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authorUlrich Drepper <drepper@redhat.com>2001-03-16 22:26:45 +0000
committerUlrich Drepper <drepper@redhat.com>2001-03-16 22:26:45 +0000
commita66f0958a1fbe5d64c3c77c01baee10bf23257dd (patch)
tree8bd667d88be5d0697fbcd2c01292b538abf5b91b
parentaeba9785a6e2e8dca120bb0b62b74ea1eda0a4a8 (diff)
downloadglibc-a66f0958a1fbe5d64c3c77c01baee10bf23257dd.tar.xz
glibc-a66f0958a1fbe5d64c3c77c01baee10bf23257dd.zip
Update.
2001-03-16 Ulrich Drepper <drepper@redhat.com> * sysdeps/ieee754/ldbl-96/s_erfl.c: New file. Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>. * sysdeps/i386/fpu/libm-test-ulps: Adjust for addition of erfl and erfcl. * sysdeps/ia64/fpu/libm-test-ulps: Likewise. * sysdeps/unix/sysv/linux/ia64/swapcontext.c: New file.
-rw-r--r--ChangeLog10
-rw-r--r--NEWS7
-rw-r--r--linuxthreads/ChangeLog9
-rw-r--r--linuxthreads/attr.c11
-rw-r--r--linuxthreads/internals.h1
-rw-r--r--linuxthreads/pthread.c34
-rw-r--r--sysdeps/i386/fpu/libm-test-ulps11
-rw-r--r--sysdeps/ia64/fpu/libm-test-ulps8
-rw-r--r--sysdeps/ieee754/ldbl-96/s_erfl.c445
-rw-r--r--sysdeps/s390/s390-32/bits/huge_val.h73
-rw-r--r--sysdeps/s390/s390-32/ffs.c68
-rw-r--r--sysdeps/s390/s390-64/bits/huge_val.h69
-rw-r--r--sysdeps/s390/s390-64/ffs.c68
-rw-r--r--sysdeps/unix/sysv/linux/ia64/swapcontext.c40
14 files changed, 550 insertions, 304 deletions
diff --git a/ChangeLog b/ChangeLog
index b0636e37ba..db343511e0 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+2001-03-16 Ulrich Drepper <drepper@redhat.com>
+
+ * sysdeps/ieee754/ldbl-96/s_erfl.c: New file.
+ Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>.
+
+ * sysdeps/i386/fpu/libm-test-ulps: Adjust for addition of erfl and
+ erfcl.
+ * sysdeps/ia64/fpu/libm-test-ulps: Likewise.
+
2001-03-16 David Mosberger <davidm@hpl.hp.com>
* sysdeps/unix/sysv/linux/ia64/bits/sigcontext.h (struct sigcontext):
@@ -23,6 +32,7 @@
* sysdeps/unix/sysv/linux/ia64/getcontext.S: New file.
* sysdeps/unix/sysv/linux/ia64/__start_context.S: New file.
* sysdeps/unix/sysv/linux/ia64/makecontext.c: New file.
+ * sysdeps/unix/sysv/linux/ia64/swapcontext.c: New file.
* sysdeps/unix/sysv/linux/ia64/__longjmp.S (__longjmp): Use extr.u
instead of shift & and.
diff --git a/NEWS b/NEWS
index 489e3bf14c..c6a1aa5c29 100644
--- a/NEWS
+++ b/NEWS
@@ -13,8 +13,8 @@ Version 2.2.3
accurate implementatations for most basic and standard math functions
in float, double, and long double format.
-* Stephen Moshier implemented j0, j1, jn, y0, y1, yn, and lgamma for the
- 96-bit long double format.
+* Stephen Moshier implemented j0, j1, jn, y0, y1, yn, lgamma, erf, and
+ erfc for the 96-bit long double format.
* The beginning of a last-bit accurate math library by IBM Haifa were added.
The basic double functions exist today. Contributed by Abraham Ziv
@@ -27,6 +27,9 @@ Version 2.2.3
* Port to S390/64bit contributed by Martin Schwidefsky
<schwidefsky@de.ibm.com>.
