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Improve tgamma accuracy (bugs 2546, 2560, 5159, 15426)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Thu, 2 May 2013 22:35:05 +0000
- Subject: Improve tgamma accuracy (bugs 2546, 2560, 5159, 15426)
This patch fixes various bugs relating to inaccuracy of results from
tgamma. Bugs 2546, 2560 and 5159 are different cases of inaccurate
finite results, arising from the use of exp (lgamma) which inevitably
results in large errors for results with large (positive or negative)
exponent. Bug 15426, found by the new testcases prepared for this
patch, is wrong sign of infinity on overflow for negative arguments
close to 0. (Bugs 15425 and 15427 were also found by testing unfixed
glibc with the testcases included in this patch; this patch does
nothing about those bugs in lgammaf and exp, although they no longer
affect the results of tgamma after the tgamma implementation changes
in this patch.)
Because of the inaccuracy resulting from exp (lgamma) when the result
of lgamma is large, after this patch lgamma is only called by tgamma
on arguments in the range 0.5 to 1.5. For larger positive arguments,
the recurrence gamma(z+1) = z * gamma(z) is used to reduce either to a
value in that range where exp (lgamma) does not introduce large
errors, or to a value large enough to apply Stirling's approximation.
When using Stirling's approximation, pow is then used to avoid large
errors from the use of exp on large values, and care is taken that
errors in arguments of exp and exp2 are small (measured in ulps of 1,
not ulps of the argument of exp, since ulps of 1 are what's relevant
to avoid large errors in the final result); a power of 2 is split out
in the calculation to avoid internal overflows when the final result
is finite. Negative arguments (other than those very close to 0) are
handled through gamma(z) = pi/(-z)sin(pi*z)gamma(-z).
To reduce accumulation of errors in the reduction, __gamma_product
keeps an estimate of how much the exact product differs from the
computed value. (The estimation in the ldbl-128ibm version is less
thorough; it deals with errors arising from an adjusted version of the
argument being used in the product because the result of adding a
small integer to the unadjusted argument may not be exactly
representable, but not with errors from each successive multiplication
step. The former kind of errors would all be in the same direction,
whereas the latter would generally be in random directions, but this
is still expected to make the ldbl-128ibm version slightly less
accurate - although such reduced accuracy doesn't show in the
testsuite.)
Before this patch, on x86_64, the testcases added by this patch showed
errors of up to 203 ulp for float, 1713 ulp for double and 12714 ulp
for long double; the patch reduces the maximum errors for its
testcases to 3 ulp, 4 ulp and 4 ulp respectively.
Tested x86_64 and x86 and ulps updated accordingly. Also did spot
tests on mips64 to sanity test the ldbl-128 version, and powerpc32 to
sanity test the ldbl-128ibm version. The former showed errors of at
most 4 ulp and the latter errors of at most 3 ulp. There are spurious
underflows for ldbl-128ibm testing inputs 0x1p-1023, 0x1p-1024,
0x1p-1074, which I think (like some other underflows seen on tests of
other functions) just reflect problems with the underlying long double
arithmetic giving spurious underflow exceptions when dealing with
norma long doubles whose lower part is a subnormal double (because of
the discontiguous mantissa bits), not actual problems with libm itself
(such issues would need fixing in libgcc's multiplication / division
code).
(There are other open bugs about inaccuracy of lgamma. Those have an
independent cause - large cancellation when the gamma function has
value close to +/- 1 - and will need their own fix. The IA64 version
of lgammal addresses those by using 35 different degree-19 polynomials
for values near roots of lgamma (less needed for float and double
versions, of course); I haven't looked in detail at how feasible it is
to be accurate near roots of lgamma without so much precomputed data.)
2013-05-02 Joseph Myers <joseph@codesourcery.com>
[BZ #2546]
[BZ #2560]
[BZ #5159]
[BZ #15426]
* sysdeps/ieee754/k_standard.c (__kernel_standard): Copy sign of
input to result for tgamma overflow.
* sysdeps/ieee754/dbl-64/e_gamma_r.c: Include <float.h>.
(gamma_coeff): New variable.
(NCOEFF): New macro.
(gamma_positive): New function.
(__ieee754_gamma_r): Handle positive infinity, NaN, overflow and
underflow here. Use gamma_positive instead of exp (lgamma) for
other arguments.
* sysdeps/ieee754/flt-32/e_gammaf_r.c: Include <float.h>.
(gamma_coeff): New variable.
(NCOEFF): New macro.
(gammaf_positive): New function.
(__ieee754_gammaf_r): Handle positive infinity, NaN, overflow and
underflow here. Use gamma_positive instead of exp (lgamma) for
other arguments.
* sysdeps/ieee754/ldbl-128/e_gammal_r.c: Include <float.h>.
(gamma_coeff): New variable.
(NCOEFF): New macro.
(gammal_positive): New function.
(__ieee754_gammal_r): Handle positive infinity, NaN, overflow and
underflow here. Use gamma_positive instead of exp (lgamma) for
other arguments.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: Include <float.h>.
(gamma_coeff): New variable.
(NCOEFF): New macro.
(gammal_positive): New function.
(__ieee754_gammal_r): Handle positive infinity, overflow and
underflow here. Handle NaN the same as positive infinity. Remove
check x < 0xffffffff for negative integers. Use gamma_positive
instead of exp (lgamma) for other arguments.
* sysdeps/ieee754/ldbl-96/e_gammal_r.c: Include <float.h>.
(gamma_coeff): New variable.
(NCOEFF): New macro.
(gammal_positive): New function.
* sysdeps/ieee754/dbl-64/gamma_product.c: New file.
* sysdeps/ieee754/dbl-64/gamma_productf.c: Likewise.
* sysdeps/ieee754/ldbl-128/gamma_productl.c: Likewise.
* sysdeps/ieee754/ldbl-128ibm/gamma_productl.c: Likewise.
* sysdeps/ieee754/ldbl-96/gamma_product.c: Likewise.
* sysdeps/ieee754/ldbl-96/gamma_productl.c: Likewise.
* sysdeps/generic/math_private.h (__gamma_productf): New
prototype.
(__gamma_product): Likewise.
(__gamma_productl): Likewise.
* math/Makefile (libm-calls): Add gamma_product.
* math/libm-test.inc (tgamma_test): Add more tests.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
diff --git a/math/Makefile b/math/Makefile
index 9f0bf72..5bbf9d3 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -58,7 +58,8 @@ libm-calls = e_acos e_acosh e_asin e_atan2 e_atanh e_cosh e_exp e_fmod \
s_catan s_casin s_ccos s_csin s_ctan s_ctanh s_cacos \
s_casinh s_cacosh s_catanh s_csqrt s_cpow s_cproj s_clog10 \
s_fma s_lrint s_llrint s_lround s_llround e_exp10 w_log2 \
- s_isinf_ns s_issignaling $(calls:s_%=m_%) x2y2m1 k_casinh
+ s_isinf_ns s_issignaling $(calls:s_%=m_%) x2y2m1 k_casinh \
+ gamma_product
include ../Makeconfig
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 8feb0a6..46f42b6 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -13482,11 +13482,511 @@ tgamma_test (void)
TEST_f_f (tgamma, -0.5, -M_2_SQRT_PIl);
TEST_f_f (tgamma, 1, 1);
+ TEST_f_f (tgamma, 2, 1);
+ TEST_f_f (tgamma, 3, 2);
TEST_f_f (tgamma, 4, 6);
+ TEST_f_f (tgamma, 5, 24);
+ TEST_f_f (tgamma, 6, 120);
+ TEST_f_f (tgamma, 7, 720);
+ TEST_f_f (tgamma, 8, 5040);
+ TEST_f_f (tgamma, 9, 40320);
+ TEST_f_f (tgamma, 10, 362880);
TEST_f_f (tgamma, 0.7L, 1.29805533264755778568117117915281162L);
TEST_f_f (tgamma, 1.2L, 0.918168742399760610640951655185830401L);
+ TEST_f_f (tgamma, 1.5L, 8.8622692545275801364908374167057259139877e-01L);
+ TEST_f_f (tgamma, 2.5L, 1.3293403881791370204736256125058588870982e+00L);
+ TEST_f_f (tgamma, 3.5L, 3.3233509704478425511840640312646472177454e+00L);
+ TEST_f_f (tgamma, 4.5L, 1.1631728396567448929144224109426265262109e+01L);
+ TEST_f_f (tgamma, 5.5L, 5.2342777784553520181149008492418193679490e+01L);
+ TEST_f_f (tgamma, 6.5L, 2.8788527781504436099631954670830006523720e+02L);
+ TEST_f_f (tgamma, 7.5L, 1.8712543057977883464760770536039504240418e+03L);
+ TEST_f_f (tgamma, 8.5L, 1.4034407293483412598570577902029628180313e+04L);
+ TEST_f_f (tgamma, 9.5L, 1.1929246199460900708784991216725183953266e+05L);
+ TEST_f_f (tgamma, -1.5L, 2.3632718012073547030642233111215269103967e+00L);
+ TEST_f_f (tgamma, -2.5L, -9.4530872048294188122568932444861076415869e-01L);
+ TEST_f_f (tgamma, -3.5L, 2.7008820585226910892162552127103164690248e-01L);
+ TEST_f_f (tgamma, -4.5L, -6.0019601300504246427027893615784810422774e-02L);
+ TEST_f_f (tgamma, -5.5L, 1.0912654781909862986732344293779056440504e-02L);
+ TEST_f_f (tgamma, -6.5L, -1.6788699664476712287280529682737009908468e-03L);
+ TEST_f_f (tgamma, -7.5L, 2.2384932885968949716374039576982679877958e-04L);
+ TEST_f_f (tgamma, -8.5L, -2.6335215159963470254557693619979623385833e-05L);
+ TEST_f_f (tgamma, -9.5L, 2.7721279115751021320587045915768024616666e-06L);
+ TEST_f_f (tgamma, 0x1p-24L, 1.6777215422784394050795179874582764575261e+07L);
+ TEST_f_f (tgamma, -0x1p-24L, -1.6777216577215723853867349114260580375249e+07L);
+ TEST_f_f (tgamma, 0x1p-53L, 9.0071992547409914227843350984672492007618e+15L);
+ TEST_f_f (tgamma, -0x1p-53L, -9.0071992547409925772156649015329704137860e+15L);
+ TEST_f_f (tgamma, 0x1p-64L, 1.8446744073709551615422784335098467139447e+19L);
+ TEST_f_f (tgamma, -0x1p-64L, -1.8446744073709551616577215664901532860660e+19L);
+ TEST_f_f (tgamma, 0x1p-106L, 8.1129638414606681695789005144063422784335e+31L);
+ TEST_f_f (tgamma, -0x1p-106L, -8.1129638414606681695789005144064577215665e+31L);
+ TEST_f_f (tgamma, 0x1p-113L, 1.0384593717069655257060992658440191422784e+34L);
+ TEST_f_f (tgamma, -0x1p-113L, -1.0384593717069655257060992658440192577216e+34L);
+ TEST_f_f (tgamma, 0x1p-127L, 1.7014118346046923173168730371588410572742e+38L);
+ TEST_f_f (tgamma, -0x1p-127L, -1.7014118346046923173168730371588410572858e+38L);
+#ifdef TEST_FLOAT
+ TEST_f_f (tgamma, 0x1p-128L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-128L, minus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, 0x1p-149L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-149L, minus_infty, OVERFLOW_EXCEPTION);
+#else
+ TEST_f_f (tgamma, 0x1p-128L, 3.4028236692093846346337460743176821145542e+38L);
+ TEST_f_f (tgamma, -0x1p-128L, -3.4028236692093846346337460743176821145658e+38L);
+ TEST_f_f (tgamma, 0x1p-149L, 7.1362384635297994052914298472474756819137e+44L);
+ TEST_f_f (tgamma, -0x1p-149L, -7.1362384635297994052914298472474756819137e+44L);
+#endif
+#ifndef TEST_FLOAT
+ TEST_f_f (tgamma, 0x1p-1023L, 8.9884656743115795386465259539451236680899e+307L);
+ TEST_f_f (tgamma, -0x1p-1023L, -8.9884656743115795386465259539451236680899e+307L);
+# if !defined TEST_LDOUBLE || LDBL_MAX_EXP <= 1024
+ TEST_f_f (tgamma, 0x1p-1024L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-1024L, minus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, 0x1p-1074L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-1074L, minus_infty, OVERFLOW_EXCEPTION);
+# else
+ TEST_f_f (tgamma, 0x1p-1024L, 1.7976931348623159077293051907890247336180e+308L);
+ TEST_f_f (tgamma, -0x1p-1024L, -1.7976931348623159077293051907890247336180e+308L);
+ TEST_f_f (tgamma, 0x1p-1074L, 2.0240225330731061835249534671891730704956e+323L);
+ TEST_f_f (tgamma, -0x1p-1074L, -2.0240225330731061835249534671891730704956e+323L);
+# endif
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+ TEST_f_f (tgamma, 0x1p-16383L, 5.9486574767861588254287966331400356538172e+4931L);
+ TEST_f_f (tgamma, -0x1p-16383L, -5.9486574767861588254287966331400356538172e+4931L);
+ TEST_f_f (tgamma, 0x1p-16384L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-16384L, minus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, 0x1p-16445L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-16445L, minus_infty, OVERFLOW_EXCEPTION);
+# if LDBL_MANT_DIG >= 113
+ TEST_f_f (tgamma, 0x1p-16494L, plus_infty, OVERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x1p-16494L, minus_infty, OVERFLOW_EXCEPTION);
+# endif
+#endif
+ TEST_f_f (tgamma, 0x8.00001p0L, 5.0400096882277802019946778420223050233915e+03L);
+ TEST_f_f (tgamma, 0x7.fffff8p0L, 5.0399951558933225045148935487583089307135e+03L);
+ TEST_f_f (tgamma, 0x7.000008p0L, 7.2000064296977505705636258629805621178587e+02L);
+ TEST_f_f (tgamma, 0x6.fffff8p0L, 7.1999935703082425988147448928288557689866e+02L);
+ TEST_f_f (tgamma, 0x6.000008p0L, 1.2000009762487825358530770343720418162783e+02L);
+ TEST_f_f (tgamma, 0x5.fffff8p0L, 1.1999990237520611552119807476573441975106e+02L);
+ TEST_f_f (tgamma, 0x5.000008p0L, 2.4000017236155647574166073485628713443799e+01L);
+ TEST_f_f (tgamma, 0x4.fffff8p0L, 2.3999982763857938712639837029547357501709e+01L);
+ TEST_f_f (tgamma, 0x4.000008p0L, 6.0000035937827461765660468073471093546129e+00L);
+ TEST_f_f (tgamma, 0x3.fffffcp0L, 5.9999982031095793171233994481968816873643e+00L);
+ TEST_f_f (tgamma, 0x3.000004p0L, 2.0000004400179308360529417942462250547999e+00L);
+ TEST_f_f (tgamma, 0x2.fffffcp0L, 1.9999995599822108706107786027549565954046e+00L);
+ TEST_f_f (tgamma, 0x2.000004p0L, 1.0000001007996638509889062631687945799175e+00L);
+ TEST_f_f (tgamma, 0x1.fffffep0L, 9.9999994960018563231526611134590489120697e-01L);
+ TEST_f_f (tgamma, 0x1.000002p0L, 9.9999993119054472483596471908942669644327e-01L);
+ TEST_f_f (tgamma, 0x0.ffffffp0L, 1.0000000344047381790797322460568297132998e+00L);
+ TEST_f_f (tgamma, -0x0.ffffffp0L, -1.6777216422784419250710305882992376932423e+07L);
+ TEST_f_f (tgamma, -0x1.000002p0L, 8.3886075772158332060084424806449513922858e+06L);
+ TEST_f_f (tgamma, -0x1.fffffep0L, 4.1943044613922792026014320172298377770578e+06L);
+ TEST_f_f (tgamma, -0x2.000004p0L, -2.0971515386080557574407223895988378776747e+06L);
+ TEST_f_f (tgamma, -0x2.fffffcp0L, -6.9905087601970247876992248591045142913324e+05L);
+ TEST_f_f (tgamma, -0x3.000004p0L, 6.9905045731381300146131914617735687322025e+05L);
+ TEST_f_f (tgamma, -0x3.fffffcp0L, 1.7476272942159602684441970627092458855771e+05L);
+ TEST_f_f (tgamma, -0x4.000008p0L, -8.7381270578483499672965708923121931082305e+04L);
+ TEST_f_f (tgamma, -0x4.fffff8p0L, -1.7476280884325863043793087474680780379554e+04L);
+ TEST_f_f (tgamma, -0x5.000008p0L, 1.7476252449031389167286893378510439443844e+04L);
+ TEST_f_f (tgamma, -0x5.fffff8p0L, 2.9127137122026653716311560165769071985443e+03L);
+ TEST_f_f (tgamma, -0x6.000008p0L, -2.9127085100239567622341538102130981196910e+03L);
+ TEST_f_f (tgamma, -0x6.fffff8p0L, -4.1610198723079349791939054365613377035519e+02L);
