man7/math_error.7

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  24 .TH MATH_ERROR 7 2008-07-30 "Linux" "Linux Programmer's Manual"
  25 .SH NAME
  26 math_error \- detecting errors from mathematical functions
  27 .SH SYNOPSIS
  28 .nf
  29 .B #include <math.h>
  30 .B #include <errno.h>
  31 .B #include <fenv.h>
  32 .fi
  33 .SH DESCRIPTION
  34 On error, many of the mathematical functions declared in
  35 .IR <math.h>
  36 return a NaN (not a number).
  37 However, rather than looking at the return value
  38 (which is not always possible)
  39 one can also check whether an error was signaled.
  40 There are two signaling mechanisms:
  41 the older one sets
  42 .IR errno ;
  43 the newer one uses the floating-point exception mechanism (the use of
  44 .BR feclearexcept (3)
  45 and
  46 .BR fetestexcept (3),
  47 as outlined below)
  48 described in
  49 .BR fenv (3).
  50
  51 A portable program that needs to check for an error from a mathematical
  52 function should set
  53 .I errno
  54 to zero, and make the following call
  55 .in +4n
  56 .nf
  57
  58 feclearexcept(FE_ALL_EXCEPT);
  59
  60 .fi
  61 .in
  62 before calling a mathematical function.
  63
  64 Upon return from the mathematical function, if
  65 .I errno
  66 is non-zero, or the following call (see
  67 .BR fenv (3))
  68 returns non-zero
  69 .in +4n
  70 .nf
  71
  72 fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
  73              FE_UNDERFLOW);
  74
  75 .fi
  76 .in
  77 .\" enum
  78 .\" {
  79 .\" FE_INVALID = 0x01,
  80 .\" __FE_DENORM = 0x02,
  81 .\" FE_DIVBYZERO = 0x04,
  82 .\" FE_OVERFLOW = 0x08,
  83 .\" FE_UNDERFLOW = 0x10,
  84 .\" FE_INEXACT = 0x20
  85 .\" };
  86 then an error occurred in the mathematical function.
  87
  88 The error conditions that can occur for mathematical functions
  89 are described below.
  90 .SS Domain Error
  91 A
  92 .I domain error
  93 occurs when a mathematical function is supplied with an argument whose
  94 value falls outside the domain for which the function
  95 is defined (e.g., giving a negative argument to
  96 .BR log (3)).
  97 When a domain error occurs,
  98 .I errno
  99 is set to
 100 .BR EDOM ,
 101 and an "invalid"
 102 .RB ( FE_INVALID )
 103 floating-point exception is raised.
 104 .SS Pole Error
 105 A
 106 .I pole error
 107 occurs when the mathematical result of a function is an exact infinity
 108 (e.g., the logarithm of 0 is negative infinity).
 109 When a pole error occurs,
 110 the function returns the (signed) value
 111 .BR HUGE_VAL ,
 112 .BR HUGE_VALF ,
 113 or
 114 .BR HUGE_VALL ,
 115 depending on whether the function result type is
 116 .IR double ,
 117 .IR float ,
 118 or
 119 .IR "long double" .
 120 The sign of the result is that which is mathematically correct for
 121 the function.
 122 .I errno
 123 is set to
 124 .BR ERANGE ,
 125 and a "divide-by-zero"
 126 .RB ( FE_DIVBYZERO )
 127 floating-point exception is raised.
 128 .SS Range Error
 129 A
 130 .I range error
 131 occurs when the magnitude of the function result means that it
 132 cannot be represented in the result type of the function.
 133 The return value of the function depends on whether the range error
 134 was an overflow or an underflow.
 135
 136 A floating result
 137 .I overflows
 138 if the  result is finite,
 139 but is too large to represented in the result type.
 140 When an overflow occurs,
 141 the function returns the value
 142 .BR HUGE_VAL ,
 143 .BR HUGE_VALF ,
 144 or
 145 .BR HUGE_VALL ,
 146 depending on whether the function result type is
 147 .IR double ,
 148 .IR float ,
 149 or
 150 .IR "long double" .
