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-rw-r--r--lib/msun/Makefile16
-rw-r--r--lib/msun/Symbol.map6
-rw-r--r--lib/msun/arm/Makefile.inc8
-rw-r--r--lib/msun/arm/Symbol.map3
-rw-r--r--lib/msun/arm/fenv-mangle.h53
-rw-r--r--lib/msun/arm/fenv-softfp.c32
-rw-r--r--lib/msun/arm/fenv-vfp.c33
-rw-r--r--lib/msun/arm/fenv.c261
-rw-r--r--lib/msun/arm/fenv.h109
-rw-r--r--lib/msun/ld128/k_expl.h328
-rw-r--r--lib/msun/ld128/s_expl.c298
-rw-r--r--lib/msun/ld80/k_expl.h305
-rw-r--r--lib/msun/ld80/s_expl.c275
-rw-r--r--lib/msun/man/cosh.314
-rw-r--r--lib/msun/man/sinh.315
-rw-r--r--lib/msun/man/tanh.319
-rw-r--r--lib/msun/src/e_cosh.c6
-rw-r--r--lib/msun/src/e_coshl.c130
-rw-r--r--lib/msun/src/e_sinh.c6
-rw-r--r--lib/msun/src/e_sinhl.c131
-rw-r--r--lib/msun/src/fenv-softfloat.h6
-rw-r--r--lib/msun/src/imprecise.c3
-rw-r--r--lib/msun/src/math.h6
-rw-r--r--lib/msun/src/s_round.c21
-rw-r--r--lib/msun/src/s_roundf.c19
-rw-r--r--lib/msun/src/s_roundl.c31
-rw-r--r--lib/msun/src/s_tanh.c6
-rw-r--r--lib/msun/src/s_tanhl.c172
28 files changed, 1744 insertions, 568 deletions
diff --git a/lib/msun/Makefile b/lib/msun/Makefile
index 5264aeb..800e0ab 100644
--- a/lib/msun/Makefile
+++ b/lib/msun/Makefile
@@ -45,6 +45,7 @@ LIB= m
SHLIBDIR?= /lib
SHLIB_MAJOR= 5
WARNS?= 1
+IGNORE_PRAGMA=
COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
@@ -73,7 +74,7 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
s_lround.c s_lroundf.c s_lroundl.c s_modff.c \
s_nan.c s_nearbyint.c s_nextafter.c s_nextafterf.c \
s_nexttowardf.c s_remquo.c s_remquof.c \
- s_rint.c s_rintf.c s_round.c s_roundf.c s_roundl.c \
+ s_rint.c s_rintf.c s_round.c s_roundf.c \
s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \
s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \
s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \
@@ -98,13 +99,14 @@ COMMON_SRCS+= s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c
.if ${LDBL_PREC} != 53
# If long double != double use these; otherwise, we alias the double versions.
COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \
- e_fmodl.c e_hypotl.c e_remainderl.c e_sqrtl.c \
+ e_coshl.c e_fmodl.c e_hypotl.c \
+ e_remainderl.c e_sinhl.c e_sqrtl.c \
invtrig.c k_cosl.c k_sinl.c k_tanl.c \
s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \
s_csqrtl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \
s_frexpl.c s_logbl.c s_logl.c s_nanl.c s_nextafterl.c \
- s_nexttoward.c s_remquol.c s_rintl.c s_scalbnl.c \
- s_sinl.c s_tanl.c s_truncl.c w_cabsl.c
+ s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c s_scalbnl.c \
+ s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c
.endif
# C99 complex functions
@@ -162,7 +164,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3
MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
MLINKS+=cos.3 cosf.3 cos.3 cosl.3
-MLINKS+=cosh.3 coshf.3
+MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3
MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3
MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \
@@ -210,11 +212,11 @@ MLINKS+=round.3 roundf.3 round.3 roundl.3
MLINKS+=scalbn.3 scalbln.3 scalbn.3 scalblnf.3 scalbn.3 scalblnl.3
MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3
MLINKS+=sin.3 sinf.3 sin.3 sinl.3
-MLINKS+=sinh.3 sinhf.3
+MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3
MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \
sqrt.3 sqrtl.3
MLINKS+=tan.3 tanf.3 tan.3 tanl.3
-MLINKS+=tanh.3 tanhf.3
+MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3
MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3
.include <bsd.lib.mk>
diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map
index 037659d..c36472b 100644
--- a/lib/msun/Symbol.map
+++ b/lib/msun/Symbol.map
@@ -260,6 +260,7 @@ FBSD_1.3 {
ccosf;
ccosh;
ccoshf;
+ coshl;
ctan;
ctanf;
ctanh;
@@ -270,13 +271,12 @@ FBSD_1.3 {
log1pl;
log2l;
logl;
+ sinhl;
+ tanhl;
/* Implemented as weak aliases for imprecise versions */
- coshl;
erfcl;
erfl;
lgammal;
powl;
- sinhl;
- tanhl;
tgammal;
};
diff --git a/lib/msun/arm/Makefile.inc b/lib/msun/arm/Makefile.inc
index 7d9e10b..09f08d8 100644
--- a/lib/msun/arm/Makefile.inc
+++ b/lib/msun/arm/Makefile.inc
@@ -2,3 +2,11 @@
LDBL_PREC = 53
SYM_MAPS += ${.CURDIR}/arm/Symbol.map
+
+.if ${TARGET_ARCH} == "armv6"
+ARCH_SRCS = fenv-softfp.c fenv-vfp.c
+.endif
+
+CFLAGS.fenv-vfp.c= -mfloat-abi=softfp
+CFLAGS+= ${CFLAGS.${.IMPSRC:T}}
+
diff --git a/lib/msun/arm/Symbol.map b/lib/msun/arm/Symbol.map
index c43d8cf..081294c 100644
--- a/lib/msun/arm/Symbol.map
+++ b/lib/msun/arm/Symbol.map
@@ -15,4 +15,7 @@ FBSD_1.3 {
fegetenv;
feholdexcept;
feupdateenv;
+ feenableexcept;
+ fedisableexcept;
+ fegetexcept;
};
diff --git a/lib/msun/arm/fenv-mangle.h b/lib/msun/arm/fenv-mangle.h
new file mode 100644
index 0000000..476f7b2
--- /dev/null
+++ b/lib/msun/arm/fenv-mangle.h
@@ -0,0 +1,53 @@
+/*-
+ * Copyright (c) 2013 Andrew Turner <andrew@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * $FreeBSD$
+ */
+
+#ifdef _FENV_MANGLE_H_
+#error Only include fenv-mangle.h once
+#endif
+
+#define _FENV_MANGLE_H_
+
+#ifndef FENV_MANGLE
+#error FENV_MANGLE is undefined
+#endif
+
+#define feclearexcept FENV_MANGLE(feclearexcept)
+#define fegetexceptflag FENV_MANGLE(fegetexceptflag)
+#define fesetexceptflag FENV_MANGLE(fesetexceptflag)
+#define feraiseexcept FENV_MANGLE(feraiseexcept)
+#define fetestexcept FENV_MANGLE(fetestexcept)
+#define fegetround FENV_MANGLE(fegetround)
+#define fesetround FENV_MANGLE(fesetround)
+#define fegetenv FENV_MANGLE(fegetenv)
+#define feholdexcept FENV_MANGLE(feholdexcept)
+#define fesetenv FENV_MANGLE(fesetenv)
+#define feupdateenv FENV_MANGLE(feupdateenv)
+#define feenableexcept FENV_MANGLE(feenableexcept)
+#define fedisableexcept FENV_MANGLE(fedisableexcept)
+#define fegetexcept FENV_MANGLE(fegetexcept)
+
diff --git a/lib/msun/arm/fenv-softfp.c b/lib/msun/arm/fenv-softfp.c
new file mode 100644
index 0000000..c32c1c2
--- /dev/null
+++ b/lib/msun/arm/fenv-softfp.c
@@ -0,0 +1,32 @@
+/*-
+ * Copyright (c) 2013 Andrew Turner <andrew@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * $FreeBSD$
+ */
+
+#define FENV_MANGLE(x) __softfp_ ##x
+#include "fenv-mangle.h"
+#include "fenv.c"
+
diff --git a/lib/msun/arm/fenv-vfp.c b/lib/msun/arm/fenv-vfp.c
new file mode 100644
index 0000000..fd615f3
--- /dev/null
+++ b/lib/msun/arm/fenv-vfp.c
@@ -0,0 +1,33 @@
+/*-
+ * Copyright (c) 2013 Andrew Turner <andrew@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * $FreeBSD$
+ */
+
+#define FENV_MANGLE(x) __vfp_ ##x
+#include "fenv-mangle.h"
+#define __ARM_PCS_VFP
+#include "fenv.c"
+
diff --git a/lib/msun/arm/fenv.c b/lib/msun/arm/fenv.c
index c94f9b4..2dd1933 100644
--- a/lib/msun/arm/fenv.c
+++ b/lib/msun/arm/fenv.c
@@ -1,5 +1,6 @@
/*-
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
+ * Copyright (c) 2013 Andrew Turner <andrew@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
@@ -29,11 +30,34 @@
#define __fenv_static
#include "fenv.h"
+#if defined(__FreeBSD_ARCH_armv6__) || (defined(__ARM_ARCH) && __ARM_ARCH >= 6)
+#define FENV_ARMv6
+#endif
+
+/* When SOFTFP_ABI is defined we are using the softfp ABI. */
+#if defined(__VFP_FP__) && !defined(__ARM_PCS_VFP)
+#define SOFTFP_ABI
+#endif
+
+
+#ifndef FENV_MANGLE
+/*
+ * Hopefully the system ID byte is immutable, so it's valid to use
+ * this as a default environment.
+ */
+const fenv_t __fe_dfl_env = 0;
+#endif
+
+
+/* If this is a non-mangled softfp version special processing is required */
+#if defined(FENV_MANGLE) || !defined(SOFTFP_ABI) || !defined(FENV_ARMv6)
+
/*
* The following macros map between the softfloat emulator's flags and
* the hardware's FPSR. The hardware this file was written for doesn't
* have rounding control bits, so we stick those in the system ID byte.
*/
+#ifndef __ARM_PCS_VFP
#define __set_env(env, flags, mask, rnd) env = ((flags) \
| (mask)<<_FPUSW_SHIFT \
| (rnd) << 24)
@@ -42,17 +66,12 @@
& FE_ALL_EXCEPT)
#define __env_round(env) (((env) >> 24) & _ROUND_MASK)
#include "fenv-softfloat.h"
+#endif
#ifdef __GNUC_GNU_INLINE__
#error "This file must be compiled with C99 'inline' semantics"
#endif
-/*
- * Hopefully the system ID byte is immutable, so it's valid to use
- * this as a default environment.