+
+* David Mosberger <davidm@hpl.hp.com> implemented the setcontext family
+ of functions for Linux/IA-64.
Version 2.2.2
diff --git a/linuxthreads/ChangeLog b/linuxthreads/ChangeLog
index 3eb7bcbdeb..8d680babb3 100644
--- a/linuxthreads/ChangeLog
+++ b/linuxthreads/ChangeLog
@@ -1,3 +1,12 @@
+2001-02-23 Jakub Jelinek <jakub@redhat.com>
+
+ * internals.h (__pthread_init_max_stacksize): New prototype.
+ * attr.c (__pthread_attr_setstacksize): Call
+ __pthread_init_max_stacksize if not yet initialized.
+ * pthread.c (__pthread_init_max_stacksize): New function.
+ (__pthread_initialize_manager): Call it.
+ Patch by <dtc@cmucl.cons.org>.
+
2001-03-16 Ulrich Drepper <drepper@redhat.com>
* attr.c (pthread_getattr_np): Fix __stacksize computation for IA-64.
diff --git a/linuxthreads/attr.c b/linuxthreads/attr.c
index 3553069c2e..623b9ba64d 100644
--- a/linuxthreads/attr.c
+++ b/linuxthreads/attr.c
@@ -193,16 +193,7 @@ int __pthread_attr_setstacksize(pthread_attr_t *attr, size_t stacksize)
problem if the manager is already started and we determined it. If
this hasn't happened, we have to find the limit outself. */
if (__pthread_max_stacksize == 0)
- {
- struct rlimit limit;
-
- getrlimit(RLIMIT_STACK, &limit);
-# ifdef NEED_SEPARATE_REGISTER_STACK
- __pthread_max_stacksize = limit.rlim_max / 2;
-# else
- __pthread_max_stacksize = limit.rlim_max;
-# endif
- }
+ __pthread_init_max_stacksize ();
if (stacksize > __pthread_max_stacksize)
return EINVAL;
diff --git a/linuxthreads/internals.h b/linuxthreads/internals.h
index f3f8af2c8e..ba0c14d29d 100644
--- a/linuxthreads/internals.h
+++ b/linuxthreads/internals.h
@@ -430,6 +430,7 @@ static inline pthread_descr thread_self (void)
extern void __pthread_destroy_specifics (void);
extern void __pthread_perform_cleanup (void);
+extern void __pthread_init_max_stacksize (void);
extern int __pthread_initialize_manager (void);
extern void __pthread_message (char * fmt, ...);
extern int __pthread_manager (void *reqfd);
diff --git a/linuxthreads/pthread.c b/linuxthreads/pthread.c
index 5a2ade7446..b1c6186683 100644
--- a/linuxthreads/pthread.c
+++ b/linuxthreads/pthread.c
@@ -456,19 +456,10 @@ void __pthread_initialize(void)
pthread_initialize();
}
-int __pthread_initialize_manager(void)
+void __pthread_init_max_stacksize(void)
{
- int manager_pipe[2];
- int pid;
- struct pthread_request request;
struct rlimit limit;
- int max_stack;
-
-#ifndef HAVE_Z_NODELETE
- if (__builtin_expect (&__dso_handle != NULL, 1))
- __cxa_atexit ((void (*) (void *)) pthread_atexit_retcode, NULL,
- __dso_handle);
-#endif
+ size_t max_stack;
getrlimit(RLIMIT_STACK, &limit);
#ifdef FLOATING_STACKS
@@ -478,9 +469,7 @@ int __pthread_initialize_manager(void)
max_stack = limit.rlim_cur / 2;
# else
max_stack = limit.rlim_cur;
-#endif
-
- __pthread_max_stacksize = max_stack;
+# endif
#else
/* Play with the stack size limit to make sure that no stack ever grows
beyond STACK_SIZE minus one page (to act as a guard page). */
@@ -496,6 +485,23 @@ int __pthread_initialize_manager(void)
setrlimit(RLIMIT_STACK, &limit);
}
#endif
+ __pthread_max_stacksize = max_stack;
+}
+
+int __pthread_initialize_manager(void)
+{
+ int manager_pipe[2];