 151 .I errno
 152 is set to
 153 .BR ERANGE ,
 154 and an "overflow"
 155 .RB ( FE_OVERFLOW )
 156 floating-point exception is raised.
 157
 158 A floating result
 159 .I underflows
 160 if the result is too small to be represented in the result type.
 161 If an underflow occurs,
 162 a mathematical function typically returns 0.0
 163 (C99 says a function shall return "an implementation-defined value
 164 whose magnitude is no greater than the smallest normalized
 165 positive number in the specified type").
 166 .\" FIXME(mtk) POSIX.1 says "may" for the following two cases; need to
 167 .\" investigate this further for specific functions.
 168 .I errno
 169 may be set to
 170 .BR ERANGE ,
 171 and an "overflow"
 172 .RB ( FE_UNDERFLOW )
 173 floating-point exception may be raised.
 174
 175 Some functions deliver a range error if the supplied argument value,
 176 or the correct function result, would be
 177 .IR subnormal .
 178 A subnormal value is one that is non-zero,
 179 but with a magnitude that is so small that
 180 it can't be presented in normalized form
 181 (i.e., with a 1 in the most significant bit of the significand).
 182 The representation of a subnormal number will contain one
 183 or more leading zeros in the significand.
 184 .SH NOTES
 185 The
 186 .I math_errhandling
 187 identifier specified by C99 and POSIX.1-2001 is not supported by glibc.
 188 .\" See CONFORMANCE in the glibc 2.8 (and earlier) source.
 189 This identifer is supposed to indicate which of the two
 190 error-notification mechanisms
 191 .RI ( errno ,
 192 exceptions retrievable via
 193 .BR fettestexcept (3))
 194 is in use.
 195 The standards require that at least one be in use,
 196 but permit both to be available.
 197 The current (version 2.8) situation under glibc is messy.
 198 Most (but not all) functions raise exceptions on errors.
 199 Some also set
 200 .IR errno .
 201 A few functions set
 202 .IR errno ,
 203 but don't raise an exception.
 204 A very few functions do neither.
 205 See the individual manual pages for details.
 206
 207 To avoid the complexities of using
 208 .I errno
 209 and
 210 .BR fetestexcept (3)
 211 for error checking,
 212 it is often advised that one should instead check for bad argument
 213 values before each call.
 214 .\" http://www.securecoding.cert.org/confluence/display/seccode/FLP32-C.+Prevent+or+detect+domain+and+range+errors+in+math+functions
 215 For example, the following code ensures that
 216 .BR log (3)'s
 217 argument is not a NaN and is not zero (a pole error) or
 218 less than zero (a domain error):
 219 .in +4n
 220 .nf
 221
 222 double x, r;
 223
 224 if (isnan(x) || islessequal(x, 0)) {
 225     /* Deal with NaN / pole error / domain error */
 226 }
 227
 228 r = log(x);
 229
 230 .fi
 231 .in
 232 The discussion on this page does not apply to the complex
 233 mathematical functions (i.e., those declared by
 234 .IR <complex.h> ),
 235 which in general are not required to return errors by C99
 236 and POSIX.1-2001.
 237
 238 The
 239 .BR gcc (1)
 240 .I "-fno-math-errno"
 241 option causes the executable to employ implementations of some
 242 mathematical functions that are faster than the standard
 243 implementations, but do not set
 244 .I errno
 245 on error.
 246 (The
 247 .BR gcc (1)
 248 .I "-ffast-math"
 249 option also enables
 250 .IR "-fno-math-errno" .)
 251 An error can still be tested for using
 252 .BR fetestexcept (3).
 253 .SH SEE ALSO
 254 .BR gcc (1),
 255 .BR errno (3),
 256 .BR fenv (3),
 257 .BR fpclassify (3),
 258 .BR INFINITY (3),
 259 .BR isgreater (3),
 260 .BR matherr (3),
 261 .BR nan (3)
 262 .br
 263 .I "info libc"