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8303798: REDO - Remove fdlibm C sources

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Reviewed-by: alanb, iris, jwaters, erikj, kvn, dholmes
This commit is contained in:
Joe Darcy 2023-04-03 23:57:01 +00:00
parent 9ce5fdc962
commit ccbb0e8d89
64 changed files with 30 additions and 6496 deletions
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3
make/common/modules/LauncherCommon.gmk
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@ -1,5 +1,5 @@
#
# Copyright (c) 2011, 2022, Oracle and/or its affiliates. All rights reserved.
# Copyright (c) 2011, 2023, Oracle and/or its affiliates. All rights reserved.
# DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
#
# This code is free software; you can redistribute it and/or modify it
@ -130,7 +130,6 @@ define SetupBuildLauncherBody
$$(shell $(FIND) $(SUPPORT_OUTPUTDIR)/modules_libs/java.base -name "*.a") \
$(SUPPORT_OUTPUTDIR)/modules_libs/jdk.jdwp.agent/libdt_socket.a \
$(SUPPORT_OUTPUTDIR)/modules_libs/jdk.jdwp.agent/libjdwp.a \
$(SUPPORT_OUTPUTDIR)/native/java.base/$(LIBRARY_PREFIX)fdlibm$(STATIC_LIBRARY_SUFFIX) \
-framework CoreFoundation \
-framework Foundation \
-framework SystemConfiguration \

40
make/modules/java.base/lib/CoreLibraries.gmk
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@ -23,43 +23,6 @@
# questions.
#
##########################################################################################
# libfdlibm is statically linked with libjava below and not delivered into the
# product on its own.
BUILD_LIBFDLIBM_OPTIMIZATION := NONE
# If FDLIBM_CFLAGS is non-empty we know that we can optimize
# fdlibm when adding those extra C flags. Currently GCC,
# and clang only.
ifneq ($(FDLIBM_CFLAGS), )
BUILD_LIBFDLIBM_OPTIMIZATION := LOW
endif
LIBFDLIBM_SRC := $(TOPDIR)/src/java.base/share/native/libfdlibm
LIBFDLIBM_CFLAGS := -I$(LIBFDLIBM_SRC) $(FDLIBM_CFLAGS)
$(eval $(call SetupNativeCompilation, BUILD_LIBFDLIBM, \
NAME := fdlibm, \
TYPE := STATIC_LIBRARY, \
OUTPUT_DIR := $(SUPPORT_OUTPUTDIR)/native/$(MODULE), \
SRC := $(LIBFDLIBM_SRC), \
OPTIMIZATION := $(BUILD_LIBFDLIBM_OPTIMIZATION), \
CFLAGS := $(CFLAGS_JDKLIB) $(LIBFDLIBM_CFLAGS), \
CFLAGS_windows_debug := -DLOGGING, \
CFLAGS_aix := -qfloat=nomaf, \
DISABLED_WARNINGS_gcc := sign-compare, \
DISABLED_WARNINGS_gcc_k_rem_pio2.c := maybe-uninitialized, \
DISABLED_WARNINGS_clang := sign-compare, \
DISABLED_WARNINGS_microsoft := 4146, \
DISABLED_WARNINGS_microsoft_e_exp.c := 4244, \
DISABLED_WARNINGS_microsoft_s_ceil.c := 4018, \
DISABLED_WARNINGS_microsoft_s_expm1.c := 4244, \
DISABLED_WARNINGS_microsoft_s_floor.c := 4018, \
ARFLAGS := $(ARFLAGS), \
OBJECT_DIR := $(SUPPORT_OUTPUTDIR)/native/$(MODULE)/libfdlibm, \
))
##########################################################################################
LIBVERIFY_OPTIMIZATION := HIGH
@ -96,14 +59,12 @@ $(eval $(call SetupJdkLibrary, BUILD_LIBJAVA, \
CFLAGS := $(CFLAGS_JDKLIB) \
$(LIBJAVA_CFLAGS), \
jdk_util.c_CFLAGS := $(VERSION_CFLAGS), \
EXTRA_HEADER_DIRS := libfdlibm, \
WARNINGS_AS_ERRORS_xlc := false, \
DISABLED_WARNINGS_gcc_ProcessImpl_md.c := unused-result, \
LDFLAGS := $(LDFLAGS_JDKLIB) \
$(call SET_SHARED_LIBRARY_ORIGIN), \
LDFLAGS_macosx := -L$(SUPPORT_OUTPUTDIR)/native/$(MODULE)/, \
LDFLAGS_windows := -delayload:shell32.dll, \
LIBS := $(BUILD_LIBFDLIBM_TARGET), \
LIBS_unix := -ljvm, \
LIBS_linux := $(LIBDL), \
LIBS_aix := $(LIBDL) $(LIBM),\
@ -119,7 +80,6 @@ TARGETS += $(BUILD_LIBJAVA)
$(BUILD_LIBJAVA): $(BUILD_LIBVERIFY)
$(BUILD_LIBJAVA): $(BUILD_LIBFDLIBM)
##########################################################################################

7
src/hotspot/os/windows/sharedRuntimeRem.cpp
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@ -1,5 +1,5 @@
/*
* Copyright (c) 2015, 2018, Oracle and/or its affiliates. All rights reserved.
* Copyright (c) 2015, 2023, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
@ -26,13 +26,12 @@
#include "runtime/sharedRuntime.hpp"
#ifdef _WIN64
// These are copied defines from fdlibm.h, this allows us to keep the code
// the same as in the JDK, for easier maintenance.
// These are copied defines originally from fdlibm.h.
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
// This code is a copy of __ieee754_fmod() from the JDK's libfdlibm and is
// This code is a copy of __ieee754_fmod() formerly from the JDK's libfdlibm and is
// used as a workaround for issues with the Windows x64 CRT implementation
// of fmod. Microsoft has acknowledged that this is an issue in Visual Studio
// 2012 and forward, but has not provided a time frame for a fix other than that

13
src/hotspot/share/runtime/sharedRuntimeTrig.cpp
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@ -1,5 +1,5 @@
/*
* Copyright (c) 2001, 2022, Oracle and/or its affiliates. All rights reserved.
* Copyright (c) 2001, 2023, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
@ -28,14 +28,9 @@
#include "runtime/sharedRuntime.hpp"
#include "runtime/sharedRuntimeMath.hpp"
// This file contains copies of the fdlibm routines used by
// StrictMath. It turns out that it is almost always required to use
// these runtime routines; the Intel CPU doesn't meet the Java
// specification for sin/cos outside a certain limited argument range,
// and the SPARC CPU doesn't appear to have sin/cos instructions. It
// also turns out that avoiding the indirect call through function
// pointer out to libjava.so in SharedRuntime speeds these routines up
// by roughly 15% on both Win32/x86 and Solaris/SPARC.
// This file contains copies of the C fdlibm routines originally used
// by StrictMath. The StrictMath sin, cos, and tan methods now use a
// Java port of the algorithm in java.lang.Fdlibm.java.
/*
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)

24
src/java.base/share/classes/java/lang/StrictMath.java
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@ -42,8 +42,28 @@ import jdk.internal.vm.annotation.IntrinsicCandidate;
* Library," <a
* href="https://www.netlib.org/fdlibm/">{@code fdlibm}</a>. These
* algorithms, which are written in the C programming language, are
* then to be understood as executed with all floating-point
* operations following the rules of Java floating-point arithmetic.
* then to be understood to be transliterated into Java and executed
* with all floating-point and integer operations following the rules
* of Java arithmetic. The following transformations are used in the
* transliteration:
*
* <ul>
* <li>Extraction and setting of the high and low halves of a 64-bit
* {@code double} in C is expressed using Java platform methods that
* perform bit-wise conversions {@linkplain
* Double#doubleToRawLongBits(double) from {@code double} to {@code
* long}} and {@linkplain Double#longBitsToDouble(long) {@code long}
* to {@code double}}.
*
* <li>Unsigned {@code int} values in C are mapped to signed {@code
* int} values in Java with updates to operations to replicate
* unsigned semantics where the results on the same textual operation
* would differ. For example, {@code >>} shifts on unsigned C values
* are replaced with {@code >>>} shifts on signed Java values. Sized
* comparisons on unsigned C values ({@code <}, {@code <=}, {@code >},
* {@code >=}) are replaced with semantically equivalent calls to
* {@link Integer#compareUnsigned(int, int) compareUnsigned}.
* </ul>
*
* <p>The Java math library is defined with respect to
* {@code fdlibm} version 5.3. Where {@code fdlibm} provides

117
src/java.base/share/native/libfdlibm/e_acos.c
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@ -1,117 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_acos(double x)
#else
double __ieee754_acos(x)
double x;
#endif
{
double z,p,q,r,w,s,c,df;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x3ff00000) { /* |x| >= 1 */
if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
}
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3fe00000) { /* |x| < 0.5 */
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = sqrt(z);
r = p/q;
w = r*s-pio2_lo;
return pi - 2.0*(s+w);
} else { /* x > 0.5 */
z = (one-x)*0.5;
s = sqrt(z);
df = s;
__LO(df) = 0;
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return 2.0*(df+w);
}
}

126
src/java.base/share/native/libfdlibm/e_asin.c
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@ -1,126 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* where
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
* and its remez error is bounded by
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
*
* For x in [0.5,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_asin(double x)
#else
double __ieee754_asin(x)
double x;
#endif
{
double t=0,w,p,q,c,r,s;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>= 0x3ff00000) { /* |x|>= 1 */
if(((ix-0x3ff00000)|__LO(x))==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3fe00000) { /* |x|<0.5 */
if(ix<0x3e400000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabs(x);
t = w*0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = sqrt(t);
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
} else {
w = s;
__LO(w) = 0;
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}