+ TEST_f_f (tgamma, -0x7.000008p0L, 4.1610118737306415004517215226199741948733e+02L);
+ TEST_f_f (tgamma, -0x7.fffff8p0L, 5.2012751504050764429534086402871289946986e+01L);
+ TEST_f_f (tgamma, -0x8.00001p0L, -2.6006296115134418896533598545925084576702e+01L);
+ TEST_f_f (tgamma, -0x9.fffffp0L, 2.8896008370721717567612135720915723136310e-01L);
+ TEST_f_f (tgamma, -0xa.00001p0L, -2.8895878754728051776830454190076999107021e-01L);
+ TEST_f_f (tgamma, -0x13.ffffep0L, 2.1550026214525536756224040483579183652119e-13L);
+ TEST_f_f (tgamma, -0x14.00002p0L, -2.1549777908265594916405421768142757507179e-13L);
+ TEST_f_f (tgamma, -0x1d.ffffep0L, 1.9765721589464867957912772592816027583176e-27L);
+ TEST_f_f (tgamma, -0x1e.00002p0L, -1.9765463890341964384070157599286498212650e-27L);
+ TEST_f_f (tgamma, -0x27.ffffcp0L, 3.2129279441390812141195076945616975790225e-43L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_f_f (tgamma, -0x28.00004p0L, -3.2128372159115252365699015758097981155793e-43L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_f_f (tgamma, -0x28.ffffcp0L, -7.8364103489619817539676737414096652170685e-45L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_f_f (tgamma, -0x29.00004p0L, 7.8361876024016854597745353972619195760515e-45L, UNDERFLOW_EXCEPTION_FLOAT);
+#ifdef TEST_FLOAT
+ TEST_f_f (tgamma, -0x29.ffffcp0L, plus_zero, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_f_f (tgamma, -0x2a.00004p0L, minus_zero, UNDERFLOW_EXCEPTION_FLOAT);
+#else
+ TEST_f_f (tgamma, -0x29.ffffcp0L, 1.8658121573125798145204120066590953505132e-46L);
+ TEST_f_f (tgamma, -0x2a.00004p0L, -1.8657587834931410688246126853566488626385e-46L);
+#endif
+#ifndef TEST_FLOAT
+ TEST_f_f (tgamma, 0x8.0000000000008p0L, 5.0400000000000180457125667322294144477136e+03L);
+ TEST_f_f (tgamma, 0x7.ffffffffffffcp0L, 5.0399999999999909771437166339103165198442e+03L);
+ TEST_f_f (tgamma, 0x7.0000000000004p0L, 7.2000000000000119762397445457359071259652e+02L);
+ TEST_f_f (tgamma, 0x6.ffffffffffffcp0L, 7.1999999999999880237602554542848858572672e+02L);
+ TEST_f_f (tgamma, 0x6.0000000000004p0L, 1.2000000000000018184042734842640022086408e+02L);
+ TEST_f_f (tgamma, 0x5.ffffffffffffcp0L, 1.1999999999999981815957265157389249327533e+02L);
+ TEST_f_f (tgamma, 0x5.0000000000004p0L, 2.4000000000000032104829055124673225982803e+01L);
+ TEST_f_f (tgamma, 0x4.ffffffffffffcp0L, 2.3999999999999967895170944875373910918544e+01L);
+ TEST_f_f (tgamma, 0x4.0000000000004p0L, 6.0000000000000066939396342309789716341613e+00L);
+ TEST_f_f (tgamma, 0x3.ffffffffffffep0L, 5.9999999999999966530301828845138185025345e+00L);
+ TEST_f_f (tgamma, 0x3.0000000000002p0L, 2.0000000000000008195971324717875960213536e+00L);
+ TEST_f_f (tgamma, 0x2.ffffffffffffep0L, 1.9999999999999991804028675282128956223990e+00L);
+ TEST_f_f (tgamma, 0x2.0000000000002p0L, 1.0000000000000001877539613108624482361963e+00L);
+ TEST_f_f (tgamma, 0x1.fffffffffffffp0L, 9.9999999999999990612301934456883679778984e-01L);
+ TEST_f_f (tgamma, 0x1.0000000000001p0L, 9.9999999999999987183237573039992418700531e-01L);
+ TEST_f_f (tgamma, 0x0.fffffffffffff8p0L, 1.0000000000000000640838121348000744796665e+00L);
+ TEST_f_f (tgamma, -0x0.fffffffffffff8p0L, -9.0071992547409924227843350984672961392521e+15L);
+ TEST_f_f (tgamma, -0x1.0000000000001p0L, 4.5035996273704955772156649015331740980405e+15L);
+ TEST_f_f (tgamma, -0x1.fffffffffffffp0L, 2.2517998136852484613921675492337776673289e+15L);
+ TEST_f_f (tgamma, -0x2.0000000000002p0L, -1.1258999068426235386078324507668462444260e+15L);
+ TEST_f_f (tgamma, -0x2.ffffffffffffep0L, -3.7529996894754154268627807196691509198813e+14L);
+ TEST_f_f (tgamma, -0x3.0000000000002p0L, 3.7529996894754112398038859470009084971438e+14L);
+ TEST_f_f (tgamma, -0x3.ffffffffffffep0L, 9.3824992236885396088236184658402406857503e+13L);
+ TEST_f_f (tgamma, -0x4.0000000000004p0L, -4.6912496118442603911763815341745722862351e+13L);
+ TEST_f_f (tgamma, -0x4.ffffffffffffcp0L, -9.3824992236885475509805702650262155809819e+12L);
+ TEST_f_f (tgamma, -0x5.0000000000004p0L, 9.3824992236885191156860964016850034672946e+12L);
+ TEST_f_f (tgamma, -0x5.ffffffffffffcp0L, 1.5637498706147581566449098589862357835505e+12L);
+ TEST_f_f (tgamma, -0x6.0000000000004p0L, -1.5637498706147529544662012521330708016396e+12L);
+ TEST_f_f (tgamma, -0x6.ffffffffffffcp0L, -2.2339283865925119357965832452642909859289e+11L);
+ TEST_f_f (tgamma, -0x7.0000000000004p0L, 2.2339283865925039372192897706214475877342e+11L);
+ TEST_f_f (tgamma, -0x7.ffffffffffffcp0L, 2.7924104832406402297655703264222230055898e+10L);
+ TEST_f_f (tgamma, -0x8.0000000000008p0L, -1.3962052416203121511868106259843527348026e+10L);
+ TEST_f_f (tgamma, -0x9.ffffffffffff8p0L, 1.5513391573559147700413058496716749249803e+08L);
+ TEST_f_f (tgamma, -0xa.0000000000008p0L, -1.5513391573559018084419393002828541166901e+08L);
+ TEST_f_f (tgamma, -0x13.ffffffffffffp0L, 1.1569515572952029402736625857313236848570e-04L);
+ TEST_f_f (tgamma, -0x14.000000000001p0L, -1.1569515572951781096476686854873801225397e-04L);
+ TEST_f_f (tgamma, -0x1d.ffffffffffffp0L, 1.0611571800204311628217068863959963842891e-18L);
+ TEST_f_f (tgamma, -0x1e.000000000001p0L, -1.0611571800204053929094168642022073530425e-18L);
+ TEST_f_f (tgamma, -0x27.fffffffffffep0L, 1.7249032006742266376460389310340465554361e-34L);
+ TEST_f_f (tgamma, -0x28.000000000002p0L, -1.7249032006741359094184881234822934593822e-34L);
+ TEST_f_f (tgamma, -0x28.fffffffffffep0L, -4.2070809772542120404320040128839297118648e-36L);
+ TEST_f_f (tgamma, -0x29.000000000002p0L, 4.2070809772539892938717205103652583609422e-36L);
+ TEST_f_f (tgamma, -0x29.fffffffffffep0L, 1.0016859469652887505173040814397197718981e-37L);
+ TEST_f_f (tgamma, -0x2a.000000000002p0L, -1.0016859469652353766978684241048308120274e-37L);
+ TEST_f_f (tgamma, -0x31.fffffffffffep0L, 4.6273774273632946947805289899230181990085e-51L);
+ TEST_f_f (tgamma, -0x32.000000000002p0L, -4.6273774273630367887073532197576655720178e-51L);
+ TEST_f_f (tgamma, -0x63.fffffffffffcp0L, 7.5400833348840965463348754984345825364294e-145L);
+ TEST_f_f (tgamma, -0x64.000000000004p0L, -7.5400833348831085791638490135462230991587e-145L);
+ TEST_f_f (tgamma, -0x95.fffffffffff8p0L, 6.1582369322723207086020016423767264008839e-250L);
+ TEST_f_f (tgamma, -0x96.000000000008p0L, -6.1582369322705655439003240743176243138734e-250L);
+ TEST_f_f (tgamma, -0xb4.fffffffffff8p0L, -9.6760879059917574597728750098636253931457e-319L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb5.000000000008p0L, 9.6760879059888966544677044221698800670218e-319L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb5.fffffffffff8p0L, 5.3165318164789884455066481673086605454904e-321L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb6.000000000008p0L, -5.3165318164774149139661976747137185876909e-321L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb6.fffffffffff8p0L, -2.9052086428846935908287469917922960610289e-323L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb7.000000000008p0L, 2.9052086428838328351126988236541632950925e-323L, UNDERFLOW_EXCEPTION_DOUBLE);
+# if !defined TEST_LDOUBLE || LDBL_MAX_EXP <= 1024
+ TEST_f_f (tgamma, -0xb7.fffffffffff8p0L, plus_zero, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb8.000000000008p0L, minus_zero, UNDERFLOW_EXCEPTION_DOUBLE);
+# else
+ TEST_f_f (tgamma, -0xb7.fffffffffff8p0L, 1.5789177406982032823826953250736039527543e-325L);
+ TEST_f_f (tgamma, -0xb8.000000000008p0L, -1.5789177406977349925854817486109369828857e-325L);
+# endif
+#endif
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106
+ TEST_f_f (tgamma, 0x8.00000000000000000000000004p0L, 5.0400000000000000000000000000020034765587e+03L);
+ TEST_f_f (tgamma, 0x7.fffffffffffffffffffffffffep0L, 5.0399999999999999999999999999989982617206e+03L);
+ TEST_f_f (tgamma, 0x7.00000000000000000000000002p0L, 7.2000000000000000000000000000013296297113e+02L);
+ TEST_f_f (tgamma, 0x6.fffffffffffffffffffffffffep0L, 7.1999999999999999999999999999986703702887e+02L);
+ TEST_f_f (tgamma, 0x6.00000000000000000000000002p0L, 1.2000000000000000000000000000002018834292e+02L);
+ TEST_f_f (tgamma, 0x5.fffffffffffffffffffffffffep0L, 1.1999999999999999999999999999997981165708e+02L);
+ TEST_f_f (tgamma, 0x5.00000000000000000000000002p0L, 2.4000000000000000000000000000003564352042e+01L);
+ TEST_f_f (tgamma, 0x4.fffffffffffffffffffffffffep0L, 2.3999999999999999999999999999996435647958e+01L);
+ TEST_f_f (tgamma, 0x4.00000000000000000000000002p0L, 6.0000000000000000000000000000007431765907e+00L);
+ TEST_f_f (tgamma, 0x3.ffffffffffffffffffffffffffp0L, 5.9999999999999999999999999999996284117046e+00L);
+ TEST_f_f (tgamma, 0x3.00000000000000000000000001p0L, 2.0000000000000000000000000000000909935607e+00L);
+ TEST_f_f (tgamma, 0x2.ffffffffffffffffffffffffffp0L, 1.9999999999999999999999999999999090064393e+00L);
+ TEST_f_f (tgamma, 0x2.00000000000000000000000001p0L, 1.0000000000000000000000000000000208448771e+00L);
+ TEST_f_f (tgamma, 0x1.ffffffffffffffffffffffffff8p0L, 9.9999999999999999999999999999998957756146e-01L);
+ TEST_f_f (tgamma, 0x1.000000000000000000000000008p0L, 9.9999999999999999999999999999998577053525e-01L);
+ TEST_f_f (tgamma, 0x0.ffffffffffffffffffffffffffcp0L, 1.0000000000000000000000000000000071147324e+00L);
+ TEST_f_f (tgamma, -0x0.ffffffffffffffffffffffffffcp0L, -8.1129638414606681695789005144064422784335e+31L);
+ TEST_f_f (tgamma, -0x1.000000000000000000000000008p0L, 4.0564819207303340847894502572031577215665e+31L);
+ TEST_f_f (tgamma, -0x1.ffffffffffffffffffffffffff8p0L, 2.0282409603651670423947251286016461392168e+31L);
+ TEST_f_f (tgamma, -0x2.00000000000000000000000001p0L, -1.0141204801825835211973625643007538607832e+31L);
+ TEST_f_f (tgamma, -0x2.ffffffffffffffffffffffffffp0L, -3.3804016006086117373245418810028760196114e+30L);
+ TEST_f_f (tgamma, -0x3.00000000000000000000000001p0L, 3.3804016006086117373245418810024573137219e+30L);
+ TEST_f_f (tgamma, -0x3.ffffffffffffffffffffffffffp0L, 8.4510040015215293433113547025072942156952e+29L);
+ TEST_f_f (tgamma, -0x4.00000000000000000000000002p0L, -4.2255020007607646716556773512527057843048e+29L);
+ TEST_f_f (tgamma, -0x4.fffffffffffffffffffffffffep0L, -8.4510040015215293433113547025080884313904e+28L);
+ TEST_f_f (tgamma, -0x5.00000000000000000000000002p0L, 8.4510040015215293433113547025052449019430e+28L);
+ TEST_f_f (tgamma, -0x5.fffffffffffffffffffffffffep0L, 1.4085006669202548905518924504180378867132e+28L);
+ TEST_f_f (tgamma, -0x6.00000000000000000000000002p0L, -1.4085006669202548905518924504175176688423e+28L);
+ TEST_f_f (tgamma, -0x6.fffffffffffffffffffffffffep0L, -2.0121438098860784150741320720257967542615e+27L);
+ TEST_f_f (tgamma, -0x7.00000000000000000000000002p0L, 2.0121438098860784150741320720249968965322e+27L);
+ TEST_f_f (tgamma, -0x7.fffffffffffffffffffffffffep0L, 2.5151797623575980188426650900322769448110e+26L);
+ TEST_f_f (tgamma, -0x8.00000000000000000000000004p0L, -1.2575898811787990094213325450153421028080e+26L);
+ TEST_f_f (tgamma, -0x9.fffffffffffffffffffffffffcp0L, 1.3973220901986655660237028277960625420495e+24L);
+ TEST_f_f (tgamma, -0xa.00000000000000000000000004p0L, -1.3973220901986655660237028277947663821128e+24L);
+ TEST_f_f (tgamma, -0x13.fffffffffffffffffffffffff8p0L, 1.0420893204640670202556853709074896123293e+12L);
+ TEST_f_f (tgamma, -0x14.00000000000000000000000008p0L, -1.0420893204640670202556853709050065497299e+12L);
+ TEST_f_f (tgamma, -0x1d.fffffffffffffffffffffffff8p0L, 9.5580541610429641982963434151488827190079e-03L);
+ TEST_f_f (tgamma, -0x1e.00000000000000000000000008p0L, -9.5580541610429641982963434151231128067179e-03L);
+ TEST_f_f (tgamma, -0x27.fffffffffffffffffffffffffp0L, 1.5536546823612837336494536911280147806523e-18L);
+ TEST_f_f (tgamma, -0x28.0000000000000000000000001p0L, -1.5536546823612837336494536911189419578973e-18L);
+ TEST_f_f (tgamma, -0x28.fffffffffffffffffffffffffp0L, -3.7894016642958139845108626612879138384405e-20L);
+ TEST_f_f (tgamma, -0x29.0000000000000000000000001p0L, 3.7894016642958139845108626612656391824122e-20L);
+ TEST_f_f (tgamma, -0x29.fffffffffffffffffffffffffp0L, 9.0223849149900332964544349078285357440663e-22L);
+ TEST_f_f (tgamma, -0x2a.0000000000000000000000001p0L, -9.0223849149900332964544349077751619246306e-22L);
+ TEST_f_f (tgamma, -0x31.fffffffffffffffffffffffffp0L, 4.1679710515150795310771069868348482819424e-35L);
+ TEST_f_f (tgamma, -0x32.0000000000000000000000001p0L, -4.1679710515150795310771069868090576746248e-35L);
+ TEST_f_f (tgamma, -0x63.ffffffffffffffffffffffffep0L, 6.7915032994648558610510614163560656864280e-129L);
+ TEST_f_f (tgamma, -0x64.0000000000000000000000002p0L, -6.7915032994648558610510614162572689693253e-129L);
+ TEST_f_f (tgamma, -0x95.ffffffffffffffffffffffffcp0L, 5.5468467106873795353190582463444660395353e-234L);
+ TEST_f_f (tgamma, -0x96.0000000000000000000000004p0L, -5.5468467106873795353190582461689495693675e-234L);
+ TEST_f_f (tgamma, -0xb4.ffffffffffffffffffffffffcp0L, -8.7154451775644399729745472278589884205029e-303L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb5.0000000000000000000000004p0L, 8.7154451775644399729745472275729078899858e-303L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb5.ffffffffffffffffffffffffcp0L, 4.7887061415189230620739270482742524864974e-305L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb6.0000000000000000000000004p0L, -4.7887061415189230620739270481168993324524e-305L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb6.ffffffffffffffffffffffffcp0L, -2.6167793123054224382917634143575601407067e-307L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb7.0000000000000000000000004p0L, 2.6167793123054224382917634142714845691019e-307L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+ TEST_f_f (tgamma, -0xb7.ffffffffffffffffffffffffcp0L, 1.4221626697312078468976975078030462044826e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xb8.0000000000000000000000004p0L, -1.4221626697312078468976975077562172247612e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbb.ffffffffffffffffffffffffcp0L, 1.1756150745511026776007338998283058108448e-318L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbc.0000000000000000000000004p0L, -1.1756150745511026776007338997894360215107e-318L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbc.ffffffffffffffffffffffffcp0L, -6.2201855796354639026493857133773832713743e-321L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbd.0000000000000000000000004p0L, 6.2201855796354639026493857131715153125175e-321L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbd.ffffffffffffffffffffffffcp0L, 3.2737818840186652119207293228302560914295e-323L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbe.0000000000000000000000004p0L, -3.2737818840186652119207293227217957948294e-323L, UNDERFLOW_EXCEPTION_DOUBLE);
