[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 | The macro @code{HUGE_VALF} is a corresponding value for @code{float}. |
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| 13 | |
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| 14 | @item |
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| 15 | The structure @code{exception} is used when you write customized error |
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| 16 | handlers for the mathematical functions. You can customize error |
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| 17 | handling for most of these functions by defining your own version of |
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| 18 | @code{matherr}; see the section on @code{matherr} for details. |
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| 19 | @end enumerate |
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| 20 | |
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| 21 | @cindex system calls |
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| 22 | @cindex support subroutines |
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| 23 | @cindex stubs |
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| 24 | @cindex OS stubs |
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| 25 | Since the error handling code calls @code{fputs}, the mathematical |
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| 26 | subroutines require stubs or minimal implementations for the same list |
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| 27 | of OS subroutines as @code{fputs}: @code{close}, @code{fstat}, |
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| 28 | @code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}. |
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| 29 | @xref{syscalls,,System Calls, libc.info, The Red Hat newlib C Library}, |
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| 30 | for a discussion and for sample minimal implementations of these support |
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| 31 | subroutines. |
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| 32 | |
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| 33 | Alternative declarations of the mathematical functions, which exploit |
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| 34 | specific machine capabilities to operate faster---but generally have |
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| 35 | less error checking and may reflect additional limitations on some |
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| 36 | machines---are available when you include @file{fastmath.h} instead of |
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| 37 | @file{math.h}. |
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| 38 | |
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| 39 | @menu |
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| 40 | * version:: Version of library |
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| 41 | * acos:: Arccosine |
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| 42 | * acosh:: Inverse hyperbolic cosine |
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| 43 | * asin:: Arcsine |
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| 44 | * asinh:: Inverse hyperbolic sine |
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| 45 | * atan:: Arctangent |
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| 46 | * atan2:: Arctangent of y/x |
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| 47 | * atanh:: Inverse hyperbolic tangent |
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| 48 | * jN:: Bessel functions (jN, yN) |
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| 49 | * cbrt:: Cube root |
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| 50 | * copysign:: Sign of Y, magnitude of X |
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| 51 | * cosh:: Hyperbolic cosine |
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| 52 | * erf:: Error function (erf, erfc) |
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| 53 | * exp:: Exponential, base e |
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| 54 | * exp10:: Exponential, base 10 |
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| 55 | * exp2:: Exponential, base 2 |
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| 56 | * expm1:: Exponential, base e, of x - 1 |
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| 57 | * fabs:: Absolute value (magnitude) |
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| 58 | * fdim:: Positive difference |
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| 59 | * floor:: Floor and ceiling (floor, ceil) |
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| 60 | * fma:: Floating multiply add |
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| 61 | * fmax:: Maximum |
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| 62 | * fmin:: Minimum |
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| 63 | * fmod:: Floating-point remainder (modulo) |
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| 64 | * fpclassify:: Floating-point classification macro |
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| 65 | * frexp:: Split floating-point number |
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| 66 | * gamma:: Logarithmic gamma function |
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| 67 | * hypot:: Distance from origin |
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| 68 | * ilogb:: Get exponent |
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| 69 | * infinity:: Floating infinity |
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| 70 | * isgreater:: Comparison macros |
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| 71 | * ldexp:: Scale by a power of 2 |
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| 72 | * log:: Natural logarithms |
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| 73 | * log10:: Base 10 logarithms |
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| 74 | * log1p:: Log of 1 + X |
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| 75 | * log2:: Base 2 logarithms |
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| 76 | * logb:: Get exponent |
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| 77 | * lrint:: Round to integer |
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| 78 | * lround:: Round to integer, away from zero (lround, llround) |
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| 79 | * matherr:: Modifiable math error handler |
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| 80 | * modf:: Split fractional and integer parts |
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| 81 | * nan:: Floating Not a Number |
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| 82 | * nearbyint:: Round to integer |
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| 83 | * nextafter:: Get next representable number |
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| 84 | * pow:: X to the power Y |
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| 85 | * pow10:: 10 to the power X |
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| 86 | * remainder:: remainder of X divided by Y |
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| 87 | * remquo:: Remainder and part of quotient |
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| 88 | * rint:: Round to integer |
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| 89 | * round:: Round to integer, away from zero |
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| 90 | * scalbn:: Scale by a power of FLT_RADIX (2) |
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| 91 | * signbit:: Does floating-point number have negative sign? |
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| 92 | * sin:: Sine or cosine (sin, cos) |
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| 93 | * sinh:: Hyperbolic sine |
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| 94 | * sqrt:: Positive square root |
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| 95 | * tan:: Tangent |
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| 96 | * tanh:: Hyperbolic tangent |