- */
-const fenv_t __fe_dfl_env = 0;
-
extern inline int feclearexcept(int __excepts);
extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts);
extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts);
@@ -64,3 +83,233 @@ extern inline int fegetenv(fenv_t *__envp);
extern inline int feholdexcept(fenv_t *__envp);
extern inline int fesetenv(const fenv_t *__envp);
extern inline int feupdateenv(const fenv_t *__envp);
+extern inline int feenableexcept(int __mask);
+extern inline int fedisableexcept(int __mask);
+extern inline int fegetexcept(void);
+
+#else /* !FENV_MANGLE && SOFTFP_ABI */
+/* Set by libc when the VFP unit is enabled */
+extern int _libc_arm_fpu_present;
+
+int __softfp_feclearexcept(int __excepts);
+int __softfp_fegetexceptflag(fexcept_t *__flagp, int __excepts);
+int __softfp_fesetexceptflag(const fexcept_t *__flagp, int __excepts);
+int __softfp_feraiseexcept(int __excepts);
+int __softfp_fetestexcept(int __excepts);
+int __softfp_fegetround(void);
+int __softfp_fesetround(int __round);
+int __softfp_fegetenv(fenv_t *__envp);
+int __softfp_feholdexcept(fenv_t *__envp);
+int __softfp_fesetenv(const fenv_t *__envp);
+int __softfp_feupdateenv(const fenv_t *__envp);
+int __softfp_feenableexcept(int __mask);
+int __softfp_fedisableexcept(int __mask);
+int __softfp_fegetexcept(void);
+
+int __vfp_feclearexcept(int __excepts);
+int __vfp_fegetexceptflag(fexcept_t *__flagp, int __excepts);
+int __vfp_fesetexceptflag(const fexcept_t *__flagp, int __excepts);
+int __vfp_feraiseexcept(int __excepts);
+int __vfp_fetestexcept(int __excepts);
+int __vfp_fegetround(void);
+int __vfp_fesetround(int __round);
+int __vfp_fegetenv(fenv_t *__envp);
+int __vfp_feholdexcept(fenv_t *__envp);
+int __vfp_fesetenv(const fenv_t *__envp);
+int __vfp_feupdateenv(const fenv_t *__envp);
+int __vfp_feenableexcept(int __mask);
+int __vfp_fedisableexcept(int __mask);
+int __vfp_fegetexcept(void);
+
+static int
+__softfp_round_to_vfp(int round)
+{
+
+ switch (round) {
+ case FE_TONEAREST:
+ default:
+ return VFP_FE_TONEAREST;
+ case FE_TOWARDZERO:
+ return VFP_FE_TOWARDZERO;
+ case FE_UPWARD:
+ return VFP_FE_UPWARD;
+ case FE_DOWNWARD:
+ return VFP_FE_DOWNWARD;
+ }
+}
+
+static int
+__softfp_round_from_vfp(int round)
+{
+
+ switch (round) {
+ case VFP_FE_TONEAREST:
+ default:
+ return FE_TONEAREST;
+ case VFP_FE_TOWARDZERO:
+ return FE_TOWARDZERO;
+ case VFP_FE_UPWARD:
+ return FE_UPWARD;
+ case VFP_FE_DOWNWARD:
+ return FE_DOWNWARD;
+ }
+}
+
+int feclearexcept(int __excepts)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_feclearexcept(__excepts);
+ __softfp_feclearexcept(__excepts);
+
+ return (0);
+}
+
+int fegetexceptflag(fexcept_t *__flagp, int __excepts)
+{
+ fexcept_t __vfp_flagp;
+
+ __vfp_flagp = 0;
+ if (_libc_arm_fpu_present)
+ __vfp_fegetexceptflag(&__vfp_flagp, __excepts);
+ __softfp_fegetexceptflag(__flagp, __excepts);
+
+ *__flagp |= __vfp_flagp;
+
+ return (0);
+}
+
+int fesetexceptflag(const fexcept_t *__flagp, int __excepts)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_fesetexceptflag(__flagp, __excepts);
+ __softfp_fesetexceptflag(__flagp, __excepts);
+
+ return (0);
+}
+
+int feraiseexcept(int __excepts)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_feraiseexcept(__excepts);
+ __softfp_feraiseexcept(__excepts);
+
+ return (0);
+}
+
+int fetestexcept(int __excepts)
+{
+ int __got_excepts;
+
+ __got_excepts = 0;
+ if (_libc_arm_fpu_present)
+ __got_excepts = __vfp_fetestexcept(__excepts);
+ __got_excepts |= __softfp_fetestexcept(__excepts);
+
+ return (__got_excepts);
+}
+
+int fegetround(void)
+{
+
+ if (_libc_arm_fpu_present)
+ return __softfp_round_from_vfp(__vfp_fegetround());
+ return __softfp_fegetround();
+}
+
+int fesetround(int __round)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_fesetround(__softfp_round_to_vfp(__round));
+ __softfp_fesetround(__round);
+
+ return (0);
+}
+
+int fegetenv(fenv_t *__envp)
+{
+ fenv_t __vfp_envp;
+
+ __vfp_envp = 0;
+ if (_libc_arm_fpu_present)
+ __vfp_fegetenv(&__vfp_envp);
+ __softfp_fegetenv(__envp);
+ *__envp |= __vfp_envp;
+
+ return (0);
+}
+
+int feholdexcept(fenv_t *__envp)
+{
+ fenv_t __vfp_envp;
+
+ __vfp_envp = 0;
+ if (_libc_arm_fpu_present)
+ __vfp_feholdexcept(&__vfp_envp);
+ __softfp_feholdexcept(__envp);
+ *__envp |= __vfp_envp;
+
+ return (0);
+}
+
+int fesetenv(const fenv_t *__envp)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_fesetenv(__envp);
+ __softfp_fesetenv(__envp);
+
+ return (0);
+}
+
+int feupdateenv(const fenv_t *__envp)
+{
+
+ if (_libc_arm_fpu_present)
+ __vfp_feupdateenv(__envp);
+ __softfp_feupdateenv(__envp);
+
+ return (0);
+}
+
+int feenableexcept(int __mask)
+{
+ int __unmasked;
+
+ __unmasked = 0;
+ if (_libc_arm_fpu_present)
+ __unmasked = __vfp_feenableexcept(__mask);
+ __unmasked |= __softfp_feenableexcept(__mask);
+
+ return (__unmasked);
+}
+
+int fedisableexcept(int __mask)
+{
+ int __unmasked;
+
+ __unmasked = 0;
+ if (_libc_arm_fpu_present)
+ __unmasked = __vfp_fedisableexcept(__mask);
+ __unmasked |= __softfp_fedisableexcept(__mask);
+
+ return (__unmasked);
+}
+
+int fegetexcept(void)
+{
+ int __unmasked;
+
+ __unmasked = 0;
+ if (_libc_arm_fpu_present)
+ __unmasked = __vfp_fegetexcept();
+ __unmasked |= __softfp_fegetexcept();
+
+ return (__unmasked);
+}
+
+#endif
+
diff --git a/lib/msun/arm/fenv.h b/lib/msun/arm/fenv.h
index e245fb0..280532f 100644
--- a/lib/msun/arm/fenv.h
+++ b/lib/msun/arm/fenv.h
@@ -44,14 +44,32 @@ typedef __uint32_t fexcept_t;
#define FE_OVERFLOW 0x0004
#define FE_UNDERFLOW 0x0008
#define FE_INEXACT 0x0010
+#ifdef __ARM_PCS_VFP
+#define FE_DENORMAL 0x0080
+#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \
+ FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW | FE_DENORMAL)
+#else
#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \
FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW)
+#endif
/* Rounding modes */
+#define VFP_FE_TONEAREST 0x00000000
+#define VFP_FE_UPWARD 0x00400000
+#define VFP_FE_DOWNWARD 0x00800000
+#define VFP_FE_TOWARDZERO 0x00c00000
+
+#ifdef __ARM_PCS_VFP
+#define FE_TONEAREST VFP_FE_TONEAREST
+#define FE_UPWARD VFP_FE_UPWARD
+#define FE_DOWNWARD VFP_FE_DOWNWARD
+#define FE_TOWARDZERO VFP_FE_TOWARDZERO
+#else
#define FE_TONEAREST 0x0000
#define FE_TOWARDZERO 0x0001
#define FE_UPWARD 0x0002
#define FE_DOWNWARD 0x0003
+#endif
#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \
FE_UPWARD | FE_TOWARDZERO)
__BEGIN_DECLS
@@ -61,10 +79,12 @@ extern const fenv_t __fe_dfl_env;
#define FE_DFL_ENV (&__fe_dfl_env)
/* We need to be able to map status flag positions to mask flag positions */
-#define _FPUSW_SHIFT 16
+#ifndef __ARM_PCS_VFP
+#define _FPUSW_SHIFT 16
#define _ENABLE_MASK (FE_ALL_EXCEPT << _FPUSW_SHIFT)
+#endif
-#ifndef ARM_HARD_FLOAT
+#ifndef __ARM_PCS_VFP
int feclearexcept(int __excepts);
int fegetexceptflag(fexcept_t *__flagp, int __excepts);
@@ -77,20 +97,27 @@ int fegetenv(fenv_t *__envp);
int feholdexcept(fenv_t *__envp);
int fesetenv(const fenv_t *__envp);
int feupdateenv(const fenv_t *__envp);
+#if __BSD_VISIBLE
+int feenableexcept(int __mask);
+int fedisableexcept(int __mask);
+int fegetexcept(void);
+#endif
+
+#else /* __ARM_PCS_VFP */
-#else /* ARM_HARD_FLOAT */
+#define vmrs_fpscr(__r) __asm __volatile("vmrs %0, fpscr" : "=&r"(__r))
+#define vmsr_fpscr(__r) __asm __volatile("vmsr fpscr, %0" : : "r"(__r))
-#define __rfs(__fpsr) __asm __volatile("rfs %0" : "=r" (*(__fpsr)))
-#define __wfs(__fpsr) __asm __volatile("wfs %0" : : "r" (__fpsr))
+#define _FPU_MASK_SHIFT 8
__fenv_static inline int
feclearexcept(int __excepts)
{
fexcept_t __fpsr;
- __rfs(&__fpsr);
+ vmrs_fpscr(__fpsr);
__fpsr &= ~__excepts;
- __wfs(__fpsr);
+ vmsr_fpscr(__fpsr);
return (0);
}
@@ -99,7 +126,7 @@ fegetexceptflag(fexcept_t *__flagp, int __excepts)
{
fexcept_t __fpsr;
- __rfs(&__fpsr);
+ vmrs_fpscr(__fpsr);
*__flagp = __fpsr & __excepts;
return (0);
}
@@ -109,10 +136,10 @@ fesetexceptflag(const fexcept_t *__flagp, int __excepts)
{
fexcept_t __fpsr;
- __rfs(&__fpsr);
+ vmrs_fpscr(__fpsr);
__fpsr &= ~__excepts;
__fpsr |= *__flagp & __excepts;
- __wfs(__fpsr);
+ vmsr_fpscr(__fpsr);
return (0);
}
@@ -130,34 +157,36 @@ fetestexcept(int __excepts)
{
fexcept_t __fpsr;
- __rfs(&__fpsr);
+ vmrs_fpscr(__fpsr);
return (__fpsr & __excepts);
}
__fenv_static inline int
fegetround(void)
{
+ fenv_t __fpsr;
- /*
- * Apparently, the rounding mode is specified as part of the
- * instruction format on ARM, so the dynamic rounding mode is
- * indeterminate. Some FPUs may differ.
