man7/math_error.7

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  24 .TH MATH_ERROR 7 2008-08-11 "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 When an error occurs,
  35 most library functions indicate this fact by returning a special value
  36 (e.g., \-1 or NULL).
  37 Because they typically return a floating-point number,
  38 the mathematical functions declared in
  39 .IR <math.h>
  40 indicate an error using other mechanisms.
  41 There are two error-reporting mechanisms:
  42 the older one sets
  43 .IR errno ;
  44 the newer one uses the floating-point exception mechanism (the use of
  45 .BR feclearexcept (3)
  46 and
  47 .BR fetestexcept (3),
  48 as outlined below)
  49 described in
  50 .BR fenv (3).
  51
  52 A portable program that needs to check for an error from a mathematical
  53 function should set
  54 .I errno
  55 to zero, and make the following call
  56 .in +4n
  57 .nf
  58
  59 feclearexcept(FE_ALL_EXCEPT);
  60
  61 .fi
  62 .in
  63 before calling a mathematical function.
  64
  65 Upon return from the mathematical function, if
  66 .I errno
  67 is non-zero, or the following call (see
  68 .BR fenv (3))
  69 returns non-zero
  70 .in +4n
  71 .nf
  72
  73 fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
  74              FE_UNDERFLOW);
  75
  76 .fi
  77 .in
  78 .\" enum
  79 .\" {
  80 .\" FE_INVALID = 0x01,
  81 .\" __FE_DENORM = 0x02,
  82 .\" FE_DIVBYZERO = 0x04,
  83 .\" FE_OVERFLOW = 0x08,
  84 .\" FE_UNDERFLOW = 0x10,
  85 .\" FE_INEXACT = 0x20
  86 .\" };
  87 then an error occurred in the mathematical function.
  88
  89 The error conditions that can occur for mathematical functions
  90 are described below.
  91 .SS Domain Error
  92 A
  93 .I domain error
  94 occurs when a mathematical function is supplied with an argument whose
  95 value falls outside the domain for which the function
  96 is defined (e.g., giving a negative argument to
  97 .BR log (3)).
  98 When a domain error occurs,
  99 math functions commonly return a NaN
 100 (though some functions return a different value in this case);
 101 .I errno
 102 is set to
 103 .BR EDOM ,
 104 and an "invalid"
 105 .RB ( FE_INVALID )
 106 floating-point exception is raised.
 107 .SS Pole Error
 108 A
 109 .I pole error
 110 occurs when the mathematical result of a function is an exact infinity
 111 (e.g., the logarithm of 0 is negative infinity).
 112 When a pole error occurs,
 113 the function returns the (signed) value
 114 .BR HUGE_VAL ,
 115 .BR HUGE_VALF ,
 116 or
 117 .BR HUGE_VALL ,
 118 depending on whether the function result type is
 119 .IR double ,
 120 .IR float ,
 121 or
 122 .IR "long double" .
 123 The sign of the result is that which is mathematically correct for
 124 the function.
 125 .I errno
 126 is set to
 127 .BR ERANGE ,
 128 and a "divide-by-zero"
 129 .RB ( FE_DIVBYZERO )
 130 floating-point exception is raised.
 131 .SS Range Error
 132 A
 133 .I range error
 134 occurs when the magnitude of the function result means that it
 135 cannot be represented in the result type of the function.
 136 The return value of the function depends on whether the range error
 137 was an overflow or an underflow.
 138
 139 A floating result
 140 .I overflows
 141 if the  result is finite,
 142 but is too large to represented in the result type.
 143 When an overflow occurs,
 144 the function returns the value
 145 .BR HUGE_VAL ,
 146 .BR HUGE_VALF ,
 147 or
 148 .BR HUGE_VALL ,
 149 depending on whether the function result type is
 150 .IR double ,
 151 .IR float ,
 152 or
 153 .IR "long double" .