+ int pid;
+ struct pthread_request request;
+
+#ifndef HAVE_Z_NODELETE
+ if (__builtin_expect (&amp;__dso_handle != NULL, 1))
+ __cxa_atexit ((void (*) (void *)) pthread_atexit_retcode, NULL,
+ __dso_handle);
+#endif
+
+ if (__pthread_max_stacksize == 0)
+ __pthread_init_max_stacksize ();
/* If basic initialization not done yet (e.g. we're called from a
constructor run before our constructor), do it now */
if (__pthread_initial_thread_bos == NULL) pthread_initialize();
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 41d8d22665..1f14566a71 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -522,11 +522,15 @@ ldouble: 3074
Test "erfc (0.7) == 0.32219880616258152702":
double: 1
idouble: 1
+ldouble: 1
+ildouble: 1
Test "erfc (1.2) == 0.089686021770364619762":
float: 1
double: 1
idouble: 1
ifloat: 1
+ldouble: 3
+ildouble: 3
Test "erfc (2.0) == 0.0046777349810472658379":
double: 1
idouble: 1
@@ -535,6 +539,11 @@ double: 24
float: 12
idouble: 24
ifloat: 12
+ldouble: 4
+ildouble: 4
+Test "erfc (9) == 0.41370317465138102381e-36":
+ldouble: 36
+ildouble: 36
# exp
Test "exp (0.7) == 2.0137527074704765216":
@@ -1417,6 +1426,8 @@ double: 24
float: 12
idouble: 24
ifloat: 12
+ldouble: 36
+ildouble: 36
Function: "exp":
ildouble: 412
diff --git a/sysdeps/ia64/fpu/libm-test-ulps b/sysdeps/ia64/fpu/libm-test-ulps
index 383d4a7fcb..a79eefd615 100644
--- a/sysdeps/ia64/fpu/libm-test-ulps
+++ b/sysdeps/ia64/fpu/libm-test-ulps
@@ -566,11 +566,15 @@ ldouble: 3074
Test "erfc (0.7) == 0.32219880616258152702":
double: 1
idouble: 1
+ldouble: 1
+ildouble: 1
Test "erfc (1.2) == 0.089686021770364619762":
float: 2
double: 1
idouble: 1
ifloat: 2
+ldouble: 2
+ildouble: 2
Test "erfc (2.0) == 0.0046777349810472658379":
double: 1
idouble: 1
@@ -579,6 +583,8 @@ double: 24
float: 12
idouble: 24
ifloat: 12
+ldouble: 12
+ildouble: 12
# exp
Test "exp (0.7) == 2.0137527074704765216":
@@ -1487,6 +1493,8 @@ double: 24
float: 12
idouble: 24
ifloat: 12
+ldouble: 12
+ildouble: 12
Function: "exp":
ildouble: 412
diff --git a/sysdeps/ieee754/ldbl-96/s_erfl.c b/sysdeps/ieee754/ldbl-96/s_erfl.c
new file mode 100644
index 0000000000..69c0eb805c
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/s_erfl.c
@@ -0,0 +1,445 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* Long double expansions contributed by
+ Stephen L. Moshier <moshier@na-net.ornl.gov> */
+
+/* double erf(double x)
+ * double erfc(double x)
+ * x
+ * 2 |\
+ * erf(x) = --------- | exp(-t*t)dt
+ * sqrt(pi) \|
+ * 0
+ *
+ * erfc(x) = 1-erf(x)
+ * Note that
+ * erf(-x) = -erf(x)
+ * erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ * 1. For |x| in [0, 0.84375]
+ * erf(x) = x + x*R(x^2)
+ * erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
+ * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
+ * Remark. The formula is derived by noting
+ * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ * and that
+ * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ * is close to one. The interval is chosen because the fix
+ * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
+ * near 0.6174), and by some experiment, 0.84375 is chosen to
+ * guarantee the error is less than one ulp for erf.
