306e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, -0.0L, -0x1.fp127L, -1.570796326794896619231321691639751442099L, -3.033533808573645181854803967025150136306e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, 0x1.fp127L, 0x1.fp127L, 1.570796326794896619231321691639751442097L, 1.516766904286822590927401983512575068153e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, 0x1.fp127L, -0x1.fp127L, 1.570796326794896619231321691639751442097L, -1.516766904286822590927401983512575068153e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, -0x1.fp127L, 0x1.fp127L, -1.570796326794896619231321691639751442097L, 1.516766904286822590927401983512575068153e-39L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catan, -0x1.fp127L, -0x1.fp127L, -1.570796326794896619231321691639751442097L, -1.516766904286822590927401983512575068153e-39L, UNDERFLOW_EXCEPTION_FLOAT);
#ifndef TEST_FLOAT
TEST_c_c (catan, 0x1p900L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, 0x1p900L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, -0x1p900L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, -0x1p900L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1p900L, 1.570796326794896619231321691639751442099L, 1.183052186166774710972751597518026531652e-271L);
TEST_c_c (catan, -0.0L, 0x1p900L, -1.570796326794896619231321691639751442099L, 1.183052186166774710972751597518026531652e-271L);
TEST_c_c (catan, 0.0L, -0x1p900L, 1.570796326794896619231321691639751442099L, -1.183052186166774710972751597518026531652e-271L);
TEST_c_c (catan, -0.0L, -0x1p900L, -1.570796326794896619231321691639751442099L, -1.183052186166774710972751597518026531652e-271L);
TEST_c_c (catan, 0x1.fp1023L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, 0x1.fp1023L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, -0x1.fp1023L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, -0x1.fp1023L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1.fp1023L, 1.570796326794896619231321691639751442099L, 5.742126086470197117652213464083623391533e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, -0.0L, 0x1.fp1023L, -1.570796326794896619231321691639751442099L, 5.742126086470197117652213464083623391533e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, 0.0L, -0x1.fp1023L, 1.570796326794896619231321691639751442099L, -5.742126086470197117652213464083623391533e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, -0.0L, -0x1.fp1023L, -1.570796326794896619231321691639751442099L, -5.742126086470197117652213464083623391533e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, 0x1.fp1023L, 0x1.fp1023L, 1.570796326794896619231321691639751442099L, 2.871063043235098558826106732041811695767e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, 0x1.fp1023L, -0x1.fp1023L, 1.570796326794896619231321691639751442099L, -2.871063043235098558826106732041811695767e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, -0x1.fp1023L, 0x1.fp1023L, -1.570796326794896619231321691639751442099L, 2.871063043235098558826106732041811695767e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catan, -0x1.fp1023L, -0x1.fp1023L, -1.570796326794896619231321691639751442099L, -2.871063043235098558826106732041811695767e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
#endif
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
TEST_c_c (catan, 0x1p10000L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, 0x1p10000L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, -0x1p10000L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, -0x1p10000L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1p10000L, 1.570796326794896619231321691639751442099L, 5.012372749206452009297555933742977749322e-3011L);
TEST_c_c (catan, -0.0L, 0x1p10000L, -1.570796326794896619231321691639751442099L, 5.012372749206452009297555933742977749322e-3011L);
TEST_c_c (catan, 0.0L, -0x1p10000L, 1.570796326794896619231321691639751442099L, -5.012372749206452009297555933742977749322e-3011L);
TEST_c_c (catan, -0.0L, -0x1p10000L, -1.570796326794896619231321691639751442099L, -5.012372749206452009297555933742977749322e-3011L);