- */
- return (-1);
+ vmrs_fpscr(__fpsr);
+ return (__fpsr & _ROUND_MASK);
}
__fenv_static inline int
fesetround(int __round)
{
+ fenv_t __fpsr;
- return (-1);
+ vmrs_fpscr(__fpsr);
+ __fpsr &= ~(_ROUND_MASK);
+ __fpsr |= __round;
+ vmsr_fpscr(__fpsr);
+ return (0);
}
__fenv_static inline int
fegetenv(fenv_t *__envp)
{
- __rfs(__envp);
+ vmrs_fpscr(*__envp);
return (0);
}
@@ -166,10 +195,10 @@ feholdexcept(fenv_t *__envp)
{
fenv_t __env;
- __rfs(&__env);
+ vmrs_fpscr(__env);
*__envp = __env;
- __env &= ~(FE_ALL_EXCEPT | _ENABLE_MASK);
- __wfs(__env);
+ __env &= ~(FE_ALL_EXCEPT);
+ vmsr_fpscr(__env);
return (0);
}
@@ -177,7 +206,7 @@ __fenv_static inline int
fesetenv(const fenv_t *__envp)
{
- __wfs(*__envp);
+ vmsr_fpscr(*__envp);
return (0);
}
@@ -186,8 +215,8 @@ feupdateenv(const fenv_t *__envp)
{
fexcept_t __fpsr;
- __rfs(&__fpsr);
- __wfs(*__envp);
+ vmrs_fpscr(__fpsr);
+ vmsr_fpscr(*__envp);
feraiseexcept(__fpsr & FE_ALL_EXCEPT);
return (0);
}
@@ -196,40 +225,42 @@ feupdateenv(const fenv_t *__envp)
/* We currently provide no external definitions of the functions below. */
-static inline int
+__fenv_static inline int
feenableexcept(int __mask)
{
fenv_t __old_fpsr, __new_fpsr;
- __rfs(&__old_fpsr);
- __new_fpsr = __old_fpsr | (__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT;
- __wfs(__new_fpsr);
- return ((__old_fpsr >> _FPUSW_SHIFT) & FE_ALL_EXCEPT);
+ vmrs_fpscr(__old_fpsr);
+ __new_fpsr = __old_fpsr |
+ ((__mask & FE_ALL_EXCEPT) << _FPU_MASK_SHIFT);
+ vmsr_fpscr(__new_fpsr);
+ return ((__old_fpsr >> _FPU_MASK_SHIFT) & FE_ALL_EXCEPT);
}
-static inline int
+__fenv_static inline int
fedisableexcept(int __mask)
{
fenv_t __old_fpsr, __new_fpsr;
- __rfs(&__old_fpsr);
- __new_fpsr = __old_fpsr & ~((__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT);
- __wfs(__new_fpsr);
- return ((__old_fpsr >> _FPUSW_SHIFT) & FE_ALL_EXCEPT);
+ vmrs_fpscr(__old_fpsr);
+ __new_fpsr = __old_fpsr &
+ ~((__mask & FE_ALL_EXCEPT) << _FPU_MASK_SHIFT);
+ vmsr_fpscr(__new_fpsr);
+ return ((__old_fpsr >> _FPU_MASK_SHIFT) & FE_ALL_EXCEPT);
}
-static inline int
+__fenv_static inline int
fegetexcept(void)
{
fenv_t __fpsr;
- __rfs(&__fpsr);
- return ((__fpsr & _ENABLE_MASK) >> _FPUSW_SHIFT);
+ vmrs_fpscr(__fpsr);
+ return (__fpsr & FE_ALL_EXCEPT);
}
#endif /* __BSD_VISIBLE */
-#endif /* ARM_HARD_FLOAT */
+#endif /* __ARM_PCS_VFP */
__END_DECLS
diff --git a/lib/msun/ld128/k_expl.h b/lib/msun/ld128/k_expl.h
new file mode 100644
index 0000000..a5668fd
--- /dev/null
+++ b/lib/msun/ld128/k_expl.h
@@ -0,0 +1,328 @@
+/* from: FreeBSD: head/lib/msun/ld128/s_expl.c 251345 2013-06-03 20:09:22Z kargl */
+
+/*-
+ * Copyright (c) 2009-2013 Steven G. Kargl
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice unmodified, this list of conditions, and the following
+ * disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * Optimized by Bruce D. Evans.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_expl.h. See ../ld80/s_expl.c for most comments.
+ *
+ * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments
+ * about the secondary kernels.
+ */
+
+#define INTERVALS 128
+#define LOG2_INTERVALS 7
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const double
+/*
+ * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
+ * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
+ * bits zero so that multiplication of it by n is exact.
+ */
+INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
+L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
+static const long double
+/* 0x1.62e42fefa39ef35793c768000000p-8 */
+L1 = 5.41521234812457272982212595914567508e-3L;
+
+/*
+ * XXX values in hex in comments have been lost (or were never present)
+ * from here.
+ */
+static const long double
+/*
+ * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
+ * |exp(x) - p(x)| < 2**-124.9
+ * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
+ *
+ * XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits.
+ */
+A2 = 0.5,
+A3 = 1.66666666666666666666666666651085500e-1L,
+A4 = 4.16666666666666666666666666425885320e-2L,
+A5 = 8.33333333333333333334522877160175842e-3L,
+A6 = 1.38888888888888888889971139751596836e-3L;
+
+static const double
+A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */
+A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */
+A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */
+A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */
+
+static const struct {
+ /*
+ * hi must be rounded to at most 106 bits so that multiplication
+ * by r1 in expm1l() is exact, but it is rounded to 88 bits due to
+ * historical accidents.
+ *
+ * XXX it is wasteful to use long double for both hi and lo. ld128
+ * exp2l() uses only float for lo (in a very differently organized
+ * table; ld80 exp2l() is different again. It uses 2 doubles in a
+ * table organized like this one. 1 double and 1 float would
+ * suffice). There are different packing/locality/alignment/caching
+ * problems with these methods.
+ *
+ * XXX C's bad %a format makes the bits unreadable. They happen
+ * to all line up for the hi values 1 before the point and 88
+ * in 22 nybbles, but for the low values the nybbles are shifted
+ * randomly.
+ */
+ long double hi;
+ long double lo;
+} tbl[INTERVALS] = {
+ 0x1p0L, 0x0p0L,
+ 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
+ 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
+ 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L,
+ 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L,
+ 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L,
+ 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L,
+ 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L,
+ 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L,
+ 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L,
+ 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L,
+ 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L,
+ 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L,
+ 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L,
+ 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L,
+ 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L,
+ 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L,
+ 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L,
+ 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L,
+ 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L,
+ 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L,
+ 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L,
+ 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L,
+ 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L,
+ 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L,
+ 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L,
+ 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L,
+ 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L,
+ 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L,
+ 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L,
+ 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L,
+ 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L,
+ 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L,
+ 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L,
+ 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L,
+ 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L,
+ 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L,
+ 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L,
+ 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L,
+ 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L,
+ 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L,
+ 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L,
+ 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L,
+ 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L,
+ 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L,
+ 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L,
+ 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L,
+ 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L,
+ 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L,
+ 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L,
+ 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L,
+ 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L,
+ 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L,
+ 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L,
+ 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L,
+ 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L,
+ 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L,
+ 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L,
+ 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L,
+ 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L,
+ 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L,
+ 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L,
+ 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L,
+ 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L,
+ 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L,
+ 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L,
+ 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L,
+ 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L,
+ 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L,
+ 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L,
+ 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L,
+ 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L,
+ 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L,
+ 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L,
+ 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L,
+ 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L,
+ 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L,
+ 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L,
+ 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L,
+ 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L,
+ 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L,
+ 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L,
+ 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L,
+ 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L,
+ 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L,
+ 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L,
+ 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L,
+ 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L,
+ 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L,
+ 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L,
+ 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L,
+ 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L,
+ 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L,
+ 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L,
+ 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L,
+ 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L,
+ 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L,
+ 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L,
+ 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L,
+ 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L,
+ 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L,
+ 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L,
+ 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L,
+ 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L,
+ 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L,
+ 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L,
+ 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L,
+ 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L,
+ 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L,
+ 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L,
+ 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L,
+ 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L,
+ 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L,
+ 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L,
+ 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L,
+ 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L,
+ 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L,
+ 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L,
+ 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L,
+ 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L,
+ 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L,
+ 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L,
+ 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L,
+ 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
+ 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
+ 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
+ 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
+ 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
+};
+
+/*
+ * Kernel for expl(x). x must be finite and not tiny or huge.
+ * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN).
+ * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2).
+ */
+static inline void
+__k_expl(long double x, long double *hip, long double *lop, int *kp)
+{
+ long double q, r, r1, t;
+ double dr, fn, r2;
+ int n, n2;
+
+ /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ /* XXX assume no extra precision for the additions, as for trig fns. */
+ /* XXX this set of comments is now quadruplicated. */
+ /* XXX but see ../src/e_exp.c for a fix using double_t. */
+ fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52;
+#if defined(HAVE_EFFICIENT_IRINT)
+ n = irint(fn);
+#else
+ n = (int)fn;
+#endif
+ n2 = (unsigned)n % INTERVALS;
+ /* Depend on the sign bit being propagated: */
+ *kp = n >> LOG2_INTERVALS;
+ r1 = x - fn * L1;
+ r2 = fn * -L2;
+ r = r1 + r2;
+
+ /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
+ dr = r;
+ q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
+ dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
+ t = tbl[n2].lo + tbl[n2].hi;
+ *hip = tbl[n2].hi;
+ *lop = tbl[n2].lo + t * (q + r1);
+}
+
+/*
+ * XXX: the rest of the functions are identical for ld80 and ld128.
+ * However, we should use scalbnl() for ld128, since long double
+ * multiplication is very slow on the only supported ld128 arch (sparc64).
+ */
+
+static inline void
+k_hexpl(long double x, long double *hip, long double *lop)
+{
+ float twopkm1;
+ int k;
+
+ __k_expl(x, hip, lop, &k);
+ SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23));
+ *hip *= twopkm1;
+ *lop *= twopkm1;
+}
+
+static inline long double
+hexpl(long double x)
+{
+ long double hi, lo, twopkm2;
+ int k;
+
+ twopkm2 = 1;
+ __k_expl(x, &hi, &lo, &k);
+ SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2);
+ return (lo + hi) * 2 * twopkm2;
+}
+
+#ifdef _COMPLEX_H
+/*
+ * See ../src/k_exp.c for details.
+ */
+static inline long double complex
+__ldexp_cexpl(long double complex z, int expt)
+{
+ long double exp_x, hi, lo;
+ long double x, y, scale1, scale2;
+ int half_expt, k;
+
+ x = creall(z);
+ y = cimagl(z);
+ __k_expl(x, &hi, &lo, &k);
+
+ exp_x = (lo + hi) * 0x1p16382;
+ expt += k - 16382;
+
+ scale1 = 1;
+ half_expt = expt / 2;
+ SET_LDBL_EXPSIGN(scale1, BIAS + half_expt);
+ scale2 = 1;
+ SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt);
+
+ return (cpackl(cos(y) * exp_x * scale1 * scale2,
+ sinl(y) * exp_x * scale1 * scale2));
+}
+#endif /* _COMPLEX_H */
diff --git a/lib/msun/ld128/s_expl.c b/lib/msun/ld128/s_expl.c
index 176c932..a6a9676 100644
--- a/lib/msun/ld128/s_expl.c
+++ b/lib/msun/ld128/s_expl.c
@@ -38,16 +38,15 @@ __FBSDID("$FreeBSD$");
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
+#include "k_expl.h"
-#define INTERVALS 128
-#define LOG2_INTERVALS 7
-#define BIAS (LDBL_MAX_EXP - 1)
+/* XXX Prevent compilers from erroneously constant folding these: */
+static const volatile long double
+huge = 0x1p10000L,
+tiny = 0x1p-10000L;
static const long double
-huge = 0x1p10000L,
twom10000 = 0x1p-10000L;
-/* XXX Prevent gcc from erroneously constant folding this: */
-static volatile const long double tiny = 0x1p-10000L;
static const long double
/* log(2**16384 - 0.5) rounded towards zero: */
@@ -56,184 +55,16 @@ o_threshold = 11356.523406294143949491931077970763428L,
/* log(2**(-16381-64-1)) rounded towards zero: */
u_threshold = -11433.462743336297878837243843452621503L;
-static const double
-/*
- * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
- * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
- * bits zero so that multiplication of it by n is exact.