+ *
+ * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
+ * c = 0.84506291151 rounded to single (24 bits)
+ * erf(x) = sign(x) * (c + P1(s)/Q1(s))
+ * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
+ * 1+(c+P1(s)/Q1(s)) if x < 0
+ * Remark: here we use the taylor series expansion at x=1.
+ * erf(1+s) = erf(1) + s*Poly(s)
+ * = 0.845.. + P1(s)/Q1(s)
+ * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ *
+ * 3. For x in [1.25,1/0.35(~2.857143)],
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z))
+ * z=1/x^2
+ * erf(x) = 1 - erfc(x)
+ *
+ * 4. For x in [1/0.35,107]
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
+ * = 2.0 - (1/x)*exp(-x*x-0.5625+R2(z)/S2(z))
+ * if -6.666<x<0
+ * = 2.0 - tiny (if x <= -6.666)
+ * z=1/x^2
+ * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6.666, else
+ * erf(x) = sign(x)*(1.0 - tiny)
+ * Note1:
+ * To compute exp(-x*x-0.5625+R/S), let s be a single
+ * precision number and s := x; then
+ * -x*x = -s*s + (s-x)*(s+x)
+ * exp(-x*x-0.5626+R/S) =
+ * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ * Note2:
+ * Here 4 and 5 make use of the asymptotic series
+ * exp(-x*x)
+ * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ * x*sqrt(pi)
+ *
+ * 5. For inf > x >= 107
+ * erf(x) = sign(x) *(1 - tiny) (raise inexact)
+ * erfc(x) = tiny*tiny (raise underflow) if x > 0
+ * = 2 - tiny if x<0
+ *
+ * 7. Special case:
+ * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
+ * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ * erfc/erf(NaN) is NaN
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+tiny = 1e-4931L,
+ half = 0.5L,
+ one = 1.0L,
+ two = 2.0L,
+ /* c = (float)0.84506291151 */
+ erx = 0.845062911510467529296875L,
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+ /* 2/sqrt(pi) - 1 */
+ efx = 1.2837916709551257389615890312154517168810E-1L,
+ /* 8 * (2/sqrt(pi) - 1) */
+ efx8 = 1.0270333367641005911692712249723613735048E0L,
+
+ pp[6] = {
+ 1.122751350964552113068262337278335028553E6L,
+ -2.808533301997696164408397079650699163276E6L,
+ -3.314325479115357458197119660818768924100E5L,
+ -6.848684465326256109712135497895525446398E4L,
+ -2.657817695110739185591505062971929859314E3L,
+ -1.655310302737837556654146291646499062882E2L,
+ },
+
+ qq[6] = {
+ 8.745588372054466262548908189000448124232E6L,
+ 3.746038264792471129367533128637019611485E6L,
+ 7.066358783162407559861156173539693900031E5L,
+ 7.448928604824620999413120955705448117056E4L,
+ 4.511583986730994111992253980546131408924E3L,
+ 1.368902937933296323345610240009071254014E2L,
+ /* 1.000000000000000000000000000000000000000E0 */
+ },
+
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+/* erf(x+1) = 0.845062911510467529296875 + pa(x)/qa(x)
+ -0.15625 <= x <= +.25
+ Peak relative error 8.5e-22 */
+
+ pa[8] = {
+ -1.076952146179812072156734957705102256059E0L,
+ 1.884814957770385593365179835059971587220E2L,
+ -5.339153975012804282890066622962070115606E1L,
+ 4.435910679869176625928504532109635632618E1L,
+ 1.683219516032328828278557309642929135179E1L,
+ -2.360236618396952560064259585299045804293E0L,
+ 1.852230047861891953244413872297940938041E0L,
