[444] | 1 | @node Math |
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| 2 | @chapter Mathematical Functions (@file{math.h}) |
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| 3 | |
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| 4 | This chapter groups a wide variety of mathematical functions. The |
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| 5 | corresponding definitions and declarations are in @file{math.h}. |
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| 6 | Two definitions from @file{math.h} are of particular interest. |
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| 7 | |
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| 8 | @enumerate |
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| 9 | @item |
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| 10 | The representation of infinity as a @code{double} is defined as |
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| 11 | @code{HUGE_VAL}; this number is returned on overflow by many functions. |
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| 12 | |
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| 13 | @item |
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| 14 | The structure @code{exception} is used when you write customized error |
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| 15 | handlers for the mathematical functions. You can customize error |
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| 16 | handling for most of these functions by defining your own version of |
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| 17 | @code{matherr}; see the section on @code{matherr} for details. |
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| 18 | @end enumerate |
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| 19 | |
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| 20 | @cindex system calls |
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| 21 | @cindex support subroutines |
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| 22 | @cindex stubs |
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| 23 | @cindex OS stubs |
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| 24 | Since the error handling code calls @code{fputs}, the mathematical |
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| 25 | subroutines require stubs or minimal implementations for the same list |
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| 26 | of OS subroutines as @code{fputs}: @code{close}, @code{fstat}, |
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| 27 | @code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}. |
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| 28 | @xref{syscalls,,System Calls, libc.info, The Red Hat newlib C Library}, |
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| 29 | for a discussion and for sample minimal implementations of these support |
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| 30 | subroutines. |
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| 31 | |
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| 32 | Alternative declarations of the mathematical functions, which exploit |
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| 33 | specific machine capabilities to operate faster---but generally have |
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| 34 | less error checking and may reflect additional limitations on some |
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| 35 | machines---are available when you include @file{fastmath.h} instead of |
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| 36 | @file{math.h}. |
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| 37 | |
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| 38 | @menu |
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| 39 | * version:: Version of library |
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| 40 | * acos:: Arccosine |
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| 41 | * acosh:: Inverse hyperbolic cosine |
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| 42 | * asin:: Arcsine |
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| 43 | * asinh:: Inverse hyperbolic sine |
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| 44 | * atan:: Arctangent |
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| 45 | * atan2:: Arctangent of y/x |
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| 46 | * atanh:: Inverse hyperbolic tangent |
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| 47 | * jN:: Bessel functions (jN, yN) |
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| 48 | * cbrt:: Cube root |
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| 49 | * copysign:: Sign of Y, magnitude of X |
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| 50 | * cosh:: Hyperbolic cosine |
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| 51 | * erf:: Error function (erf, erfc) |
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| 52 | * exp:: Exponential |
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| 53 | * expm1:: Exponential of x, - 1 |
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| 54 | * fabs:: Absolute value (magnitude) |
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| 55 | * floor:: Floor and ceiling (floor, ceil) |
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| 56 | * fmod:: Floating-point remainder (modulo) |
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| 57 | * frexp:: Split floating-point number |
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| 58 | * gamma:: Logarithmic gamma function |
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| 59 | * hypot:: Distance from origin |
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| 60 | * ilogb:: Get exponent |
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| 61 | * infinity:: Floating infinity |
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| 62 | * isnan:: Check type of number |
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| 63 | * ldexp:: Load exponent |
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| 64 | * log:: Natural logarithms |
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| 65 | * log10:: Base 10 logarithms |
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| 66 | * log1p:: Log of 1 + X |
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| 67 | * matherr:: Modifiable math error handler |
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| 68 | * modf:: Split fractional and integer parts |
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| 69 | * nan:: Floating Not a Number |
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| 70 | * nextafter:: Get next representable number |
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| 71 | * pow:: X to the power Y |
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| 72 | * remainder:: remainder of X divided by Y |
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| 73 | * scalbn:: scalbn |
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| 74 | * sin:: Sine or cosine (sin, cos) |
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| 75 | * sinh:: Hyperbolic sine |
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| 76 | * sqrt:: Positive square root |
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| 77 | * tan:: Tangent |
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| 78 | * tanh:: Hyperbolic tangent |
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| 79 | @end menu |
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| 80 | |
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| 81 | @page |
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| 82 | @node version |
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| 83 | @section Version of library |
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| 84 | |
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| 85 | There are four different versions of the math library routines: IEEE, |
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| 86 | POSIX, X/Open, or SVID. The version may be selected at runtime by |
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| 87 | setting the global variable @code{_LIB_VERSION}, defined in |
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| 88 | @file{math.h}. It may be set to one of the following constants defined |
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| 89 | in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or |
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| 90 | @code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any |
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| 91 | thread, and changing it will affect all threads. |
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| 92 | |
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| 93 | The versions of the library differ only in how errors are handled. |
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| 94 | |
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| 95 | In IEEE mode, the @code{matherr} function is never called, no warning |
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| 96 | messages are printed, and @code{errno} is never set. |
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| 97 | |
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| 98 | In POSIX mode, @code{errno} is set correctly, but the @code{matherr} |
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| 99 | function is never called and no warning messages are printed. |
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| 100 | |
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| 101 | In X/Open mode, @code{errno} is set correctly, and @code{matherr} is |
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| 102 | called, but warning message are not printed. |
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| 103 | |