- */
-INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
-L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
-static const long double
-/* 0x1.62e42fefa39ef35793c768000000p-8 */
-L1 = 5.41521234812457272982212595914567508e-3L;
-
-static const long double
-/*
- * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
- * |exp(x) - p(x)| < 2**-124.9
- * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
- */
-A2 = 0.5,
-A3 = 1.66666666666666666666666666651085500e-1L,
-A4 = 4.16666666666666666666666666425885320e-2L,
-A5 = 8.33333333333333333334522877160175842e-3L,
-A6 = 1.38888888888888888889971139751596836e-3L;
-
-static const double
-A7 = 1.9841269841269471e-4,
-A8 = 2.4801587301585284e-5,
-A9 = 2.7557324277411234e-6,
-A10 = 2.7557333722375072e-7;
-
-static const struct {
- /*
- * hi must be rounded to at most 106 bits so that multiplication
- * by r1 in expm1l() is exact, but it is rounded to 88 bits due to
- * historical accidents.
- */
- long double hi;
- long double lo;
-} tbl[INTERVALS] = {
- 0x1p0L, 0x0p0L,
- 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
- 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
- 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L,
- 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L,
- 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L,
- 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L,
- 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L,
- 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L,
- 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L,
- 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L,
- 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L,
- 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L,
- 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L,
- 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L,
- 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L,
- 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L,
- 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L,
- 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L,
- 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L,
- 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L,
- 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L,
- 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L,
- 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L,
- 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L,
- 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L,
- 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L,
- 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L,
- 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L,
- 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L,
- 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L,
- 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L,
- 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L,
- 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L,
- 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L,
- 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L,
- 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L,
- 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L,
- 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L,
- 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L,
- 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L,
- 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L,
- 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L,
- 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L,
- 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L,
- 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L,
- 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L,
- 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L,
- 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L,
- 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L,
- 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L,
- 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L,
- 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L,
- 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L,
- 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L,
- 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L,
- 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L,
- 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L,
- 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L,
- 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L,
- 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L,
- 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L,
- 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L,
- 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L,
- 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L,
- 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L,
- 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L,
- 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L,
- 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L,
- 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L,
- 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L,
- 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L,
- 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L,
- 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L,
- 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L,
- 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L,
- 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L,
- 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L,
- 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L,
- 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L,
- 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L,
- 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L,
- 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L,
- 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L,
- 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L,
- 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L,
- 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L,
- 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L,
- 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L,
- 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L,
- 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L,
- 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L,
- 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L,
- 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L,
- 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L,
- 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L,
- 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L,
- 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L,
- 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L,
- 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L,
- 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L,
- 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L,
- 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L,
- 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L,
- 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L,
- 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L,
- 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L,
- 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L,
- 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L,
- 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L,
- 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L,
- 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L,
- 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L,
- 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L,
- 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L,
- 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L,
- 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L,
- 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L,
- 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L,
- 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L,
- 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L,
- 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L,
- 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L,
- 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
- 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
- 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
- 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
- 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
-};
-
long double
expl(long double x)
{
- union IEEEl2bits u, v;
- long double q, r, r1, t, twopk, twopkp10000;
- double dr, fn, r2;
- int k, n, n2;
+ union IEEEl2bits u;
+ long double hi, lo, t, twopk;
+ int k;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -241,60 +72,33 @@ expl(long double x)
if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
- return (-1 / x);
- return (x + x); /* x is +Inf or +NaN */
+ RETURNP(-1 / x);
+ RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
if (x < u_threshold)
- return (tiny * tiny);
+ RETURNP(tiny * tiny);
} else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */
- return (1 + x); /* 1 with inexact iff x != 0 */
+ RETURN2P(1, x); /* 1 with inexact iff x != 0 */
}
ENTERI();
- /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
- /* Use a specialized rint() to get fn. Assume round-to-nearest. */
- /* XXX assume no extra precision for the additions, as for trig fns. */
- /* XXX this set of comments is now quadruplicated. */
- fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52;
-#if defined(HAVE_EFFICIENT_IRINT)
- n = irint(fn);
-#else
- n = (int)fn;
-#endif
- n2 = (unsigned)n % INTERVALS;
- k = n >> LOG2_INTERVALS;
- r1 = x - fn * L1;
- r2 = fn * -L2;
- r = r1 + r2;
-
- /* Prepare scale factors. */
- /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */
- v.e = 1;
- if (k >= LDBL_MIN_EXP) {
- v.xbits.expsign = BIAS + k;
- twopk = v.e;
- } else {
- v.xbits.expsign = BIAS + k + 10000;
- twopkp10000 = v.e;
- }
-
- /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
- dr = r;
- q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
- dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
- t = tbl[n2].lo + tbl[n2].hi;
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ twopk = 1;
+ __k_expl(x, &hi, &lo, &k);
+ t = SUM2P(hi, lo);
/* Scale by 2**k. */
+ /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */
if (k >= LDBL_MIN_EXP) {
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k);
RETURNI(t * twopk);
} else {
- RETURNI(t * twopkp10000 * twom10000);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000);
+ RETURNI(t * twopk * twom10000);
}
}
@@ -312,6 +116,12 @@ expl(long double x)
* Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear
* in both subintervals, so set T3 = 2**-5, which places the condition
* into the [T1, T3] interval.
+ *
+ * XXX we now do this more to (partially) balance the number of terms
+ * in the C and D polys than to avoid checking the condition in both
+ * intervals.
+ *
+ * XXX these micro-optimizations are excessive.
*/
static const double
T1 = -0.1659, /* ~-30.625/128 * log(2) */
@@ -321,6 +131,12 @@ T3 = 0.03125;
/*
* Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03
+ *
+ * XXX none of the long double C or D coeffs except C10 is correctly printed.
+ * If you re-print their values in %.35Le format, the result is always
+ * different. For example, the last 2 digits in C3 should be 59, not 67.
+ * 67 is apparently from rounding an extra-precision value to 36 decimal
+ * places.
*/
static const long double
C3 = 1.66666666666666666666666666666666667e-1L,
@@ -335,6 +151,13 @@ C11 = 2.50521083854417203619031960151253944e-8L,
C12 = 2.08767569878679576457272282566520649e-9L,
C13 = 1.60590438367252471783548748824255707e-10L;
+/*
+ * XXX this has 1 more coeff than needed.
+ * XXX can start the double coeffs but not the double mults at C10.
+ * With my coeffs (C10-C17 double; s = best_s):
+ * Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]:
+ * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
+ */
static const double
C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */
C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */
@@ -359,6 +182,13 @@ D11 = 2.50521083855084570046480450935267433e-8L,
D12 = 2.08767569819738524488686318024854942e-9L,
D13 = 1.60590442297008495301927448122499313e-10L;
+/*
+ * XXX this has 1 more coeff than needed.
+ * XXX can start the double coeffs but not the double mults at D11.
+ * With my coeffs (D11-D16 double):
+ * Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]:
+ * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
+ */
static const double
D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */
D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */
@@ -375,6 +205,8 @@ expm1l(long double x)
int k, n, n2;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -382,11 +214,11 @@ expm1l(long double x)
if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
- return (-1 / x - 1);
- return (x + x); /* x is +Inf or +NaN */
+ RETURNP(-1 / x - 1);
+ RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
/*
* expm1l() never underflows, but it must avoid
* unrepresentable large negative exponents. We used a
@@ -395,7 +227,7 @@ expm1l(long double x)
* in the same way as large ones here.
*/
if (hx & 0x8000) /* x <= -128 */
- return (tiny - 1); /* good for x < -114ln2 - eps */
+ RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */
}
ENTERI();
@@ -407,7 +239,7 @@ expm1l(long double x)
if (x < T3) {
if (ix < BIAS - 113) { /* |x| < 0x1p-113 */
/* x (rounded) with inexact if x != 0: */
- RETURNI(x == 0 ? x :
+ RETURNPI(x == 0 ? x :
(0x1p200 * x + fabsl(x)) * 0x1p-200);
}
q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 +
@@ -428,9 +260,9 @@ expm1l(long double x)
hx2_hi = x_hi * x_hi / 2;
hx2_lo = x_lo * (x + x_hi) / 2;
if (ix >= BIAS - 7)
- RETURNI(hx2_lo + x_lo + q + (hx2_hi + x_hi));
+ RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q);
else
- RETURNI(hx2_lo + q + hx2_hi + x);
+ RETURN2PI(x, hx2_lo + q + hx2_hi);
}
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
@@ -463,21 +295,21 @@ expm1l(long double x)
t = tbl[n2].lo + tbl[n2].hi;
if (k == 0) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 1);
+ t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t);
}
if (k == -1) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 2);
+ t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t / 2);
}
if (k < -7) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk - 1);
}
if (k > 2 * LDBL_MANT_DIG - 1) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L - 1);
RETURNI(t * twopk - 1);
@@ -487,8 +319,8 @@ expm1l(long double x)
twomk = v.e;
if (k > LDBL_MANT_DIG - 1)
- t = tbl[n2].lo - twomk + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1));
else
- t = tbl[n2].lo + t * (q + r1) + (tbl[n2].hi - twomk);
+ t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk);
}
diff --git a/lib/msun/ld80/k_expl.h b/lib/msun/ld80/k_expl.h
new file mode 100644
index 0000000..ebfb9a8
--- /dev/null
+++ b/lib/msun/ld80/k_expl.h
@@ -0,0 +1,305 @@
+/* from: FreeBSD: head/lib/msun/ld80/s_expl.c 251343 2013-06-03 19:51:32Z kargl */
+
+/*-
+ * Copyright (c) 2009-2013 Steven G. Kargl
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice unmodified, this list of conditions, and the following
+ * disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * Optimized by Bruce D. Evans.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See s_expl.c for more comments about __k_expl().
+ *
+ * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments
+ * about the secondary kernels.
+ */
+
+#define INTERVALS 128
+#define LOG2_INTERVALS 7
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const double
+/*
+ * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
+ * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
+ * bits zero so that multiplication of it by n is exact.
+ */
+INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
+L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */
+L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */
+/*
+ * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]:
+ * |exp(x) - p(x)| < 2**-77.2
+ * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
+ */
+A2 = 0.5,
+A3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
+A4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */
+A5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
+A6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
+
+/*
+ * 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where
+ * the first 53 bits of the significand are stored in hi and the next 53
+ * bits are in lo. Tang's paper states that the trailing 6 bits of hi must
+ * be zero for his algorithm in both single and double precision, because
+ * the table is re-used in the implementation of expm1() where a floating
+ * point addition involving hi must be exact. Here hi is double, so
+ * converting it to long double gives 11 trailing zero bits.
+ */
+static const struct {
+ double hi;
+ double lo;
+} tbl[INTERVALS] = {
+ 0x1p+0, 0x0p+0,
+ /*
+ * XXX hi is rounded down, and the formatting is not quite normal.
+ * But I rather like both. The 0x1.*p format is good for 4N+1
+ * mantissa bits. Rounding down makes the lo terms positive,
+ * so that the columnar formatting can be simpler.