+ 9.394994446747752308256773044667843200719E-2L,
+ },
+
+ qa[7] = {
+ 4.559263722294508998149925774781887811255E2L,
+ 3.289248982200800575749795055149780689738E2L,
+ 2.846070965875643009598627918383314457912E2L,
+ 1.398715859064535039433275722017479994465E2L,
+ 6.060190733759793706299079050985358190726E1L,
+ 2.078695677795422351040502569964299664233E1L,
+ 4.641271134150895940966798357442234498546E0L,
+ /* 1.000000000000000000000000000000000000000E0 */
+ },
+
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + ra(x^2)/sa(x^2))
+ 1/2.85711669921875 < 1/x < 1/1.25
+ Peak relative error 3.1e-21 */
+
+ ra[] = {
+ 1.363566591833846324191000679620738857234E-1L,
+ 1.018203167219873573808450274314658434507E1L,
+ 1.862359362334248675526472871224778045594E2L,
+ 1.411622588180721285284945138667933330348E3L,
+ 5.088538459741511988784440103218342840478E3L,
+ 8.928251553922176506858267311750789273656E3L,
+ 7.264436000148052545243018622742770549982E3L,
+ 2.387492459664548651671894725748959751119E3L,
+ 2.220916652813908085449221282808458466556E2L,
+ },
+
+ sa[] = {
+ -1.382234625202480685182526402169222331847E1L,
+ -3.315638835627950255832519203687435946482E2L,
+ -2.949124863912936259747237164260785326692E3L,
+ -1.246622099070875940506391433635999693661E4L,
+ -2.673079795851665428695842853070996219632E4L,
+ -2.880269786660559337358397106518918220991E4L,
+ -1.450600228493968044773354186390390823713E4L,
+ -2.874539731125893533960680525192064277816E3L,
+ -1.402241261419067750237395034116942296027E2L,
+ /* 1.000000000000000000000000000000000000000E0 */
+ },
+/*
+ * Coefficients for approximation to erfc in [1/.35,107]
+ */
+/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rb(x^2)/sb(x^2))
+ 1/6.6666259765625 < 1/x < 1/2.85711669921875
+ Peak relative error 4.2e-22 */
+ rb[] = {
+ -4.869587348270494309550558460786501252369E-5L,
+ -4.030199390527997378549161722412466959403E-3L,
+ -9.434425866377037610206443566288917589122E-2L,
+ -9.319032754357658601200655161585539404155E-1L,
+ -4.273788174307459947350256581445442062291E0L,
+ -8.842289940696150508373541814064198259278E0L,
+ -7.069215249419887403187988144752613025255E0L,
+ -1.401228723639514787920274427443330704764E0L,
+ },
+
+ sb[] = {
+ 4.936254964107175160157544545879293019085E-3L,
+ 1.583457624037795744377163924895349412015E-1L,
+ 1.850647991850328356622940552450636420484E0L,
+ 9.927611557279019463768050710008450625415E0L,
+ 2.531667257649436709617165336779212114570E1L,
+ 2.869752886406743386458304052862814690045E1L,
+ 1.182059497870819562441683560749192539345E1L,
+ /* 1.000000000000000000000000000000000000000E0 */
+ },
+/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rc(x^2)/sc(x^2))
+ 1/107 <= 1/x <= 1/6.6666259765625
+ Peak relative error 1.1e-21 */
+ rc[] = {
+ -8.299617545269701963973537248996670806850E-5L,
+ -6.243845685115818513578933902532056244108E-3L,
+ -1.141667210620380223113693474478394397230E-1L,
+ -7.521343797212024245375240432734425789409E-1L,
+ -1.765321928311155824664963633786967602934E0L,
+ -1.029403473103215800456761180695263439188E0L,
+ },
+
+ sc[] = {
+ 8.413244363014929493035952542677768808601E-3L,