+# if LDBL_MAX_EXP <= 1024
+ TEST_f_f (tgamma, -0xbe.ffffffffffffffffffffffffcp0L, minus_zero, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_f_f (tgamma, -0xbf.0000000000000000000000004p0L, plus_zero, UNDERFLOW_EXCEPTION_DOUBLE);
+# else
+ TEST_f_f (tgamma, -0xbe.ffffffffffffffffffffffffcp0L, -1.7140219288055838805867692789687487834686e-325L);
+ TEST_f_f (tgamma, -0xbf.0000000000000000000000004p0L, 1.7140219288055838805867692789119066543632e-325L);
+# endif
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+ TEST_f_f (tgamma, 0x8.000000000000001p0L, 5.0400000000000000088113830892247051102283e+03L);
+ TEST_f_f (tgamma, 0x7.fffffffffffffff8p0L, 5.0399999999999999955943084553876474508520e+03L);
+ TEST_f_f (tgamma, 0x7.0000000000000008p0L, 7.2000000000000000058477733127664675369681e+02L);
+ TEST_f_f (tgamma, 0x6.fffffffffffffff8p0L, 7.1999999999999999941522266872335324679893e+02L);
+ TEST_f_f (tgamma, 0x6.0000000000000008p0L, 1.2000000000000000008878927116622375680433e+02L);
+ TEST_f_f (tgamma, 0x5.fffffffffffffff8p0L, 1.1999999999999999991121072883377624326546e+02L);
+ TEST_f_f (tgamma, 0x5.0000000000000008p0L, 2.4000000000000000015676186062072582846211e+01L);
+ TEST_f_f (tgamma, 0x4.fffffffffffffff8p0L, 2.3999999999999999984323813937927417165027e+01L);
+ TEST_f_f (tgamma, 0x4.0000000000000008p0L, 6.0000000000000000032685252120268430507939e+00L);
+ TEST_f_f (tgamma, 0x3.fffffffffffffffcp0L, 5.9999999999999999983657373939865784753909e+00L);
+ TEST_f_f (tgamma, 0x3.0000000000000004p0L, 2.0000000000000000004001939123397399171482e+00L);
+ TEST_f_f (tgamma, 0x2.fffffffffffffffcp0L, 1.9999999999999999995998060876602600829690e+00L);
+ TEST_f_f (tgamma, 0x2.0000000000000004p0L, 1.0000000000000000000916767389213195151634e+00L);
+ TEST_f_f (tgamma, 0x1.fffffffffffffffep0L, 9.9999999999999999995416163053934024243282e-01L);
+ TEST_f_f (tgamma, 0x1.0000000000000002p0L, 9.9999999999999999993741815221210931418291e-01L);
+ TEST_f_f (tgamma, 0x0.ffffffffffffffffp0L, 1.0000000000000000000312909238939453429173e+00L);
+ TEST_f_f (tgamma, -0x0.ffffffffffffffffp0L, -1.8446744073709551616422784335098467139470e+19L);
+ TEST_f_f (tgamma, -0x1.0000000000000002p0L, 9.2233720368547758075772156649015328607596e+18L);
+ TEST_f_f (tgamma, -0x1.fffffffffffffffep0L, 4.6116860184273879044613921675492335697983e+18L);
+ TEST_f_f (tgamma, -0x2.0000000000000004p0L, -2.3058430092136939515386078324507664305064e+18L);
+ TEST_f_f (tgamma, -0x2.fffffffffffffffcp0L, -7.6861433640456465087601961140530007887063e+17L);
+ TEST_f_f (tgamma, -0x3.0000000000000004p0L, 7.6861433640456465045731372192803325462836e+17L);
+ TEST_f_f (tgamma, -0x3.fffffffffffffffcp0L, 1.9215358410114116272942156951799168638773e+17L);
+ TEST_f_f (tgamma, -0x4.0000000000000008p0L, -9.6076792050570581270578430482008313684602e+16L);
+ TEST_f_f (tgamma, -0x4.fffffffffffffff8p0L, -1.9215358410114116280884313903598337283601e+16L);
+ TEST_f_f (tgamma, -0x5.0000000000000008p0L, 1.9215358410114116252449019429734996071487e+16L);
+ TEST_f_f (tgamma, -0x5.fffffffffffffff8p0L, 3.2025597350190193803788671320812043622696e+15L);
+ TEST_f_f (tgamma, -0x6.0000000000000008p0L, -3.2025597350190193751766884234743511972877e+15L);
+ TEST_f_f (tgamma, -0x6.fffffffffffffff8p0L, -4.5750853357414562579675426149912896787735e+14L);
+ TEST_f_f (tgamma, -0x7.0000000000000008p0L, 4.5750853357414562499689653215166468353753e+14L);
+ TEST_f_f (tgamma, -0x7.fffffffffffffff8p0L, 5.7188566696768203227694481100089533685959e+13L);
+ TEST_f_f (tgamma, -0x8.000000000000001p0L, -2.8594283348384101534210280804672371201060e+13L);
+ TEST_f_f (tgamma, -0x9.fffffffffffffffp0L, 3.1771425942649001828476427167843945971988e+11L);
+ TEST_f_f (tgamma, -0xa.000000000000001p0L, -3.1771425942649001698860433502350057763905e+11L);
+ TEST_f_f (tgamma, -0x13.ffffffffffffffep0L, 2.3694367893405502075347562184931828448654e-01L);
+ TEST_f_f (tgamma, -0x14.000000000000002p0L, -2.3694367893405501827041302245929389013031e-01L);
+ TEST_f_f (tgamma, -0x1d.ffffffffffffffep0L, 2.1732499046818166459536268654187775086902e-15L);
+ TEST_f_f (tgamma, -0x1e.000000000000002p0L, -2.1732499046818166201837145753965837196590e-15L);
+ TEST_f_f (tgamma, -0x27.ffffffffffffffcp0L, 3.5326017549807232935581894777156474496719e-31L);
+ TEST_f_f (tgamma, -0x28.000000000000004p0L, -3.5326017549807232028299619269080956965758e-31L);
+ TEST_f_f (tgamma, -0x28.ffffffffffffffcp0L, -8.6161018414163982777002940498289948893044e-33L);
+ TEST_f_f (tgamma, -0x29.000000000000004p0L, 8.6161018414163980549537337663264762179535e-33L);
+ TEST_f_f (tgamma, -0x29.ffffffffffffffcp0L, 2.0514528193848567329552463626090806737389e-34L);
+ TEST_f_f (tgamma, -0x2a.000000000000004p0L, -2.0514528193848566795814269269517457847791e-34L);
+ TEST_f_f (tgamma, -0x31.ffffffffffffffcp0L, 9.4768689712397635680446279661359728835046e-48L);
+ TEST_f_f (tgamma, -0x32.000000000000004p0L, -9.4768689712397633101385547903658075308777e-48L);
+ TEST_f_f (tgamma, -0x63.ffffffffffffff8p0L, 1.5442090669841618542494279375256856430049e-141L);
+ TEST_f_f (tgamma, -0x64.000000000000008p0L, -1.5442090669841617554527108348771968070612e-141L);
+ TEST_f_f (tgamma, -0x95.ffffffffffffffp0L, 1.2612069237291916400144732227892704713839e-246L);
+ TEST_f_f (tgamma, -0x96.00000000000001p0L, -1.2612069237291914644980030550324645611752e-246L);
+ TEST_f_f (tgamma, -0xb4.ffffffffffffffp0L, -1.9816628031468191243385005680879281767694e-315L);
+ TEST_f_f (tgamma, -0xb5.00000000000001p0L, 1.9816628031468188382579700510291588022368e-315L);
+ TEST_f_f (tgamma, -0xb5.ffffffffffffffp0L, 1.0888257160147357826865964233809723297472e-317L);
+ TEST_f_f (tgamma, -0xb6.00000000000001p0L, -1.0888257160147356253334423783317128355514e-317L);
+ TEST_f_f (tgamma, -0xb6.ffffffffffffffp0L, -5.9498673006269714905418984659220067091260e-320L);
+ TEST_f_f (tgamma, -0xb7.00000000000001p0L, 5.9498673006269706297861824177538685763601e-320L);
+ TEST_f_f (tgamma, -0xb7.ffffffffffffffp0L, 3.2336235329494410277123118903958061569834e-322L);
+ TEST_f_f (tgamma, -0xb8.00000000000001p0L, -3.2336235329494405594225146768193434900135e-322L);
+ TEST_f_f (tgamma, -0xbb.ffffffffffffffp0L, 2.6730392040715350119087465463119939092815e-331L);
+ TEST_f_f (tgamma, -0xbc.00000000000001p0L, -2.6730392040715346232108532050343031951651e-331L);
+ TEST_f_f (tgamma, -0xbc.ffffffffffffffp0L, -1.4143064571807063556111222197839950086445e-333L);
+ TEST_f_f (tgamma, -0xbd.00000000000001p0L, 1.4143064571807061497431633629389135273431e-333L);
+ TEST_f_f (tgamma, -0xbd.ffffffffffffffp0L, 7.4437181956879281879706555863416819210399e-336L);
+ TEST_f_f (tgamma, -0xbe.00000000000001p0L, -7.4437181956879271033676895858841525581153e-336L);
+ TEST_f_f (tgamma, -0xbe.ffffffffffffffp0L, -3.8972346574282346536709453101948570578636e-338L);
+ TEST_f_f (tgamma, -0xbf.00000000000001p0L, 3.8972346574282340852496542564155275274974e-338L);
+ TEST_f_f (tgamma, -0xf9.ffffffffffffffp0L, 2.2289142548411573883553287678043297937797e-476L);
+ TEST_f_f (tgamma, -0xfa.00000000000001p0L, -2.2289142548411570466476165308364665814265e-476L);
+ TEST_f_f (tgamma, -0x1f3.fffffffffffffep0L, 2.9528489142763141594943668922610562530068e-1118L);
+ TEST_f_f (tgamma, -0x1f4.00000000000002p0L, -2.9528489142763131406565394149878256133744e-1118L);
+ TEST_f_f (tgamma, -0x2ed.fffffffffffffcp0L, 6.9801511765871818502006905472380418430269e-1817L);
+ TEST_f_f (tgamma, -0x2ee.00000000000004p0L, -6.9801511765871767194421856376592926002995e-1817L);
+ TEST_f_f (tgamma, -0x3e7.fffffffffffffcp0L, 4.4768809295877296071892611539415773519036e-2552L);
+ TEST_f_f (tgamma, -0x3e8.00000000000004p0L, -4.4768809295877261735541135972060089530309e-2552L);
+ TEST_f_f (tgamma, -0x4e1.fffffffffffff8p0L, 5.4651488569236507565341414077911790252381e-3315L);
+ TEST_f_f (tgamma, -0x4e2.00000000000008p0L, -5.4651488569236421026544487194247355967789e-3315L);
+ TEST_f_f (tgamma, -0x5db.fffffffffffff8p0L, 1.8718211510339187689122114747834510481993e-4099L);
+ TEST_f_f (tgamma, -0x5dc.00000000000008p0L, -1.8718211510339157291960718369454861898499e-4099L);
+ TEST_f_f (tgamma, -0x6d5.fffffffffffff8p0L, 4.2925786447266492555651378780094011518063e-4902L);
+ TEST_f_f (tgamma, -0x6d6.00000000000008p0L, -4.2925786447266421378134368786479937285900e-4902L);
+ TEST_f_f (tgamma, -0x6e2.fffffffffffff8p0L, -2.8229173528168668283609231628661510187536e-4944L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e3.00000000000008p0L, 2.8229173528168621428945467532322397890424e-4944L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e3.fffffffffffff8p0L, 1.6002932839097884515524894602387278842659e-4947L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e4.00000000000008p0L, -1.6002932839097857951909742110188634438017e-4947L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e4.fffffffffffff8p0L, -9.0668174725767051085164382743343408095146e-4951L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e5.00000000000008p0L, 9.0668174725766900571689083050287838090189e-4951L, UNDERFLOW_EXCEPTION);
+# if LDBL_MANT_DIG <= 64
+ TEST_f_f (tgamma, -0x6e5.fffffffffffff8p0L, plus_zero, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e6.00000000000008p0L, minus_zero, UNDERFLOW_EXCEPTION);
+# else
+ TEST_f_f (tgamma, -0x6e5.fffffffffffff8p0L, 5.1340982290921319983501912122292601780326e-4954L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e6.00000000000008p0L, -5.1340982290921234748578193083614111497314e-4954L, UNDERFLOW_EXCEPTION);
+# endif
+# if LDBL_MANT_DIG >= 113
+ TEST_f_f (tgamma, 0x8.0000000000000000000000000008p0L, 5.0400000000000000000000000000000156521606e+03L);
+ TEST_f_f (tgamma, 0x7.fffffffffffffffffffffffffffcp0L, 5.0399999999999999999999999999999921739197e+03L);
+ TEST_f_f (tgamma, 0x7.0000000000000000000000000004p0L, 7.2000000000000000000000000000000103877321e+02L);
+ TEST_f_f (tgamma, 0x6.fffffffffffffffffffffffffffcp0L, 7.1999999999999999999999999999999896122679e+02L);
+ TEST_f_f (tgamma, 0x6.0000000000000000000000000004p0L, 1.2000000000000000000000000000000015772143e+02L);
+ TEST_f_f (tgamma, 0x5.fffffffffffffffffffffffffffcp0L, 1.1999999999999999999999999999999984227857e+02L);
+ TEST_f_f (tgamma, 0x5.0000000000000000000000000004p0L, 2.4000000000000000000000000000000027846500e+01L);
+ TEST_f_f (tgamma, 0x4.fffffffffffffffffffffffffffcp0L, 2.3999999999999999999999999999999972153500e+01L);
+ TEST_f_f (tgamma, 0x4.0000000000000000000000000004p0L, 6.0000000000000000000000000000000058060671e+00L);
+ TEST_f_f (tgamma, 0x3.fffffffffffffffffffffffffffep0L, 5.9999999999999999999999999999999970969664e+00L);
+ TEST_f_f (tgamma, 0x3.0000000000000000000000000002p0L, 2.0000000000000000000000000000000007108872e+00L);
+ TEST_f_f (tgamma, 0x2.fffffffffffffffffffffffffffep0L, 1.9999999999999999999999999999999992891128e+00L);
+ TEST_f_f (tgamma, 0x2.0000000000000000000000000002p0L, 1.0000000000000000000000000000000001628506e+00L);
+ TEST_f_f (tgamma, 0x1.ffffffffffffffffffffffffffffp0L, 9.9999999999999999999999999999999991857470e-01L);
+ TEST_f_f (tgamma, 0x1.0000000000000000000000000001p0L, 9.9999999999999999999999999999999988883231e-01L);
+ TEST_f_f (tgamma, 0x0.ffffffffffffffffffffffffffff8p0L, 1.0000000000000000000000000000000000555838e+00L);
+ TEST_f_f (tgamma, -0x0.ffffffffffffffffffffffffffff8p0L, -1.0384593717069655257060992658440192422784e+34L);
+ TEST_f_f (tgamma, -0x1.0000000000000000000000000001p0L, 5.1922968585348276285304963292200955772157e+33L);
+ TEST_f_f (tgamma, -0x1.ffffffffffffffffffffffffffffp0L, 2.5961484292674138142652481646100484613922e+33L);
+ TEST_f_f (tgamma, -0x2.0000000000000000000000000002p0L, -1.2980742146337069071326240823050235386078e+33L);
+ TEST_f_f (tgamma, -0x2.fffffffffffffffffffffffffffep0L, -4.3269140487790230237754136076834154268628e+32L);
+ TEST_f_f (tgamma, -0x3.0000000000000000000000000002p0L, 4.3269140487790230237754136076834112398039e+32L);
+ TEST_f_f (tgamma, -0x3.fffffffffffffffffffffffffffep0L, 1.0817285121947557559438534019208539608824e+32L);
+ TEST_f_f (tgamma, -0x4.0000000000000000000000000004p0L, -5.4086425609737787797192670096042603911764e+31L);
+ TEST_f_f (tgamma, -0x4.fffffffffffffffffffffffffffcp0L, -1.0817285121947557559438534019208547550981e+31L);
+ TEST_f_f (tgamma, -0x5.0000000000000000000000000004p0L, 1.0817285121947557559438534019208519115686e+31L);
+ TEST_f_f (tgamma, -0x5.fffffffffffffffffffffffffffcp0L, 1.8028808536579262599064223365347581566449e+30L);
+ TEST_f_f (tgamma, -0x6.0000000000000000000000000004p0L, -1.8028808536579262599064223365347529544662e+30L);
+ TEST_f_f (tgamma, -0x6.fffffffffffffffffffffffffffcp0L, -2.5755440766541803712948890521925119357966e+29L);
+ TEST_f_f (tgamma, -0x7.0000000000000000000000000004p0L, 2.5755440766541803712948890521925039372193e+29L);
+ TEST_f_f (tgamma, -0x7.fffffffffffffffffffffffffffcp0L, 3.2194300958177254641186113152406402297656e+28L);
+ TEST_f_f (tgamma, -0x8.0000000000000000000000000008p0L, -1.6097150479088627320593056576203121511868e+28L);
+ TEST_f_f (tgamma, -0x9.fffffffffffffffffffffffffff8p0L, 1.7885722754542919245103396195781369922635e+26L);
+ TEST_f_f (tgamma, -0xa.0000000000000000000000000008p0L, -1.7885722754542919245103396195781240306642e+26L);
+ TEST_f_f (tgamma, -0x13.fffffffffffffffffffffffffffp0L, 1.3338743301940057859272772747600099590309e+14L);
+ TEST_f_f (tgamma, -0x14.000000000000000000000000001p0L, -1.3338743301940057859272772747599851284049e+14L);
+ TEST_f_f (tgamma, -0x1d.fffffffffffffffffffffffffffp0L, 1.2234309326134994173819319571374205986026e+00L);
+ TEST_f_f (tgamma, -0x1e.000000000000000000000000001p0L, -1.2234309326134994173819319571373948286903e+00L);
+ TEST_f_f (tgamma, -0x27.ffffffffffffffffffffffffffep0L, 1.9886779934224431790713007246380976767855e-16L);
+ TEST_f_f (tgamma, -0x28.000000000000000000000000002p0L, -1.9886779934224431790713007246380069485580e-16L);
+ TEST_f_f (tgamma, -0x28.ffffffffffffffffffffffffffep0L, -4.8504341302986419001739042064343853066259e-18L);
+ TEST_f_f (tgamma, -0x29.000000000000000000000000002p0L, 4.8504341302986419001739042064341625600656e-18L);
+ TEST_f_f (tgamma, -0x29.ffffffffffffffffffffffffffep0L, 1.1548652691187242619461676681986633377063e-19L);
+ TEST_f_f (tgamma, -0x2a.000000000000000000000000002p0L, -1.1548652691187242619461676681986099638869e-19L);
+ TEST_f_f (tgamma, -0x31.ffffffffffffffffffffffffffep0L, 5.3350029459393017997786969431322287652396e-33L);