134
src/java.base/share/native/libfdlibm/e_atan2.c
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@ -1,134 +0,0 @@
/*
* Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
tiny = 1.0e-300,
zero = 0.0,
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
#ifdef __STDC__
double __ieee754_atan2(double y, double x)
#else
double __ieee754_atan2(y,x)
double y,x;
#endif
{
double z;
int k,m,hx,hy,ix,iy;
unsigned lx,ly;
hx = __HI(x); ix = hx&0x7fffffff;
lx = __LO(x);
hy = __HI(y); iy = hy&0x7fffffff;
ly = __LO(y);
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
return x+y;
if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff00000) {
if(iy==0x7ff00000) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -1.0*zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>20;
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
else z=atan(fabs(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: __HI(z) ^= 0x80000000;
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
*
* Special cases:
* atanh(x) is NaN if |x| > 1 with signal;
* atanh(NaN) is that NaN with no signal;
* atanh(+-1) is +-INF with signal.
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, huge = 1e300;
#else
static double one = 1.0, huge = 1e300;
#endif
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_atanh(double x)
#else
double __ieee754_atanh(x)
double x;
#endif
{
double t;
int hx,ix;
unsigned lx;
hx = __HI(x); /* high word */
lx = __LO(x); /* low word */
ix = hx&0x7fffffff;
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3ff00000)
return x/zero;
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
__HI(x) = ix; /* x <- |x| */
if(ix<0x3fe00000) { /* x < 0.5 */
t = x+x;
t = 0.5*log1p(t+t*x/(one-x));
} else
t = 0.5*log1p((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, half=0.5, huge = 1.0e300;
#else
static double one = 1.0, half=0.5, huge = 1.0e300;
#endif
#ifdef __STDC__
double __ieee754_cosh(double x)
#else
double __ieee754_cosh(x)
double x;
#endif
{
double t,w;
int ix;
unsigned lx;
/* High word of |x|. */
ix = __HI(x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
t = expm1(fabs(x));
w = one+t;
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x40360000) {
t = __ieee754_exp(fabs(x));
return half*t+half/t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
if (ix<0x408633CE ||
((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
w = __ieee754_exp(half*fabs(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_exp(x)
* Returns the exponential of x.
*
* Method
* 1. Argument reduction:
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2.
*
* Here r will be represented as r = hi-lo for better
* accuracy.
*
* 2. Approximation of exp(r) by a special rational function on
* the interval [0,0.34658]:
* Write
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
* We use a special Reme algorithm on [0,0.34658] to generate
* a polynomial of degree 5 to approximate R. The maximum error
* of this polynomial approximation is bounded by 2**-59. In
* other words,
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
* (where z=r*r, and the values of P1 to P5 are listed below)
* and
* | 5 | -59
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
* | |
* The computation of exp(r) thus becomes
* 2*r
* exp(r) = 1 + -------
* R - r
* r*R1(r)
* = 1 + r + ----------- (for better accuracy)
* 2 - R1(r)
* where
* 2 4 10
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
*
* 3. Scale back to obtain exp(x):
* From step 1, we have
* exp(x) = 2^k * exp(r)
*
* Special cases:
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF) is 0, and
* for finite argument, only exp(0)=1 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then exp(x) overflow
* if x < -7.45133219101941108420e+02 then exp(x) underflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+300,
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
#ifdef __STDC__
double __ieee754_exp(double x) /* default IEEE double exp */
#else
double __ieee754_exp(x) /* default IEEE double exp */
double x;
#endif
{
double y,hi=0,lo=0,c,t;
int k=0,xsb;
unsigned hx;
hx = __HI(x); /* high word of x */
xsb = (hx>>31)&1; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out non-finite argument */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
if(((hx&0xfffff)|__LO(x))!=0)
return x+x; /* NaN */
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
}
if(x > o_threshold) return huge*huge; /* overflow */
if(x < u_threshold) return twom1000*twom1000; /* underflow */
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
} else {
k = invln2*x+halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
x = hi - lo;
}
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-2.0)-x);
else y = one-((lo-(x*c)/(2.0-c))-hi);
if(k >= -1021) {
__HI(y) += (k<<20); /* add k to y's exponent */
return y;
} else {
__HI(y) += ((k+1000)<<20);/* add k to y's exponent */
return y*twom1000;
}
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* __ieee754_fmod(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, Zero[] = {0.0, -0.0,};
#else
static double one = 1.0, Zero[] = {0.0, -0.0,};
#endif
#ifdef __STDC__
double __ieee754_fmod(double x, double y)
#else
double __ieee754_fmod(x,y)
double x,y ;
#endif
{
int n,hx,hy,hz,ix,iy,sx,i;
unsigned lx,ly,lz;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hy = __HI(y); /* high word of y */
ly = __LO(y); /* low word of y */
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x00100000) { /* subnormal x */
if(hx==0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
}
} else ix = (hx>>20)-1023;
/* determine iy = ilogb(y) */
if(hy<0x00100000) { /* subnormal y */
if(hy==0) {
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
}
} else iy = (hy>>20)-1023;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -1022)
hx = 0x00100000|(0x000fffff&hx);
else { /* subnormal x, shift x to normal */
n = -1022-ix;
if(n<=31) {
hx = (hx<<n)|(lx>>(32-n));
lx <<= n;
} else {
hx = lx<<(n-32);
lx = 0;
}
}
if(iy >= -1022)
hy = 0x00100000|(0x000fffff&hy);
else { /* subnormal y, shift y to normal */
n = -1022-iy;
if(n<=31) {
hy = (hy<<n)|(ly>>(32-n));
ly <<= n;
} else {
hy = ly<<(n-32);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(unsigned)sx>>31];
hx = hz+hz+(lz>>31); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(unsigned)sx>>31];
while(hx<0x00100000) { /* normalize x */
hx = hx+hx+(lx>>31); lx = lx+lx;
iy -= 1;
}
if(iy>= -1022) { /* normalize output */
hx = ((hx-0x00100000)|((iy+1023)<<20));
__HI(x) = hx|sx;
__LO(x) = lx;
} else { /* subnormal output */
n = -1022 - iy;
if(n<=20) {
lx = (lx>>n)|((unsigned)hx<<(32-n));
hx >>= n;
} else if (n<=31) {
lx = (hx<<(32-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-32); hx = sx;
}
__HI(x) = hx|sx;
__LO(x) = lx;
x *= one; /* create necessary signal */
}
return x; /* exact output */
}

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/*
* Copyright (c) 1998, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_log(x)
* Return the logarithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_log(double x)
#else
double __ieee754_log(x)
double x;
#endif
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) {
if (k==0) return zero;
else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;}
}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}

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@ -1,103 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_log10(x)
* Return the base 10 logarithm of x
*
* Method :
* Let log10_2hi = leading 40 bits of log10(2) and
* log10_2lo = log10(2) - log10_2hi,
* ivln10 = 1/log(10) rounded.
* Then
* n = ilogb(x),
* if(n<0) n = n+1;
* x = scalbn(x,-n);
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
*
* Note 1:
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
* mode must set to Round-to-Nearest.
* Note 2:
* [1/log(10)] rounded to 53 bits has error .198 ulps;
* log10 is monotonic at all binary break points.
*
* Special cases:
* log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal;
* log10(10**N) = N for N=0,1,...,22.
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_log10(double x)
#else
double __ieee754_log10(x)
double x;
#endif
{
double y,z;
int i,k,hx;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
i = ((unsigned)k&0x80000000)>>31;
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
__HI(x) = hx;
z = y*log10_2lo + ivln10*__ieee754_log(x);
return z+y*log10_2hi;
}

186
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@ -1,186 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#include "fdlibm.h"
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const int two_over_pi[] = {
#else
static int two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
#ifdef __STDC__
static const int npio2_hw[] = {
#else
static int npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
#ifdef __STDC__
int __ieee754_rem_pio2(double x, double *y)
#else
int __ieee754_rem_pio2(x,y)
double x,y[];
#endif
{
double z,w,t,r,fn;
double tx[3];
int e0,i,j,nx,n,ix,hx;
hx = __HI(x); /* high word of x */
ix = hx&0x7fffffff;
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;}
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
if(hx>0) {
z = x - pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1;
} else { /* negative x */
z = x + pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1;
}
}
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
t = fabs(x);
n = (int) (t*invpio2+half);
fn = (double)n;
r = t-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 85 bit */
if(n<32&&ix!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
j = ix>>20;
y[0] = r-w;
i = j-(((__HI(y[0]))>>20)&0x7ff);
if(i>16) { /* 2nd iteration needed, good to 118 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
i = j-(((__HI(y[0]))>>20)&0x7ff);
if(i>49) { /* 3rd iteration need, 151 bits acc */
t = r; /* will cover all possible cases */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
}
y[1] = (r-y[0])-w;
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
else return n;
}
/*
* all other (large) arguments
*/
if(ix>=0x7ff00000) { /* x is inf or NaN */
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
__LO(z) = __LO(x);
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
__HI(z) = ix - (e0<<20);
for(i=0;i<2;i++) {
tx[i] = (double)((int)(z));
z = (z-tx[i])*two24;
}
tx[2] = z;
nx = 3;
while(tx[nx-1]==zero) nx--; /* skip zero term */
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}

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@ -1,89 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_remainder(x,p)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* integer nearest x/p (in half way case choose the even one).
* Method :
* Based on fmod() return x-[x/p]chopped*p exactlp.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
#ifdef __STDC__
double __ieee754_remainder(double x, double p)
#else
double __ieee754_remainder(x,p)
double x,p;
#endif
{
int hx,hp;
unsigned sx,lx,lp;
double p_half;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hp = __HI(p); /* high word of p */
lp = __LO(p); /* low word of p */
sx = hx&0x80000000;
hp &= 0x7fffffff;
hx &= 0x7fffffff;
/* purge off exception values */
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff00000)|| /* x not finite */
((hp>=0x7ff00000)&& /* p is NaN */
(((hp-0x7ff00000)|lp)!=0)))
return (x*p)/(x*p);
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabs(x);
p = fabs(p);
if (hp<0x00200000) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
__HI(x) ^= sx;
return x;
}

