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体验新版 GitCode,发现更多精彩内容 >>
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f1434582
编写于
12月 16, 2012
作者:
S
Szabolcs Nagy
浏览文件
操作
浏览文件
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电子邮件补丁
差异文件
math: sinh.c cleanup similar to the cosh one
comments are kept in the double version of the function
上级
1aec620f
变更
3
显示空白变更内容
内联
并排
Showing
3 changed file
with
72 addition
and
171 deletion
+72
-171
src/math/sinh.c
src/math/sinh.c
+29
-61
src/math/sinhf.c
src/math/sinhf.c
+20
-46
src/math/sinhl.c
src/math/sinhl.c
+23
-64
未找到文件。
src/math/sinh.c
浏览文件 @
f1434582
/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* 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 "libm.h"
#include "libm.h"
static
const
double
huge
=
1.0e307
;
/* sinh(x) = (exp(x) - 1/exp(x))/2
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
* = x + x^3/6 + o(x^5)
*/
double
sinh
(
double
x
)
double
sinh
(
double
x
)
{
{
double
t
,
h
;
union
{
double
f
;
uint64_t
i
;}
u
=
{.
f
=
x
};
int32_t
ix
,
jx
;
uint32_t
w
;
double
t
,
h
,
absx
;
/* High word of |x|. */
GET_HIGH_WORD
(
jx
,
x
);
ix
=
jx
&
0x7fffffff
;
/* x is INF or NaN */
if
(
ix
>=
0x7ff00000
)
return
x
+
x
;
h
=
0
.
5
;
h
=
0
.
5
;
if
(
jx
<
0
)
h
=
-
h
;
if
(
u
.
i
>>
63
)
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
h
=
-
h
;
if
(
ix
<
0x40360000
)
{
/* |x|<22 */
/* |x| */
if
(
ix
<
0x3e300000
)
/* |x|<2**-28 */
u
.
i
&=
(
uint64_t
)
-
1
/
2
;
/* raise inexact, return x */
absx
=
u
.
f
;
if
(
huge
+
x
>
1
.
0
)
w
=
u
.
i
>>
32
;
/* |x| < log(DBL_MAX) */
if
(
w
<
0x40862e42
)
{
t
=
expm1
(
absx
);
if
(
w
<
0x3ff00000
)
{
if
(
w
<
0x3ff00000
-
(
26
<<
20
))
/* note: inexact is raised by expm1 */
/* note: this branch avoids underflow */
return
x
;
return
x
;
t
=
expm1
(
fabs
(
x
));
return
h
*
(
2
*
t
-
t
*
t
/
(
t
+
1
));
if
(
ix
<
0x3ff00000
)
}
return
h
*
(
2
.
0
*
t
-
t
*
t
/
(
t
+
1
.
0
));
/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
return
h
*
(
t
+
t
/
(
t
+
1
.
0
));
return
h
*
(
t
+
t
/
(
t
+
1
));
}
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
/* |x| > log(DBL_MAX) or nan */
if
(
ix
<
0x40862E42
)
/* note: the result is stored to handle overflow */
return
h
*
exp
(
fabs
(
x
));
t
=
2
*
h
*
__expo2
(
absx
);
return
t
;
/* |x| in [log(maxdouble), overflowthresold] */
if
(
ix
<=
0x408633CE
)
return
h
*
2
.
0
*
__expo2
(
fabs
(
x
));
/* h is for sign only */
/* |x| > overflowthresold, sinh(x) overflow */
return
x
*
huge
;
}
}
src/math/sinhf.c
浏览文件 @
f1434582
/* origin: FreeBSD /usr/src/lib/msun/src/e_sinhf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "libm.h"
#include "libm.h"
static
const
float
huge
=
1.0e37
;
float
sinhf
(
float
x
)
float
sinhf
(
float
x
)
{
{
float
t
,
h
;
union
{
float
f
;
uint32_t
i
;}
u
=
{.
f
=
x
};
int32_t
ix
,
jx
;
uint32_t
w
;
float
t
,
h
,
absx
;
GET_FLOAT_WORD
(
jx
,
x
);
ix
=
jx
&
0x7fffffff
;
/* x is INF or NaN */
if
(
ix
>=
0x7f800000
)
return
x
+
x
;
h
=
0
.
5
;
h
=
0
.
5
;
if
(
jx
<
0
)
if
(
u
.
i
>>
31
)
h
=
-
h
;
h
=
-
h
;
/* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */
/* |x| */
if
(
ix
<
0x41100000
)
{
/* |x|<9 */
u
.
i
&=
0x7fffffff
;
if
(
ix
<
0x39800000
)
/* |x|<2**-12 */
absx
=
u
.
f
;
/* raise inexact, return x */
w
=
u
.
i
;
if
(
huge
+
x
>
1
.