+ TEST_f_f (tgamma, -0x32.000000000000000000000000002p0L, -5.3350029459393017997786969431319708591664e-33L);
+ TEST_f_f (tgamma, -0x63.ffffffffffffffffffffffffffcp0L, 8.6931242233150155021453586128730281632676e-127L);
+ TEST_f_f (tgamma, -0x64.000000000000000000000000004p0L, -8.6931242233150155021453586128720401960966e-127L);
+ TEST_f_f (tgamma, -0x95.ffffffffffffffffffffffffff8p0L, 7.0999637896798458052083945552094635720486e-232L);
+ TEST_f_f (tgamma, -0x96.000000000000000000000000008p0L, -7.0999637896798458052083945552077084073470e-232L);
+ TEST_f_f (tgamma, -0xb4.ffffffffffffffffffffffffff8p0L, -1.1155769827282483165407420451477844041365e-300L);
+ TEST_f_f (tgamma, -0xb5.000000000000000000000000008p0L, 1.1155769827282483165407420451474983236060e-300L);
+ TEST_f_f (tgamma, -0xb5.ffffffffffffffffffffffffff8p0L, 6.1295438611442215194546266216911239298981e-303L);
+ TEST_f_f (tgamma, -0xb6.000000000000000000000000008p0L, -6.1295438611442215194546266216895503983577e-303L);
+ TEST_f_f (tgamma, -0xb6.ffffffffffffffffffffffffff8p0L, -3.3494775197509407210134571703230189921356e-305L);
+ TEST_f_f (tgamma, -0xb7.000000000000000000000000008p0L, 3.3494775197509407210134571703221582364195e-305L);
+ TEST_f_f (tgamma, -0xb7.ffffffffffffffffffffffffff8p0L, 1.8203682172559460440290528099581627396147e-307L);
+ TEST_f_f (tgamma, -0xb8.000000000000000000000000008p0L, -1.8203682172559460440290528099576944498174e-307L);
+ TEST_f_f (tgamma, -0xbb.ffffffffffffffffffffffffff8p0L, 1.5047872954254114273289393917555491216542e-316L);
+ TEST_f_f (tgamma, -0xbc.000000000000000000000000008p0L, -1.5047872954254114273289393917551604237609e-316L);
+ TEST_f_f (tgamma, -0xbc.ffffffffffffffffffffffffff8p0L, -7.9618375419333937953912137129923244334851e-319L);
+ TEST_f_f (tgamma, -0xbd.000000000000000000000000008p0L, 7.9618375419333937953912137129902657538965e-319L);
+ TEST_f_f (tgamma, -0xbd.ffffffffffffffffffffffffff8p0L, 4.1904408115438914712585335331538555086887e-321L);
+ TEST_f_f (tgamma, -0xbe.000000000000000000000000008p0L, -4.1904408115438914712585335331527709057227e-321L);
+ TEST_f_f (tgamma, -0xbe.ffffffffffffffffffffffffff8p0L, -2.1939480688711473671510646770439036908579e-323L);
+ TEST_f_f (tgamma, -0xbf.000000000000000000000000008p0L, 2.1939480688711473671510646770433352695669e-323L);
+ TEST_f_f (tgamma, -0xf9.ffffffffffffffffffffffffff8p0L, 1.2547671759429278005937024349858508569625e-461L);
+ TEST_f_f (tgamma, -0xfa.000000000000000000000000008p0L, -1.2547671759429278005937024349855091492502e-461L);
+ TEST_f_f (tgamma, -0x1f3.ffffffffffffffffffffffffffp0L, 1.6623061587520224800948170558276526986560e-1103L);
+ TEST_f_f (tgamma, -0x1f4.00000000000000000000000001p0L, -1.6623061587520224800948170558266338608285e-1103L);
+ TEST_f_f (tgamma, -0x2ed.fffffffffffffffffffffffffep0L, 3.9294757797334687313030998663853566763041e-1802L);
+ TEST_f_f (tgamma, -0x2ee.00000000000000000000000002p0L, -3.9294757797334687313030998663802259177992e-1802L);
+ TEST_f_f (tgamma, -0x3e7.fffffffffffffffffffffffffep0L, 2.5202599107841713834679953735597552855978e-2537L);
+ TEST_f_f (tgamma, -0x3e8.00000000000000000000000002p0L, -2.5202599107841713834679953735563216504503e-2537L);
+ TEST_f_f (tgamma, -0x4e1.fffffffffffffffffffffffffcp0L, 3.0766052944457032773369415396747635242705e-3300L);
+ TEST_f_f (tgamma, -0x4e2.00000000000000000000000004p0L, -3.0766052944457032773369415396661096445778e-3300L);
+ TEST_f_f (tgamma, -0x5db.fffffffffffffffffffffffffcp0L, 1.0537416297875703295453200836588944487917e-4084L);
+ TEST_f_f (tgamma, -0x5dc.00000000000000000000000004p0L, -1.0537416297875703295453200836558547326520e-4084L);
+ TEST_f_f (tgamma, -0x6d5.fffffffffffffffffffffffffcp0L, 2.4165069481061837867659591369998698607387e-4887L);
+ TEST_f_f (tgamma, -0x6d6.00000000000000000000000004p0L, -2.4165069481061837867659591369927521090377e-4887L);
+ TEST_f_f (tgamma, -0x6e2.fffffffffffffffffffffffffcp0L, -1.5891611922804672355414813803008070609431e-4929L);
+ TEST_f_f (tgamma, -0x6e3.00000000000000000000000004p0L, 1.5891611922804672355414813802961215945667e-4929L);
+ TEST_f_f (tgamma, -0x6e3.fffffffffffffffffffffffffcp0L, 9.0088502963745308137272187091882496519917e-4933L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e4.00000000000000000000000004p0L, -9.0088502963745308137272187091616860368392e-4933L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e4.fffffffffffffffffffffffffcp0L, -5.1041644738665896961627301468488672286746e-4936L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e5.00000000000000000000000004p0L, 5.1041644738665896961627301468338158811446e-4936L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e5.fffffffffffffffffffffffffcp0L, 2.8902403589278537350864836618623260468143e-4939L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6e6.00000000000000000000000004p0L, -2.8902403589278537350864836618538025544424e-4939L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6eb.fffffffffffffffffffffffffcp0L, 9.4152481960798287090819640211017219042636e-4959L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ec.00000000000000000000000004p0L, -9.4152481960798287090819640210739431797168e-4959L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ec.fffffffffffffffffffffffffcp0L, -5.3103486723518492437010513373388172315540e-4962L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ed.00000000000000000000000004p0L, 5.3103486723518492437010513373231484108489e-4962L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ed.fffffffffffffffffffffffffcp0L, 2.9934321715624854812294539669328172615019e-4965L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ee.00000000000000000000000004p0L, -2.9934321715624854812294539669239841152754e-4965L, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ee.fffffffffffffffffffffffffcp0L, minus_zero, UNDERFLOW_EXCEPTION);
+ TEST_f_f (tgamma, -0x6ef.00000000000000000000000004p0L, plus_zero, UNDERFLOW_EXCEPTION);
+# endif
+#endif
+ TEST_f_f (tgamma, -0x1.0a32a2p+5L, 1.8125267978155035272941154746083439329912e-37L);
+#ifndef TEST_FLOAT
+ TEST_f_f (tgamma, -0x1.5800000080001p+7L, -3.1439271448823567326093363350637118195240e-304L, UNDERFLOW_EXCEPTION_LDOUBLE_IBM);
+#endif
+ TEST_f_f (tgamma, 18.5L, 1.4986120533153361177371791123515513270334e+15L);
+ TEST_f_f (tgamma, 19.5L, 2.7724322986333718178137813578503699550119e+16L);
+ TEST_f_f (tgamma, 23.5L, 5.3613035875444147334274983856108155717836e+21L);
+ TEST_f_f (tgamma, 29.5L, 1.6348125198274266444378807806868221866931e+30L);
+ TEST_f_f (tgamma, 30.5L, 4.8226969334909086010917483030261254507447e+31L);
+ TEST_f_f (tgamma, 31.5L, 1.4709225647147271233329832324229682624771e+33L);
+ TEST_f_f (tgamma, 32.5L, 4.6334060788513904384988971821323500268029e+34L);
+ TEST_f_f (tgamma, 33.5L, 1.5058569756267018925121415841930137587110e+36L);
+ TEST_f_f (tgamma, 34.5L, 5.0446208683494513399156743070465960916817e+37L);
+ TEST_f_f (tgamma, 0x2.30a43cp+4L, 3.4027979115654976101247558405326779640190e+38L);
+#ifdef TEST_FLOAT
+ TEST_f_f (tgamma, 0x2.30a44p+4L, plus_infty, OVERFLOW_EXCEPTION);
+#else
+ TEST_f_f (tgamma, 0x2.30a44p+4L, 3.4028438913396451054667218138127983367181e+38L);
+#endif
+#ifndef TEST_FLOAT
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb238p+4L, 1.7976931348622298700886249281842651388250e+308L);
+# if !defined TEST_LDOUBLE || LDBL_MAX_EXP <= 1024
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb24p+4L, plus_infty, OVERFLOW_EXCEPTION);
+# else
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb24p+4L, 1.7976931348624926129589466917917870782484e+308L);
+# endif
+#endif
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb23a9ddbf0d3804f4p+4L, 1.7976931348623158079372897140307719334857e+308L);
+# if LDBL_MAX_EXP <= 1024
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb23a9ddbf0d3804f8p+4L, plus_infty, OVERFLOW_EXCEPTION);
+# else
+ TEST_f_f (tgamma, 0xa.b9fd72b0fb23a9ddbf0d3804f8p+4L, 1.7976931348623158079372897140599422519044e+308L);
+# endif
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+ TEST_f_f (tgamma, 0x6.db8c603359a97108p+8L, 1.1897314953572317517071551278058233700012e+4932L);
+ TEST_f_f (tgamma, 0x6.db8c603359a9711p+8L, plus_infty, OVERFLOW_EXCEPTION);
+# if LDBL_MANT_DIG >= 113
+ TEST_f_f (tgamma, 0x6.db8c603359a971081bc4a2e9dfdp+8L, 1.1897314953572317650857593266265995494998e+4932L);
+ TEST_f_f (tgamma, 0x6.db8c603359a971081bc4a2e9dfd4p+8L, plus_infty, OVERFLOW_EXCEPTION);
+# endif
+#endif
+
END (tgamma);
}
diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h
index 7661788..9d6ecad 100644
--- a/sysdeps/generic/math_private.h
+++ b/sysdeps/generic/math_private.h
@@ -371,6 +371,18 @@ extern float __x2y2m1f (float x, float y);
extern double __x2y2m1 (double x, double y);
extern long double __x2y2m1l (long double x, long double y);
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+extern float __gamma_productf (float x, float x_eps, int n, float *eps);
+extern double __gamma_product (double x, double x_eps, int n, double *eps);
+extern long double __gamma_productl (long double x, long double x_eps,
+ int n, long double *eps);
+
#ifndef math_opt_barrier
# define math_opt_barrier(x) \
({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; })
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 0815592..8761d3a 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -6165,6 +6165,379 @@ idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
+Test "tgamma (-0x0.ffffffffffffffffp0) == -1.8446744073709551616422784335098467139470e+19":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1.000002p0) == 8.3886075772158332060084424806449513922858e+06":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1.0a32a2p+5) == 1.8125267978155035272941154746083439329912e-37":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1.5800000080001p+7) == -3.1439271448823567326093363350637118195240e-304":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x1.fffffffffffffp0) == 2.2517998136852484613921675492337776673289e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x13.ffffep0) == 2.1550026214525536756224040483579183652119e-13":
+float: 1
+ifloat: 1
+Test "tgamma (-0x13.ffffffffffffffep0) == 2.3694367893405502075347562184931828448654e-01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x13.ffffffffffffp0) == 1.1569515572952029402736625857313236848570e-04":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x14.000000000001p0) == -1.1569515572951781096476686854873801225397e-04":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x1d.ffffep0) == 1.9765721589464867957912772592816027583176e-27":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1d.ffffffffffffffep0) == 2.1732499046818166459536268654187775086902e-15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1e.000000000000002p0) == -2.1732499046818166201837145753965837196590e-15":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x1e.00002p0) == -1.9765463890341964384070157599286498212650e-27":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1f4.00000000000002p0) == -2.9528489142763131406565394149878256133744e-1118":
+ildouble: 3
+ldouble: 3
+Test "tgamma (-0x1p-24) == -1.6777216577215723853867349114260580375249e+07":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.0000000000000004p0) == -2.3058430092136939515386078324507664305064e+18":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.0000000000002p0) == -1.1258999068426235386078324507668462444260e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.000004p0) == -2.0971515386080557574407223895988378776747e+06":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.fffffcp0) == -6.9905087601970247876992248591045142913324e+05":
+double: 1
+idouble: 1
+Test "tgamma (-0x27.ffffcp0) == 3.2129279441390812141195076945616975790225e-43":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x27.fffffffffffep0) == 1.7249032006742266376460389310340465554361e-34":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.000000000002p0) == -1.7249032006741359094184881234822934593822e-34":
+double: 1
+idouble: 1
+Test "tgamma (-0x28.00004p0) == -3.2128372159115252365699015758097981155793e-43":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.ffffcp0) == -7.8364103489619817539676737414096652170685e-45":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.fffffffffffep0) == -4.2070809772542120404320040128839297118648e-36":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.ffffffffffffffcp0) == -8.6161018414163982777002940498289948893044e-33":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.000000000000004p0) == 8.6161018414163980549537337663264762179535e-33":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.000000000002p0) == 4.2070809772539892938717205103652583609422e-36":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.00004p0) == 7.8361876024016854597745353972619195760515e-45":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.ffffcp0) == 1.8658121573125798145204120066590953505132e-46":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2a.00004p0) == -1.8657587834931410688246126853566488626385e-46":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2ed.fffffffffffffcp0) == 6.9801511765871818502006905472380418430269e-1817":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3.0000000000002p0) == 3.7529996894754112398038859470009084971438e+14":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3.000004p0) == 6.9905045731381300146131914617735687322025e+05":
+double: 1
+idouble: 1
+Test "tgamma (-0x3.fffffcp0) == 1.7476272942159602684441970627092458855771e+05":
+float: 1
+ifloat: 1
+Test "tgamma (-0x3.ffffffffffffep0) == 9.3824992236885396088236184658402406857503e+13":
+double: 1
+idouble: 1
+Test "tgamma (-0x3.fffffffffffffffcp0) == 1.9215358410114116272942156951799168638773e+17":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x31.fffffffffffep0) == 4.6273774273632946947805289899230181990085e-51":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x32.000000000000004p0) == -9.4768689712397633101385547903658075308777e-48":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x32.000000000002p0) == -4.6273774273630367887073532197576655720178e-51":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3e7.fffffffffffffcp0) == 4.4768809295877296071892611539415773519036e-2552":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3e8.00000000000004p0) == -4.4768809295877261735541135972060089530309e-2552":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.0000000000000008p0) == -9.6076792050570581270578430482008313684602e+16":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.000008p0) == -8.7381270578483499672965708923121931082305e+04":