TEST_c_c (catan, 0x1.fp16383L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, 0x1.fp16383L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, -0x1.fp16383L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
TEST_c_c (catan, -0x1.fp16383L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
TEST_c_c (catan, 0.0L, 0x1.fp16383L, 1.570796326794896619231321691639751442099L, 8.676395208031209048419813722120651877672e-4933L, UNDERFLOW_EXCEPTION);
TEST_c_c (catan, -0.0L, 0x1.fp16383L, -1.570796326794896619231321691639751442099L, 8.676395208031209048419813722120651877672e-4933L, UNDERFLOW_EXCEPTION);
TEST_c_c (catan, 0.0L, -0x1.fp16383L, 1.570796326794896619231321691639751442099L, -8.676395208031209048419813722120651877672e-4933L, UNDERFLOW_EXCEPTION);
TEST_c_c (catan, -0.0L, -0x1.fp16383L, -1.570796326794896619231321691639751442099L, -8.676395208031209048419813722120651877672e-4933L, UNDERFLOW_EXCEPTION);
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);
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, 0.75L, 1.25L, 1.10714871779409050301706546017853704L, 0.549306144334054845697622618461262852L);
TEST_c_c (catan, -2, -3, -1.4099210495965755225306193844604208L, -0.22907268296853876629588180294200276L);
@ -4496,6 +4560,70 @@ catanh_test (void)
TEST_c_c (catanh, 0.5L, -0x1p8191L, 1.681051571556046753131338908660876301299e-4932L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
TEST_c_c (catanh, -0.5L, -0x1p8191L, -1.681051571556046753131338908660876301299e-4932L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
#endif
TEST_c_c (catanh, 0x1p100L, 0.0L, 7.888609052210118054117285652827862296732e-31L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1p100L, -0.0L, 7.888609052210118054117285652827862296732e-31L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p100L, 0.0L, -7.888609052210118054117285652827862296732e-31L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p100L, -0.0L, -7.888609052210118054117285652827862296732e-31L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, 0x1p100L, 0.0L, 1.570796326794896619231321691638962581193L);
TEST_c_c (catanh, -0.0L, 0x1p100L, -0.0L, 1.570796326794896619231321691638962581193L);
TEST_c_c (catanh, 0.0L, -0x1p100L, 0.0L, -1.570796326794896619231321691638962581193L);
TEST_c_c (catanh, -0.0L, -0x1p100L, -0.0L, -1.570796326794896619231321691638962581193L);
TEST_c_c (catanh, 0x1.fp127L, 0.0L, 3.033533808573645181854803967025150136306e-39L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, 0x1.fp127L, -0.0L, 3.033533808573645181854803967025150136306e-39L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, -0x1.fp127L, 0.0L, -3.033533808573645181854803967025150136306e-39L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, -0x1.fp127L, -0.0L, -3.033533808573645181854803967025150136306e-39L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, 0.0L, 0x1.fp127L, 0.0L, 1.570796326794896619231321691639751442096L);
TEST_c_c (catanh, -0.0L, 0x1.fp127L, -0.0L, 1.570796326794896619231321691639751442096L);
TEST_c_c (catanh, 0.0L, -0x1.fp127L, 0.0L, -1.570796326794896619231321691639751442096L);
TEST_c_c (catanh, -0.0L, -0x1.fp127L, -0.0L, -1.570796326794896619231321691639751442096L);
TEST_c_c (catanh, 0x1.fp127L, 0x1.fp127L, 1.516766904286822590927401983512575068153e-39L, 1.570796326794896619231321691639751442097L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, 0x1.fp127L, -0x1.fp127L, 1.516766904286822590927401983512575068153e-39L, -1.570796326794896619231321691639751442097L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, -0x1.fp127L, 0x1.fp127L, -1.516766904286822590927401983512575068153e-39L, 1.570796326794896619231321691639751442097L, UNDERFLOW_EXCEPTION_FLOAT);
TEST_c_c (catanh, -0x1.fp127L, -0x1.fp127L, -1.516766904286822590927401983512575068153e-39L, -1.570796326794896619231321691639751442097L, UNDERFLOW_EXCEPTION_FLOAT);
#ifndef TEST_FLOAT