0
f
)
/* |x| < log(FLT_MAX) */
if
(
w
<
0x42b17217
)
{
t
=
expm1f
(
absx
);
if
(
w
<
0x3f800000
)
{
if
(
w
<
0x3f800000
-
(
12
<<
23
))
return
x
;
return
x
;
t
=
expm1f
(
fabsf
(
x
));
return
h
*
(
2
*
t
-
t
*
t
/
(
t
+
1
));
if
(
ix
<
0x3f800000
)
}
return
h
*
(
2
.
0
f
*
t
-
t
*
t
/
(
t
+
1
.
0
f
));
return
h
*
(
t
+
t
/
(
t
+
1
));
return
h
*
(
t
+
t
/
(
t
+
1
.
0
f
));
}
}
/* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */
/* |x| > logf(FLT_MAX) or nan */
if
(
ix
<
0x42b17217
)
t
=
2
*
h
*
__expo2f
(
absx
);
return
h
*
expf
(
fabsf
(
x
));
return
t
;
/* |x| in [logf(maxfloat), overflowthresold] */
if
(
ix
<=
0x42b2d4fc
)
return
h
*
2
.
0
f
*
__expo2f
(
fabsf
(
x
));
/* h is for sign only */
/* |x| > overflowthresold, sinh(x) overflow */
return
x
*
huge
;
}
}
src/math/sinhl.c
浏览文件 @
f1434582
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* sinhl(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
* 2
*
* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
* ln2ovft < x : sinhl(x) := x*huge (overflow)
*
* Special cases:
* sinhl(x) is |x| if x is +INF, -INF, or NaN.
* only sinhl(0)=0 is exact for finite x.
*/
#include "libm.h"
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
...
@@ -35,47 +6,35 @@ long double sinhl(long double x)
...
@@ -35,47 +6,35 @@ long double sinhl(long double x)
return
sinh
(
x
);
return
sinh
(
x
);
}
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static
const
long
double
huge
=
1.0e4931L
;
long
double
sinhl
(
long
double
x
)
long
double
sinhl
(
long
double
x
)
{
{
long
double
t
,
w
,
h
;
union
{
uint32_t
jx
,
ix
,
i0
,
i1
;
long
double
f
;
struct
{
uint64_t
m
;
uint16_t
se
;
uint16_t
pad
;}
i
;
/* Words of |x|. */
}
u
=
{.
f
=
x
};
GET_LDOUBLE_WORDS
(
jx
,
i0
,
i1
,
x
);
unsigned
ex
=
u
.
i
.
se
&
0x7fff
;
ix
=
jx
&
0x7fff
;
long
double
h
,
t
,
absx
;
/* x is INF or NaN */
if
(
ix
==
0x7fff
)
return
x
+
x
;
h
=
0
.
5
;
h
=
0
.
5
;
if
(
jx
&
0x8000
)
if
(
u
.
i
.
se
&
0x8000
)
h
=
-
h
;
h
=
-
h
;
/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
/* |x| */
if
(
ix
<
0x4003
||
(
ix
==
0x4003
&&
i0
<=
0xc8000000
))
{
/* |x| < 25 */
u
.
i
.
se
=
ex
;
if
(
ix
<
0x3fdf
)
/* |x|<2**-32 */
absx
=
u
.
f
;
if
(
huge
+
x
>
1
.
0
)
return
x
;
/* sinh(tiny) = tiny with inexact */
/* |x| < log(LDBL_MAX) */
t
=
expm1l
(
fabsl
(
x
));
if
(
ex
<
0x3fff
+
13
||
(
ex
==
0x3fff
+
13
&&
u
.
i
.
m
>>
32
<
0xb17217f7
))
{
if
(
ix
<
0x3fff
)
t
=
expm1l
(
absx
);
return
h
*
(
2
.
0
*
t
-
t
*
t
/
(
t
+
1
.
0
));
if
(
ex
<
0x3fff
)
{
return
h
*
(
t
+
t
/
(
t
+
1
.
0
));
if
(
ex
<
0x3fff
-
32
)
return
x
;
return
h
*
(
2
*
t
-
t
*
t
/
(
1
+
t
));
}
}
return
h
*
(
t
+
t
/
(
t
+
1
));
/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
if
(
ix
<
0x400c
||
(
ix
==
0x400c
&&
i0
<
0xb17217f7
))
return
h
*
expl
(
fabsl
(
x
));
/* |x| in [log(maxdouble), overflowthreshold] */
if
(
ix
<
0x400c
||
(
ix
==
0x400c
&&
(
i0
<
0xb174ddc0
||
(
i0
==
0xb174ddc0
&&
i1
<=
0x31aec0ea
))))
{
w
=
expl
(
0
.
5
*
fabsl
(
x
));
t
=
h
*
w
;
return
t
*
w
;
}
}
/* |x| > overflowthreshold, sinhl(x) overflow */
/* |x| > log(LDBL_MAX) or nan */
return
x
*
huge
;
t
=
expl
(
0
.
5
*
absx
);
return
h
*
t
*
t
;
}
}
#endif
#endif
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