+float: 2
+ifloat: 2
+Test "tgamma (-0x4.fffff8p0) == -1.7476280884325863043793087474680780379554e+04":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.ffffffffffffcp0) == -9.3824992236885475509805702650262155809819e+12":
+double: 1
+idouble: 1
+Test "tgamma (-0x4e2.00000000000008p0) == -5.4651488569236421026544487194247355967789e-3315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.0000000000000008p0) == 1.9215358410114116252449019429734996071487e+16":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.0000000000004p0) == 9.3824992236885191156860964016850034672946e+12":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.000008p0) == 1.7476252449031389167286893378510439443844e+04":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.fffff8p0) == 2.9127137122026653716311560165769071985443e+03":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (-0x5.ffffffffffffcp0) == 1.5637498706147581566449098589862357835505e+12":
+double: 1
+idouble: 1
+Test "tgamma (-0x5db.fffffffffffff8p0) == 1.8718211510339187689122114747834510481993e-4099":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x6.0000000000000008p0) == -3.2025597350190193751766884234743511972877e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x6.000008p0) == -2.9127085100239567622341538102130981196910e+03":
+double: 1
+idouble: 1
+Test "tgamma (-0x6.fffff8p0) == -4.1610198723079349791939054365613377035519e+02":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x6.ffffffffffffcp0) == -2.2339283865925119357965832452642909859289e+11":
+double: 3
+idouble: 3
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x63.fffffffffffcp0) == 7.5400833348840965463348754984345825364294e-145":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x63.ffffffffffffff8p0) == 1.5442090669841618542494279375256856430049e-141":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x64.000000000000008p0) == -1.5442090669841617554527108348771968070612e-141":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x64.000000000004p0) == -7.5400833348831085791638490135462230991587e-145":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x6d6.00000000000008p0) == -4.2925786447266421378134368786479937285900e-4902":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.0000000000000008p0) == 4.5750853357414562499689653215166468353753e+14":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.0000000000004p0) == 2.2339283865925039372192897706214475877342e+11":
+double: 4
+idouble: 4
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.000008p0) == 4.1610118737306415004517215226199741948733e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.fffff8p0) == 5.2012751504050764429534086402871289946986e+01":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.ffffffffffffcp0) == 2.7924104832406402297655703264222230055898e+10":
+double: 2
+idouble: 2
+Test "tgamma (-0x7.fffffffffffffff8p0) == 5.7188566696768203227694481100089533685959e+13":
+ildouble: 4
+ldouble: 4
+Test "tgamma (-0x8.000000000000001p0) == -2.8594283348384101534210280804672371201060e+13":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x8.00001p0) == -2.6006296115134418896533598545925084576702e+01":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x9.ffffffffffff8p0) == 1.5513391573559147700413058496716749249803e+08":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x95.fffffffffff8p0) == 6.1582369322723207086020016423767264008839e-250":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x95.ffffffffffffffp0) == 1.2612069237291916400144732227892704713839e-246":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x96.000000000008p0) == -6.1582369322705655439003240743176243138734e-250":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xa.000000000000001p0) == -3.1771425942649001698860433502350057763905e+11":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xa.0000000000008p0) == -1.5513391573559018084419393002828541166901e+08":
+double: 1
+idouble: 1
+Test "tgamma (-0xa.00001p0) == -2.8895878754728051776830454190076999107021e-01":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb4.ffffffffffffffp0) == -1.9816628031468191243385005680879281767694e-315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb5.00000000000001p0) == 1.9816628031468188382579700510291588022368e-315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb5.000000000008p0) == 9.6760879059888966544677044221698800670218e-319":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xb5.ffffffffffffffp0) == 1.0888257160147357826865964233809723297472e-317":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.00000000000001p0) == -1.0888257160147356253334423783317128355514e-317":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.fffffffffff8p0) == -2.9052086428846935908287469917922960610289e-323":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.ffffffffffffffp0) == -5.9498673006269714905418984659220067091260e-320":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb7.fffffffffff8p0) == 1.5789177406982032823826953250736039527543e-325":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb7.ffffffffffffffp0) == 3.2336235329494410277123118903958061569834e-322":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xb8.000000000008p0) == -1.5789177406977349925854817486109369828857e-325":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbb.ffffffffffffffp0) == 2.6730392040715350119087465463119939092815e-331":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xbc.00000000000001p0) == -2.6730392040715346232108532050343031951651e-331":
+ildouble: 3
+ldouble: 3
+Test "tgamma (-0xbd.00000000000001p0) == 1.4143064571807061497431633629389135273431e-333":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbe.00000000000001p0) == -7.4437181956879271033676895858841525581153e-336":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbe.ffffffffffffffp0) == -3.8972346574282346536709453101948570578636e-338":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbf.00000000000001p0) == 3.8972346574282340852496542564155275274974e-338":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xf9.ffffffffffffffp0) == 2.2289142548411573883553287678043297937797e-476":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xfa.00000000000001p0) == -2.2289142548411570466476165308364665814265e-476":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-1.5) == 2.3632718012073547030642233111215269103967e+00":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-2.5) == -9.4530872048294188122568932444861076415869e-01":
+double: 1
+idouble: 1
+Test "tgamma (-4.5) == -6.0019601300504246427027893615784810422774e-02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-5.5) == 1.0912654781909862986732344293779056440504e-02":
+float: 1
+ifloat: 1
+Test "tgamma (-6.5) == -1.6788699664476712287280529682737009908468e-03":
+float: 1
+ifloat: 1
+Test "tgamma (-7.5) == 2.2384932885968949716374039576982679877958e-04":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-8.5) == -2.6335215159963470254557693619979623385833e-05":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-9.5) == 2.7721279115751021320587045915768024616666e-06":
+ildouble: 2
+ldouble: 2
Test "tgamma (0.5) == sqrt (pi)":
float: 1
ifloat: 1
@@ -6173,7 +6546,218 @@ double: 1
float: 1
idouble: 1
ifloat: 1
+Test "tgamma (0x1.fffffep0) == 9.9999994960018563231526611134590489120697e-01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x1.fffffffffffffffep0) == 9.9999999999999999995416163053934024243282e-01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x1p-24) == 1.6777215422784394050795179874582764575261e+07":
+float: 1
+ifloat: 1
+Test "tgamma (0x1p-53) == 9.0071992547409914227843350984672492007618e+15":
+double: 1
+idouble: 1
+Test "tgamma (0x1p-64) == 1.8446744073709551615422784335098467139447e+19":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.0000000000002p0) == 1.0000000000000001877539613108624482361963e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.000004p0) == 1.0000001007996638509889062631687945799175e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.30a43cp+4) == 3.4027979115654976101247558405326779640190e+38":
+double: 1
+idouble: 1
+Test "tgamma (0x2.fffffcp0) == 1.9999995599822108706107786027549565954046e+00":
+float: 2
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.ffffffffffffep0) == 1.9999999999999991804028675282128956223990e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.0000000000002p0) == 2.0000000000000008195971324717875960213536e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.fffffcp0) == 5.9999982031095793171233994481968816873643e+00":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.fffffffffffffffcp0) == 5.9999999999999999983657373939865784753909e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.0000000000000008p0) == 6.0000000000000000032685252120268430507939e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.000008p0) == 6.0000035937827461765660468073471093546129e+00":
+float: 1
+ifloat: 1
+Test "tgamma (0x4.fffff8p0) == 2.3999982763857938712639837029547357501709e+01":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.fffffffffffffff8p0) == 2.3999999999999999984323813937927417165027e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.0000000000000008p0) == 2.4000000000000000015676186062072582846211e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.000008p0) == 2.4000017236155647574166073485628713443799e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.fffff8p0) == 1.1999990237520611552119807476573441975106e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.ffffffffffffcp0) == 1.1999999999999981815957265157389249327533e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.0000000000000008p0) == 1.2000000000000000008878927116622375680433e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.000008p0) == 1.2000009762487825358530770343720418162783e+02":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.fffff8p0) == 7.1999935703082425988147448928288557689866e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.ffffffffffffcp0) == 7.1999999999999880237602554542848858572672e+02":
+double: 3
+idouble: 3
+Test "tgamma (0x7.0000000000000008p0) == 7.2000000000000000058477733127664675369681e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.0000000000004p0) == 7.2000000000000119762397445457359071259652e+02":
+double: 4
+idouble: 4
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.000008p0) == 7.2000064296977505705636258629805621178587e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.fffff8p0) == 5.0399951558933225045148935487583089307135e+03":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.ffffffffffffcp0) == 5.0399999999999909771437166339103165198442e+03":
+double: 2
+idouble: 2
+Test "tgamma (0x7.fffffffffffffff8p0) == 5.0399999999999999955943084553876474508520e+03":
+ildouble: 3
+ldouble: 3
+Test "tgamma (0x8.000000000000001p0) == 5.0400000000000000088113830892247051102283e+03":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x8.0000000000008p0) == 5.0400000000000180457125667322294144477136e+03":
+double: 1
+idouble: 1
+Test "tgamma (0x8.00001p0) == 5.0400096882277802019946778420223050233915e+03":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0xa.b9fd72b0fb238p+4) == 1.7976931348622298700886249281842651388250e+308":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (10) == 362880":
+double: 1
+idouble: 1
+Test "tgamma (18.5) == 1.4986120533153361177371791123515513270334e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (19.5) == 2.7724322986333718178137813578503699550119e+16":
+double: 1
+idouble: 1
+Test "tgamma (2.5) == 1.3293403881791370204736256125058588870982e+00":
+float: 1
+ifloat: 1
+Test "tgamma (23.5) == 5.3613035875444147334274983856108155717836e+21":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (29.5) == 1.6348125198274266444378807806868221866931e+30":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (3) == 2":
+float: 1
+ifloat: 1
+Test "tgamma (3.5) == 3.3233509704478425511840640312646472177454e+00":
+float: 1
+ifloat: 1
+Test "tgamma (30.5) == 4.8226969334909086010917483030261254507447e+31":
+float: 1
+ifloat: 1
+Test "tgamma (31.5) == 1.4709225647147271233329832324229682624771e+33":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (32.5) == 4.6334060788513904384988971821323500268029e+34":
+ildouble: 1
+ldouble: 1
+Test "tgamma (34.5) == 5.0446208683494513399156743070465960916817e+37":
+ildouble: 1
+ldouble: 1
Test "tgamma (4) == 6":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (4.5) == 1.1631728396567448929144224109426265262109e+01":
+double: 1
+idouble: 1
+Test "tgamma (5.5) == 5.2342777784553520181149008492418193679490e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (6.5) == 2.8788527781504436099631954670830006523720e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (7.5) == 1.8712543057977883464760770536039504240418e+03":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (8) == 5040":
+ildouble: 1
+ldouble: 1
+Test "tgamma (8.5) == 1.4034407293483412598570577902029628180313e+04":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (9) == 40320":
+ildouble: 1
+ldouble: 1
+Test "tgamma (9.5) == 1.1929246199460900708784991216725183953266e+05":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
ildouble: 1
ldouble: 1
@@ -7103,12 +7687,12 @@ ildouble: 2
ldouble: 2
Function: "tgamma":
-double: 2
-float: 1
-idouble: 2
-ifloat: 1
-ildouble: 1
-ldouble: 1
+double: 4
+float: 2
+idouble: 4
+ifloat: 2
+ildouble: 4
+ldouble: 4
Function: "y0":
double: 2
diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c
index 9873551..5b17f7b 100644
--- a/sysdeps/ieee754/dbl-64/e_gamma_r.c
+++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c
@@ -19,14 +19,104 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const double gamma_coeff[] =
+ {
+ 0x1.5555555555555p-4,
+ -0xb.60b60b60b60b8p-12,
+ 0x3.4034034034034p-12,
+ -0x2.7027027027028p-12,
+ 0x3.72a3c5631fe46p-12,
+ -0x7.daac36664f1f4p-12,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 184, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static double
+gamma_positive (double x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5)
+ {
+ *exp2_adj = 0;
+ return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5)
+ {
+ *exp2_adj = 0;
+ return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
+ }
+ else if (x < 6.5)
+ {
+ /* Adjust into the range for using exp (lgamma). */
+ *exp2_adj = 0;
+ double n = __ceil (x - 1.5);
+ double x_adj = x - n;
+ double eps;