 154 .I errno
 155 is set to
 156 .BR ERANGE ,
 157 and an "overflow"
 158 .RB ( FE_OVERFLOW )
 159 floating-point exception is raised.
 160
 161 A floating result
 162 .I underflows
 163 if the result is too small to be represented in the result type.
 164 If an underflow occurs,
 165 a mathematical function typically returns 0.0
 166 (C99 says a function shall return "an implementation-defined value
 167 whose magnitude is no greater than the smallest normalized
 168 positive number in the specified type").
 169 .\" FIXME(mtk) POSIX.1 says "may" for the following two cases; need to
 170 .\" investigate this further for specific functions.
 171 .I errno
 172 may be set to
 173 .BR ERANGE ,
 174 and an "overflow"
 175 .RB ( FE_UNDERFLOW )
 176 floating-point exception may be raised.
 177
 178 Some functions deliver a range error if the supplied argument value,
 179 or the correct function result, would be
 180 .IR subnormal .
 181 A subnormal value is one that is non-zero,
 182 but with a magnitude that is so small that
 183 it can't be presented in normalized form
 184 (i.e., with a 1 in the most significant bit of the significand).
 185 The representation of a subnormal number will contain one
 186 or more leading zeros in the significand.
 187 .SH NOTES
 188 The
 189 .I math_errhandling
 190 identifier specified by C99 and POSIX.1-2001 is not supported by glibc.
 191 .\" See CONFORMANCE in the glibc 2.8 (and earlier) source.
 192 This identifer is supposed to indicate which of the two
 193 error-notification mechanisms
 194 .RI ( errno ,
 195 exceptions retrievable via
 196 .BR fettestexcept (3))
 197 is in use.
 198 The standards require that at least one be in use,
 199 but permit both to be available.
 200 The current (version 2.8) situation under glibc is messy.
 201 Most (but not all) functions raise exceptions on errors.
 202 Some also set
 203 .IR errno .
 204 A few functions set
 205 .IR errno ,
 206 but don't raise an exception.
 207 A very few functions do neither.
 208 See the individual manual pages for details.
 209
 210 To avoid the complexities of using
 211 .I errno
 212 and
 213 .BR fetestexcept (3)
 214 for error checking,
 215 it is often advised that one should instead check for bad argument
 216 values before each call.
 217 .\" http://www.securecoding.cert.org/confluence/display/seccode/FLP32-C.+Prevent+or+detect+domain+and+range+errors+in+math+functions
 218 For example, the following code ensures that
 219 .BR log (3)'s
 220 argument is not a NaN and is not zero (a pole error) or
 221 less than zero (a domain error):
 222 .in +4n
 223 .nf
 224
 225 double x, r;
 226
 227 if (isnan(x) || islessequal(x, 0)) {
 228     /* Deal with NaN / pole error / domain error */
 229 }
 230
 231 r = log(x);
 232
 233 .fi
 234 .in
 235 The discussion on this page does not apply to the complex
 236 mathematical functions (i.e., those declared by
 237 .IR <complex.h> ),
 238 which in general are not required to return errors by C99
 239 and POSIX.1-2001.
 240
 241 The
 242 .BR gcc (1)
 243 .I "-fno-math-errno"
 244 option causes the executable to employ implementations of some
 245 mathematical functions that are faster than the standard
 246 implementations, but do not set
 247 .I errno
 248 on error.
 249 (The
 250 .BR gcc (1)
 251 .I "-ffast-math"
 252 option also enables
 253 .IR "-fno-math-errno" .)
 254 An error can still be tested for using
 255 .BR fetestexcept (3).
 256 .SH SEE ALSO
 257 .BR gcc (1),
 258 .BR errno (3),
 259 .BR fenv (3),
 260 .BR fpclassify (3),
 261 .BR INFINITY (3),
 262 .BR isgreater (3),
 263 .BR matherr (3),
 264 .BR nan (3)
 265 .br
 266 .I "info libc"