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| 97 | * trunc:: Round to integer, towards zero |
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| 98 | @end menu |
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| 99 | |
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| 100 | @page |
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| 101 | @node version |
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| 102 | @section Error Handling |
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| 103 | |
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| 104 | There are four different versions of the math library routines: IEEE, |
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| 105 | POSIX, X/Open, or SVID. The version may be selected at runtime by |
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| 106 | setting the global variable @code{_LIB_VERSION}, defined in |
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| 107 | @file{math.h}. It may be set to one of the following constants defined |
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| 108 | in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or |
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| 109 | @code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any |
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| 110 | thread, and changing it will affect all threads. |
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| 111 | |
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| 112 | The versions of the library differ only in how errors are handled. |
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| 113 | |
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| 114 | In IEEE mode, the @code{matherr} function is never called, no warning |
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| 115 | messages are printed, and @code{errno} is never set. |
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| 116 | |
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| 117 | In POSIX mode, @code{errno} is set correctly, but the @code{matherr} |
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| 118 | function is never called and no warning messages are printed. |
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| 119 | |
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| 120 | In X/Open mode, @code{errno} is set correctly, and @code{matherr} is |
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| 121 | called, but warning message are not printed. |
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| 122 | |
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| 123 | In SVID mode, functions which overflow return 3.40282346638528860e+38, |
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| 124 | the maximum single-precision floating-point value, rather than infinity. |
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| 125 | Also, @code{errno} is set correctly, @code{matherr} is called, and, if |
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| 126 | @code{matherr} returns 0, warning messages are printed for some errors. |
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| 127 | For example, by default @samp{log(-1.0)} writes this message on standard |
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| 128 | error output: |
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| 129 | |
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| 130 | @example |
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| 131 | log: DOMAIN error |
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| 132 | @end example |
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| 133 | |
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| 134 | The library is set to X/Open mode by default. |
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| 135 | |
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| 136 | The aforementioned error reporting is the supported Newlib libm error |
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| 137 | handling method. However, the majority of the functions are written |
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| 138 | so as to produce the floating-point exceptions (e.g. "invalid", |
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| 139 | "divide-by-zero") as required by the C and POSIX standards, for |
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| 140 | floating-point implementations that support them. Newlib does not provide |
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| 141 | the floating-point exception access routines defined in the standards |
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| 142 | for fenv.h, though, which is why they are considered unsupported. It is |
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| 143 | mentioned in case you have separately-provided access routines so that |
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| 144 | you are aware that they can be caused. |
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| 145 | |
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| 146 | @section Standards Compliance And Portability |
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| 147 | Most of the individual function descriptions describe the standards to which |
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| 148 | each function complies. However, these descriptions are mostly out of date, |
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| 149 | having been written before C99 was released. One of these days we'll get |
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| 150 | around to updating the rest of them. (If you'd like to help, please let us |
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| 151 | know.) |
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| 152 | |
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| 153 | ``C99'' refers to ISO/IEC 9899:1999, ``Programming languages--C''. |
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| 154 | ``POSIX'' refers to IEEE Standard 1003.1. POSIX@registeredsymbol{} is a |
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| 155 | registered trademark of The IEEE. |
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| 156 | |
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| 157 | @c To sort the include list easily, keep the indentation right because want to |
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| 158 | @c skip the s_|w_ at the start of most--but not all--of the file names. |
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| 159 | @c (e.g., isgreater.def does not have a leading s nor w.) Then, sort |
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| 160 | @c based on the column. For example: "sort -t@ -k3.17" |
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| 161 | @c A few hand-edits might be appropriate after a sort, although not necessary |
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| 162 | @c and are a nuisance as ought to be kept in sync with menu list above: |
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| 163 | @c atan2 after atan, exp2 after exp, log first in log list, and w_j0 to place |
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| 164 | @c to reflect function name of Bessel (as opposed to j; e.g. after atanh, |
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| 165 | @c before cbrt). |
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| 166 | |
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| 167 | @page |
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| 168 | @include math/w_acos.def |
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| 169 | @page |
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| 170 | @include math/w_acosh.def |
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| 171 | @page |
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| 172 | @include math/w_asin.def |
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| 173 | @page |
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| 174 | @include math/s_asinh.def |
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| 175 | @page |
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| 176 | @include math/s_atan.def |