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@ -1,63 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* __ieee754_scalb(x, fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
#include "fdlibm.h"
#ifdef _SCALB_INT
#ifdef __STDC__
double __ieee754_scalb(double x, int fn)
#else
double __ieee754_scalb(x,fn)
double x; int fn;
#endif
#else
#ifdef __STDC__
double __ieee754_scalb(double x, double fn)
#else
double __ieee754_scalb(x,fn)
double x, fn;
#endif
#endif
{
#ifdef _SCALB_INT
return scalbn(x,fn);
#else
if (isnan(x)||isnan(fn)) return x*fn;
if (!finite(fn)) {
if(fn>0.0) return x*fn;
else return x/(-fn);
}
if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
if ( fn > 65000.0) return scalbn(x, 65000);
if (-fn > 65000.0) return scalbn(x,-65000);
return scalbn(x,(int)fn);
#endif
}

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@ -1,94 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, shuge = 1.0e307;
#else
static double one = 1.0, shuge = 1.0e307;
#endif
#ifdef __STDC__
double __ieee754_sinh(double x)
#else
double __ieee754_sinh(x)
double x;
#endif
{
double t,w,h;
int ix,jx;
unsigned lx;
/* High word of |x|. */
jx = __HI(x);
ix = jx&0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3e300000) /* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = expm1(fabs(x));
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
w = __ieee754_exp(0.5*fabs(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}

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@ -1,462 +0,0 @@
/*
* Copyright (c) 1998, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __ieee754_sqrt(x)
* Return correctly rounded sqrt.
* ------------------------------------------
* | Use the hardware sqrt if you have one |
* ------------------------------------------
* Method:
* Bit by bit method using integer arithmetic. (Slow, but portable)
* 1. Normalization
* Scale x to y in [1,4) with even powers of 2:
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
* sqrt(x) = 2^k * sqrt(y)
* 2. Bit by bit computation
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
* i 0
* i+1 2
* s = 2*q , and y = 2 * ( y - q ). (1)
* i i i i
*
* To compute q from q , one checks whether
* i+1 i
*
* -(i+1) 2
* (q + 2 ) <= y. (2)
* i
* -(i+1)
* If (2) is false, then q = q ; otherwise q = q + 2 .
* i+1 i i+1 i
*
* With some algebraic manipulation, it is not difficult to see
* that (2) is equivalent to
* -(i+1)
* s + 2 <= y (3)
* i i
*
* The advantage of (3) is that s and y can be computed by
* i i
* the following recurrence formula:
* if (3) is false
*
* s = s , y = y ; (4)
* i+1 i i+1 i
*
* otherwise,
* -i -(i+1)
* s = s + 2 , y = y - s - 2 (5)
* i+1 i i+1 i i
*
* One may easily use induction to prove (4) and (5).
* Note. Since the left hand side of (3) contain only i+2 bits,
* it does not necessary to do a full (53-bit) comparison
* in (3).
* 3. Final rounding
* After generating the 53 bits result, we compute one more bit.
* Together with the remainder, we can decide whether the
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
* (it will never equal to 1/2ulp).
* The rounding mode can be detected by checking whether
* huge + tiny is equal to huge, and whether huge - tiny is
* equal to huge for some floating point number "huge" and "tiny".
*
* Special cases:
* sqrt(+-0) = +-0 ... exact
* sqrt(inf) = inf
* sqrt(-ve) = NaN ... with invalid signal
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
*
* Other methods : see the appended file at the end of the program below.
*---------------
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, tiny=1.0e-300;
#else
static double one = 1.0, tiny=1.0e-300;
#endif
#ifdef __STDC__
double __ieee754_sqrt(double x)
#else
double __ieee754_sqrt(x)
double x;
#endif
{
double z;
int sign = (int)0x80000000;
unsigned r,t1,s1,ix1,q1;
int ix0,s0,q,m,t,i;
ix0 = __HI(x); /* high word of x */
ix1 = __LO(x); /* low word of x */
/* take care of Inf and NaN */
if((ix0&0x7ff00000)==0x7ff00000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix0<=0) {
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
else if(ix0<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix0>>20);
if(m==0) { /* subnormal x */
while(ix0==0) {
m -= 21;
ix0 |= (ix1>>11); ix1 <<= 21;
}
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
m -= i-1;
ix0 |= (ix1>>(32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if(m&1){ /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
while(r!=0) {
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
r = sign;
while(r!=0) {
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
if (ix1 < t1) ix0 -= 1;
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
/* use floating add to find out rounding direction */
if((ix0|ix1)!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(unsigned)0xfffffffe) q+=1;
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1)+0x3fe00000;
ix1 = q1>>1;
if ((q&1)==1) ix1 |= sign;
ix0 += (m <<20);
__HI(z) = ix0;
__LO(z) = ix1;
return z;
}
/*
Other methods (use floating-point arithmetic)
-------------
(This is a copy of a drafted paper by Prof W. Kahan
and K.C. Ng, written in May, 1986)
Two algorithms are given here to implement sqrt(x)
(IEEE double precision arithmetic) in software.
Both supply sqrt(x) correctly rounded. The first algorithm (in
Section A) uses newton iterations and involves four divisions.
The second one uses reciproot iterations to avoid division, but
requires more multiplications. Both algorithms need the ability
to chop results of arithmetic operations instead of round them,
and the INEXACT flag to indicate when an arithmetic operation
is executed exactly with no roundoff error, all part of the
standard (IEEE 754-1985). The ability to perform shift, add,
subtract and logical AND operations upon 32-bit words is needed
too, though not part of the standard.
A. sqrt(x) by Newton Iteration
(1) Initial approximation
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
1 11 52 ...widths
------------------------------------------------------
x: |s| e | f |
------------------------------------------------------
msb lsb msb lsb ...order
------------------------ ------------------------
x0: |s| e | f1 | x1: | f2 |
------------------------ ------------------------
By performing shifts and subtracts on x0 and x1 (both regarded
as integers), we obtain an 8-bit approximation of sqrt(x) as
follows.
k := (x0>>1) + 0x1ff80000;
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
Here k is a 32-bit integer and T1[] is an integer array containing
correction terms. Now magically the floating value of y (y's
leading 32-bit word is y0, the value of its trailing word is 0)
approximates sqrt(x) to almost 8-bit.
Value of T1:
static int T1[32]= {
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
(2) Iterative refinement
Apply Heron's rule three times to y, we have y approximates
sqrt(x) to within 1 ulp (Unit in the Last Place):
y := (y+x/y)/2 ... almost 17 sig. bits
y := (y+x/y)/2 ... almost 35 sig. bits
y := y-(y-x/y)/2 ... within 1 ulp
Remark 1.
Another way to improve y to within 1 ulp is:
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
2
(x-y )*y
y := y + 2* ---------- ...within 1 ulp
2
3y + x
This formula has one division fewer than the one above; however,
it requires more multiplications and additions. Also x must be
scaled in advance to avoid spurious overflow in evaluating the
expression 3y*y+x. Hence it is not recommended uless division
is slow. If division is very slow, then one should use the
reciproot algorithm given in section B.
(3) Final adjustment
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
I := FALSE; ... reset INEXACT flag I
R := RZ; ... set rounding mode to round-toward-zero
z := x/y; ... chopped quotient, possibly inexact
If(not I) then { ... if the quotient is exact
if(z=y) {
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
} else {
z := z - ulp; ... special rounding
}
}
i := TRUE; ... sqrt(x) is inexact
If (r=RN) then z=z+ulp ... rounded-to-nearest
If (r=RP) then { ... round-toward-+inf
y = y+ulp; z=z+ulp;
}
y := y+z; ... chopped sum
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
(4) Special cases
Square root of +inf, +-0, or NaN is itself;
Square root of a negative number is NaN with invalid signal.
B. sqrt(x) by Reciproot Iteration
(1) Initial approximation
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
(see section A). By performing shifs and subtracts on x0 and y0,
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
k := 0x5fe80000 - (x0>>1);
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
Here k is a 32-bit integer and T2[] is an integer array
containing correction terms. Now magically the floating
value of y (y's leading 32-bit word is y0, the value of
its trailing word y1 is set to zero) approximates 1/sqrt(x)
to almost 7.8-bit.
Value of T2:
static int T2[64]= {
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
(2) Iterative refinement
Apply Reciproot iteration three times to y and multiply the
result by x to get an approximation z that matches sqrt(x)
to about 1 ulp. To be exact, we will have
-1ulp < sqrt(x)-z<1.0625ulp.
... set rounding mode to Round-to-nearest
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
... special arrangement for better accuracy
z := x*y ... 29 bits to sqrt(x), with z*y<1
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
(a) the term z*y in the final iteration is always less than 1;
(b) the error in the final result is biased upward so that
-1 ulp < sqrt(x) - z < 1.0625 ulp
instead of |sqrt(x)-z|<1.03125ulp.
(3) Final adjustment
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
R := RZ; ... set rounding mode to round-toward-zero
switch(r) {
case RN: ... round-to-nearest
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
break;
case RZ:case RM: ... round-to-zero or round-to--inf
R:=RP; ... reset rounding mod to round-to-+inf
if(x<z*z ... rounded up) z = z - ulp; else
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
break;
case RP: ... round-to-+inf
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
if(x>z*z ...chopped) z = z+ulp;
break;
}
Remark 3. The above comparisons can be done in fixed point. For
example, to compare x and w=z*z chopped, it suffices to compare
x1 and w1 (the trailing parts of x and w), regarding them as
two's complement integers.
...Is z an exact square root?
To determine whether z is an exact square root of x, let z1 be the
trailing part of z, and also let x0 and x1 be the leading and
trailing parts of x.
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
I := 1; ... Raise Inexact flag: z is not exact
else {
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
k := z1 >> 26; ... get z's 25-th and 26-th
fraction bits
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
}
R:= r ... restore rounded mode
return sqrt(x):=z.
If multiplication is cheaper then the foregoing red tape, the
Inexact flag can be evaluated by
I := i;
I := (z*z!=x) or I.
Note that z*z can overwrite I; this value must be sensed if it is
True.
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
zero.
--------------------
z1: | f2 |
--------------------
bit 31 bit 0
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
or even of logb(x) have the following relations:
-------------------------------------------------
bit 27,26 of z1 bit 1,0 of x1 logb(x)
-------------------------------------------------
00 00 odd and even
01 01 even
10 10 odd
10 00 even
11 01 even
-------------------------------------------------
(4) Special cases (see (4) of Section A).
*/