+ 2.065114333816877479753334599639158060979E-1L,
+ 1.639064941530797583766364412782135680148E0L,
+ 4.936788463787115555582319302981666347450E0L,
+ 5.005177727208955487404729933261347679090E0L,
+ /* 1.000000000000000000000000000000000000000E0 */
+ };
+
+#ifdef __STDC__
+long double
+__erfl (long double x)
+#else
+double
+__erfl (x)
+ long double x;
+#endif
+{
+ long double R, S, P, Q, s, y, z, r;
+ int32_t ix, i;
+ u_int32_t se, i0, i1;
+
+ GET_LDOUBLE_WORDS (se, i0, i1, x);
+ ix = se & 0x7fff;
+
+ if (ix >= 0x7fff)
+ { /* erf(nan)=nan */
+ i = ((se & 0xffff) >> 15) << 1;
+ return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */
+ }
+
+ ix = (ix << 16) | (i0 >> 16);
+ if (ix < 0x3ffed800) /* |x|<0.84375 */
+ {
+ if (ix < 0x3fde8000) /* |x|<2**-33 */
+ {
+ if (ix < 0x00080000)
+ return 0.125 * (8.0 * x + efx8 * x); /*avoid underflow */
+ return x + efx * x;
+ }
+ z = x * x;
+ r = pp[0] + z * (pp[1]
+ + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5]))));
+ s = qq[0] + z * (qq[1]
+ + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z)))));
+ y = r / s;
+ return x + x * y;
+ }
+ if (ix < 0x3fffa000) /* 1.25 */
+ { /* 0.84375 <= |x| < 1.25 */
+ s = fabsl (x) - one;
+ P = pa[0] + s * (pa[1] + s * (pa[2]
+ + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
+ Q = qa[0] + s * (qa[1] + s * (qa[2]
+ + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
+ if ((se & 0x8000) == 0)
+ return erx + P / Q;
+ else
+ return -erx - P / Q;
+ }
+ if (ix >= 0x4001d555) /* 6.6666259765625 */
+ { /* inf>|x|>=6.666 */
+ if ((se & 0x8000) == 0)
+ return one - tiny;
+ else
+ return tiny - one;
+ }
+ x = fabsl (x);
+ s = one / (x * x);
+ if (ix < 0x4000b6db) /* 2.85711669921875 */
+ {
+ R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
+ s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
+ S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
+ s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
+ }
+ else
+ { /* |x| >= 1/0.35 */
+ R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
+ s * (rb[5] + s * (rb[6] + s * rb[7]))))));
+ S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
+ s * (sb[5] + s * (sb[6] + s))))));
+ }
+ z = x;
+ GET_LDOUBLE_WORDS (i, i0, i1, z);
+ i1 = 0;
+ SET_LDOUBLE_WORDS (z, i, i0, i1);
+ r =
+ __ieee754_expl (-z * z - 0.5625) * __ieee754_expl ((z - x) * (z + x) +
+ R / S);
+ if ((se & 0x8000) == 0)
+ return one - r / x;
+ else
+ return r / x - one;
+}
+
+weak_alias (__erfl, erfl)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__erf, __erfl)
+weak_alias (__erf, erfl)
+#endif
+#ifdef __STDC__
+ long double
+ __erfcl (long double x)
+#else
+ long double
+ __erfcl (x)
+ double
+ x;
+#endif
+{
+ int32_t hx, ix;
+ long double R, S, P, Q, s, y, z, r;
+ u_int32_t se, i0, i1;
+
+ GET_LDOUBLE_WORDS (se, i0, i1, x);
+ ix = se & 0x7fff;
+ if (ix >= 0x7fff)
+ { /* erfc(nan)=nan */
+ /* erfc(+-inf)=0,2 */
+ return (long double) (((se & 0xffff) >> 15) << 1) + one / x;
+ }
+
+ ix = (ix << 16) | (i0 >> 16);
+ if (ix < 0x3ffed800) /* |x|<0.84375 */
+ {
+ if (ix < 0x3fbe0000) /* |x|<2**-65 */
+ return one - x;
+ z = x * x;
+ r = pp