TEST_c_c (catanh, 0x1p900L, 0.0L, 1.183052186166774710972751597518026531652e-271L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1p900L, -0.0L, 1.183052186166774710972751597518026531652e-271L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p900L, 0.0L, -1.183052186166774710972751597518026531652e-271L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p900L, -0.0L, -1.183052186166774710972751597518026531652e-271L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, 0x1p900L, 0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, 0x1p900L, -0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, -0x1p900L, 0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, -0x1p900L, -0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1.fp1023L, 0.0L, 5.742126086470197117652213464083623391533e-309L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, 0x1.fp1023L, -0.0L, 5.742126086470197117652213464083623391533e-309L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, -0x1.fp1023L, 0.0L, -5.742126086470197117652213464083623391533e-309L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, -0x1.fp1023L, -0.0L, -5.742126086470197117652213464083623391533e-309L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, 0.0L, 0x1.fp1023L, 0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, 0x1.fp1023L, -0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, -0x1.fp1023L, 0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, -0x1.fp1023L, -0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1.fp1023L, 0x1.fp1023L, 2.871063043235098558826106732041811695767e-309L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, 0x1.fp1023L, -0x1.fp1023L, 2.871063043235098558826106732041811695767e-309L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, -0x1.fp1023L, 0x1.fp1023L, -2.871063043235098558826106732041811695767e-309L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
TEST_c_c (catanh, -0x1.fp1023L, -0x1.fp1023L, -2.871063043235098558826106732041811695767e-309L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION_DOUBLE);
#endif
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
TEST_c_c (catanh, 0x1p10000L, 0.0L, 5.012372749206452009297555933742977749322e-3011L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1p10000L, -0.0L, 5.012372749206452009297555933742977749322e-3011L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p10000L, 0.0L, -5.012372749206452009297555933742977749322e-3011L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0x1p10000L, -0.0L, -5.012372749206452009297555933742977749322e-3011L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, 0x1p10000L, 0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, 0x1p10000L, -0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, -0x1p10000L, 0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, -0x1p10000L, -0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0x1.fp16383L, 0.0L, 8.676395208031209048419813722120651877672e-4933L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
TEST_c_c (catanh, 0x1.fp16383L, -0.0L, 8.676395208031209048419813722120651877672e-4933L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
TEST_c_c (catanh, -0x1.fp16383L, 0.0L, -8.676395208031209048419813722120651877672e-4933L, 1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
TEST_c_c (catanh, -0x1.fp16383L, -0.0L, -8.676395208031209048419813722120651877672e-4933L, -1.570796326794896619231321691639751442099L, UNDERFLOW_EXCEPTION);
TEST_c_c (catanh, 0.0L, 0x1.fp16383L, 0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, 0x1.fp16383L, -0.0L, 1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, 0.0L, -0x1.fp16383L, 0.0L, -1.570796326794896619231321691639751442099L);
TEST_c_c (catanh, -0.0L, -0x1.fp16383L, -0.0L, -1.570796326794896619231321691639751442099L);
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);
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, 0.75L, 1.25L, 0.261492138795671927078652057366532140L, 0.996825126463918666098902241310446708L);
TEST_c_c (catanh, -2, -3, -0.14694666622552975204743278515471595L, -1.3389725222944935611241935759091443L);