+ */
+ 0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54,
+ 0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53,
+ 0x1.04315e86e7f84p+0, 0x1.7ae71f3441b49p-53,
+ 0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55,
+ 0x1.0706b29ddf6ddp+0, 0x1.8db880753b0f6p-53,
+ 0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57,
+ 0x1.09e3ecac6f383p+0, 0x1.1487818316136p-54,
+ 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54,
+ 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f71p-54,
+ 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b53p-59,
+ 0x1.0fb66affed31ap+0, 0x1.e464123bb1428p-53,
+ 0x1.11301d0125b50p+0, 0x1.49d77e35db263p-53,
+ 0x1.12abdc06c31cbp+0, 0x1.f72575a649ad2p-53,
+ 0x1.1429aaea92ddfp+0, 0x1.66820328764b1p-53,
+ 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeab0ap-55,
+ 0x1.172b83c7d517ap+0, 0x1.b9bef918a1d63p-53,
+ 0x1.18af9388c8de9p+0, 0x1.777ee1734784ap-53,
+ 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55,
+ 0x1.1bbe084045cd3p+0, 0x1.3563ce56884fcp-53,
+ 0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54,
+ 0x1.1ed5022fcd91cp+0, 0x1.71033fec2243ap-53,
+ 0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55,
+ 0x1.21f49917ddc96p+0, 0x1.2a97e9494a5eep-55,
+ 0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54,
+ 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f4a4p-55,
+ 0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55,
+ 0x1.284dfe1f56380p+0, 0x1.2d9e2b9e07941p-53,
+ 0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55,
+ 0x1.2b87fd0dad98fp+0, 0x1.fbbd48ca71f95p-53,
+ 0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54,
+ 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d52383p-56,
+ 0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55,
+ 0x1.32170fc4cd831p+0, 0x1.a9ce78e18047cp-55,
+ 0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54,
+ 0x1.356c55f929ff0p+0, 0x1.928c468ec6e76p-53,
+ 0x1.371a7373aa9cap+0, 0x1.4e28aa05e8a8fp-53,
+ 0x1.38cae6d05d865p+0, 0x1.0b53961b37da2p-53,
+ 0x1.3a7db34e59ff6p+0, 0x1.d43792533c144p-53,
+ 0x1.3c32dc313a8e4p+0, 0x1.08003e4516b1ep-53,
+ 0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55,
+ 0x1.3fa4504ac801bp+0, 0x1.417ee03548306p-53,
+ 0x1.4160a21f72e29p+0, 0x1.f0864b71e7b6cp-53,
+ 0x1.431f5d950a896p+0, 0x1.b8e088728219ap-53,
+ 0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59,
+ 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a76p-54,
+ 0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56,
+ 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be56p-54,
+ 0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56,
+ 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a7833p-54,
+ 0x1.4f9b2769d2ca6p+0, 0x1.5a67b16d3540ep-53,
+ 0x1.516daa2cf6641p+0, 0x1.8225ea5909b04p-53,
+ 0x1.5342b569d4f81p+0, 0x1.be1507893b0d5p-53,
+ 0x1.551a4ca5d920ep+0, 0x1.8a5d8c4048699p-53,
+ 0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54,
+ 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1de8p-55,
+ 0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54,
+ 0x1.5c9268a5946b7p+0, 0x1.c4b1b816986a2p-60,
+ 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54,
+ 0x1.605e1b976dc08p+0, 0x1.60edeb25490dcp-53,
+ 0x1.6247eb03a5584p+0, 0x1.63e1f40dfa5b5p-53,
+ 0x1.6434634ccc31fp+0, 0x1.8edf0e2989db3p-53,
+ 0x1.6623882552224p+0, 0x1.224fb3c5371e6p-53,
+ 0x1.68155d44ca973p+0, 0x1.038ae44f73e65p-57,
+ 0x1.6a09e667f3bccp+0, 0x1.21165f626cdd5p-53,
+ 0x1.6c012750bdabep+0, 0x1.daed533001e9ep-53,
+ 0x1.6dfb23c651a2ep+0, 0x1.e441c597c3775p-53,
+ 0x1.6ff7df9519483p+0, 0x1.9f0fc369e7c42p-53,
+ 0x1.71f75e8ec5f73p+0, 0x1.ba46e1e5de15ap-53,
+ 0x1.73f9a48a58173p+0, 0x1.7ab9349cd1562p-53,
+ 0x1.75feb564267c8p+0, 0x1.7edd354674916p-53,
+ 0x1.780694fde5d3fp+0, 0x1.866b80a02162dp-54,
+ 0x1.7a11473eb0186p+0, 0x1.afaa2047ed9b4p-53,
+ 0x1.7c1ed0130c132p+0, 0x1.f124cd1164dd6p-54,
+ 0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56,
+ 0x1.80427543e1a11p+0, 0x1.6c1bccec9346bp-53,
+ 0x1.82589994cce12p+0, 0x1.159f115f56694p-53,
+ 0x1.8471a4623c7acp+0, 0x1.9ca5ed72f8c81p-53,
+ 0x1.868d99b4492ecp+0, 0x1.01c83b21584a3p-53,
+ 0x1.88ac7d98a6699p+0, 0x1.994c2f37cb53ap-54,
+ 0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54,
+ 0x1.8cf3216b5448bp+0, 0x1.de55439a2c38bp-53,
+ 0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55,
+ 0x1.9145b0b91ffc5p+0, 0x1.114c368d3ed6ep-53,
+ 0x1.93737b0cdc5e4p+0, 0x1.e8a0387e4a814p-53,
+ 0x1.95a44cbc8520ep+0, 0x1.d36906d2b41f9p-53,
+ 0x1.97d829fde4e4fp+0, 0x1.173d241f23d18p-53,
+ 0x1.9a0f170ca07b9p+0, 0x1.7462137188ce7p-53,
+ 0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56,
+ 0x1.9e86319e32323p+0, 0x1.824ca78e64c6ep-56,
+ 0x1.a0c667b5de564p+0, 0x1.6535b51719567p-53,
+ 0x1.a309bec4a2d33p+0, 0x1.6305c7ddc36abp-54,
+ 0x1.a5503b23e255cp+0, 0x1.1684892395f0fp-53,
+ 0x1.a799e1330b358p+0, 0x1.bcb7ecac563c7p-54,
+ 0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54,
+ 0x1.ac36bbfd3f379p+0, 0x1.81b72cd4624ccp-53,
+ 0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54,
+ 0x1.b0e07298db665p+0, 0x1.2108559bf8deep-53,
+ 0x1.b33a2b84f15fap+0, 0x1.ed7fa1cf7b290p-53,
+ 0x1.b59728de55939p+0, 0x1.1c7102222c90ep-53,
+ 0x1.b7f76f2fb5e46p+0, 0x1.d54f610356a79p-53,
+ 0x1.ba5b030a10649p+0, 0x1.0819678d5eb69p-53,
+ 0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55,
+ 0x1.bf2c25bd71e08p+0, 0x1.0811ae04a31c7p-53,
+ 0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55,
+ 0x1.c40ab5fffd07ap+0, 0x1.b4537e083c60ap-54,
+ 0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54,
+ 0x1.c8f6d9406e7b5p+0, 0x1.1acbc48805c44p-56,
+ 0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56,
+ 0x1.cdf0b555dc3f9p+0, 0x1.889f12b1f58a3p-53,
+ 0x1.d072d4a07897bp+0, 0x1.1a1e45e4342b2p-53,
+ 0x1.d2f87080d89f1p+0, 0x1.15bc247313d44p-53,
+ 0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55,
+ 0x1.d80e316c98397p+0, 0x1.7709f3a09100cp-53,
+ 0x1.da9e603db3285p+0, 0x1.c2300696db532p-54,
+ 0x1.dd321f301b460p+0, 0x1.2da5778f018c3p-54,
+ 0x1.dfc97337b9b5ep+0, 0x1.72d195873da52p-53,
+ 0x1.e264614f5a128p+0, 0x1.424ec3f42f5b5p-53,
+ 0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55,
+ 0x1.e7a51fbc74c83p+0, 0x1.2d522ca0c8de2p-54,
+ 0x1.ea4afa2a490d9p+0, 0x1.0b1ee7431ebb6p-53,
+ 0x1.ecf482d8e67f0p+0, 0x1.1b60625f7293ap-53,
+ 0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54,
+ 0x1.f252b376bba97p+0, 0x1.3a1a5bf0d8e43p-54,
+ 0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54,
+ 0x1.f7bfdad9cbe13p+0, 0x1.1227697fce57bp-53,
+ 0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55,
+ 0x1.fd3c22b8f71f1p+0, 0x1.2eb74966579e7p-57
+};
+
+/*
+ * Kernel for expl(x). x must be finite and not tiny or huge.
+ * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN).
+ * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2).
+ */
+static inline void
+__k_expl(long double x, long double *hip, long double *lop, int *kp)
+{
+ long double fn, q, r, r1, r2, t, z;
+ int n, n2;
+
+ /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ fn = x * INV_L + 0x1.8p63 - 0x1.8p63;
+ r = x - fn * L1 - fn * L2; /* r = r1 + r2 done independently. */
+#if defined(HAVE_EFFICIENT_IRINTL)
+ n = irintl(fn);
+#elif defined(HAVE_EFFICIENT_IRINT)
+ n = irint(fn);
+#else
+ n = (int)fn;
+#endif
+ n2 = (unsigned)n % INTERVALS;
+ /* Depend on the sign bit being propagated: */
+ *kp = n >> LOG2_INTERVALS;
+ r1 = x - fn * L1;
+ r2 = fn * -L2;
+
+ /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
+ z = r * r;
+#if 0
+ q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6;
+#else
+ q = r2 + z * A2 + z * r * (A3 + r * A4 + z * (A5 + r * A6));
+#endif
+ t = (long double)tbl[n2].lo + tbl[n2].hi;
+ *hip = tbl[n2].hi;
+ *lop = tbl[n2].lo + t * (q + r1);
+}
+
+static inline void
+k_hexpl(long double x, long double *hip, long double *lop)
+{
+ float twopkm1;
+ int k;
+
+ __k_expl(x, hip, lop, &k);
+ SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23));
+ *hip *= twopkm1;
+ *lop *= twopkm1;
+}
+
+static inline long double
+hexpl(long double x)
+{
+ long double hi, lo, twopkm2;
+ int k;
+
+ twopkm2 = 1;
+ __k_expl(x, &hi, &lo, &k);
+ SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2);
+ return (lo + hi) * 2 * twopkm2;
+}
+
+#ifdef _COMPLEX_H
+/*
+ * See ../src/k_exp.c for details.