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| 177 | @page |
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| 178 | @include math/w_atan2.def |
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| 179 | @page |
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| 180 | @include math/w_atanh.def |
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| 181 | @page |
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| 182 | @include math/w_j0.def |
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| 183 | @page |
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| 184 | @include common/s_cbrt.def |
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| 185 | @page |
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| 186 | @include common/s_copysign.def |
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| 187 | @page |
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| 188 | @include math/w_cosh.def |
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| 189 | @page |
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| 190 | @include math/s_erf.def |
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| 191 | @page |
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| 192 | @include math/w_exp.def |
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| 193 | @page |
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| 194 | @include common/s_exp10.def |
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| 195 | @page |
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| 196 | @include math/w_exp2.def |
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| 197 | @page |
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| 198 | @include common/s_expm1.def |
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| 199 | @page |
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| 200 | @include math/s_fabs.def |
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| 201 | @page |
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| 202 | @include common/s_fdim.def |
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| 203 | @page |
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| 204 | @include math/s_floor.def |
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| 205 | @page |
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| 206 | @include common/s_fma.def |
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| 207 | @page |
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| 208 | @include common/s_fmax.def |
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| 209 | @page |
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| 210 | @include common/s_fmin.def |
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| 211 | @page |
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| 212 | @include math/w_fmod.def |
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| 213 | @page |
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| 214 | @include math/s_frexp.def |
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| 215 | @page |
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| 216 | @include math/w_gamma.def |
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| 217 | @page |
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| 218 | @include math/w_hypot.def |
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| 219 | @page |
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| 220 | @include common/s_ilogb.def |
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| 221 | @page |
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| 222 | @include common/s_infinity.def |
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| 223 | @page |
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| 224 | @include common/isgreater.def |
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| 225 | @page |
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| 226 | @include common/s_isnan.def |
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| 227 | @page |
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| 228 | @include math/s_ldexp.def |
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| 229 | @page |
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| 230 | @include math/w_log.def |
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| 231 | @page |
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| 232 | @include math/w_log10.def |
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| 233 | @page |
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| 234 | @include common/s_log1p.def |
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| 235 | @page |
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| 236 | @include common/s_log2.def |
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| 237 | @page |
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| 238 | @include common/s_logb.def |
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| 239 | @page |
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| 240 | @include common/s_lrint.def |
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| 241 | @page |
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| 242 | @include common/s_lround.def |
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| 243 | @page |
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| 244 | @include common/s_matherr.def |
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| 245 | @page |
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| 246 | @include common/s_modf.def |
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| 247 | @page |
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| 248 | @include common/s_nan.def |
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| 249 | @page |
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| 250 | @include common/s_nearbyint.def |
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| 251 | @page |
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| 252 | @include common/s_nextafter.def |
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| 253 | @page |
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| 254 | @include math/w_pow.def |
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| 255 | @page |
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| 256 | @include common/s_pow10.def |
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| 257 | @page |
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| 258 | @include math/w_remainder.def |
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| 259 | @page |
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| 260 | @include common/s_remquo.def |
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| 261 | @page |
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| 262 | @include common/s_rint.def |
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| 263 | @page |
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| 264 | @include common/s_round.def |
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| 265 | @page |
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| 266 | @include common/s_scalbn.def |
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| 267 | @page |
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| 268 | @include common/s_signbit.def |
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| 269 | @page |
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| 270 | @include math/s_sin.def |
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| 271 | @page |
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| 272 | @include math/w_sinh.def |
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| 273 | @page |
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| 274 | @include math/w_sqrt.def |
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| 275 | @page |
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| 276 | @include math/s_tan.def |
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| 277 | @page |
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| 278 | @include math/s_tanh.def |
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| 279 | @page |
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| 280 | @include common/s_trunc.def |
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