+ double prod = __gamma_product (x_adj, 0, n, &eps);
+ return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
+ * prod * (1.0 + eps));
+ }
+ else
+ {
+ double eps = 0;
+ double x_eps = 0;
+ double x_adj = x;
+ double prod = 1;
+ if (x < 12.0)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ double n = __ceil (12.0 - x);
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ double x_tmp = x + n;
+ x_adj = x_tmp;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_product (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ double exp_adj = -eps;
+ double x_adj_int = __round (x_adj);
+ double x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ double x_adj_mant = __frexp (x_adj, &x_adj_log2);
+ if (x_adj_mant < M_SQRT1_2)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ double ret = (__ieee754_pow (x_adj_mant, x_adj)
+ * __ieee754_exp2 (x_adj_log2 * x_adj_frac)
+ * __ieee754_exp (-x_adj)
+ * __ieee754_sqrt (2 * M_PI / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_log (x);
+ double bsum = gamma_coeff[NCOEFF - 1];
+ double x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1 (exp_adj);
+ }
+}
double
__ieee754_gamma_r (double x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
int32_t hx;
u_int32_t lx;
@@ -51,8 +141,48 @@ __ieee754_gamma_r (double x, int *signgamp)
*signgamp = 0;
return x - x;
}
+ if (__builtin_expect ((hx & 0x7ff00000) == 0x7ff00000, 0))
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ *signgamp = 0;
+ return x + x;
+ }
- /* XXX FIXME. */
- return __ieee754_exp (__ieee754_lgamma_r (x, signgamp));
+ if (x >= 172.0)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return DBL_MAX * DBL_MAX;
+ }
+ else if (x > 0.0)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ double ret = gamma_positive (x, &exp2_adj);
+ return __scalbn (ret, exp2_adj);
+ }
+ else if (x >= -DBL_EPSILON / 4.0)
+ {
+ *signgamp = 0;
+ return 1.0 / x;
+ }
+ else
+ {
+ double tx = __trunc (x);
+ *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
+ if (x <= -184.0)
+ /* Underflow. */
+ return DBL_MIN * DBL_MIN;
+ double frac = tx - x;
+ if (frac > 0.5)
+ frac = 1.0 - frac;
+ double sinpix = (frac <= 0.25
+ ? __sin (M_PI * frac)
+ : __cos (M_PI * (0.5 - frac)));
+ int exp2_adj;
+ double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj));
+ return __scalbn (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gamma_r, __gamma_r_finite)
diff --git a/sysdeps/ieee754/dbl-64/gamma_product.c b/sysdeps/ieee754/dbl-64/gamma_product.c
new file mode 100644
index 0000000..2a3fc1a
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/gamma_product.c
@@ -0,0 +1,75 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Calculate X * Y exactly and store the result in *HI + *LO. It is
+ given that the values are small enough that no overflow occurs and
+ large enough (or zero) that no underflow occurs. */
+
+static void
+mul_split (double *hi, double *lo, double x, double y)
+{
+#ifdef __FP_FAST_FMA
+ /* Fast built-in fused multiply-add. */
+ *hi = x * y;
+ *lo = __builtin_fma (x, y, -*hi);
+#elif defined FP_FAST_FMA
+ /* Fast library fused multiply-add, compiler before GCC 4.6. */
+ *hi = x * y;
+ *lo = __fma (x, y, -*hi);
+#else
+ /* Apply Dekker's algorithm. */
+ *hi = x * y;
+# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+ double x1 = x * C;
+ double y1 = y * C;
+# undef C
+ x1 = (x - x1) + x1;
+ y1 = (y - y1) + y1;
+ double x2 = x - x1;
+ double y2 = y - y1;
+ *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+double
+__gamma_product (double x, double x_eps, int n, double *eps)
+{
+ SET_RESTORE_ROUND (FE_TONEAREST);
+ double ret = x;
+ *eps = x_eps / x;
+ for (int i = 1; i < n; i++)
+ {
+ *eps += x_eps / (x + i);
+ double lo;
+ mul_split (&ret, &lo, ret, x + i);
+ *eps += lo / ret;
+ }
+ return ret;
+}
diff --git a/sysdeps/ieee754/dbl-64/gamma_productf.c b/sysdeps/ieee754/dbl-64/gamma_productf.c
new file mode 100644
index 0000000..46072f1
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/gamma_productf.c
@@ -0,0 +1,46 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+float
+__gamma_productf (float x, float x_eps, int n, float *eps)
+{
+ double x_full = (double) x + (double) x_eps;
+ double ret = x_full;
+ for (int i = 1; i < n; i++)
+ ret *= x_full + i;
+
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ float fret = ret;
+ *eps = (ret - fret) / fret;
+
+ return fret;
+}
diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c
index a312957..f58f4c8 100644
--- a/sysdeps/ieee754/flt-32/e_gammaf_r.c
+++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c
@@ -19,14 +19,97 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const float gamma_coeff[] =
+ {
+ 0x1.555556p-4f,
+ -0xb.60b61p-12f,
+ 0x3.403404p-12f,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 42, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static float
+gammaf_positive (float x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5f)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5f)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
+ }
+ else if (x < 2.5f)
+ {
+ *exp2_adj = 0;
+ float x_adj = x - 1;
+ return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
+ * x_adj);
+ }
+ else
+ {
+ float eps = 0;
+ float x_eps = 0;
+ float x_adj = x;
+ float prod = 1;
+ if (x < 4.0f)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ float n = __ceilf (4.0f - x);
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ float x_tmp = x + n;
+ x_adj = x_tmp;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_productf (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ float exp_adj = -eps;
+ float x_adj_int = __roundf (x_adj);
+ float x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
+ if (x_adj_mant < (float) M_SQRT1_2)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0f;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ float ret = (__ieee754_powf (x_adj_mant, x_adj)
+ * __ieee754_exp2f (x_adj_log2 * x_adj_frac)
+ * __ieee754_expf (-x_adj)
+ * __ieee754_sqrtf (2 * (float) M_PI / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_logf (x);
+ float bsum = gamma_coeff[NCOEFF - 1];
+ float x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1f (exp_adj);
+ }
+}
float
__ieee754_gammaf_r (float x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
int32_t hx;
GET_FLOAT_WORD (hx, x);
@@ -50,8 +133,49 @@ __ieee754_gammaf_r (float x, int *signgamp)
*signgamp = 0;
return x - x;
}
+ if (__builtin_expect ((hx & 0x7f800000) == 0x7f800000, 0))
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ *signgamp = 0;
+ return x + x;
+ }
- /* XXX FIXME. */
- return __ieee754_expf (__ieee754_lgammaf_r (x, signgamp));
+ if (x >= 36.0f)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return FLT_MAX * FLT_MAX;
+ }
+ else if (x > 0.0f)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ float ret = gammaf_positive (x, &exp2_adj);
+ return __scalbnf (ret, exp2_adj);
+ }
+ else if (x >= -FLT_EPSILON / 4.0f)
+ {
+ *signgamp = 0;
+ return 1.0f / x;
+ }
+ else
+ {
+ float tx = __truncf (x);
+ *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;
+ if (x <= -42.0f)
+ /* Underflow. */
+ return FLT_MIN * FLT_MIN;
+ float frac = tx - x;
+ if (frac > 0.5f)
+ frac = 1.0f - frac;
+ float sinpix = (frac <= 0.25f
+ ? __sinf ((float) M_PI * frac)
+ : __cosf ((float) M_PI * (0.5f - frac)));
+ int exp2_adj;
+ float ret = (float) M_PI / (-x * sinpix
+ * gammaf_positive (-x, &exp2_adj));
+ return __scalbnf (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gammaf_r, __gammaf_r_finite)
diff --git a/sysdeps/ieee754/k_standard.c b/sysdeps/ieee754/k_standard.c
index cd31230..150921f 100644
--- a/sysdeps/ieee754/k_standard.c
+++ b/sysdeps/ieee754/k_standard.c
@@ -837,7 +837,7 @@ __kernel_standard(double x, double y, int type)
exc.type = OVERFLOW;
exc.name = type < 100 ? "tgamma" : (type < 200
? "tgammaf" : "tgammal");
- exc.retval = HUGE_VAL;
+ exc.retval = __copysign (HUGE_VAL, x);
if (_LIB_VERSION == _POSIX_)
__set_errno (ERANGE);
else if (!matherr(&exc)) {
diff --git a/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/sysdeps/ieee754/ldbl-128/e_gammal_r.c
index b6da31c..e8d49e9 100644
--- a/sysdeps/ieee754/ldbl-128/e_gammal_r.c
+++ b/sysdeps/ieee754/ldbl-128/e_gammal_r.c
@@ -20,14 +20,108 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const long double gamma_coeff[] =
+ {
+ 0x1.5555555555555555555555555555p-4L,
+ -0xb.60b60b60b60b60b60b60b60b60b8p-12L,
+ 0x3.4034034034034034034034034034p-12L,
+ -0x2.7027027027027027027027027028p-12L,
+ 0x3.72a3c5631fe46ae1d4e700dca8f2p-12L,
+ -0x7.daac36664f1f207daac36664f1f4p-12L,
+ 0x1.a41a41a41a41a41a41a41a41a41ap-8L,
+ -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8L,
+ 0x2.dfd2c703c0cfff430edfd2c703cp-4L,
+ -0x1.6476701181f39edbdb9ce625987dp+0L,
+ 0xd.672219167002d3a7a9c886459cp+0L,
+ -0x9.cd9292e6660d55b3f712eb9e07c8p+4L,
+ 0x8.911a740da740da740da740da741p+8L,
+ -0x8.d0cc570e255bf59ff6eec24b49p+12L,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 1775, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static long double
+gammal_positive (long double x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
+ }
+ else if (x < 12.5L)
+ {
+ /* Adjust into the range for using exp (lgamma). */
+ *exp2_adj = 0;
+ long double n = __ceill (x - 1.5L);
+ long double x_adj = x - n;
+ long double eps;
+ long double prod = __gamma_productl (x_adj, 0, n, &eps);
+ return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
+ * prod * (1.0L + eps));
+ }
+ else
+ {
+ long double eps = 0;
+ long double x_eps = 0;
+ long double x_adj = x;
+ long double prod = 1;
+ if (x < 24.0L)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ long double n = __ceill (24.0L - x);
+ x_adj = x + n;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_productl (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ long double exp_adj = -eps;
+ long double x_adj_int = __roundl (x_adj);
+ long double x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
+ if (x_adj_mant < M_SQRT1_2l)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0L;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ long double ret = (__ieee754_powl (x_adj_mant, x_adj)
+ * __ieee754_exp2l (x_adj_log2 * x_adj_frac)
+ * __ieee754_expl (-x_adj)
+ * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_logl (x);
+ long double bsum = gamma_coeff[NCOEFF - 1];
+ long double x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1l (exp_adj);
+ }
+}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
int64_t hx;
u_int64_t lx;
@@ -51,8 +145,49 @@ __ieee754_gammal_r (long double x, int *signgamp)
*signgamp = 0;
return x - x;
}
+ if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL)
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ *signgamp = 0;
+ return x + x;
+ }
- /* XXX FIXME. */
- return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
+ if (x >= 1756.0L)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return LDBL_MAX * LDBL_MAX;
+ }
+ else if (x > 0.0L)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ long double ret = gammal_positive (x, &exp2_adj);
+ return __scalbnl (ret, exp2_adj);
+ }
+ else if (x >= -LDBL_EPSILON / 4.0L)
+ {
+ *signgamp = 0;
+ return 1.0f / x;
+ }
+ else
+ {
+ long double tx = __truncl (x);
+ *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
+ if (x <= -1775.0L)
+ /* Underflow. */
+ return LDBL_MIN * LDBL_MIN;
+ long double frac = tx - x;
+ if (frac > 0.5L)
+ frac = 1.0L - frac;
+ long double sinpix = (frac <= 0.25L
+ ? __sinl (M_PIl * frac)
+ : __cosl (M_PIl * (0.5L - frac)));
+ int exp2_adj;
+ long double ret = M_PIl / (-x * sinpix
+ * gammal_positive (-x, &exp2_adj));
+ return __scalbnl (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gammal_r, __gammal_r_finite)
diff --git a/sysdeps/ieee754/ldbl-128/gamma_productl.c b/sysdeps/ieee754/ldbl-128/gamma_productl.c
new file mode 100644
index 0000000..157dbab
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/gamma_productl.c
@@ -0,0 +1,75 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Calculate X * Y exactly and store the result in *HI + *LO. It is
+ given that the values are small enough that no overflow occurs and
+ large enough (or zero) that no underflow occurs. */
+
+static inline void
+mul_split (long double *hi, long double *lo, long double x, long double y)
+{
+#ifdef __FP_FAST_FMAL
+ /* Fast built-in fused multiply-add. */
+ *hi = x * y;
+ *lo = __builtin_fmal (x, y, -*hi);
+#elif defined FP_FAST_FMAL
+ /* Fast library fused multiply-add, compiler before GCC 4.6. */
+ *hi = x * y;
+ *lo = __fmal (x, y, -*hi);
+#else
+ /* Apply Dekker's algorithm. */
+ *hi = x * y;
+# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
+ long double x1 = x * C;
+ long double y1 = y * C;
+# undef C
+ x1 = (x - x1) + x1;
+ y1 = (y - y1) + y1;
+ long double x2 = x - x1;
+ long double y2 = y - y1;
+ *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+long double
+__gamma_productl (long double x, long double x_eps, int n, long double *eps)
+{
+ SET_RESTORE_ROUNDL (FE_TONEAREST);
+ long double ret = x;
+ *eps = x_eps / x;
+ for (int i = 1; i < n; i++)
+ {
+ *eps += x_eps / (x + i);
+ long double lo;
+ mul_split (&ret, &lo, ret, x + i);
+ *eps += lo / ret;
+ }
+ return ret;
+}
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c b/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c
index 52ade9e..90d8e3f 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c
@@ -20,14 +20,107 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const long double gamma_coeff[] =
+ {
+ 0x1.555555555555555555555555558p-4L,
+ -0xb.60b60b60b60b60b60b60b60b6p-12L,
+ 0x3.4034034034034034034034034p-12L,
+ -0x2.7027027027027027027027027p-12L,
+ 0x3.72a3c5631fe46ae1d4e700dca9p-12L,
+ -0x7.daac36664f1f207daac36664f2p-12L,
+ 0x1.a41a41a41a41a41a41a41a41a4p-8L,
+ -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L,
+ 0x2.dfd2c703c0cfff430edfd2c704p-4L,
+ -0x1.6476701181f39edbdb9ce625988p+0L,
+ 0xd.672219167002d3a7a9c886459cp+0L,
+ -0x9.cd9292e6660d55b3f712eb9e08p+4L,
+ 0x8.911a740da740da740da740da74p+8L,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 191, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static long double
+gammal_positive (long double x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
+ }
+ else if (x < 11.5L)
+ {
+ /* Adjust into the range for using exp (lgamma). */
+ *exp2_adj = 0;
+ long double n = __ceill (x - 1.5L);
+ long double x_adj = x - n;
+ long double eps;
+ long double prod = __gamma_productl (x_adj, 0, n, &eps);