+ */
+static inline long double complex
+__ldexp_cexpl(long double complex z, int expt)
+{
+ long double exp_x, hi, lo;
+ long double x, y, scale1, scale2;
+ int half_expt, k;
+
+ x = creall(z);
+ y = cimagl(z);
+ __k_expl(x, &hi, &lo, &k);
+
+ exp_x = (lo + hi) * 0x1p16382;
+ expt += k - 16382;
+
+ scale1 = 1;
+ half_expt = expt / 2;
+ SET_LDBL_EXPSIGN(scale1, BIAS + half_expt);
+ scale2 = 1;
+ SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt);
+
+ return (cpackl(cos(y) * exp_x * scale1 * scale2,
+ sinl(y) * exp_x * scale1 * scale2));
+}
+#endif /* _COMPLEX_H */
diff --git a/lib/msun/ld80/s_expl.c b/lib/msun/ld80/s_expl.c
index ec748d3..3147d35 100644
--- a/lib/msun/ld80/s_expl.c
+++ b/lib/msun/ld80/s_expl.c
@@ -48,16 +48,15 @@ __FBSDID("$FreeBSD$");
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
+#include "k_expl.h"
-#define INTERVALS 128
-#define LOG2_INTERVALS 7
-#define BIAS (LDBL_MAX_EXP - 1)
+/* XXX Prevent compilers from erroneously constant folding these: */
+static const volatile long double
+huge = 0x1p10000L,
+tiny = 0x1p-10000L;
static const long double
-huge = 0x1p10000L,
twom10000 = 0x1p-10000L;
-/* XXX Prevent gcc from erroneously constant folding this: */
-static volatile const long double tiny = 0x1p-10000L;
static const union IEEEl2bits
/* log(2**16384 - 0.5) rounded towards zero: */
@@ -68,178 +67,16 @@ o_thresholdu = LD80C(0xb17217f7d1cf79ab, 13, 11356.5234062941439488L),
u_thresholdu = LD80C(0xb21dfe7f09e2baa9, 13, -11399.4985314888605581L);
#define u_threshold (u_thresholdu.e)
-static const double
-/*
- * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
- * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
- * bits zero so that multiplication of it by n is exact.
- */
-INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
-L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */
-L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */
-/*
- * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]:
- * |exp(x) - p(x)| < 2**-77.2
- * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
- */
-A2 = 0.5,
-A3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
-A4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */
-A5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
-A6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
-
-/*
- * 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where
- * the first 53 bits of the significand are stored in hi and the next 53
- * bits are in lo. Tang's paper states that the trailing 6 bits of hi must
- * be zero for his algorithm in both single and double precision, because
- * the table is re-used in the implementation of expm1() where a floating
- * point addition involving hi must be exact. Here hi is double, so
- * converting it to long double gives 11 trailing zero bits.
- */
-static const struct {
- double hi;
- double lo;
-} tbl[INTERVALS] = {
- 0x1p+0, 0x0p+0,
- 0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54,
- 0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53,
- 0x1.04315e86e7f84p+0, 0x1.7ae71f3441b49p-53,
- 0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55,
- 0x1.0706b29ddf6ddp+0, 0x1.8db880753b0f6p-53,
- 0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57,
- 0x1.09e3ecac6f383p+0, 0x1.1487818316136p-54,
- 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54,
- 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f71p-54,
- 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b53p-59,
- 0x1.0fb66affed31ap+0, 0x1.e464123bb1428p-53,
- 0x1.11301d0125b50p+0, 0x1.49d77e35db263p-53,
- 0x1.12abdc06c31cbp+0, 0x1.f72575a649ad2p-53,
- 0x1.1429aaea92ddfp+0, 0x1.66820328764b1p-53,
- 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeab0ap-55,
- 0x1.172b83c7d517ap+0, 0x1.b9bef918a1d63p-53,
- 0x1.18af9388c8de9p+0, 0x1.777ee1734784ap-53,
- 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55,
- 0x1.1bbe084045cd3p+0, 0x1.3563ce56884fcp-53,
- 0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54,
- 0x1.1ed5022fcd91cp+0, 0x1.71033fec2243ap-53,
- 0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55,
- 0x1.21f49917ddc96p+0, 0x1.2a97e9494a5eep-55,
- 0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54,
- 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f4a4p-55,
- 0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55,
- 0x1.284dfe1f56380p+0, 0x1.2d9e2b9e07941p-53,
- 0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55,
- 0x1.2b87fd0dad98fp+0, 0x1.fbbd48ca71f95p-53,
- 0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54,
- 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d52383p-56,
- 0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55,
- 0x1.32170fc4cd831p+0, 0x1.a9ce78e18047cp-55,
- 0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54,
- 0x1.356c55f929ff0p+0, 0x1.928c468ec6e76p-53,
- 0x1.371a7373aa9cap+0, 0x1.4e28aa05e8a8fp-53,
- 0x1.38cae6d05d865p+0, 0x1.0b53961b37da2p-53,
- 0x1.3a7db34e59ff6p+0, 0x1.d43792533c144p-53,
- 0x1.3c32dc313a8e4p+0, 0x1.08003e4516b1ep-53,
- 0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55,
- 0x1.3fa4504ac801bp+0, 0x1.417ee03548306p-53,
- 0x1.4160a21f72e29p+0, 0x1.f0864b71e7b6cp-53,
- 0x1.431f5d950a896p+0, 0x1.b8e088728219ap-53,
- 0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59,
- 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a76p-54,
- 0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56,
- 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be56p-54,
- 0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56,
- 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a7833p-54,
- 0x1.4f9b2769d2ca6p+0, 0x1.5a67b16d3540ep-53,
- 0x1.516daa2cf6641p+0, 0x1.8225ea5909b04p-53,
- 0x1.5342b569d4f81p+0, 0x1.be1507893b0d5p-53,
- 0x1.551a4ca5d920ep+0, 0x1.8a5d8c4048699p-53,
- 0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54,
- 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1de8p-55,
- 0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54,
- 0x1.5c9268a5946b7p+0, 0x1.c4b1b816986a2p-60,
- 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54,
- 0x1.605e1b976dc08p+0, 0x1.60edeb25490dcp-53,
- 0x1.6247eb03a5584p+0, 0x1.63e1f40dfa5b5p-53,
- 0x1.6434634ccc31fp+0, 0x1.8edf0e2989db3p-53,
- 0x1.6623882552224p+0, 0x1.224fb3c5371e6p-53,
- 0x1.68155d44ca973p+0, 0x1.038ae44f73e65p-57,
- 0x1.6a09e667f3bccp+0, 0x1.21165f626cdd5p-53,
- 0x1.6c012750bdabep+0, 0x1.daed533001e9ep-53,
- 0x1.6dfb23c651a2ep+0, 0x1.e441c597c3775p-53,
- 0x1.6ff7df9519483p+0, 0x1.9f0fc369e7c42p-53,
- 0x1.71f75e8ec5f73p+0, 0x1.ba46e1e5de15ap-53,
- 0x1.73f9a48a58173p+0, 0x1.7ab9349cd1562p-53,
- 0x1.75feb564267c8p+0, 0x1.7edd354674916p-53,
- 0x1.780694fde5d3fp+0, 0x1.866b80a02162dp-54,
- 0x1.7a11473eb0186p+0, 0x1.afaa2047ed9b4p-53,
- 0x1.7c1ed0130c132p+0, 0x1.f124cd1164dd6p-54,
- 0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56,
- 0x1.80427543e1a11p+0, 0x1.6c1bccec9346bp-53,
- 0x1.82589994cce12p+0, 0x1.159f115f56694p-53,
- 0x1.8471a4623c7acp+0, 0x1.9ca5ed72f8c81p-53,
- 0x1.868d99b4492ecp+0, 0x1.01c83b21584a3p-53,
- 0x1.88ac7d98a6699p+0, 0x1.994c2f37cb53ap-54,
- 0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54,
- 0x1.8cf3216b5448bp+0, 0x1.de55439a2c38bp-53,
- 0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55,
- 0x1.9145b0b91ffc5p+0, 0x1.114c368d3ed6ep-53,
- 0x1.93737b0cdc5e4p+0, 0x1.e8a0387e4a814p-53,
- 0x1.95a44cbc8520ep+0, 0x1.d36906d2b41f9p-53,
- 0x1.97d829fde4e4fp+0, 0x1.173d241f23d18p-53,
- 0x1.9a0f170ca07b9p+0, 0x1.7462137188ce7p-53,
- 0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56,
- 0x1.9e86319e32323p+0, 0x1.824ca78e64c6ep-56,
- 0x1.a0c667b5de564p+0, 0x1.6535b51719567p-53,
- 0x1.a309bec4a2d33p+0, 0x1.6305c7ddc36abp-54,
- 0x1.a5503b23e255cp+0, 0x1.1684892395f0fp-53,
- 0x1.a799e1330b358p+0, 0x1.bcb7ecac563c7p-54,
- 0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54,
- 0x1.ac36bbfd3f379p+0, 0x1.81b72cd4624ccp-53,
- 0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54,
- 0x1.b0e07298db665p+0, 0x1.2108559bf8deep-53,
- 0x1.b33a2b84f15fap+0, 0x1.ed7fa1cf7b290p-53,
- 0x1.b59728de55939p+0, 0x1.1c7102222c90ep-53,
- 0x1.b7f76f2fb5e46p+0, 0x1.d54f610356a79p-53,
- 0x1.ba5b030a10649p+0, 0x1.0819678d5eb69p-53,
- 0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55,
- 0x1.bf2c25bd71e08p+0, 0x1.0811ae04a31c7p-53,
- 0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55,
- 0x1.c40ab5fffd07ap+0, 0x1.b4537e083c60ap-54,
- 0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54,
- 0x1.c8f6d9406e7b5p+0, 0x1.1acbc48805c44p-56,
- 0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56,
- 0x1.cdf0b555dc3f9p+0, 0x1.889f12b1f58a3p-53,
- 0x1.d072d4a07897bp+0, 0x1.1a1e45e4342b2p-53,
- 0x1.d2f87080d89f1p+0, 0x1.15bc247313d44p-53,
- 0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55,
- 0x1.d80e316c98397p+0, 0x1.7709f3a09100cp-53,
- 0x1.da9e603db3285p+0, 0x1.c2300696db532p-54,
- 0x1.dd321f301b460p+0, 0x1.2da5778f018c3p-54,
- 0x1.dfc97337b9b5ep+0, 0x1.72d195873da52p-53,
- 0x1.e264614f5a128p+0, 0x1.424ec3f42f5b5p-53,
- 0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55,
- 0x1.e7a51fbc74c83p+0, 0x1.2d522ca0c8de2p-54,
- 0x1.ea4afa2a490d9p+0, 0x1.0b1ee7431ebb6p-53,
- 0x1.ecf482d8e67f0p+0, 0x1.1b60625f7293ap-53,
- 0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54,
- 0x1.f252b376bba97p+0, 0x1.3a1a5bf0d8e43p-54,
- 0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54,
- 0x1.f7bfdad9cbe13p+0, 0x1.1227697fce57bp-53,
- 0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55,
- 0x1.fd3c22b8f71f1p+0, 0x1.2eb74966579e7p-57
-};
-
long double
expl(long double x)
{
- union IEEEl2bits u, v;
- long double fn, q, r, r1, r2, t, twopk, twopkp10000;
- long double z;
- int k, n, n2;
+ union IEEEl2bits u;
+ long double hi, lo, t, twopk;
+ int k;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -247,59 +84,32 @@ expl(long double x)
if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf, -NaN or unsupported */
- return (-1 / x);
- return (x + x); /* x is +Inf, +NaN or unsupported */
+ RETURNP(-1 / x);
+ RETURNP(x + x); /* x is +Inf, +NaN or unsupported */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
if (x < u_threshold)
- return (tiny * tiny);
- } else if (ix < BIAS - 65) { /* |x| < 0x1p-65 (includes pseudos) */
- return (1 + x); /* 1 with inexact iff x != 0 */
+ RETURNP(tiny * tiny);
+ } else if (ix < BIAS - 75) { /* |x| < 0x1p-75 (includes pseudos) */
+ RETURN2P(1, x); /* 1 with inexact iff x != 0 */
}
ENTERI();
- /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
- /* Use a specialized rint() to get fn. Assume round-to-nearest. */
- fn = x * INV_L + 0x1.8p63 - 0x1.8p63;
- r = x - fn * L1 - fn * L2; /* r = r1 + r2 done independently. */
-#if defined(HAVE_EFFICIENT_IRINTL)
- n = irintl(fn);
-#elif defined(HAVE_EFFICIENT_IRINT)
- n = irint(fn);
-#else
- n = (int)fn;
-#endif
- n2 = (unsigned)n % INTERVALS;
- /* Depend on the sign bit being propagated: */
- k = n >> LOG2_INTERVALS;
- r1 = x - fn * L1;
- r2 = fn * -L2;
-
- /* Prepare scale factors. */
- v.e = 1;
- if (k >= LDBL_MIN_EXP) {
- v.xbits.expsign = BIAS + k;
- twopk = v.e;
- } else {
- v.xbits.expsign = BIAS + k + 10000;
- twopkp10000 = v.e;
- }
-
- /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
- z = r * r;
- q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6;
- t = (long double)tbl[n2].lo + tbl[n2].hi;
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ twopk = 1;
+ __k_expl(x, &hi, &lo, &k);
+ t = SUM2P(hi, lo);
/* Scale by 2**k. */
if (k >= LDBL_MIN_EXP) {
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k);
RETURNI(t * twopk);
} else {
- RETURNI(t * twopkp10000 * twom10000);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000);
+ RETURNI(t * twopk * twom10000);
}
}
@@ -326,8 +136,11 @@ T1 = -0.1659, /* ~-30.625/128 * log(2) */
T2 = 0.1659; /* ~30.625/128 * log(2) */
/*
- * Domain [-0.1659, 0.1659], range ~[-1.2027e-22, 3.4417e-22]:
- * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-71.2
+ * Domain [-0.1659, 0.1659], range ~[-2.6155e-22, 2.5507e-23]:
+ * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-71.6
+ *
+ * XXX the coeffs aren't very carefully rounded, and I get 2.8 more bits,
+ * but unlike for ld128 we can't drop any terms.