204
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View File

@ -1,204 +0,0 @@
/*
* Copyright (c) 1998, 2019, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#ifdef _ALLBSD_SOURCE
#include <machine/endian.h>
#elif defined(__linux__)
#define __USE_BSD 1
#include <endian.h>
#endif
#include "jfdlibm.h"
#ifdef __NEWVALID /* special setup for Sun test regime */
#if defined(i386) || defined(i486) || \
defined(intel) || defined(x86) || defined(arm) || \
defined(i86pc) || defined(ia64)
#define _LITTLE_ENDIAN
#endif
#endif
#ifdef _LITTLE_ENDIAN
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
#define __HIp(x) *(1+(int*)x)
#define __LOp(x) *(int*)x
#else
#define __HI(x) *(int*)&x
#define __LO(x) *(1+(int*)&x)
#define __HIp(x) *(int*)x
#define __LOp(x) *(1+(int*)x)
#endif
#ifndef __P
#ifdef __STDC__
#define __P(p) p
#else
#define __P(p) ()
#endif
#endif
/*
* ANSI/POSIX
*/
extern int signgam;
#define MAXFLOAT ((float)3.40282346638528860e+38)
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
#define _LIB_VERSION_TYPE enum fdversion
#define _LIB_VERSION _fdlib_version
/* if global variable _LIB_VERSION is not desirable, one may
* change the following to be a constant by:
* #define _LIB_VERSION_TYPE const enum version
* In that case, after one initializes the value _LIB_VERSION (see
* s_lib_version.c) during compile time, it cannot be modified
* in the middle of a program
*/
extern _LIB_VERSION_TYPE _LIB_VERSION;
#define _IEEE_ fdlibm_ieee
#define _SVID_ fdlibm_svid
#define _XOPEN_ fdlibm_xopen
#define _POSIX_ fdlibm_posix
struct exception {
int type;
char *name;
double arg1;
double arg2;
double retval;
};
#define HUGE MAXFLOAT
/*
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
* (one may replace the following line by "#include <values.h>")
*/
#define X_TLOSS 1.41484755040568800000e+16
#define DOMAIN 1
#define SING 2
#define OVERFLOW 3
#define UNDERFLOW 4
#define TLOSS 5
#define PLOSS 6
/*
* ANSI/POSIX
*/
extern double acos __P((double));
extern double asin __P((double));
extern double atan __P((double));
extern double atan2 __P((double, double));
extern double cos __P((double));
extern double sin __P((double));
extern double tan __P((double));
extern double cosh __P((double));
extern double sinh __P((double));
extern double tanh __P((double));
extern double exp __P((double));
extern double frexp __P((double, int *));
extern double ldexp __P((double, int));
extern double log __P((double));
extern double log10 __P((double));
extern double modf __P((double, double *));
extern double sqrt __P((double));
extern double ceil __P((double));
extern double fabs __P((double));
extern double floor __P((double));
extern double fmod __P((double, double));
extern double hypot __P((double, double));
extern int isnan __P((double));
extern int finite __P((double));
extern double atanh __P((double));
extern double cbrt __P((double));
extern double logb __P((double));
extern double nextafter __P((double, double));
extern double remainder __P((double, double));
#ifdef _SCALB_INT
extern double scalb __P((double, int));
#else
extern double scalb __P((double, double));
#endif
extern int matherr __P((struct exception *));
/*
* IEEE Test Vector
*/
extern double significand __P((double));
/*
* Functions callable from C, intended to support IEEE arithmetic.
*/
extern double copysign __P((double, double));
extern int ilogb __P((double));
extern double rint __P((double));
extern double scalbn __P((double, int));
/*
* BSD math library entry points
*/
extern double expm1 __P((double));
extern double log1p __P((double));
/* ieee style elementary functions */
extern double __ieee754_sqrt __P((double));
extern double __ieee754_acos __P((double));
extern double __ieee754_log __P((double));
extern double __ieee754_atanh __P((double));
extern double __ieee754_asin __P((double));
extern double __ieee754_atan2 __P((double,double));
extern double __ieee754_exp __P((double));
extern double __ieee754_cosh __P((double));
extern double __ieee754_fmod __P((double,double));
extern double __ieee754_log10 __P((double));
extern double __ieee754_sinh __P((double));
extern double __ieee754_hypot __P((double,double));
extern double __ieee754_remainder __P((double,double));
extern int __ieee754_rem_pio2 __P((double,double*));
#ifdef _SCALB_INT
extern double __ieee754_scalb __P((double,int));
#else
extern double __ieee754_scalb __P((double,double));
#endif
/* fdlibm kernel function */
extern double __kernel_standard __P((double,double,int));
extern double __kernel_sin __P((double,double,int));
extern double __kernel_cos __P((double,double));
extern double __kernel_tan __P((double,double,int));
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));

89
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View File

@ -1,89 +0,0 @@
/*
* Copyright (c) 1998, 2012, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#ifndef _JFDLIBM_H
#define _JFDLIBM_H
#define _IEEE_LIBM
/*
* In order to resolve the conflict between fdlibm and compilers
* (such as keywords and built-in functions), the following
* function names have to be re-mapped.
*/
#define huge HUGE_NUMBER
#define acos jacos
#define asin jasin
#define atan jatan
#define atan2 jatan2
#define cos jcos
#define exp jexp
#define log jlog
#define log10 jlog10
#define pow jpow
#define sin jsin
#define sqrt jsqrt
#define cbrt jcbrt
#define tan jtan
#define floor jfloor
#define ceil jceil
#define cosh jcosh
#define fmod jmod
#define log10 jlog10
#define sinh jsinh
#define fabs jfabs
#define tanh jtanh
#define remainder jremainder
#define hypot jhypot
#define log1p jlog1p
#define expm1 jexpm1
#if defined(__linux__) || defined(_ALLBSD_SOURCE)
#define __ieee754_sqrt __j__ieee754_sqrt
#define __ieee754_acos __j__ieee754_acos
#define __ieee754_log __j__ieee754_log
#define __ieee754_atanh __j__ieee754_atanh
#define __ieee754_asin __j__ieee754_asin
#define __ieee754_atan2 __j__ieee754_atan2
#define __ieee754_exp __j__ieee754_exp
#define __ieee754_cosh __j__ieee754_cosh
#define __ieee754_fmod __j__ieee754_fmod
#define __ieee754_pow __j__ieee754_pow
#define __ieee754_log10 __j__ieee754_log10
#define __ieee754_sinh __j__ieee754_sinh
#define __ieee754_hypot __j__ieee754_hypot
#define __ieee754_remainder __j__ieee754_remainder
#define __ieee754_rem_pio2 __j__ieee754_rem_pio2
#define __ieee754_scalb __j__ieee754_scalb
#define __kernel_standard __j__kernel_standard
#define __kernel_sin __j__kernel_sin
#define __kernel_cos __j__kernel_cos
#define __kernel_tan __j__kernel_tan
#define __kernel_rem_pio2 __j__kernel_rem_pio2
#define __ieee754_log1p __j__ieee754_log1p
#define __ieee754_expm1 __j__ieee754_expm1
#endif
#endif/*_JFDLIBM_H*/

104
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@ -1,104 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* __kernel_cos( x, y )
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
*
* Algorithm
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
* 3. cos(x) is approximated by a polynomial of degree 14 on
* [0,pi/4]
* 4 14
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
* where the remez error is
*
* | 2 4 6 8 10 12 14 | -58
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
* | |
*
* 4 6 8 10 12 14
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
* cos(x) = 1 - x*x/2 + r
* since cos(x+y) ~ cos(x) - sin(x)*y
* ~ cos(x) - x*y,
* a correction term is necessary in cos(x) and hence
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
* For better accuracy when x > 0.3, let qx = |x|/4 with
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
* Then
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
* magnitude of the latter is at least a quarter of x*x/2,
* thus, reducing the rounding error in the subtraction.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
#ifdef __STDC__
double __kernel_cos(double x, double y)
#else
double __kernel_cos(x, y)
double x,y;
#endif
{
double a,hz,z,r,qx;
int ix;
ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x3e400000) { /* if x < 2**27 */
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) { /* x > 0.78125 */
qx = 0.28125;
} else {
__HI(qx) = ix-0x00200000; /* x/4 */
__LO(qx) = 0;
}
hz = 0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}