+ return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
+ * prod * (1.0L + eps));
+ }
+ else
+ {
+ long double eps = 0;
+ long double x_eps = 0;
+ long double x_adj = x;
+ long double prod = 1;
+ if (x < 23.0L)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ long double n = __ceill (23.0L - x);
+ x_adj = x + n;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_productl (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ long double exp_adj = -eps;
+ long double x_adj_int = __roundl (x_adj);
+ long double x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
+ if (x_adj_mant < M_SQRT1_2l)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0L;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ long double ret = (__ieee754_powl (x_adj_mant, x_adj)
+ * __ieee754_exp2l (x_adj_log2 * x_adj_frac)
+ * __ieee754_expl (-x_adj)
+ * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_logl (x);
+ long double bsum = gamma_coeff[NCOEFF - 1];
+ long double x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1l (exp_adj);
+ }
+}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
int64_t hx;
u_int64_t lx;
@@ -51,8 +144,49 @@ __ieee754_gammal_r (long double x, int *signgamp)
*signgamp = 0;
return x - x;
}
+ if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL)
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ *signgamp = 0;
+ return x + x;
+ }
- /* XXX FIXME. */
- return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
+ if (x >= 172.0L)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return LDBL_MAX * LDBL_MAX;
+ }
+ else if (x > 0.0L)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ long double ret = gammal_positive (x, &exp2_adj);
+ return __scalbnl (ret, exp2_adj);
+ }
+ else if (x >= -0x1p-110L)
+ {
+ *signgamp = 0;
+ return 1.0f / x;
+ }
+ else
+ {
+ long double tx = __truncl (x);
+ *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
+ if (x <= -191.0L)
+ /* Underflow. */
+ return LDBL_MIN * LDBL_MIN;
+ long double frac = tx - x;
+ if (frac > 0.5L)
+ frac = 1.0L - frac;
+ long double sinpix = (frac <= 0.25L
+ ? __sinl (M_PIl * frac)
+ : __cosl (M_PIl * (0.5L - frac)));
+ int exp2_adj;
+ long double ret = M_PIl / (-x * sinpix
+ * gammal_positive (-x, &exp2_adj));
+ return __scalbnl (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gammal_r, __gammal_r_finite)
diff --git a/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c b/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c
new file mode 100644
index 0000000..7c6186d
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c
@@ -0,0 +1,42 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+long double
+__gamma_productl (long double x, long double x_eps, int n, long double *eps)
+{
+ long double ret = x;
+ *eps = x_eps / x;
+ for (int i = 1; i < n; i++)
+ {
+ *eps += x_eps / (x + i);
+ ret *= x + i;
+ /* FIXME: no error estimates for the multiplication. */
+ }
+ return ret;
+}
diff --git a/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/sysdeps/ieee754/ldbl-96/e_gammal_r.c
index 0974351..7cb3e85 100644
--- a/sysdeps/ieee754/ldbl-96/e_gammal_r.c
+++ b/sysdeps/ieee754/ldbl-96/e_gammal_r.c
@@ -19,14 +19,102 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const long double gamma_coeff[] =
+ {
+ 0x1.5555555555555556p-4L,
+ -0xb.60b60b60b60b60bp-12L,
+ 0x3.4034034034034034p-12L,
+ -0x2.7027027027027028p-12L,
+ 0x3.72a3c5631fe46aep-12L,
+ -0x7.daac36664f1f208p-12L,
+ 0x1.a41a41a41a41a41ap-8L,
+ -0x7.90a1b2c3d4e5f708p-8L,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 1766, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static long double
+gammal_positive (long double x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5L)
+ {
+ *exp2_adj = 0;
+ return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
+ }
+ else if (x < 7.5L)
+ {
+ /* Adjust into the range for using exp (lgamma). */
+ *exp2_adj = 0;
+ long double n = __ceill (x - 1.5L);
+ long double x_adj = x - n;
+ long double eps;
+ long double prod = __gamma_productl (x_adj, 0, n, &eps);
+ return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
+ * prod * (1.0L + eps));
+ }
+ else
+ {
+ long double eps = 0;
+ long double x_eps = 0;
+ long double x_adj = x;
+ long double prod = 1;
+ if (x < 13.0L)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ long double n = __ceill (13.0L - x);
+ x_adj = x + n;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_productl (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ long double exp_adj = -eps;
+ long double x_adj_int = __roundl (x_adj);
+ long double x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
+ if (x_adj_mant < M_SQRT1_2l)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0L;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ long double ret = (__ieee754_powl (x_adj_mant, x_adj)
+ * __ieee754_exp2l (x_adj_log2 * x_adj_frac)
+ * __ieee754_expl (-x_adj)
+ * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_logl (x);
+ long double bsum = gamma_coeff[NCOEFF - 1];
+ long double x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1l (exp_adj);
+ }
+}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
u_int32_t es, hx, lx;
GET_LDOUBLE_WORDS (es, hx, lx, x);
@@ -43,22 +131,55 @@ __ieee754_gammal_r (long double x, int *signgamp)
*signgamp = 0;
return x - x;
}
- if (__builtin_expect ((es & 0x7fff) == 0x7fff, 0)
- && ((hx & 0x7fffffff) | lx) != 0)
+ if (__builtin_expect ((es & 0x7fff) == 0x7fff, 0))
{
- /* NaN, return it. */
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
*signgamp = 0;
- return x;
+ return x + x;
}
- if (__builtin_expect ((es & 0x8000) != 0, 0)
- && x < 0xffffffff && __rintl (x) == x)
+ if (__builtin_expect ((es & 0x8000) != 0, 0) && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
- /* XXX FIXME. */
- return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
+ if (x >= 1756.0L)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return LDBL_MAX * LDBL_MAX;
+ }
+ else if (x > 0.0L)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ long double ret = gammal_positive (x, &exp2_adj);
+ return __scalbnl (ret, exp2_adj);
+ }
+ else if (x >= -LDBL_EPSILON / 4.0L)
+ {
+ *signgamp = 0;
+ return 1.0f / x;
+ }
+ else
+ {
+ long double tx = __truncl (x);
+ *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
+ if (x <= -1766.0L)
+ /* Underflow. */
+ return LDBL_MIN * LDBL_MIN;
+ long double frac = tx - x;
+ if (frac > 0.5L)
+ frac = 1.0L - frac;
+ long double sinpix = (frac <= 0.25L
+ ? __sinl (M_PIl * frac)
+ : __cosl (M_PIl * (0.5L - frac)));
+ int exp2_adj;
+ long double ret = M_PIl / (-x * sinpix
+ * gammal_positive (-x, &exp2_adj));
+ return __scalbnl (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gammal_r, __gammal_r_finite)
diff --git a/sysdeps/ieee754/ldbl-96/gamma_product.c b/sysdeps/ieee754/ldbl-96/gamma_product.c
new file mode 100644
index 0000000..d464e70
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/gamma_product.c
@@ -0,0 +1,46 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+double
+__gamma_product (double x, double x_eps, int n, double *eps)
+{
+ long double x_full = (long double) x + (long double) x_eps;
+ long double ret = x_full;
+ for (int i = 1; i < n; i++)
+ ret *= x_full + i;
+
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ double fret = ret;
+ *eps = (ret - fret) / fret;
+
+ return fret;
+}
diff --git a/sysdeps/ieee754/ldbl-96/gamma_productl.c b/sysdeps/ieee754/ldbl-96/gamma_productl.c
new file mode 100644
index 0000000..157dbab
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/gamma_productl.c
@@ -0,0 +1,75 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Calculate X * Y exactly and store the result in *HI + *LO. It is
+ given that the values are small enough that no overflow occurs and
+ large enough (or zero) that no underflow occurs. */
+
+static inline void
+mul_split (long double *hi, long double *lo, long double x, long double y)
+{
+#ifdef __FP_FAST_FMAL
+ /* Fast built-in fused multiply-add. */
+ *hi = x * y;
+ *lo = __builtin_fmal (x, y, -*hi);
+#elif defined FP_FAST_FMAL
+ /* Fast library fused multiply-add, compiler before GCC 4.6. */
+ *hi = x * y;
+ *lo = __fmal (x, y, -*hi);
+#else
+ /* Apply Dekker's algorithm. */
+ *hi = x * y;
+# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
+ long double x1 = x * C;
+ long double y1 = y * C;
+# undef C
+ x1 = (x - x1) + x1;
+ y1 = (y - y1) + y1;
+ long double x2 = x - x1;
+ long double y2 = y - y1;
+ *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+long double
+__gamma_productl (long double x, long double x_eps, int n, long double *eps)
+{
+ SET_RESTORE_ROUNDL (FE_TONEAREST);
+ long double ret = x;
+ *eps = x_eps / x;
+ for (int i = 1; i < n; i++)
+ {
+ *eps += x_eps / (x + i);
+ long double lo;
+ mul_split (&ret, &lo, ret, x + i);
+ *eps += lo / ret;
+ }
+ return ret;
+}
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index d84a898..3827b9d 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -7142,6 +7142,417 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "tgamma (-0x0.fffffffffffff8p0) == -9.0071992547409924227843350984672961392521e+15":
+double: 1
+idouble: 1
+Test "tgamma (-0x0.ffffffffffffffffp0) == -1.8446744073709551616422784335098467139470e+19":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x0.ffffffp0) == -1.6777216422784419250710305882992376932423e+07":
+float: 1
+ifloat: 1
+Test "tgamma (-0x1.000002p0) == 8.3886075772158332060084424806449513922858e+06":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1.0a32a2p+5) == 1.8125267978155035272941154746083439329912e-37":
+float: 2
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1.5800000080001p+7) == -3.1439271448823567326093363350637118195240e-304":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x1.fffffffffffffp0) == 2.2517998136852484613921675492337776673289e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x13.ffffep0) == 2.1550026214525536756224040483579183652119e-13":
+float: 2
+ifloat: 2
+Test "tgamma (-0x13.ffffffffffffffep0) == 2.3694367893405502075347562184931828448654e-01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x13.ffffffffffffp0) == 1.1569515572952029402736625857313236848570e-04":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x14.000000000001p0) == -1.1569515572951781096476686854873801225397e-04":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x14.00002p0) == -2.1549777908265594916405421768142757507179e-13":
+float: 1
+ifloat: 1
+Test "tgamma (-0x1d.ffffep0) == 1.9765721589464867957912772592816027583176e-27":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1d.ffffffffffffffep0) == 2.1732499046818166459536268654187775086902e-15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1e.000000000000002p0) == -2.1732499046818166201837145753965837196590e-15":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x1e.000000000001p0) == -1.0611571800204053929094168642022073530425e-18":
+double: 3
+idouble: 3
+Test "tgamma (-0x1e.00002p0) == -1.9765463890341964384070157599286498212650e-27":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x1f4.00000000000002p0) == -2.9528489142763131406565394149878256133744e-1118":
+ildouble: 3
+ldouble: 3
+Test "tgamma (-0x1p-24) == -1.6777216577215723853867349114260580375249e+07":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.0000000000000004p0) == -2.3058430092136939515386078324507664305064e+18":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.0000000000002p0) == -1.1258999068426235386078324507668462444260e+15":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.000004p0) == -2.0971515386080557574407223895988378776747e+06":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2.fffffcp0) == -6.9905087601970247876992248591045142913324e+05":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (-0x27.ffffcp0) == 3.2129279441390812141195076945616975790225e-43":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x27.fffffffffffep0) == 1.7249032006742266376460389310340465554361e-34":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.000000000002p0) == -1.7249032006741359094184881234822934593822e-34":
+double: 1
+idouble: 1
+Test "tgamma (-0x28.00004p0) == -3.2128372159115252365699015758097981155793e-43":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.ffffcp0) == -7.8364103489619817539676737414096652170685e-45":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.fffffffffffep0) == -4.2070809772542120404320040128839297118648e-36":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x28.ffffffffffffffcp0) == -8.6161018414163982777002940498289948893044e-33":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.000000000000004p0) == 8.6161018414163980549537337663264762179535e-33":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.000000000002p0) == 4.2070809772539892938717205103652583609422e-36":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.00004p0) == 7.8361876024016854597745353972619195760515e-45":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x29.ffffcp0) == 1.8658121573125798145204120066590953505132e-46":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2a.00004p0) == -1.8657587834931410688246126853566488626385e-46":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x2ed.fffffffffffffcp0) == 6.9801511765871818502006905472380418430269e-1817":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3.0000000000002p0) == 3.7529996894754112398038859470009084971438e+14":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3.000004p0) == 6.9905045731381300146131914617735687322025e+05":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+Test "tgamma (-0x3.fffffcp0) == 1.7476272942159602684441970627092458855771e+05":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (-0x3.ffffffffffffep0) == 9.3824992236885396088236184658402406857503e+13":
+double: 2
+idouble: 2
+Test "tgamma (-0x3.fffffffffffffffcp0) == 1.9215358410114116272942156951799168638773e+17":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x31.fffffffffffep0) == 4.6273774273632946947805289899230181990085e-51":
+double: 3
+idouble: 3
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x32.000000000000004p0) == -9.4768689712397633101385547903658075308777e-48":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x32.000000000002p0) == -4.6273774273630367887073532197576655720178e-51":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3e7.fffffffffffffcp0) == 4.4768809295877296071892611539415773519036e-2552":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x3e8.00000000000004p0) == -4.4768809295877261735541135972060089530309e-2552":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.0000000000000008p0) == -9.6076792050570581270578430482008313684602e+16":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.000008p0) == -8.7381270578483499672965708923121931082305e+04":
