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< div class = "textblock" > < code > #include " < a class = "el" href = "real_2prim_8h_source.html" > prim.h< / a > " < / code > < br / >
< code > #include " < a class = "el" href = "math_8h_source.html" > math.h< / a > " < / code > < br / >
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Include dependency graph for acosh.c:< / div >
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< map name = "lib_2real_2acosh_8c" id = "lib_2real_2acosh_8c" >
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< p > < a href = "acosh_8c_source.html" > Go to the source code of this file.< / a > < / p >
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Functions< / h2 > < / td > < / tr >
< tr class = "memitem:ac862445bcb46911b1782c284829d5e46" > < td class = "memItemLeft" align = "right" valign = "top" > double  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "acosh_8c.html#ac862445bcb46911b1782c284829d5e46" > acosh< / a > (double x)< / td > < / tr >
< tr class = "memdesc:ac862445bcb46911b1782c284829d5e46" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Inverse hyperbolic cosine function. < a href = "#ac862445bcb46911b1782c284829d5e46" > More...< / a > < br / > < / td > < / tr >
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Variables< / h2 > < / td > < / tr >
< tr class = "memitem:ada85e349d35971b32c8ea4238881ff8b" > < td class = "memItemLeft" align = "right" valign = "top" > static const double  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b" > one< / a > = 1.0< / td > < / tr >
< tr class = "separator:ada85e349d35971b32c8ea4238881ff8b" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:a703f4fc93e5a57058ce6ba2ba196918d" > < td class = "memItemLeft" align = "right" valign = "top" > static const double  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d" > ln2< / a > = 6.93147180559945286227e-01< / td > < / tr >
< tr class = "separator:a703f4fc93e5a57058ce6ba2ba196918d" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< h2 class = "groupheader" > Function Documentation< / h2 >
< a class = "anchor" id = "ac862445bcb46911b1782c284829d5e46" > < / a >
< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > double acosh < / td >
< td > (< / td >
< td class = "paramtype" > double  < / td >
< td class = "paramname" > < em > x< / em > < / td > < td > )< / td >
< td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
< p > Inverse hyperbolic cosine function. < / p >
< dl class = "section version" > < dt > Version< / dt > < dd > 1.3 < / dd > < / dl >
< dl class = "section date" > < dt > Date< / dt > < dd > 95/01/18< / dd > < / dl >
< pre >
Method :
Based on
acosh(x) = log [ x + sqrt(x*x-1) ]
we have
acosh(x) := log(x)+ln2, if x is large; else
acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x> 2; else
acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.< / pre > < pre > Special cases:
acosh(x) is NaN with signal if x< 1.
acosh(NaN) is NaN without signal.
< / pre > < dl class = "section copyright" > < dt > Copyright< / dt > < dd > 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. < / dd > < / dl >
< p > Definition at line < a class = "el" href = "acosh_8c_source.html#l00075" > 75< / a > of file < a class = "el" href = "acosh_8c_source.html" > acosh.c< / a > .< / p >
< p > References < a class = "el" href = "acosh_8c_source.html#l00049" > ln2< / a > , < a class = "el" href = "log1p_8c_source.html#l00125" > log1p()< / a > , < a class = "el" href = "acosh_8c_source.html#l00048" > one< / a > , and < a class = "el" href = "sqrt_8c_source.html#l00127" > sqrt()< / a > .< / p >
< p > Referenced by < a class = "el" href = "real_8cpp_source.html#l00477" > RealNumber::HypArcCosine()< / a > , and < a class = "el" href = "real_8cpp_source.html#l00487" > RealNumber::HypArcSecant()< / a > .< / p >
< div class = "fragment" > < div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   {< / div > < div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "keywordtype" > double< / span > t;< / div > < div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   < a class = "code" href = "real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77" > sword< / a > hx, lx;< / div > < div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   < a class = "code" href = "real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195" > GET_HIGH_WORD< / a > (hx,x);< / div > < div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < a class = "code" href = "real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22" > GET_LOW_WORD< / a > (lx,x);< / div > < div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < / div > < div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "keywordflow" > if< / span > (hx< 0x3ff00000) { < span class = "comment" > /* x < 1 */< / span > < / div > < div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "keywordflow" > return< / span > (x-x)/(x-x);< / div > < div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   } < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (hx > =0x41b00000) { < span class = "comment" > /* x > 2**28 */< / span > < / div > < div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "keywordflow" > if< / span > (hx > =0x7ff00000) { < span class = "comment" > /* x is inf of NaN */< / span > < / div > < div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "keywordflow" > return< / span > x+x;< / div > < div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   } < span class = "keywordflow" > else< / span > < / div > < div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "math_8h.html#adb302c9aafbaa5e180d9f60ee954bb82" > log< / a > (x)+< a class = "code" href = "acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d" > ln2< / a > ; < span class = "comment" > /* acosh(huge)=log(2x) */< / span > < / div > < div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   } < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (((hx-0x3ff00000)|lx)==0) {< / div > < div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "keywordflow" > return< / span > 0.0; < span class = "comment" > /* acosh(1) = 0 */< / span > < / div > < div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   } < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (hx > 0x40000000) { < span class = "comment" > /* 2**28 > x > 2 */< / span > < / div > < div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   t=x*x;< / div > < div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "math_8h.html#adb302c9aafbaa5e180d9f60ee954bb82" > log< / a > (2.0*x-< a class = "code" href = "acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b" > one< / a > /(x+< a class = "code" href = "math_8h.html#ab87521a75ef827a85807f89a6c10629a" > sqrt< / a > (t-< a class = "code" href = "acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b" > one< / a > )));< / div > < div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   } < span class = "keywordflow" > else< / span > { < span class = "comment" > /* 1< x< 2 */< / span > < / div > < div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   t = x-< a class = "code" href = "acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b" > one< / a > ;< / div > < div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "math_8h.html#ac2aac20ab1347498e6e4f209148fea84" > log1p< / a > (t+< a class = "code" href = "math_8h.html#ab87521a75ef827a85807f89a6c1062
< div class = "ttc" id = "real_2prim_8h_html_ae62ee08d06ab4cc06d61dc1246b73195" > < div class = "ttname" > < a href = "real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195" > GET_HIGH_WORD< / a > < / div > < div class = "ttdeci" > #define GET_HIGH_WORD(i, d)< / div > < div class = "ttdoc" > Get the more significant 32 bit int from a double. < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "real_2prim_8h_source.html#l00165" > prim.h:165< / a > < / div > < / div >
< div class = "ttc" id = "math_8h_html_ac2aac20ab1347498e6e4f209148fea84" > < div class = "ttname" > < a href = "math_8h.html#ac2aac20ab1347498e6e4f209148fea84" > log1p< / a > < / div > < div class = "ttdeci" > double log1p(double x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "log1p_8c_source.html#l00125" > log1p.c:125< / a > < / div > < / div >
< div class = "ttc" id = "real_2prim_8h_html_adee023704c856ea8f310e8e3fd765a22" > < div class = "ttname" > < a href = "real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22" > GET_LOW_WORD< / a > < / div > < div class = "ttdeci" > #define GET_LOW_WORD(i, d)< / div > < div class = "ttdoc" > Get the less significant 32 bit int from a double. < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "real_2prim_8h_source.html#l00176" > prim.h:176< / a > < / div > < / div >
< div class = "ttc" id = "real_2prim_8h_html_ae91287c8a5f73a8a22a100f50dc4de77" > < div class = "ttname" > < a href = "real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77" > sword< / a > < / div > < div class = "ttdeci" > signed int sword< / div > < div class = "ttdoc" > 32 bit signed integer. < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "real_2prim_8h_source.html#l00107" > prim.h:107< / a > < / div > < / div >
< div class = "ttc" id = "math_8h_html_ab87521a75ef827a85807f89a6c10629a" > < div class = "ttname" > < a href = "math_8h.html#ab87521a75ef827a85807f89a6c10629a" > sqrt< / a > < / div > < div class = "ttdeci" > double sqrt(double x)< / div > < div class = "ttdoc" > Square root function. < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sqrt_8c_source.html#l00127" > sqrt.c:127< / a > < / div > < / div >
< div class = "ttc" id = "math_8h_html_adb302c9aafbaa5e180d9f60ee954bb82" > < div class = "ttname" > < a href = "math_8h.html#adb302c9aafbaa5e180d9f60ee954bb82" > log< / a > < / div > < div class = "ttdeci" > double log(double x)< / div > < div class = "ttdoc" > Natural logarithm function (base e). < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "log_8c_source.html#l00118" > log.c:118< / a > < / div > < / div >
< div class = "ttc" id = "acosh_8c_html_a703f4fc93e5a57058ce6ba2ba196918d" > < div class = "ttname" > < a href = "acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d" > ln2< / a > < / div > < div class = "ttdeci" > static const double ln2< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "acosh_8c_source.html#l00049" > acosh.c:49< / a > < / div > < / div >
< / div > <!-- fragment -->
< p > < div class = "dynheader" >
Here is the call graph for this function:< / div >
< div class = "dyncontent" >
< div class = "center" > < img src = "acosh_8c_ac862445bcb46911b1782c284829d5e46_cgraph.png" border = "0" usemap = "#acosh_8c_ac862445bcb46911b1782c284829d5e46_cgraph" alt = "" / > < / div >
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Here is the caller graph for this function:< / div >
< div class = "dyncontent" >
< div class = "center" > < img src = "acosh_8c_ac862445bcb46911b1782c284829d5e46_icgraph.png" border = "0" usemap = "#acosh_8c_ac862445bcb46911b1782c284829d5e46_icgraph" alt = "" / > < / div >
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< h2 class = "groupheader" > Variable Documentation< / h2 >
< a class = "anchor" id = "a703f4fc93e5a57058ce6ba2ba196918d" > < / a >
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< td class = "memname" > const double ln2 = 6.93147180559945286227e-01< / td >
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< span class = "mlabels" > < span class = "mlabel" > static< / span > < / span > < / td >
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< p > Definition at line < a class = "el" href = "acosh_8c_source.html#l00049" > 49< / a > of file < a class = "el" href = "acosh_8c_source.html" > acosh.c< / a > .< / p >
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< p > Definition at line < a class = "el" href = "acosh_8c_source.html#l00048" > 48< / a > of file < a class = "el" href = "acosh_8c_source.html" > acosh.c< / a > .< / p >
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