329
src/java.base/share/native/libfdlibm/k_rem_pio2.c
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@ -1,329 +0,0 @@
/*
* Copyright (c) 1998, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
* double x[],y[]; int e0,nx,prec; int ipio2[];
*
* __kernel_rem_pio2 return the last three digits of N with
* y = x - N*pi/2
* so that |y| < pi/2.
*
* The method is to compute the integer (mod 8) and fraction parts of
* (2/pi)*x without doing the full multiplication. In general we
* skip the part of the product that are known to be a huge integer (
* more accurately, = 0 mod 8 ). Thus the number of operations are
* independent of the exponent of the input.
*
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
*
* Input parameters:
* x[] The input value (must be positive) is broken into nx
* pieces of 24-bit integers in double precision format.
* x[i] will be the i-th 24 bit of x. The scaled exponent
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
* match x's up to 24 bits.
*
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
* e0 = ilogb(z)-23
* z = scalbn(z,-e0)
* for i = 0,1,2
* x[i] = floor(z)
* z = (z-x[i])*2**24
*
*
* y[] output result in an array of double precision numbers.
* The dimension of y[] is:
* 24-bit precision 1
* 53-bit precision 2
* 64-bit precision 2
* 113-bit precision 3
* The actual value is the sum of them. Thus for 113-bit
* precision, one may have to do something like:
*
* long double t,w,r_head, r_tail;
* t = (long double)y[2] + (long double)y[1];
* w = (long double)y[0];
* r_head = t+w;
* r_tail = w - (r_head - t);
*
* e0 The exponent of x[0]
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 0 24 bits (single)
* 1 53 bits (double)
* 2 64 bits (extended)
* 3 113 bits (quad)
*
* ipio2[]
* integer array, contains the (24*i)-th to (24*i+23)-th
* bit of 2/pi after binary point. The corresponding
* floating value is
*
* ipio2[i] * 2^(-24(i+1)).
*
* External function:
* double scalbn(), floor();
*
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* in the computation. The recommended value is 2,3,4,
* 6 for single, double, extended,and quad.
*
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
* jv index for pointing to the suitable ipio2[] for the
* computation. In general, we want
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
* is an integer. Thus
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
* Hence jv = max(0,(e0-3)/24).
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 24-bits chunk of the product of x and 2/pi.
*
* q0 the corresponding exponent of q[0]. Note that the
* exponent for q[i] would be q0-24*i.
*
* PIo2[] double precision array, obtained by cutting pi/2
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
*
* ih integer. If >0 it indicates q[] is >= 0.5, hence
* it also indicates the *sign* of the result.
*
*/
/*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6};
#endif
#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.0,
one = 1.0,
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
#else
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
double x[], y[]; int e0,nx,prec; int ipio2[];
#endif
{
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/24; if(jv<0) jv=0;
q0 = e0-24*(jv+1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (double)((int)(twon24* z));
iq[i] = (int)(z-two24*fw);
z = q[j-1]+fw;
}
/* compute n */
z = scalbn(z,q0); /* actual value of z */
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
n = (int) z;
z -= (double)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(24-q0)); n += i;
iq[jz-1] -= i<<(24-q0);
ih = iq[jz-1]>>(23-q0);
}
else if(q0==0) ih = iq[jz-1]>>23;
else if(z>=0.5) ih=2;
if(ih>0) { /* q > 0.5 */
n += 1; carry = 0;
for(i=0;i<jz ;i++) { /* compute 1-q */
j = iq[i];
if(carry==0) {
if(j!=0) {
carry = 1; iq[i] = 0x1000000- j;
}
} else iq[i] = 0xffffff - j;
}
if(q0>0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7fffff; break;
case 2:
iq[jz-1] &= 0x3fffff; break;
}
}
if(ih==2) {
z = one - z;
if(carry!=0) z -= scalbn(one,q0);
}
}
/* check if recomputation is needed */
if(z==zero) {
j = 0;
for (i=jz-1;i>=jk;i--) j |= iq[i];
if(j==0) { /* need recomputation */
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (double) ipio2[jv+i];
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
/* chop off zero terms */
if(z==0.0) {
jz -= 1; q0 -= 24;
while(iq[jz]==0) { jz--; q0-=24;}
} else { /* break z into 24-bit if necessary */
z = scalbn(z,-q0);
if(z>=two24) {
fw = (double)((int)(twon24*z));
iq[jz] = (int)(z-two24*fw);
jz += 1; q0 += 24;
iq[jz] = (int) fw;
} else iq[jz] = (int) z ;
}
/* convert integer "bit" chunk to floating-point value */
fw = scalbn(one,q0);
for(i=jz;i>=0;i--) {
q[i] = fw*(double)iq[i]; fw*=twon24;
}
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz;i>=0;i--) {
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
fw = fq[0]-fw;
for (i=1;i<=jz;i++) fw += fq[i];
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz;i>1;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
if(ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}

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src/java.base/share/native/libfdlibm/k_sin.c
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@ -1,86 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __kernel_sin( x, y, iy)
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
*
* Algorithm
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
* 3. sin(x) is approximated by a polynomial of degree 13 on
* [0,pi/4]
* 3 13
* sin(x) ~ x + S1*x + ... + S6*x
* where
*
* |sin(x) 2 4 6 8 10 12 | -58
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
* | x |
*
* 4. sin(x+y) = sin(x) + sin'(x')*y
* ~ sin(x) + (1-x*x/2)*y
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
#ifdef __STDC__
double __kernel_sin(double x, double y, int iy)
#else
double __kernel_sin(x, y, iy)
double x,y; int iy; /* iy=0 if y is zero */
#endif
{
double z,r,v;
int ix;
ix = __HI(x)&0x7fffffff; /* high word of x */
if(ix<0x3e400000) /* |x| < 2**-27 */
{if((int)x==0) return x;} /* generate inexact */
z = x*x;
v = z*x;
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}

748
src/java.base/share/native/libfdlibm/k_standard.c
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@ -1,748 +0,0 @@
/*
* Copyright (c) 1998, 2020, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#include "fdlibm.h"
#include <errno.h>
#ifndef _USE_WRITE
#include <stdio.h> /* fputs(), stderr */
#define WRITE2(u,v) fputs(u, stderr)
#else /* !defined(_USE_WRITE) */
#include <unistd.h> /* write */
#define WRITE2(u,v) write(2, u, v)
#undef fflush
#endif /* !defined(_USE_WRITE) */
static double zero = 0.0; /* used as const */
/*
* Standard conformance (non-IEEE) on exception cases.
* Mapping:
* 1 -- acos(|x|>1)
* 2 -- asin(|x|>1)
* 3 -- atan2(+-0,+-0)
* 4 -- hypot overflow
* 5 -- cosh overflow
* 6 -- exp overflow
* 7 -- exp underflow
* 8 -- y0(0)
* 9 -- y0(-ve)
* 10-- y1(0)
* 11-- y1(-ve)
* 12-- yn(0)
* 13-- yn(-ve)
* 14-- lgamma(finite) overflow
* 15-- lgamma(-integer)
* 16-- log(0)
* 17-- log(x<0)
* 18-- log10(0)
* 19-- log10(x<0)
* 20-- pow(0.0,0.0)
* 21-- pow(x,y) overflow
* 22-- pow(x,y) underflow
* 23-- pow(0,negative)
* 24-- pow(neg,non-integral)
* 25-- sinh(finite) overflow
* 26-- sqrt(negative)
* 27-- fmod(x,0)
* 28-- remainder(x,0)
* 29-- acosh(x<1)
* 30-- atanh(|x|>1)
* 31-- atanh(|x|=1)
* 32-- scalb overflow
* 33-- scalb underflow
* 34-- j0(|x|>X_TLOSS)
* 35-- y0(x>X_TLOSS)
* 36-- j1(|x|>X_TLOSS)
* 37-- y1(x>X_TLOSS)
* 38-- jn(|x|>X_TLOSS, n)
* 39-- yn(x>X_TLOSS, n)
* 40-- gamma(finite) overflow
* 41-- gamma(-integer)
* 42-- pow(NaN,0.0)
*/
#ifdef __STDC__
double __kernel_standard(double x, double y, int type)
#else
double __kernel_standard(x,y,type)
double x,y; int type;
#endif
{
struct exception exc;
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
#define HUGE_VAL inf
double inf = 0.0;
__HI(inf) = 0x7ff00000; /* set inf to infinite */
#endif
#ifdef _USE_WRITE
(void) fflush(stdout);
#endif
exc.arg1 = x;
exc.arg2 = y;
switch(type) {
case 1:
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = "acos";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("acos: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 2:
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = "asin";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("asin: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 3:
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = "atan2";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("atan2: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 4:
/* hypot(finite,finite) overflow */
exc.type = OVERFLOW;
exc.name = "hypot";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 5:
/* cosh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "cosh";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 6:
/* exp(finite) overflow */
exc.type = OVERFLOW;
exc.name = "exp";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 7:
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "exp";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 8:
/* y0(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 9:
/* y0(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 10:
/* y1(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 11:
/* y1(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 12:
/* yn(n,0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 13:
/* yn(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 14:
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 15:
/* lgamma(-integer) or lgamma(0) */
exc.type = SING;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("lgamma: SING error\n", 19);
}
errno = EDOM;
}
break;
case 16:
/* log(0) */
exc.type = SING;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: SING error\n", 16);
}
errno = EDOM;
}
break;
case 17:
/* log(x<0) */
exc.type = DOMAIN;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: DOMAIN error\n", 18);
}
errno = EDOM;
}
break;
case 18:
/* log10(0) */
exc.type = SING;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: SING error\n", 18);
}
errno = EDOM;
}
break;
case 19:
/* log10(x<0) */
exc.type = DOMAIN;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 20:
/* pow(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = zero;
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
else if (!matherr(&exc)) {
(void) WRITE2("pow(0,0): DOMAIN error\n", 23);
errno = EDOM;
}
break;
case 21:
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "pow";
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
}
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 22:
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "pow";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 23:
/* 0**neg */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
}
errno = EDOM;
}
break;
case 24:
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero; /* X/Open allow NaN */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
}
errno = EDOM;
}
break;
case 25:
/* sinh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "sinh";
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>zero) ? HUGE : -HUGE);
else
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 26:
/* sqrt(x<0) */
exc.type = DOMAIN;
exc.name = "sqrt";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("sqrt: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 27:
/* fmod(x,0) */
exc.type = DOMAIN;
exc.name = "fmod";
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("fmod: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 28:
/* remainder(x,0) */
exc.type = DOMAIN;
exc.name = "remainder";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("remainder: DOMAIN error\n", 24);
}
errno = EDOM;
}
break;
case 29:
/* acosh(x<1) */
exc.type = DOMAIN;
exc.name = "acosh";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("acosh: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 30:
/* atanh(|x|>1) */
exc.type = DOMAIN;
exc.name = "atanh";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 31:
/* atanh(|x|=1) */
exc.type = SING;
exc.name = "atanh";
exc.retval = x/zero; /* sign(x)*inf */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: SING error\n", 18);
}
errno = EDOM;
}
break;
case 32:
/* scalb overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = "scalb";
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 33:
/* scalb underflow */
exc.type = UNDERFLOW;
exc.name = "scalb";
exc.retval = copysign(zero,x);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 34:
/* j0(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j0";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 35:
/* y0(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y0";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 36:
/* j1(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j1";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 37:
/* y1(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y1";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 38:
/* jn(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "jn";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 39:
/* yn(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "yn";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 40:
/* gamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!matherr(&exc)) {
errno = ERANGE;
}
break;
case 41:
/* gamma(-integer) or gamma(0) */
exc.type = SING;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("gamma: SING error\n", 18);
}
errno = EDOM;
}
break;
case 42:
/* pow(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = x;
if (_LIB_VERSION == _IEEE_ ||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
else if (!matherr(&exc)) {
errno = EDOM;
}
break;
default:
exc.retval = zero / zero;
errno = EINVAL;
break;
}
return exc.retval;
}