+float: 1
+ifloat: 1
+Test "tgamma (-0x4.fffff8p0) == -1.7476280884325863043793087474680780379554e+04":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x4.ffffffffffffcp0) == -9.3824992236885475509805702650262155809819e+12":
+double: 1
+idouble: 1
+Test "tgamma (-0x4e2.00000000000008p0) == -5.4651488569236421026544487194247355967789e-3315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.0000000000000008p0) == 1.9215358410114116252449019429734996071487e+16":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.0000000000004p0) == 9.3824992236885191156860964016850034672946e+12":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.000008p0) == 1.7476252449031389167286893378510439443844e+04":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x5.ffffffffffffcp0) == 1.5637498706147581566449098589862357835505e+12":
+double: 1
+idouble: 1
+Test "tgamma (-0x5db.fffffffffffff8p0) == 1.8718211510339187689122114747834510481993e-4099":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x6.0000000000000008p0) == -3.2025597350190193751766884234743511972877e+15":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x6.000008p0) == -2.9127085100239567622341538102130981196910e+03":
+float: 2
+ifloat: 2
+Test "tgamma (-0x6.fffff8p0) == -4.1610198723079349791939054365613377035519e+02":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x6.ffffffffffffcp0) == -2.2339283865925119357965832452642909859289e+11":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x63.fffffffffffcp0) == 7.5400833348840965463348754984345825364294e-145":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x63.ffffffffffffff8p0) == 1.5442090669841618542494279375256856430049e-141":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x64.000000000000008p0) == -1.5442090669841617554527108348771968070612e-141":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x64.000000000004p0) == -7.5400833348831085791638490135462230991587e-145":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x6d6.00000000000008p0) == -4.2925786447266421378134368786479937285900e-4902":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.0000000000000008p0) == 4.5750853357414562499689653215166468353753e+14":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.0000000000004p0) == 2.2339283865925039372192897706214475877342e+11":
+double: 3
+idouble: 3
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.000008p0) == 4.1610118737306415004517215226199741948733e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.fffff8p0) == 5.2012751504050764429534086402871289946986e+01":
+double: 3
+float: 1
+idouble: 3
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x7.ffffffffffffcp0) == 2.7924104832406402297655703264222230055898e+10":
+double: 3
+idouble: 3
+Test "tgamma (-0x7.fffffffffffffff8p0) == 5.7188566696768203227694481100089533685959e+13":
+ildouble: 4
+ldouble: 4
+Test "tgamma (-0x8.000000000000001p0) == -2.8594283348384101534210280804672371201060e+13":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0x8.00001p0) == -2.6006296115134418896533598545925084576702e+01":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x9.ffffffffffff8p0) == 1.5513391573559147700413058496716749249803e+08":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x9.fffffp0) == 2.8896008370721717567612135720915723136310e-01":
+float: 1
+ifloat: 1
+Test "tgamma (-0x95.fffffffffff8p0) == 6.1582369322723207086020016423767264008839e-250":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x95.ffffffffffffffp0) == 1.2612069237291916400144732227892704713839e-246":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0x96.000000000008p0) == -6.1582369322705655439003240743176243138734e-250":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xa.000000000000001p0) == -3.1771425942649001698860433502350057763905e+11":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xa.00001p0) == -2.8895878754728051776830454190076999107021e-01":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb4.ffffffffffffffp0) == -1.9816628031468191243385005680879281767694e-315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb5.00000000000001p0) == 1.9816628031468188382579700510291588022368e-315":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb5.000000000008p0) == 9.6760879059888966544677044221698800670218e-319":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xb5.ffffffffffffffp0) == 1.0888257160147357826865964233809723297472e-317":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.00000000000001p0) == -1.0888257160147356253334423783317128355514e-317":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.fffffffffff8p0) == -2.9052086428846935908287469917922960610289e-323":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb6.ffffffffffffffp0) == -5.9498673006269714905418984659220067091260e-320":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb7.fffffffffff8p0) == 1.5789177406982032823826953250736039527543e-325":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xb7.ffffffffffffffp0) == 3.2336235329494410277123118903958061569834e-322":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xb8.000000000008p0) == -1.5789177406977349925854817486109369828857e-325":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbb.ffffffffffffffp0) == 2.6730392040715350119087465463119939092815e-331":
+ildouble: 2
+ldouble: 2
+Test "tgamma (-0xbc.00000000000001p0) == -2.6730392040715346232108532050343031951651e-331":
+ildouble: 3
+ldouble: 3
+Test "tgamma (-0xbd.00000000000001p0) == 1.4143064571807061497431633629389135273431e-333":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbe.00000000000001p0) == -7.4437181956879271033676895858841525581153e-336":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbe.ffffffffffffffp0) == -3.8972346574282346536709453101948570578636e-338":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xbf.00000000000001p0) == 3.8972346574282340852496542564155275274974e-338":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xf9.ffffffffffffffp0) == 2.2289142548411573883553287678043297937797e-476":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-0xfa.00000000000001p0) == -2.2289142548411570466476165308364665814265e-476":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-1.5) == 2.3632718012073547030642233111215269103967e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (-2.5) == -9.4530872048294188122568932444861076415869e-01":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+Test "tgamma (-3.5) == 2.7008820585226910892162552127103164690248e-01":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (-4.5) == -6.0019601300504246427027893615784810422774e-02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-5.5) == 1.0912654781909862986732344293779056440504e-02":
+double: 1
+idouble: 1
+Test "tgamma (-6.5) == -1.6788699664476712287280529682737009908468e-03":
+float: 1
+ifloat: 1
+Test "tgamma (-7.5) == 2.2384932885968949716374039576982679877958e-04":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-8.5) == -2.6335215159963470254557693619979623385833e-05":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (-9.5) == 2.7721279115751021320587045915768024616666e-06":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
Test "tgamma (0.5) == sqrt (pi)":
float: 1
ifloat: 1
@@ -7150,7 +7561,260 @@ double: 1
float: 1
idouble: 1
ifloat: 1
+Test "tgamma (0x1.fffffep0) == 9.9999994960018563231526611134590489120697e-01":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x1.fffffffffffffffep0) == 9.9999999999999999995416163053934024243282e-01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x1.fffffffffffffp0) == 9.9999999999999990612301934456883679778984e-01":
+double: 1
+idouble: 1
+Test "tgamma (0x1p-24) == 1.6777215422784394050795179874582764575261e+07":
+float: 1
+ifloat: 1
+Test "tgamma (0x1p-53) == 9.0071992547409914227843350984672492007618e+15":
+double: 1
+idouble: 1
+Test "tgamma (0x1p-64) == 1.8446744073709551615422784335098467139447e+19":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.0000000000002p0) == 1.0000000000000001877539613108624482361963e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.000004p0) == 1.0000001007996638509889062631687945799175e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.30a43cp+4) == 3.4027979115654976101247558405326779640190e+38":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+Test "tgamma (0x2.fffffcp0) == 1.9999995599822108706107786027549565954046e+00":
+float: 3
+ifloat: 3
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x2.ffffffffffffep0) == 1.9999999999999991804028675282128956223990e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.0000000000002p0) == 2.0000000000000008195971324717875960213536e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.fffffcp0) == 5.9999982031095793171233994481968816873643e+00":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x3.ffffffffffffep0) == 5.9999999999999966530301828845138185025345e+00":
+double: 1
+idouble: 1
+Test "tgamma (0x3.fffffffffffffffcp0) == 5.9999999999999999983657373939865784753909e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.0000000000000008p0) == 6.0000000000000000032685252120268430507939e+00":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.0000000000004p0) == 6.0000000000000066939396342309789716341613e+00":
+double: 1
+idouble: 1
+Test "tgamma (0x4.fffff8p0) == 2.3999982763857938712639837029547357501709e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x4.ffffffffffffcp0) == 2.3999999999999967895170944875373910918544e+01":
+double: 1
+idouble: 1
+Test "tgamma (0x4.fffffffffffffff8p0) == 2.3999999999999999984323813937927417165027e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.0000000000000008p0) == 2.4000000000000000015676186062072582846211e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.0000000000004p0) == 2.4000000000000032104829055124673225982803e+01":
+double: 1
+idouble: 1
+Test "tgamma (0x5.000008p0) == 2.4000017236155647574166073485628713443799e+01":
+float: 2
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.fffff8p0) == 1.1999990237520611552119807476573441975106e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x5.ffffffffffffcp0) == 1.1999999999999981815957265157389249327533e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.0000000000000008p0) == 1.2000000000000000008878927116622375680433e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.0000000000004p0) == 1.2000000000000018184042734842640022086408e+02":
+double: 1
+idouble: 1
+Test "tgamma (0x6.000008p0) == 1.2000009762487825358530770343720418162783e+02":
+float: 2
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.fffff8p0) == 7.1999935703082425988147448928288557689866e+02":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x6.ffffffffffffcp0) == 7.1999999999999880237602554542848858572672e+02":
+double: 3
+idouble: 3
+Test "tgamma (0x7.0000000000000008p0) == 7.2000000000000000058477733127664675369681e+02":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.0000000000004p0) == 7.2000000000000119762397445457359071259652e+02":
+double: 4
+idouble: 4
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.000008p0) == 7.2000064296977505705636258629805621178587e+02":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.fffff8p0) == 5.0399951558933225045148935487583089307135e+03":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x7.ffffffffffffcp0) == 5.0399999999999909771437166339103165198442e+03":
+double: 2
+idouble: 2
+Test "tgamma (0x7.fffffffffffffff8p0) == 5.0399999999999999955943084553876474508520e+03":
+ildouble: 3
+ldouble: 3
+Test "tgamma (0x8.000000000000001p0) == 5.0400000000000000088113830892247051102283e+03":
+ildouble: 1
+ldouble: 1
+Test "tgamma (0x8.00001p0) == 5.0400096882277802019946778420223050233915e+03":
+double: 2
+idouble: 2
+ildouble: 1
+ldouble: 1
+Test "tgamma (0xa.b9fd72b0fb238p+4) == 1.7976931348622298700886249281842651388250e+308":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (10) == 362880":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (18.5) == 1.4986120533153361177371791123515513270334e+15":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (19.5) == 2.7724322986333718178137813578503699550119e+16":
+double: 2
+idouble: 2
+Test "tgamma (2.5) == 1.3293403881791370204736256125058588870982e+00":
+float: 2
+ifloat: 2
+Test "tgamma (23.5) == 5.3613035875444147334274983856108155717836e+21":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (29.5) == 1.6348125198274266444378807806868221866931e+30":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (3) == 2":
+float: 1
+ifloat: 1
+Test "tgamma (3.5) == 3.3233509704478425511840640312646472177454e+00":
+float: 2
+ifloat: 2
+Test "tgamma (30.5) == 4.8226969334909086010917483030261254507447e+31":
+float: 1
+ifloat: 1
+Test "tgamma (32.5) == 4.6334060788513904384988971821323500268029e+34":
+ildouble: 1
+ldouble: 1
+Test "tgamma (33.5) == 1.5058569756267018925121415841930137587110e+36":
+float: 1
+ifloat: 1
+Test "tgamma (34.5) == 5.0446208683494513399156743070465960916817e+37":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
Test "tgamma (4) == 6":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (4.5) == 1.1631728396567448929144224109426265262109e+01":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "tgamma (5.5) == 5.2342777784553520181149008492418193679490e+01":
+ildouble: 1
+ldouble: 1
+Test "tgamma (6) == 120":
+float: 1
+ifloat: 1
+Test "tgamma (6.5) == 2.8788527781504436099631954670830006523720e+02":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (7) == 720":
+double: 1
+idouble: 1
+Test "tgamma (7.5) == 1.8712543057977883464760770536039504240418e+03":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (8) == 5040":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (8.5) == 1.4034407293483412598570577902029628180313e+04":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "tgamma (9) == 40320":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "tgamma (9.5) == 1.1929246199460900708784991216725183953266e+05":
+double: 1
+idouble: 1
ildouble: 1
ldouble: 1
@@ -8052,12 +8716,12 @@ ildouble: 2
ldouble: 2
Function: "tgamma":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
-ildouble: 1
-ldouble: 1
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 4
+ldouble: 4
Function: "y0":
double: 2
--
Joseph S. Myers
joseph@codesourcery.com