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Fix catan, catanh spurious overflows (bug 15409)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Fri, 26 Apr 2013 20:47:23 +0000
- Subject: Fix catan, catanh spurious overflows (bug 15409)
Bug 15409 is spurious overflows from catan and catanh, arising from
squaring a large real or imaginary part of the argument. This patch
fixes these overflows by using different expressions in those cases
that are sufficiently accurate there and avoid the problematic
squaring.
(There's another spurious overflow possibility, when r2 in catan is
subnormal and __imag__ x is exactly 1, resulting in overflow from
division when calculating the argument to log. That will need
addressing separately along with various spurious underflow
possibilities.)
Tested x86_64 and x86 and ulps updated accordingly.
2013-04-26 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.
diff --git a/math/libm-test.inc b/math/libm-test.inc
index a62ae9a..b91035b 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -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);
diff --git a/math/s_catan.c b/math/s_catan.c
index 6a1016e..4b7fbad 100644
--- a/math/s_catan.c
+++ b/math/s_catan.c
@@ -61,27 +61,44 @@ __catan (__complex__ double x)
}
else
{
- double r2, num, den, 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
+ {
+ double r2, num, den, f;
- r2 = __real__ x * __real__ x;
+ r2 = __real__ x * __real__ x;
- den = 1 - r2 - __imag__ x * __imag__ x;
+ den = 1 - r2 - __imag__ x * __imag__ x;
- __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
+ __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
- num = __imag__ x + 1.0;
- num = r2 + num * num;
+ num = __imag__ x + 1.0;
+ num = r2 + num * num;
- den = __imag__ x - 1.0;
- den = r2 + den * den;
+ 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);
+ 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)
diff --git a/math/s_catanf.c b/math/s_catanf.c
index d0d188c..aa71e5e 100644
--- a/math/s_catanf.c
+++ b/math/s_catanf.c
@@ -61,27 +61,45 @@ __catanf (__complex__ float x)
}
else
{
- float r2, num, den, 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
+ {
+ float r2, num, den, f;
- r2 = __real__ x * __real__ x;
+ r2 = __real__ x * __real__ x;
- den = 1 - r2 - __imag__ x * __imag__ x;
+ den = 1 - r2 - __imag__ x * __imag__ x;
- __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
+ __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
- num = __imag__ x + 1.0f;
- num = r2 + num * num;
+ num = __imag__ x + 1.0f;
+ num = r2 + num * num;
- den = __imag__ x - 1.0f;
- den = r2 + den * den;
+ 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);
+ 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)
diff --git a/math/s_catanh.c b/math/s_catanh.c
index 5d18cd6..55c5628 100644
--- a/math/s_catanh.c
+++ b/math/s_catanh.c
@@ -56,26 +56,43 @@ __catanh (__complex__ double x)
}
else
{
- double i2 = __imag__ x * __imag__ x;
+ 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
+ {
+ double i2 = __imag__ x * __imag__ x;
- double num = 1.0 + __real__ x;
- num = i2 + num * num;
+ double num = 1.0 + __real__ x;
+ num = i2 + num * num;
- double den = 1.0 - __real__ x;
- den = i2 + den * den;
+ 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);
- }
+ 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;
+ den = 1 - __real__ x * __real__ x - i2;
- __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
+ __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
+ }
if (fabs (__real__ res) < DBL_MIN)
{
diff --git a/math/s_catanhf.c b/math/s_catanhf.c
index 6376a2c..3e87942 100644
--- a/math/s_catanhf.c
+++ b/math/s_catanhf.c
@@ -56,26 +56,44 @@ __catanhf (__complex__ float x)
}
else
{
- float i2 = __imag__ x * __imag__ x;
+ 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
+ {
+ float i2 = __imag__ x * __imag__ x;
- float num = 1.0f + __real__ x;
- num = i2 + num * num;
+ float num = 1.0f + __real__ x;
+ num = i2 + num * num;
- float den = 1.0f - __real__ x;
- den = i2 + den * den;
+ 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);
- }
+ 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;
+ den = 1 - __real__ x * __real__ x - i2;
- __imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
+ __imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
+ }
if (fabsf (__real__ res) < FLT_MIN)
{
diff --git a/math/s_catanhl.c b/math/s_catanhl.c
index 30fd277..64c30b5 100644
--- a/math/s_catanhl.c
+++ b/math/s_catanhl.c
@@ -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)
{
@@ -56,26 +63,44 @@ __catanhl (__complex__ long double x)
}
else
{
- long double i2 = __imag__ x * __imag__ x;
+ 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
+ {
+ long double i2 = __imag__ x * __imag__ x;
- long double num = 1.0L + __real__ x;
- num = i2 + num * num;
+ long double num = 1.0L + __real__ x;
+ num = i2 + num * num;
- long double den = 1.0L - __real__ x;
- den = i2 + den * den;
+ 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);
- }
+ 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;
+ den = 1 - __real__ x * __real__ x - i2;
- __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
+ __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
+ }
if (fabsl (__real__ res) < LDBL_MIN)
{
diff --git a/math/s_catanl.c b/math/s_catanl.c
index 2440e6d..17ab62d 100644
--- a/math/s_catanl.c
+++ b/math/s_catanl.c
@@ -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;
+ 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
+ {
+ long double r2, num, den, f;
- r2 = __real__ x * __real__ x;
+ r2 = __real__ x * __real__ x;
- den = 1 - r2 - __imag__ x * __imag__ x;
+ den = 1 - r2 - __imag__ x * __imag__ x;
- __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
+ __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
- num = __imag__ x + 1.0L;
- num = r2 + num * num;
+ num = __imag__ x + 1.0L;
+ num = r2 + num * num;
- den = __imag__ x - 1.0L;
- den = r2 + den * den;
+ 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);
+ 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)
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index a6d9b0f..b6fe897 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -3400,13 +3400,49 @@ 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
@@ -3419,6 +3455,18 @@ 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":
@@ -6156,6 +6204,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
+ildouble: 1
+ldouble: 1
Function: Real part of "catanh":
double: 2
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 9588481..43b5595 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -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
--
Joseph S. Myers
joseph@codesourcery.com