55
math/s_catan.c
View File

@ -61,27 +61,44 @@ __catan (__complex__ double x)
}
else
{
double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
num = __imag__ x + 1.0;
num = r2 + num * num;
den = __imag__ x - 1.0;
den = r2 + den * den;
f = num / den;
if (f < 0.5)
__imag__ res = 0.25 * __ieee754_log (f);
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__real__ res = __copysign (M_PI_2, __real__ x);
if (fabs (__real__ x) <= 1.0)
__imag__ res = 1.0 / __imag__ x;
else if (fabs (__imag__ x) <= 1.0)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__imag__ res = __imag__ x / h / h / 4.0;
}
}
else
{
num = 4.0 * __imag__ x;
__imag__ res = 0.25 * __log1p (num / den);
double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
num = __imag__ x + 1.0;
num = r2 + num * num;
den = __imag__ x - 1.0;
den = r2 + den * den;
f = num / den;
if (f < 0.5)
__imag__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __imag__ x;
__imag__ res = 0.25 * __log1p (num / den);
}
}
if (fabs (__real__ res) < DBL_MIN)

56
math/s_catanf.c
View File

@ -61,27 +61,45 @@ __catanf (__complex__ float x)
}
else
{
float r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
num = __imag__ x + 1.0f;
num = r2 + num * num;
den = __imag__ x - 1.0f;
den = r2 + den * den;
f = num / den;
if (f < 0.5f)
__imag__ res = 0.25f * __ieee754_logf (f);
if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON
|| fabsf (__imag__ x) >= 16.0f / FLT_EPSILON)
{
__real__ res = __copysignf ((float) M_PI_2, __real__ x);
if (fabsf (__real__ x) <= 1.0f)
__imag__ res = 1.0f / __imag__ x;
else if (fabsf (__imag__ x) <= 1.0f)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
float h = __ieee754_hypotf (__real__ x / 2.0f,
__imag__ x / 2.0f);
__imag__ res = __imag__ x / h / h / 4.0f;
}
}
else
{
num = 4.0f * __imag__ x;
__imag__ res = 0.25f * __log1pf (num / den);
float r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
num = __imag__ x + 1.0f;
num = r2 + num * num;
den = __imag__ x - 1.0f;
den = r2 + den * den;
f = num / den;
if (f < 0.5f)
__imag__ res = 0.25f * __ieee754_logf (f);
else
{
num = 4.0f * __imag__ x;
__imag__ res = 0.25f * __log1pf (num / den);
}
}
if (fabsf (__real__ res) < FLT_MIN)

51
math/s_catanh.c
View File

@ -56,27 +56,44 @@ __catanh (__complex__ double x)
}
else
{
double i2 = __imag__ x * __imag__ x;
double num = 1.0 + __real__ x;
num = i2 + num * num;
double den = 1.0 - __real__ x;
den = i2 + den * den;
double f = num / den;
if (f < 0.5)
__real__ res = 0.25 * __ieee754_log (f);
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__imag__ res = __copysign (M_PI_2, __imag__ x);
if (fabs (__imag__ x) <= 1.0)
__real__ res = 1.0 / __real__ x;
else if (fabs (__real__ x) <= 1.0)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__real__ res = __real__ x / h / h / 4.0;
}
}
else
{
num = 4.0 * __real__ x;
__real__ res = 0.25 * __log1p (num / den);
double i2 = __imag__ x * __imag__ x;
double num = 1.0 + __real__ x;
num = i2 + num * num;
double den = 1.0 - __real__ x;
den = i2 + den * den;
double f = num / den;
if (f < 0.5)
__real__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __real__ x;
__real__ res = 0.25 * __log1p (num / den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
if (fabs (__real__ res) < DBL_MIN)
{
volatile double force_underflow = __real__ res * __real__ res;

52
math/s_catanhf.c
View File

@ -56,27 +56,45 @@ __catanhf (__complex__ float x)
}
else
{
float i2 = __imag__ x * __imag__ x;
float num = 1.0f + __real__ x;
num = i2 + num * num;
float den = 1.0f - __real__ x;
den = i2 + den * den;
float f = num / den;
if (f < 0.5f)
__real__ res = 0.25f * __ieee754_logf (f);
if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON
|| fabsf (__imag__ x) >= 16.0f / FLT_EPSILON)
{
__imag__ res = __copysignf ((float) M_PI_2, __imag__ x);
if (fabsf (__imag__ x) <= 1.0f)
__real__ res = 1.0f / __real__ x;
else if (fabsf (__real__ x) <= 1.0f)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
float h = __ieee754_hypotf (__real__ x / 2.0f,
__imag__ x / 2.0f);
__real__ res = __real__ x / h / h / 4.0f;
}
}
else
{
num = 4.0f * __real__ x;
__real__ res = 0.25f * __log1pf (num / den);
float i2 = __imag__ x * __imag__ x;
float num = 1.0f + __real__ x;
num = i2 + num * num;
float den = 1.0f - __real__ x;
den = i2 + den * den;
float f = num / den;
if (f < 0.5f)
__real__ res = 0.25f * __ieee754_logf (f);
else
{
num = 4.0f * __real__ x;
__real__ res = 0.25f * __log1pf (num / den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
if (fabsf (__real__ res) < FLT_MIN)
{
volatile float force_underflow = __real__ res * __real__ res;

