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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