*/
static const union IEEEl2bits
B3 = LD80C(0xaaaaaaaaaaaaaaab, -3, 1.66666666666666666671e-1L),
@@ -353,6 +166,8 @@ expm1l(long double x)
int k, n, n2;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -360,11 +175,11 @@ expm1l(long double x)
if (ix >= BIAS + 6) { /* |x| >= 64 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf, -NaN or unsupported */
- return (-1 / x - 1);
- return (x + x); /* x is +Inf, +NaN or unsupported */
+ RETURNP(-1 / x - 1);
+ RETURNP(x + x); /* x is +Inf, +NaN or unsupported */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
/*
* expm1l() never underflows, but it must avoid
* unrepresentable large negative exponents. We used a
@@ -373,15 +188,15 @@ expm1l(long double x)
* in the same way as large ones here.
*/
if (hx & 0x8000) /* x <= -64 */
- return (tiny - 1); /* good for x < -65ln2 - eps */
+ RETURN2P(tiny, -1); /* good for x < -65ln2 - eps */
}
ENTERI();
if (T1 < x && x < T2) {
- if (ix < BIAS - 64) { /* |x| < 0x1p-64 (includes pseudos) */
+ if (ix < BIAS - 74) { /* |x| < 0x1p-74 (includes pseudos) */
/* x (rounded) with inexact if x != 0: */
- RETURNI(x == 0 ? x :
+ RETURNPI(x == 0 ? x :
(0x1p100 * x + fabsl(x)) * 0x1p-100);
}
@@ -402,9 +217,9 @@ expm1l(long double x)
hx2_hi = x_hi * x_hi / 2;
hx2_lo = x_lo * (x + x_hi) / 2;
if (ix >= BIAS - 7)
- RETURNI(hx2_lo + x_lo + q + (hx2_hi + x_hi));
+ RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q);
else
- RETURNI(hx2_lo + q + hx2_hi + x);
+ RETURN2PI(x, hx2_lo + q + hx2_hi);
}
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
@@ -438,21 +253,21 @@ expm1l(long double x)
t = (long double)tbl[n2].lo + tbl[n2].hi;
if (k == 0) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 1);
+ t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t);
}
if (k == -1) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 2);
+ t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t / 2);
}
if (k < -7) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk - 1);
}
if (k > 2 * LDBL_MANT_DIG - 1) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L - 1);
RETURNI(t * twopk - 1);
@@ -462,8 +277,8 @@ expm1l(long double x)
twomk = v.e;
if (k > LDBL_MANT_DIG - 1)
- t = tbl[n2].lo - twomk + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1));
else
- t = tbl[n2].lo + t * (q + r1) + (tbl[n2].hi - twomk);
+ t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk);
}
diff --git a/lib/msun/man/cosh.3 b/lib/msun/man/cosh.3
index 96abc5a..334b564 100644
--- a/lib/msun/man/cosh.3
+++ b/lib/msun/man/cosh.3
@@ -28,12 +28,13 @@
.\" from: @(#)cosh.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
-.Dd January 14, 2005
+.Dd August 17, 2013
.Dt COSH 3
.Os
.Sh NAME
.Nm cosh ,
-.Nm coshf
+.Nm coshf ,
+.Nm coshl
.Nd hyperbolic cosine functions
.Sh LIBRARY
.Lb libm
@@ -43,11 +44,14 @@
.Fn cosh "double x"
.Ft float
.Fn coshf "float x"
+.Ft long double
+.Fn coshl "long double x"
.Sh DESCRIPTION
The
-.Fn cosh
-and the
-.Fn coshf
+.Fn cosh ,
+.Fn coshf ,
+and
+.Fn coshl
functions compute the hyperbolic cosine of
.Fa x .
.Sh SEE ALSO
diff --git a/lib/msun/man/sinh.3 b/lib/msun/man/sinh.3
index 02944cc..b34cc38 100644
--- a/lib/msun/man/sinh.3
+++ b/lib/msun/man/sinh.3
@@ -27,12 +27,14 @@
.\"
.\" from: @(#)sinh.3 6.6 (Berkeley) 4/19/91
.\" $FreeBSD$
-.Dd January 14, 2005
+.\"
+.Dd August 17, 2013
.Dt SINH 3
.Os
.Sh NAME
.Nm sinh ,
-.Nm sinhf
+.Nm sinhf ,
+.Nm sinhl
.Nd hyperbolic sine function
.Sh LIBRARY
.Lb libm
@@ -42,11 +44,14 @@
.Fn sinh "double x"
.Ft float
.Fn sinhf "float x"
+.Ft long double
+.Fn sinhl "long double x"
.Sh DESCRIPTION
The
-.Fn sinh
-and the
-.Fn sinhf
+.Fn sinh ,
+.Fn sinhf ,
+and
+.Fn sinhl
functions compute the hyperbolic sine of
.Fa x .
.Sh SEE ALSO
diff --git a/lib/msun/man/tanh.3 b/lib/msun/man/tanh.3
index 6fb185c..ea2468f 100644
--- a/lib/msun/man/tanh.3
+++ b/lib/msun/man/tanh.3
@@ -28,12 +28,13 @@
.\" from: @(#)tanh.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
-.Dd May 2, 1991
+.Dd August 17, 2013
.Dt TANH 3
.Os
.Sh NAME
.Nm tanh ,
-.Nm tanhf
+.Nm tanhf ,
+.Nm tanhl
.Nd hyperbolic tangent functions
.Sh LIBRARY
.Lb libm
@@ -43,20 +44,24 @@
.Fn tanh "double x"
.Ft float
.Fn tanhf "float x"
+.Ft long double
+.Fn tanhl "long double x"
.Sh DESCRIPTION
The
-.Fn tanh
-and the
-.Fn tanhf
+.Fn tanh ,
+.Fn tanhf ,
+and
+.Fn tanhl
functions compute the hyperbolic tangent of
.Fa x .
For a discussion of error due to roundoff, see
.Xr math 3 .
.Sh RETURN VALUES
The
-.Fn tanh
+.Fn tanh ,
+.Fn tanhf ,
and the
-.Fn tanhf
+.Fn tanhl
functions return the hyperbolic tangent value.
.Sh SEE ALSO
.Xr acos 3 ,
diff --git a/lib/msun/src/e_cosh.c b/lib/msun/src/e_cosh.c
index a363695..246b5fb 100644
--- a/lib/msun/src/e_cosh.c
+++ b/lib/msun/src/e_cosh.c
@@ -35,6 +35,8 @@ __FBSDID("$FreeBSD$");
* only cosh(0)=1 is exact for finite x.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
@@ -77,3 +79,7 @@ __ieee754_cosh(double x)
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(cosh, coshl);
+#endif
diff --git a/lib/msun/src/e_coshl.c b/lib/msun/src/e_coshl.c
new file mode 100644
index 0000000..0a21277
--- /dev/null
+++ b/lib/msun/src/e_coshl.c
@@ -0,0 +1,130 @@
+/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See e_cosh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
+ * |cosh(x) - c(x)| < 2**-68.8
+ */
+static const union IEEEl2bits
+C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L);
+#define C4 C4u.e
+static const double
+C2 = 0.5,
+C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */
+C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */
+C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */
+C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */
+C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */
+C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
+ * |cosh(x) - c(x)| < 2**-121.69
+ */
+static const long double
+C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */
+C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
+C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */
+C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */
+C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */
+C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
+C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
+static const double
+C2 = 0.5,
+C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */
+C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */
+C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */
+C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */
+C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */
+#else
+#error "Unsupported long double format"
+#endif /* LDBL_MANT_DIG == 64 */
+
+/* log(2**16385 - 0.5) rounded up: */
+static const float
+o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
+
+long double
+coshl(long double x)
+{
+ long double hi,lo,x2,x4;
+ double dx2;
+ uint16_t ix;
+
+ GET_LDBL_EXPSIGN(ix,x);
+ ix &= 0x7fff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7fff) return x*x;
+
+ ENTERI();
+
+ /* |x| < 1, return 1 or c(x) */
+ if(ix<0x3fff) {
+ if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */
+ RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */
+ x2 = x*x;
+#if LDBL_MANT_DIG == 64
+ x4 = x2*x2;
+ RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
+ ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
+#elif LDBL_MANT_DIG == 113
+ dx2 = x2;
+ RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
+ C20)*x2 + C18)*x2 +
+ C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
+ C4)*(x2*x2) + C2*x2 + 1);
+#endif
+ }
+
+ /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
+ if (ix < 0x4005) {
+ k_hexpl(fabsl(x), &hi, &lo);
+ RETURNI(lo + 0.25/(hi + lo) + hi);
+ }
+
+ /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
+ if (fabsl(x) <= o_threshold)
+ RETURNI(hexpl(fabsl(x)));
+
+ /* |x| > o_threshold, cosh(x) overflow */
+ RETURNI(huge*huge);
+}
diff --git a/lib/msun/src/e_sinh.c b/lib/msun/src/e_sinh.c
index 17442d0..6c01f4a 100644
--- a/lib/msun/src/e_sinh.c
+++ b/lib/msun/src/e_sinh.c
@@ -32,6 +32,8 @@ __FBSDID("$FreeBSD$");
* only sinh(0)=0 is exact for finite x.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
@@ -71,3 +73,7 @@ __ieee754_sinh(double x)
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(sinh, sinhl);
+#endif
diff --git a/lib/msun/src/e_sinhl.c b/lib/msun/src/e_sinhl.c
new file mode 100644
index 0000000..ce7e333
--- /dev/null
+++ b/lib/msun/src/e_sinhl.c
@@ -0,0 +1,131 @@
+/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See e_sinh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const long double shuge = 0x1p16383L;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
+ * |sinh(x)/x - s(x)| < 2**-70.3
+ */
+static const union IEEEl2bits
+S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L);
+#define S3 S3u.e
+static const double
+S5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */
+S7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */
+S9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */
+S11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */
+S13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */
+S15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */
+S17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
+ * |sinh(x)/x - s(x)| < 2**-118.0
+ */
+static const long double
+S3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */
+S5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */
+S7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */
+S9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */
+S11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */
+S13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */
+S15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */
+S17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */
+static const double
+S19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */
+S21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */
+S23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */
+S25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */
+#else
+#error "Unsupported long double format"
+#endif /* LDBL_MANT_DIG == 64 */
+
+/* log(2**16385 - 0.5) rounded up: */
+static const float
+o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
+
+long double
+sinhl(long double x)
+{
+ long double hi,lo,x2,x4;