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| 104 | In SVID mode, functions which overflow return 3.40282346638528860e+38, |
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| 105 | the maximum single-precision floating-point value, rather than infinity. |
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| 106 | Also, @code{errno} is set correctly, @code{matherr} is called, and, if |
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| 107 | @code{matherr} returns 0, warning messages are printed for some errors. |
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| 108 | For example, by default @samp{log(-1.0)} writes this message on standard |
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| 109 | error output: |
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| 110 | |
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| 111 | @example |
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| 112 | log: DOMAIN error |
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| 113 | @end example |
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| 114 | |
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| 115 | The library is set to X/Open mode by default. |
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| 116 | |
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| 117 | @page |
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| 118 | @include mathfp/sacos.def |
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| 119 | |
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| 120 | @page |
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| 121 | @include mathfp/eacosh.def |
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| 122 | |
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| 123 | @page |
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| 124 | @include mathfp/sasine.def |
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| 125 | |
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| 126 | @page |
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| 127 | @include mathfp/sasinh.def |
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| 128 | |
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| 129 | @page |
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| 130 | @include mathfp/satan.def |
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| 131 | |
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| 132 | @page |
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| 133 | @include mathfp/satan2.def |
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| 134 | |
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| 135 | @page |
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| 136 | @include mathfp/eatanh.def |
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| 137 | |
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| 138 | @page |
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| 139 | @include mathfp/wjn.def |
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| 140 | |
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| 141 | @page |
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| 142 | @include common/scbrt.def |
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| 143 | |
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| 144 | @page |
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| 145 | @include common/scopysign.def |
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| 146 | |
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| 147 | @page |
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| 148 | @include mathfp/scosh.def |
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| 149 | |
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| 150 | @page |
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| 151 | @include mathfp/serf.def |
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| 152 | |
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| 153 | @page |
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| 154 | @include mathfp/sexp.def |
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| 155 | |
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| 156 | @page |
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| 157 | @include common/sexpm1.def |
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| 158 | |
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| 159 | @page |
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| 160 | @include mathfp/sfabs.def |
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| 161 | |
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| 162 | @page |
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| 163 | @include mathfp/sfloor.def |
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| 164 | |
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| 165 | @page |
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| 166 | @include mathfp/sfmod.def |
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| 167 | |
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| 168 | @page |
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| 169 | @include mathfp/sfrexp.def |
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| 170 | |
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| 171 | @page |
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| 172 | @include mathfp/erlgamma.def |
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| 173 | |
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| 174 | @page |
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| 175 | @include mathfp/ehypot.def |
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| 176 | |
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| 177 | @page |
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| 178 | @include common/silogb.def |
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| 179 | |
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| 180 | @page |
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| 181 | @include common/sinfinity.def |
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| 182 | |
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| 183 | @page |
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| 184 | @include common/sisnan.def |
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| 185 | |
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| 186 | @page |
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| 187 | @include mathfp/sldexp.def |
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| 188 | |
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| 189 | @page |
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| 190 | @include mathfp/slogarithm.def |
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| 191 | |
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| 192 | @page |
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| 193 | @include mathfp/slog10.def |
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| 194 | |
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| 195 | @page |
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| 196 | @include common/slog1p.def |
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| 197 | |
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| 198 | @page |
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| 199 | @include common/smatherr.def |
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| 200 | |
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| 201 | @page |
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| 202 | @include common/smodf.def |
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| 203 | |
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| 204 | @page |
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| 205 | @include common/snan.def |
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| 206 | |
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| 207 | @page |
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| 208 | @include common/snextafter.def |
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| 209 | |
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| 210 | @page |
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| 211 | @include mathfp/spow.def |
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| 212 | |
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| 213 | @page |
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| 214 | @include mathfp/eremainder.def |
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| 215 | |
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| 216 | @page |
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| 217 | @include common/sscalbn.def |
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| 218 | |
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| 219 | @page |
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| 220 | @include mathfp/ssqrt.def |
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| 221 | |
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| 222 | @page |
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| 223 | @include mathfp/ssine.def |
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| 224 | |
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| 225 | @page |
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| 226 | @include mathfp/ssineh.def |
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| 227 | |
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| 228 | @page |
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| 229 | @include mathfp/stan.def |
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| 230 | |
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| 231 | @page |
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| 232 | @include mathfp/stanh.def |
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