59
math/s_catanhl.c
View File

@ -22,6 +22,13 @@
#include <math_private.h>
#include <float.h>
/* To avoid spurious overflows, use this definition to treat IBM long
double as approximating an IEEE-style format. */
#if LDBL_MANT_DIG == 106
# undef LDBL_EPSILON
# define LDBL_EPSILON 0x1p-106L
#endif
__complex__ long double
__catanhl (__complex__ long double x)
{
@ -56,27 +63,45 @@ __catanhl (__complex__ long double x)
}
else
{
long double i2 = __imag__ x * __imag__ x;
long double num = 1.0L + __real__ x;
num = i2 + num * num;
long double den = 1.0L - __real__ x;
den = i2 + den * den;
long double f = num / den;
if (f < 0.5L)
__real__ res = 0.25L * __ieee754_logl (f);
if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
{
__imag__ res = __copysignl (M_PI_2l, __imag__ x);
if (fabsl (__imag__ x) <= 1.0L)
__real__ res = 1.0L / __real__ x;
else if (fabsl (__real__ x) <= 1.0L)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
long double h = __ieee754_hypotl (__real__ x / 2.0L,
__imag__ x / 2.0L);
__real__ res = __real__ x / h / h / 4.0L;
}
}
else
{
num = 4.0L * __real__ x;
__real__ res = 0.25L * __log1pl (num / den);
long double i2 = __imag__ x * __imag__ x;
long double num = 1.0L + __real__ x;
num = i2 + num * num;
long double den = 1.0L - __real__ x;
den = i2 + den * den;
long double f = num / den;
if (f < 0.5L)
__real__ res = 0.25L * __ieee754_logl (f);
else
{
num = 4.0L * __real__ x;
__real__ res = 0.25L * __log1pl (num / den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
}
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
if (fabsl (__real__ res) < LDBL_MIN)
{
volatile long double force_underflow = __real__ res * __real__ res;

63
math/s_catanl.c
View File

@ -22,6 +22,13 @@
#include <math_private.h>
#include <float.h>
/* To avoid spurious overflows, use this definition to treat IBM long
double as approximating an IEEE-style format. */
#if LDBL_MANT_DIG == 106
# undef LDBL_EPSILON
# define LDBL_EPSILON 0x1p-106L
#endif
__complex__ long double
__catanl (__complex__ long double x)
{
@ -61,27 +68,45 @@ __catanl (__complex__ long double x)
}
else
{
long double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
num = __imag__ x + 1.0L;
num = r2 + num * num;
den = __imag__ x - 1.0L;
den = r2 + den * den;
f = num / den;
if (f < 0.5L)
__imag__ res = 0.25L * __ieee754_logl (f);
if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
{
__real__ res = __copysignl (M_PI_2l, __real__ x);
if (fabsl (__real__ x) <= 1.0L)
__imag__ res = 1.0L / __imag__ x;
else if (fabsl (__imag__ x) <= 1.0L)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
long double h = __ieee754_hypotl (__real__ x / 2.0L,
__imag__ x / 2.0L);
__imag__ res = __imag__ x / h / h / 4.0L;
}
}
else
{
num = 4.0L * __imag__ x;
__imag__ res = 0.25L * __log1pl (num / den);
long double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
num = __imag__ x + 1.0L;
num = r2 + num * num;
den = __imag__ x - 1.0L;
den = r2 + den * den;
f = num / den;
if (f < 0.5L)
__imag__ res = 0.25L * __ieee754_logl (f);
else
{
num = 4.0L * __imag__ x;
__imag__ res = 0.25L * __log1pl (num / den);
}
}
if (fabsl (__real__ res) < LDBL_MIN)