152
src/java.base/share/native/libfdlibm/k_tan.c
View File

@ -1,152 +0,0 @@
/*
* Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* __kernel_tan( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
* [0,0.67434]
* 3 27
* tan(x) ~ x + T1*x + ... + T13*x
* where
*
* |tan(x) 2 4 26 | -59.2
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
* | x |
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* 3 2 2 2 2
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
* then
* 3 2
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
*
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] = {
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};
#ifdef __STDC__
double __kernel_tan(double x, double y, int iy)
#else
double __kernel_tan(x, y, iy)
double x,y; int iy;
#endif
{
double z,r,v,w,s;
int ix,hx;
hx = __HI(x); /* high word of x */
ix = hx&0x7fffffff; /* high word of |x| */
if(ix<0x3e300000) { /* x < 2**-28 */
if((int)x==0) { /* generate inexact */
if (((ix | __LO(x)) | (iy + 1)) == 0)
return one / fabs(x);
else {
if (iy == 1)
return x;
else { /* compute -1 / (x+y) carefully */
double a, t;
z = w = x + y;
__LO(z) = 0;
v = y - (z - x);
t = a = -one / w;
__LO(t) = 0;
s = one + t * z;
return t + a * (s + t * v);
}
}
}
}
if(ix>=0x3FE59428) { /* |x|>=0.6744 */
if(hx<0) {x = -x; y = -y;}
z = pio4-x;
w = pio4lo-y;
x = z+w; y = 0.0;
}
z = x*x;
w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
if(ix>=0x3FE59428) {
v = (double)iy;
return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
}
if(iy==1) return w;
else { /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
double a,t;
z = w;
__LO(z) = 0;
v = r-(z - x); /* z+v = r+x */
t = a = -1.0/w; /* a = -1.0/w */
__LO(t) = 0;
s = 1.0+t*z;
return t+a*(s+t*v);
}
}

145
src/java.base/share/native/libfdlibm/s_atan.c
View File

@ -1,145 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* atan(x)
* Method
* 1. Reduce x to positive by atan(x) = -atan(-x).
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
* is further reduced to one of the following intervals and the
* arctangent of t is evaluated by the corresponding formula:
*
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double atanhi[] = {
#else
static double atanhi[] = {
#endif
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};
#ifdef __STDC__
static const double atanlo[] = {
#else
static double atanlo[] = {
#endif
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};
#ifdef __STDC__
static const double aT[] = {
#else
static double aT[] = {
#endif
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e300;
#ifdef __STDC__
double atan(double x)
#else
double atan(x)
double x;
#endif
{
double w,s1,s2,z;
int ix,hx,id;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x44100000) { /* if |x| >= 2^66 */
if(ix>0x7ff00000||
(ix==0x7ff00000&&(__LO(x)!=0)))
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
if (ix < 0x3e200000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabs(x);
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
id = 0; x = (2.0*x-one)/(2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x40038000) { /* |x| < 2.4375 */
id = 2; x = (x-1.5)/(one+1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}

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@ -1,90 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* ceil(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to ceil(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double ceil(double x)
#else
double ceil(x)
double x;
#endif
{
int i0,i1,j0;
unsigned i,j;
i0 = __HI(x);
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0<0) {i0=0x80000000;i1=0;}
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) {
if(j0==20) i0+=1;
else {
j = i1 + (1<<(52-j0));
if(j<i1) i0+=1; /* got a carry */
i1 = j;
}
}
i1 &= (~i);
}
}
__HI(x) = i0;
__LO(x) = i1;
return x;
}

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@ -1,43 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* copysign(double x, double y)
* copysign(x,y) returns a value with the magnitude of x and
* with the sign bit of y.
*/
#include "fdlibm.h"
#ifdef __STDC__
double copysign(double x, double y)
#else
double copysign(x,y)
double x,y;
#endif
{
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
return x;
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* cos(x)
* Return cosine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cosine function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double cos(double x)
#else
double cos(x)
double x;
#endif
{
double y[2],z=0.0;
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
/* cos(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_cos(y[0],y[1]);
case 1: return -__kernel_sin(y[0],y[1],1);
case 2: return -__kernel_cos(y[0],y[1]);
default:
return __kernel_sin(y[0],y[1],1);
}
}
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* expm1(x)
* Returns exp(x)-1, the exponential of x minus 1.
*
* Method
* 1. Argument reduction:
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
*
* Here a correction term c will be computed to compensate
* the error in r when rounded to a floating-point number.
*
* 2. Approximating expm1(r) by a special rational function on
* the interval [0,0.34658]:
* Since
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
* we define R1(r*r) by
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
* That is,
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
* We use a special Reme algorithm on [0,0.347] to generate
* a polynomial of degree 5 in r*r to approximate R1. The
* maximum error of this polynomial approximation is bounded
* by 2**-61. In other words,
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
* where Q1 = -1.6666666666666567384E-2,
* Q2 = 3.9682539681370365873E-4,
* Q3 = -9.9206344733435987357E-6,
* Q4 = 2.5051361420808517002E-7,
* Q5 = -6.2843505682382617102E-9;
* (where z=r*r, and the values of Q1 to Q5 are listed below)
* with error bounded by
* | 5 | -61
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
* | |
*
* expm1(r) = exp(r)-1 is then computed by the following
* specific way which minimize the accumulation rounding error:
* 2 3
* r r [ 3 - (R1 + R1*r/2) ]
* expm1(r) = r + --- + --- * [--------------------]
* 2 2 [ 6 - r*(3 - R1*r/2) ]
*
* To compensate the error in the argument reduction, we use
* expm1(r+c) = expm1(r) + c + expm1(r)*c
* ~ expm1(r) + c + r*c
* Thus c+r*c will be added in as the correction terms for
* expm1(r+c). Now rearrange the term to avoid optimization
* screw up:
* ( 2 2 )
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
* ( )
*
* = r - E
* 3. Scale back to obtain expm1(x):
* From step 1, we have
* expm1(x) = either 2^k*[expm1(r)+1] - 1
* = or 2^k*[expm1(r) + (1-2^-k)]
* 4. Implementation notes:
* (A). To save one multiplication, we scale the coefficient Qi
* to Qi*2^i, and replace z by (x^2)/2.
* (B). To achieve maximum accuracy, we compute expm1(x) by
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
* (ii) if k=0, return r-E
* (iii) if k=-1, return 0.5*(r-E)-0.5
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
* else return 1.0+2.0*(r-E);
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
* (vii) return 2^k(1-((E+2^-k)-r))
*
* Special cases:
* expm1(INF) is INF, expm1(NaN) is NaN;
* expm1(-INF) is -1, and
* for finite argument, only expm1(0)=0 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e+300,
tiny = 1.0e-300,
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
/* scaled coefficients related to expm1 */
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
#ifdef __STDC__
double expm1(double x)
#else
double expm1(x)
double x;
#endif
{
double y,hi,lo,c=0,t,e,hxs,hfx,r1;
int k,xsb;
unsigned hx;
hx = __HI(x); /* high word of x */
xsb = hx&0x80000000; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
if(((hx&0xfffff)|__LO(x))!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
if(x+tiny<0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?0.5:-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi - lo;
c = (hi-x)-lo;
}
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = 0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = 3.0-r1*hfx;
e = hxs*((r1-t)/(6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return 0.5*(x-e)-0.5;
if(k==1) {
if(x < -0.25) return -2.0*(e-(x+0.5));
else return one+2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
y = one-(e-x);
__HI(y) += (k<<20); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<20) {
__HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
y = t-(e-x);
__HI(y) += (k<<20); /* add k to y's exponent */
} else {
__HI(t) = ((0x3ff-k)<<20); /* 2^-k */
y = x-(e+t);
y += one;
__HI(y) += (k<<20); /* add k to y's exponent */
}
}
return y;
}

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/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* fabs(x) returns the absolute value of x.
*/
#include "fdlibm.h"
#ifdef __STDC__
double fabs(double x)
#else
double fabs(x)
double x;
#endif
{
__HI(x) &= 0x7fffffff;
return x;
}

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@ -1,43 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* finite(x) returns 1 is x is finite, else 0;
* no branching!
*/
#include "fdlibm.h"
#ifdef __STDC__
int finite(double x)
#else
int finite(x)
double x;
#endif
{
int hx;
hx = __HI(x);
return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31;
}

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@ -1,91 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* floor(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floor(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double floor(double x)
#else
double floor(x)
double x;
#endif
{
int i0,i1,j0;
unsigned i,j;
i0 = __HI(x);
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=i1=0;}
else if(((i0&0x7fffffff)|i1)!=0)
{ i0=0xbff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) {
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if(j<i1) i0 +=1 ; /* got a carry */
i1=j;
}
}
i1 &= (~i);
}
}
__HI(x) = i0;
__LO(x) = i1;
return x;
}