+ double dx2,s;
+ int16_t ix,jx;
+
+ GET_LDBL_EXPSIGN(jx,x);
+ ix = jx&0x7fff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7fff) return x+x;
+
+ ENTERI();
+
+ s = 1;
+ if (jx<0) s = -1;
+
+ /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
+ if (ix<0x4005) { /* |x|<64 */
+ if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */
+ if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */
+ if (ix<0x3fff) { /* |x|<1 */
+ x2 = x*x;
+#if LDBL_MANT_DIG == 64
+ x4 = x2*x2;
+ RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
+ ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
+#elif LDBL_MANT_DIG == 113
+ dx2 = x2;
+ RETURNI(((((((((((S25*dx2 + S23)*dx2 +
+ S21)*x2 + S19)*x2 +
+ S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
+ S5)* (x2*x*x2) +
+ S3*(x2*x) + x);
+#endif
+ }
+ k_hexpl(fabsl(x), &hi, &lo);
+ RETURNI(s*(lo - 0.25/(hi + lo) + hi));
+ }
+
+ /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
+ if (fabsl(x) <= o_threshold)
+ RETURNI(s*hexpl(fabsl(x)));
+
+ /* |x| > o_threshold, sinh(x) overflow */
+ return x*shuge;
+}
diff --git a/lib/msun/src/fenv-softfloat.h b/lib/msun/src/fenv-softfloat.h
index 02d2a2c..48c1277 100644
--- a/lib/msun/src/fenv-softfloat.h
+++ b/lib/msun/src/fenv-softfloat.h
@@ -156,7 +156,7 @@ feupdateenv(const fenv_t *__envp)
/* We currently provide no external definitions of the functions below. */
-static inline int
+__fenv_static inline int
feenableexcept(int __mask)
{
int __omask = __softfloat_float_exception_mask;
@@ -165,7 +165,7 @@ feenableexcept(int __mask)
return (__omask);
}
-static inline int
+__fenv_static inline int
fedisableexcept(int __mask)
{
int __omask = __softfloat_float_exception_mask;
@@ -174,7 +174,7 @@ fedisableexcept(int __mask)
return (__omask);
}
-static inline int
+__fenv_static inline int
fegetexcept(void)
{
diff --git a/lib/msun/src/imprecise.c b/lib/msun/src/imprecise.c
index a7503bf..5bd3d64 100644
--- a/lib/msun/src/imprecise.c
+++ b/lib/msun/src/imprecise.c
@@ -60,10 +60,7 @@ DECLARE_WEAK(powl);
long double imprecise_ ## f ## l(long double v) { return f(v); }\
DECLARE_WEAK(f ## l)
-DECLARE_IMPRECISE(cosh);
DECLARE_IMPRECISE(erfc);
DECLARE_IMPRECISE(erf);
DECLARE_IMPRECISE(lgamma);
-DECLARE_IMPRECISE(sinh);
-DECLARE_IMPRECISE(tanh);
DECLARE_IMPRECISE(tgamma);
diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h
index 1bd931c..fc4becc 100644
--- a/lib/msun/src/math.h
+++ b/lib/msun/src/math.h
@@ -451,6 +451,7 @@ long double atanl(long double);
long double cbrtl(long double);
long double ceill(long double);
long double copysignl(long double, long double) __pure2;
+long double coshl(long double);
long double cosl(long double);
long double exp2l(long double);
long double expl(long double);
@@ -488,8 +489,10 @@ long double rintl(long double);
long double roundl(long double);
long double scalblnl(long double, long);
long double scalbnl(long double, int);
+long double sinhl(long double);
long double sinl(long double);
long double sqrtl(long double);
+long double tanhl(long double);
long double tanl(long double);
long double truncl(long double);
@@ -510,13 +513,10 @@ __END_DECLS
*/
__BEGIN_DECLS
-long double coshl(long double);
long double erfcl(long double);
long double erfl(long double);
long double lgammal(long double);
long double powl(long double, long double);
-long double sinhl(long double);
-long double tanhl(long double);
long double tgammal(long double);
__END_DECLS
diff --git a/lib/msun/src/s_round.c b/lib/msun/src/s_round.c
index 65de31b..fab3019 100644
--- a/lib/msun/src/s_round.c
+++ b/lib/msun/src/s_round.c
@@ -27,25 +27,34 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <math.h>
+#include <float.h>
+
+#include "math.h"
+#include "math_private.h"
double
round(double x)
{
double t;
+ uint32_t hx;
- if (!isfinite(x))
- return (x);
+ GET_HIGH_WORD(hx, x);
+ if ((hx & 0x7fffffff) == 0x7ff00000)
+ return (x + x);
- if (x >= 0.0) {
+ if (!(hx & 0x80000000)) {
t = floor(x);
if (t - x <= -0.5)
- t += 1.0;
+ t += 1;
return (t);
} else {
t = floor(-x);
if (t + x <= -0.5)
- t += 1.0;
+ t += 1;
return (-t);
}
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(round, roundl);
+#endif
diff --git a/lib/msun/src/s_roundf.c b/lib/msun/src/s_roundf.c
index 952e8e7..e7e2eb9 100644
--- a/lib/msun/src/s_roundf.c
+++ b/lib/msun/src/s_roundf.c
@@ -27,25 +27,28 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <math.h>
+#include "math.h"
+#include "math_private.h"
float
roundf(float x)
{
float t;
+ uint32_t hx;
- if (!isfinite(x))
- return (x);
+ GET_FLOAT_WORD(hx, x);
+ if ((hx & 0x7fffffff) == 0x7f800000)
+ return (x + x);
- if (x >= 0.0) {
+ if (!(hx & 0x80000000)) {
t = floorf(x);
- if (t - x <= -0.5)
- t += 1.0;
+ if (t - x <= -0.5F)
+ t += 1;
return (t);
} else {
t = floorf(-x);
- if (t + x <= -0.5)
- t += 1.0;
+ if (t + x <= -0.5F)
+ t += 1;
return (-t);
}
}
diff --git a/lib/msun/src/s_roundl.c b/lib/msun/src/s_roundl.c
index a70b617..2d15e13 100644
--- a/lib/msun/src/s_roundl.c
+++ b/lib/msun/src/s_roundl.c
@@ -27,25 +27,36 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <math.h>
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
long double
roundl(long double x)
{
long double t;
+ uint16_t hx;
+
+ GET_LDBL_EXPSIGN(hx, x);
+ if ((hx & 0x7fff) == 0x7fff)
+ return (x + x);
- if (!isfinite(x))
- return (x);
+ ENTERI();
- if (x >= 0.0) {
+ if (!(hx & 0x8000)) {
t = floorl(x);
- if (t - x <= -0.5)
- t += 1.0;
- return (t);
+ if (t - x <= -0.5L)
+ t += 1;
+ RETURNI(t);
} else {
t = floorl(-x);
- if (t + x <= -0.5)
- t += 1.0;
- return (-t);
+ if (t + x <= -0.5L)
+ t += 1;
+ RETURNI(-t);
}
}
diff --git a/lib/msun/src/s_tanh.c b/lib/msun/src/s_tanh.c
index 96e3565..f7b71c5 100644
--- a/lib/msun/src/s_tanh.c
+++ b/lib/msun/src/s_tanh.c
@@ -37,6 +37,8 @@ __FBSDID("$FreeBSD$");
* only tanh(0)=0 is exact for finite argument.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
@@ -75,3 +77,7 @@ tanh(double x)
}
return (jx>=0)? z: -z;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(tanh, tanhl);
+#endif
diff --git a/lib/msun/src/s_tanhl.c b/lib/msun/src/s_tanhl.c
new file mode 100644
index 0000000..886158b
--- /dev/null
+++ b/lib/msun/src/s_tanhl.c
@@ -0,0 +1,172 @@
+/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
+
+/* @(#)s_tanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See s_tanh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "math.h"
+#include "math_private.h"
+#include "fpmath.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const volatile double tiny = 1.0e-300;
+static const double one = 1.0;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
+ * |tanh(x)/x - t(x)| < 2**-72.3
+ */
+static const union IEEEl2bits
+T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
+#define T3 T3u.e
+static const double
+T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */
+T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */
+T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */
+T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */
+T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */
+T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */
+T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */
+T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
+ * |tanh(x)/x - t(x)| < 2**121.6
+ */
+static const long double
+T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */
+T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */
+T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
+T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
+T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
+T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
+T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */
+static const double
+T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */
+T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */
+T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */
+T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */
+T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */
+T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */
+T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */
+T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */
+T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */
+#endif /* LDBL_MANT_DIG == 64 */
+
+static inline long double
+divl(long double a, long double b, long double c, long double d,
+ long double e, long double f)
+{
+ long double inv, r;
+ float fr, fw;
+
+ _2sumF(a, c);
+ b = b + c;
+ _2sumF(d, f);
+ e = e + f;
+
+ inv = 1 / (d + e);
+
+ r = (a + b) * inv;
+ fr = r;
+ r = fr;
+
+ fw = d + e;
+ e = d - fw + e;
+ d = fw;
+
+ r = r + (a - d * r + b - e * r) * inv;
+
+ return r;
+}
+
+long double
+tanhl(long double x)
+{
+ long double hi,lo,s,x2,x4,z;
+ double dx2;
+ int16_t jx,ix;
+
+ GET_LDBL_EXPSIGN(jx,x);
+ ix = jx&0x7fff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7fff) {
+ if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
+ else return one/x-one; /* tanh(NaN) = NaN */
+ }
+
+ ENTERI();
+
+ /* |x| < 40 */
+ if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */
+ if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
+ /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
+ return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
+ }
+ if (ix<0x3ffd) { /* |x|<0.25 */
+ x2 = x*x;
+#if LDBL_MANT_DIG == 64
+ x4 = x2*x2;
+ RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
+ ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
+ T3*(x2*x) + x);
+#elif LDBL_MANT_DIG == 113
+ dx2 = x2;
+#if 0
+ RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
+ T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
+ T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
+ (x2*x*x2) +
+ T3*(x2*x) + x);
+#else
+ long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
+ T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
+ T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
+ (x2*x*x2);
+ RETURNI(q + T3*(x2*x) + x);
+#endif
+#endif
+ }
+ k_hexpl(2*fabsl(x), &hi, &lo);
+ if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */
+ z = divl(hi, lo, -0.5, hi, lo, 0.5);
+ else
+ z = one - one/(lo+0.5+hi);
+ /* |x| >= 40, return +-1 */
+ } else {
+ z = one - tiny; /* raise inexact flag */
+ }
+ s = 1;
+ if (jx<0) s = -1;
+ RETURNI(s*z);
+}
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