50
sysdeps/i386/fpu/libm-test-ulps
View File

@ -3480,13 +3480,49 @@ double: 1
idouble: 1
# catan
Test "Imaginary part of: catan (-0x1.fp1023 + 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i":
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (-0x1.fp1023 - 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 - 2.871063043235098558826106732041811695767e-309 i":
ildouble: 1
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 (-0x1.fp127 - 0x1.fp127 i) == -1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 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 (0x1.fp1023 + 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i":
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (0x1.fp1023 - 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 - 2.871063043235098558826106732041811695767e-309 i":
ildouble: 1
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 (0x1.fp127 - 0x1.fp127 i) == 1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 i":
ildouble: 1
ldouble: 1
# catanh
Test "Real part of: catanh (-0x1.fp1023 + 0x1.fp1023 i) == -2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 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
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 (-0x1.fp127 - 0x1.fp127 i) == -1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i":
ildouble: 1
ldouble: 1
Test "Real part of: catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i":
double: 2
float: 1
@ -3499,6 +3535,18 @@ double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (0x1.fp1023 + 0x1.fp1023 i) == 2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 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
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 (0x1.fp127 - 0x1.fp127 i) == 1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i":
ildouble: 1
ldouble: 1
# cbrt
Test "cbrt (-27.0) == -3.0":
@ -6236,6 +6284,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catanh":
double: 2

82
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -4205,6 +4205,26 @@ double: 1
idouble: 1
# catan
Test "Imaginary part of: catan (-0x1.fp1023 + 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (-0x1.fp1023 - 0x1.fp1023 i) == -1.570796326794896619231321691639751442099 - 2.871063043235098558826106732041811695767e-309 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (-0x1.fp127 + 0x1.fp127 i) == -1.570796326794896619231321691639751442097 + 1.516766904286822590927401983512575068153e-39 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (-0x1.fp127 - 0x1.fp127 i) == -1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":
float: 3
ifloat: 3
@ -4216,8 +4236,48 @@ 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 (0x1.fp1023 + 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 + 2.871063043235098558826106732041811695767e-309 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (0x1.fp1023 - 0x1.fp1023 i) == 1.570796326794896619231321691639751442099 - 2.871063043235098558826106732041811695767e-309 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (0x1.fp127 + 0x1.fp127 i) == 1.570796326794896619231321691639751442097 + 1.516766904286822590927401983512575068153e-39 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: catan (0x1.fp127 - 0x1.fp127 i) == 1.570796326794896619231321691639751442097 - 1.516766904286822590927401983512575068153e-39 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
# catanh
Test "Real part of: catanh (-0x1.fp1023 + 0x1.fp1023 i) == -2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (-0x1.fp1023 - 0x1.fp1023 i) == -2.871063043235098558826106732041811695767e-309 - 1.570796326794896619231321691639751442099 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (-0x1.fp127 + 0x1.fp127 i) == -1.516766904286822590927401983512575068153e-39 + 1.570796326794896619231321691639751442097 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (-0x1.fp127 - 0x1.fp127 i) == -1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i":
double: 4
idouble: 4
@ -4234,6 +4294,26 @@ 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 (0x1.fp1023 + 0x1.fp1023 i) == 2.871063043235098558826106732041811695767e-309 + 1.570796326794896619231321691639751442099 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (0x1.fp1023 - 0x1.fp1023 i) == 2.871063043235098558826106732041811695767e-309 - 1.570796326794896619231321691639751442099 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (0x1.fp127 + 0x1.fp127 i) == 1.516766904286822590927401983512575068153e-39 + 1.570796326794896619231321691639751442097 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: catanh (0x1.fp127 - 0x1.fp127 i) == 1.516766904286822590927401983512575068153e-39 - 1.570796326794896619231321691639751442097 i":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
# cbrt
Test "cbrt (-0.001) == -0.1":
@ -6780,6 +6860,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catanh":
double: 4