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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