68
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@ -1,68 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* for non-zero x
* x = frexp(arg,&exp);
* return a double fp quantity x such that 0.5 <= |x| <1.0
* and the corresponding binary exponent "exp". That is
* arg = x*2^exp.
* If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
* with *exp=0.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
#ifdef __STDC__
double frexp(double x, int *eptr)
#else
double frexp(x, eptr)
double x; int *eptr;
#endif
{
int hx, ix, lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
*eptr = 0;
if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
if (ix<0x00100000) { /* subnormal */
x *= two54;
hx = __HI(x);
ix = hx&0x7fffffff;
*eptr = -54;
}
*eptr += (ix>>20)-1022;
hx = (hx&0x800fffff)|0x3fe00000;
__HI(x) = hx;
return x;
}

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@ -1,58 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* ilogb(double x)
* return the binary exponent of non-zero x
* ilogb(0) = 0x80000001
* ilogb(inf/NaN) = 0x7fffffff (no signal is raised)
*/
#include "fdlibm.h"
#ifdef __STDC__
int ilogb(double x)
#else
int ilogb(x)
double x;
#endif
{
int hx,lx,ix;
hx = (__HI(x))&0x7fffffff; /* high word of x */
if(hx<0x00100000) {
lx = __LO(x);
if((hx|lx)==0)
return 0x80000001; /* ilogb(0) = 0x80000001 */
else /* subnormal x */
if(hx==0) {
for (ix = -1043; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7ff00000) return (hx>>20)-1023;
else return 0x7fffffff;
}

46
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@ -1,46 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* isnan(x) returns 1 is x is nan, else 0;
* no branching!
*/
#include "fdlibm.h"
#ifdef __STDC__
int isnan(double x)
#else
int isnan(x)
double x;
#endif
{
int hx,lx;
hx = (__HI(x)&0x7fffffff);
lx = __LO(x);
hx |= (unsigned)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return ((unsigned)(hx))>>31;
}

40
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@ -1,40 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#include "fdlibm.h"
#include <errno.h>
#ifdef __STDC__
double ldexp(double value, int exp)
#else
double ldexp(value, exp)
double value; int exp;
#endif
{
if(!finite(value)||value==0.0) return value;
value = scalbn(value,exp);
if(!finite(value)||value==0.0) errno = ERANGE;
return value;
}

47
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@ -1,47 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* MACRO for standards
*/
#include "fdlibm.h"
/*
* define and initialize _LIB_VERSION
*/
#ifdef _POSIX_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
#else
#ifdef _XOPEN_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
#else
#ifdef _SVID3_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
#else /* default _IEEE_MODE */
_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
#endif
#endif
#endif

183
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@ -1,183 +0,0 @@
/*
* Copyright (c) 1998, 2003, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* double log1p(double x)
*
* Method :
* 1. Argument Reduction: find k and f such that
* 1+x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* Note. If k=0, then f=x is exact. However, if k!=0, then f
* may not be representable exactly. In that case, a correction
* term is need. Let u=1+x rounded. Let c = (1+x)-u, then
* log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
* and add back the correction term c/u.
* (Note: when x > 2**53, one can simply return log(x))
*
* 2. Approximation of log1p(f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
* (the values of Lp1 to Lp7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lp1*s +...+Lp7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log1p(f) = f - (hfsq - s*(hfsq+R)).
*
* 3. Finally, log1p(x) = k*ln2 + log1p(f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log1p(x) is NaN with signal if x < -1 (including -INF) ;
* log1p(+INF) is +INF; log1p(-1) is -INF with signal;
* log1p(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*
* Note: Assuming log() return accurate answer, the following
* algorithm can be used to compute log1p(x) to within a few ULP:
*
* u = 1+x;
* if(u==1.0) return x ; else
* return log(u)*(x/(u-1.0));
*
* See HP-15C Advanced Functions Handbook, p.193.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
#ifdef __STDC__
double log1p(double x)
#else
double log1p(x)
double x;
#endif
{
double hfsq,f=0,c=0,s,z,R,u;
int k,hx,hu=0,ax;
hx = __HI(x); /* high word of x */
ax = hx&0x7fffffff;
k = 1;
if (hx < 0x3FDA827A) { /* x < 0.41422 */
if(ax>=0x3ff00000) { /* x <= -1.0 */
/*
* Added redundant test against hx to work around VC++
* code generation problem.
*/
if(x==-1.0 && (hx==0xbff00000)) /* log1p(-1)=-inf */
return -two54/zero;
else
return (x-x)/(x-x); /* log1p(x<-1)=NaN */
}
if(ax<0x3e200000) { /* |x| < 2**-29 */
if(two54+x>zero /* raise inexact */
&&ax<0x3c900000) /* |x| < 2**-54 */
return x;
else
return x - x*x*0.5;
}
if(hx>0||hx<=((int)0xbfd2bec3)) {
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
}
if (hx >= 0x7ff00000) return x+x;
if(k!=0) {
if(hx<0x43400000) {
u = 1.0+x;
hu = __HI(u); /* high word of u */
k = (hu>>20)-1023;
c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
c /= u;
} else {
u = x;
hu = __HI(u); /* high word of u */
k = (hu>>20)-1023;
c = 0;
}
hu &= 0x000fffff;
if(hu<0x6a09e) {
__HI(u) = hu|0x3ff00000; /* normalize u */
} else {
k += 1;
__HI(u) = hu|0x3fe00000; /* normalize u/2 */
hu = (0x00100000-hu)>>2;
}
f = u-1.0;
}
hfsq=0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}}
R = hfsq*(1.0-0.66666666666666666*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
s = f/(2.0+f);
z = s*s;
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

50
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@ -1,50 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* double logb(x)
* IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
* Use ilogb instead.
*/
#include "fdlibm.h"
#ifdef __STDC__
double logb(double x)
#else
double logb(x)
double x;
#endif
{
int lx,ix;
ix = (__HI(x))&0x7fffffff; /* high |x| */
lx = __LO(x); /* low x */
if((ix|lx)==0) return -1.0/fabs(x);
if(ix>=0x7ff00000) return x*x;
if((ix>>=20)==0) /* IEEE 754 logb */
return -1022.0;
else
return (double) (ix-1023);
}

38
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@ -1,38 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#include "fdlibm.h"
#ifdef __STDC__
int matherr(struct exception *x)
#else
int matherr(x)
struct exception *x;
#endif
{
int n=0;
if(x->arg1!=x->arg1) return 0;
return n;
}

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@ -1,92 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* modf(double x, double *iptr)
* return fraction part of x, and return x's integral part in *iptr.
* Method:
* Bit twiddling.
*
* Exception:
* No exception.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0;
#else
static double one = 1.0;
#endif
#ifdef __STDC__
double modf(double x, double *iptr)
#else
double modf(x, iptr)
double x,*iptr;
#endif
{
int i0,i1,j0;
unsigned i;
i0 = __HI(x); /* high x */
i1 = __LO(x); /* low x */
j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */
if(j0<20) { /* integer part in high x */
if(j0<0) { /* |x|<1 */
__HIp(iptr) = i0&0x80000000;
__LOp(iptr) = 0; /* *iptr = +-0 */
return x;
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) { /* x is integral */
*iptr = x;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else {
__HIp(iptr) = i0&(~i);
__LOp(iptr) = 0;
return x - *iptr;
}
}
} else if (j0>51) { /* no fraction part */
*iptr = x*one;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else { /* fraction part in low x */
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) { /* x is integral */
*iptr = x;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else {
__HIp(iptr) = i0;
__LOp(iptr) = i1&(~i);
return x - *iptr;
}
}
}

90
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@ -1,90 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* IEEE functions
* nextafter(x,y)
* return the next machine floating-point number of x in the
* direction toward y.
* Special cases:
*/
#include "fdlibm.h"
#ifdef __STDC__
double nextafter(double x, double y)
#else
double nextafter(x,y)
double x,y;
#endif
{
int hx,hy,ix,iy;
unsigned lx,ly;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hy = __HI(y); /* high word of y */
ly = __LO(y); /* low word of y */
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffff; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
return x+y;
if(x==y) return x; /* x=y, return x */
if((ix|lx)==0) { /* x == 0 */
__HI(x) = hy&0x80000000; /* return +-minsubnormal */
__LO(x) = 1;
y = x*x;
if(y==x) return y; else return x; /* raise underflow flag */
}
if(hx>=0) { /* x > 0 */
if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
} else { /* x < 0 */
if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
}
hy = hx&0x7ff00000;
if(hy>=0x7ff00000) return x+x; /* overflow */
if(hy<0x00100000) { /* underflow */
y = x*x;
if(y!=x) { /* raise underflow flag */
__HI(y) = hx; __LO(y) = lx;
return y;
}
}
__HI(x) = hx; __LO(x) = lx;
return x;
}

96
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@ -1,96 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* rint(x)
* Return x rounded to integral value according to the prevailing
* rounding mode.
* Method:
* Using floating addition.
* Exception:
* Inexact flag raised if x not equal to rint(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
TWO52[2]={
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
};
#ifdef __STDC__
double rint(double x)
#else
double rint(x)
double x;
#endif
{
int i0,j0,sx;
unsigned i,i1;
double w,t;
i0 = __HI(x);
sx = (i0>>31)&1;
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) {
if(((i0&0x7fffffff)|i1)==0) return x;
i1 |= (i0&0x0fffff);
i0 &= 0xfffe0000;
i0 |= ((i1|-i1)>>12)&0x80000;
__HI(x)=i0;
w = TWO52[sx]+x;
t = w-TWO52[sx];
i0 = __HI(t);
__HI(t) = (i0&0x7fffffff)|(sx<<31);
return t;
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
i>>=1;
if(((i0&i)|i1)!=0) {
if(j0==19) i1 = 0x40000000; else
i0 = (i0&(~i))|((0x20000)>>j0);
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
i>>=1;
if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
}
__HI(x) = i0;
__LO(x) = i1;
w = TWO52[sx]+x;
return w-TWO52[sx];
}

76
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@ -1,76 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* scalbn (double x, int n)
* scalbn(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
huge = 1.0e+300,
tiny = 1.0e-300;
#ifdef __STDC__
double scalbn (double x, int n)
#else
double scalbn (x,n)
double x; int n;
#endif
{
int k,hx,lx;
hx = __HI(x);
lx = __LO(x);
k = (hx&0x7ff00000)>>20; /* extract exponent */
if (k==0) { /* 0 or subnormal x */
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
x *= two54;
hx = __HI(x);
k = ((hx&0x7ff00000)>>20) - 54;
if (n< -50000) return tiny*x; /*underflow*/
}
if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
if (k > 0) /* normal result */
{__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
if (k <= -54) {
if (n > 50000) /* in case integer overflow in n+k */
return huge*copysign(huge,x); /*overflow*/
else return tiny*copysign(tiny,x); /*underflow*/
}
k += 54; /* subnormal result */
__HI(x) = (hx&0x800fffff)|(k<<20);
return x*twom54;
}

27
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@ -1,27 +0,0 @@
/*
* Copyright (c) 1998, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
#include "fdlibm.h"
int signgam = 0;

42
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@ -1,42 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* significand(x) computes just
* scalb(x, (double) -ilogb(x)),
* for exercising the fraction-part(F) IEEE 754-1985 test vector.
*/
#include "fdlibm.h"
#ifdef __STDC__
double significand(double x)
#else
double significand(x)
double x;
#endif
{
return __ieee754_scalb(x,(double) -ilogb(x));
}

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@ -1,90 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* sin(x)
* Return sine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cose function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double sin(double x)
#else
double sin(x)
double x;
#endif
{
double y[2],z=0.0;
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_sin(y[0],y[1],1);
case 1: return __kernel_cos(y[0],y[1]);
case 2: return -__kernel_sin(y[0],y[1],1);
default:
return -__kernel_cos(y[0],y[1]);
}
}
}

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@ -1,84 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* tan(x)
* Return tangent function of x.
*
* kernel function:
* __kernel_tan ... tangent function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double tan(double x)
#else
double tan(x)
double x;
#endif
{
double y[2],z=0.0;
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
/* tan(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x; /* NaN */
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}

94
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@ -1,94 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* Tanh(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanh(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
* -t
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
* t + 2
* 2
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
* t + 2
* 22.0 < x <= INF : tanh(x) := 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one=1.0, two=2.0, tiny = 1.0e-300;
#else
static double one=1.0, two=2.0, tiny = 1.0e-300;
#endif
#ifdef __STDC__
double tanh(double x)
#else
double tanh(x)
double x;
#endif
{
double t,z;
int jx,ix;
/* High word of |x|. */
jx = __HI(x);
ix = jx&0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
/* |x| < 22 */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3c800000) /* |x|<2**-55 */
return x*(one+x); /* tanh(small) = small */
if (ix>=0x3ff00000) { /* |x|>=1 */
t = expm1(two*fabs(x));
z = one - two/(t+two);
} else {
t = expm1(-two*fabs(x));
z= -t/(t+two);
}
/* |x| > 22, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}

52
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@ -1,52 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrap_acos(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double acos(double x) /* wrapper acos */
#else
double acos(x) /* wrapper acos */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_acos(x);
#else
double z;
z = __ieee754_acos(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>1.0) {
return __kernel_standard(x,x,1); /* acos(|x|>1) */
} else
return z;
#endif
}

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@ -1,53 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper asin(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double asin(double x) /* wrapper asin */
#else
double asin(x) /* wrapper asin */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_asin(x);
#else
double z;
z = __ieee754_asin(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>1.0) {
return __kernel_standard(x,x,2); /* asin(|x|>1) */
} else
return z;
#endif
}

52
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@ -1,52 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper atan2(y,x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double atan2(double y, double x) /* wrapper atan2 */
#else
double atan2(y,x) /* wrapper atan2 */
double y,x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atan2(y,x);
#else
double z;
z = __ieee754_atan2(y,x);
if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z;
if(x==0.0&&y==0.0) {
return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
} else
return z;
#endif
}

55
src/java.base/share/native/libfdlibm/w_atanh.c
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@ -1,55 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper atanh(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double atanh(double x) /* wrapper atanh */
#else
double atanh(x) /* wrapper atanh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_atanh(x);
#else
double z,y;
z = __ieee754_atanh(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
y = fabs(x);
if(y>=1.0) {
if(y>1.0)
return __kernel_standard(x,x,30); /* atanh(|x|>1) */
else
return __kernel_standard(x,x,31); /* atanh(|x|==1) */
} else
return z;
#endif
}

51
src/java.base/share/native/libfdlibm/w_cosh.c
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@ -1,51 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper cosh(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double cosh(double x) /* wrapper cosh */
#else
double cosh(x) /* wrapper cosh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_cosh(x);
#else
double z;
z = __ieee754_cosh(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>7.10475860073943863426e+02) {
return __kernel_standard(x,x,5); /* cosh overflow */
} else
return z;
#endif
}

62
src/java.base/share/native/libfdlibm/w_exp.c
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@ -1,62 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper exp(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
#ifdef __STDC__
double exp(double x) /* wrapper exp */
#else
double exp(x) /* wrapper exp */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_exp(x);
#else
double z;
z = __ieee754_exp(x);
if(_LIB_VERSION == _IEEE_) return z;
if(finite(x)) {
if(x>o_threshold)
return __kernel_standard(x,x,6); /* exp overflow */
else if(x<u_threshold)
return __kernel_standard(x,x,7); /* exp underflow */
}
return z;
#endif
}

52
src/java.base/share/native/libfdlibm/w_fmod.c
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@ -1,52 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper fmod(x,y)
*/
#include "fdlibm.h"
#ifdef __STDC__
double fmod(double x, double y) /* wrapper fmod */
#else
double fmod(x,y) /* wrapper fmod */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_fmod(x,y);
#else
double z;
z = __ieee754_fmod(x,y);
if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z;
if(y==0.0) {
return __kernel_standard(x,y,27); /* fmod(x,0) */
} else
return z;
#endif
}

52
src/java.base/share/native/libfdlibm/w_log.c
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@ -1,52 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper log(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double log(double x) /* wrapper log */
#else
double log(x) /* wrapper log */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_log(x);
#else
double z;
z = __ieee754_log(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
if(x==0.0)
return __kernel_standard(x,x,16); /* log(0) */
else
return __kernel_standard(x,x,17); /* log(x<0) */
#endif
}

55
src/java.base/share/native/libfdlibm/w_log10.c
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@ -1,55 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper log10(X)
*/
#include "fdlibm.h"
#ifdef __STDC__
double log10(double x) /* wrapper log10 */
#else
double log10(x) /* wrapper log10 */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_log10(x);
#else
double z;
z = __ieee754_log10(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<=0.0) {
if(x==0.0)
return __kernel_standard(x,x,18); /* log10(0) */
else
return __kernel_standard(x,x,19); /* log10(x<0) */
} else
return z;
#endif
}

51
src/java.base/share/native/libfdlibm/w_remainder.c
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@ -1,51 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper remainder(x,p)
*/
#include "fdlibm.h"
#ifdef __STDC__
double remainder(double x, double y) /* wrapper remainder */
#else
double remainder(x,y) /* wrapper remainder */
double x,y;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_remainder(x,y);
#else
double z;
z = __ieee754_remainder(x,y);
if(_LIB_VERSION == _IEEE_ || isnan(y)) return z;
if(y==0.0)
return __kernel_standard(x,y,28); /* remainder(x,0) */
else
return z;
#endif
}

69
src/java.base/share/native/libfdlibm/w_scalb.c
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@ -1,69 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper scalb(double x, double fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
#include "fdlibm.h"
#include <errno.h>
#ifdef __STDC__
#ifdef _SCALB_INT
double scalb(double x, int fn) /* wrapper scalb */
#else
double scalb(double x, double fn) /* wrapper scalb */
#endif
#else
double scalb(x,fn) /* wrapper scalb */
#ifdef _SCALB_INT
double x; int fn;
#else
double x,fn;
#endif
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_scalb(x,fn);
#else
double z;
z = __ieee754_scalb(x,fn);
if(_LIB_VERSION == _IEEE_) return z;
if(!(finite(z)||isnan(z))&&finite(x)) {
return __kernel_standard(x,(double)fn,32); /* scalb overflow */
}
if(z==0.0&&z!=x) {
return __kernel_standard(x,(double)fn,33); /* scalb underflow */
}
#ifndef _SCALB_INT
if(!finite(fn)) errno = ERANGE;
#endif
return z;
#endif
}

51
src/java.base/share/native/libfdlibm/w_sinh.c
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@ -1,51 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper sinh(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double sinh(double x) /* wrapper sinh */
#else
double sinh(x) /* wrapper sinh */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sinh(x);
#else
double z;
z = __ieee754_sinh(x);
if(_LIB_VERSION == _IEEE_) return z;
if(!finite(z)&&finite(x)) {
return __kernel_standard(x,x,25); /* sinh overflow */
} else
return z;
#endif
}

51
src/java.base/share/native/libfdlibm/w_sqrt.c
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@ -1,51 +0,0 @@
/*
* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* wrapper sqrt(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double sqrt(double x) /* wrapper sqrt */
#else
double sqrt(x) /* wrapper sqrt */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sqrt(x);
#else
double z;
z = __ieee754_sqrt(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<0.0) {
return __kernel_standard(x,x,26); /* sqrt(negative) */
} else
return z;
#endif
}