mirror of https://github.com/mkerrisk/man-pages
488 lines
15 KiB
Plaintext
488 lines
15 KiB
Plaintext
.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved
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.TH "<math.h>" P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual"
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.\" <math.h>
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.SH NAME
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math.h \- mathematical declarations
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.SH SYNOPSIS
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.LP
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\fB#include <math.h>\fP
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.SH DESCRIPTION
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.LP
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Some of the functionality described on this reference page extends
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the ISO\ C standard. Applications shall define
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the appropriate feature test macro (see the System Interfaces volume
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of IEEE\ Std\ 1003.1-2001, Section 2.2, The Compilation Environment)
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to enable the visibility of these symbols in this
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header.
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.LP
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The \fI<math.h>\fP header shall include definitions for at least the
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following types:
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.TP 7
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\fBfloat_t\fP
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A real-floating type at least as wide as \fBfloat\fP.
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.TP 7
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\fBdouble_t\fP
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A real-floating type at least as wide as \fBdouble\fP, and at least
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as wide as \fBfloat_t\fP.
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.sp
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.LP
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If FLT_EVAL_METHOD equals 0, \fBfloat_t\fP and \fBdouble_t\fP shall
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be \fBfloat\fP and \fBdouble\fP, respectively; if
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FLT_EVAL_METHOD equals 1, they shall both be \fBdouble\fP; if FLT_EVAL_METHOD
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equals 2, they shall both be \fBlong double\fP; for
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other values of FLT_EVAL_METHOD, they are otherwise implementation-defined.
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.LP
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The \fI<math.h>\fP header shall define the following macros, where
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real-floating indicates that the argument shall be an
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expression of real-floating type:
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.sp
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.RS
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.nf
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\fBint fpclassify(real-floating x);
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int isfinite(real-floating x);
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int isinf(real-floating x);
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int isnan(real-floating x);
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int isnormal(real-floating x);
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int signbit(real-floating x);
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int isgreater(real-floating x, real-floating y);
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int isgreaterequal(real-floating x, real-floating y);
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int isless(real-floating x, real-floating y);
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int islessequal(real-floating x, real-floating y);
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int islessgreater(real-floating x, real-floating y);
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int isunordered(real-floating x, real-floating y);
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\fP
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.fi
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.RE
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.LP
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The \fI<math.h>\fP header shall provide for the following constants.
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The values are of type \fBdouble\fP and are
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accurate within the precision of the \fBdouble\fP type.
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.TP 7
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M_E
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Value of \fIe\fP
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.TP 7
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M_LOG2E
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Value of log_2\fIe\fP
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.TP 7
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M_LOG10E
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Value of log_10\fIe\fP
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.TP 7
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M_LN2
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Value of log_e2
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.TP 7
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M_LN10
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Value of log_e10
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.TP 7
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M_PI
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Value of pi
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.TP 7
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M_PI_2
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Value of pi/2
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.TP 7
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M_PI_4
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Value of pi/4
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.TP 7
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M_1_PI
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Value of 1/pi
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.TP 7
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M_2_PI
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Value of 2/pi
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.TP 7
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M_2_SQRTPI
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Value of 2/ sqrt pi
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.TP 7
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M_SQRT2
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Value of sqrt 2
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.TP 7
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M_SQRT1_2
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Value of 1/sqrt 2
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.sp
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.LP
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The header shall define the following symbolic constants:
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.TP 7
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MAXFLOAT
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Value of maximum non-infinite single-precision floating-point number.
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.TP 7
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HUGE_VAL
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A positive \fBdouble\fP expression, not necessarily representable
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as a \fBfloat\fP. Used as an error value returned by the
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mathematics library. HUGE_VAL evaluates to +infinity on systems supporting
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IEEE\ Std\ 754-1985.
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.TP 7
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HUGE_VALF
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A positive \fBfloat\fP constant expression. Used as an error value
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returned by the mathematics library. HUGE_VALF evaluates to
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+infinity on systems supporting IEEE\ Std\ 754-1985.
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.TP 7
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HUGE_VALL
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A positive \fBlong double\fP constant expression. Used as an error
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value returned by the mathematics library. HUGE_VALL
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evaluates to +infinity on systems supporting IEEE\ Std\ 754-1985.
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.TP 7
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INFINITY
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A constant expression of type \fBfloat\fP representing positive or
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unsigned infinity, if available; else a positive constant
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of type \fBfloat\fP that overflows at translation time.
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.TP 7
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NAN
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A constant expression of type \fBfloat\fP representing a quiet NaN.
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This symbolic constant is only defined if the
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implementation supports quiet NaNs for the \fBfloat\fP type.
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.sp
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.LP
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The following macros shall be defined for number classification. They
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represent the mutually-exclusive kinds of floating-point
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values. They expand to integer constant expressions with distinct
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values. Additional implementation-defined floating-point
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classifications, with macro definitions beginning with FP_ and an
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uppercase letter, may also be specified by the
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implementation.
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.sp
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.RS
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.nf
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FP_INFINITE
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FP_NAN
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FP_NORMAL
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FP_SUBNORMAL
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FP_ZERO
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.fi
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.RE
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.LP
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The following optional macros indicate whether the \fIfma\fP() family
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of functions are fast
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compared with direct code:
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.sp
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.RS
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.nf
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FP_FAST_FMA
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FP_FAST_FMAF
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FP_FAST_FMAL
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.fi
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.RE
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.LP
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The FP_FAST_FMA macro shall be defined to indicate that the \fIfma\fP()
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function generally
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executes about as fast as, or faster than, a multiply and an add of
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\fBdouble\fP operands. The other macros have the equivalent
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meaning for the \fBfloat\fP and \fBlong double\fP versions.
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.LP
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The following macros shall expand to integer constant expressions
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whose values are returned by \fIilogb\fP( \fIx\fP) if
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\fIx\fP is zero or NaN, respectively. The value of FP_ILOGB0 shall
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be either {INT_MIN} or - {INT_MAX}. The value of FP_ILOGBNAN
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shall be either {INT_MAX} or {INT_MIN}.
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.sp
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.RS
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.nf
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FP_ILOGB0
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FP_ILOGBNAN
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.fi
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.RE
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.LP
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The following macros shall expand to the integer constants 1 and 2,
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respectively;
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.sp
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.RS
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.nf
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MATH_ERRNO
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MATH_ERREXCEPT
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.fi
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.RE
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.LP
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The following macro shall expand to an expression that has type \fBint\fP
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and the value MATH_ERRNO, MATH_ERREXCEPT, or the
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bitwise-inclusive OR of both:
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.sp
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.RS
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.nf
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math_errhandling
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.fi
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.RE
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.LP
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The value of math_errhandling is constant for the duration of the
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program. It is unspecified whether math_errhandling is a macro
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or an identifier with external linkage. If a macro definition is suppressed
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or a program defines an identifier with the name
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math_errhandling , the behavior is undefined. If the expression (math_errhandling
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& MATH_ERREXCEPT) can be non-zero, the
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implementation shall define the macros FE_DIVBYZERO, FE_INVALID, and
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FE_OVERFLOW in \fI<fenv.h>\fP.
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.LP
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The following shall be declared as functions and may also be defined
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as macros. Function prototypes shall be provided.
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.sp
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.RS
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.nf
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\fBdouble acos(double);
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float acosf(float);
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double acosh(double);
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float acoshf(float);
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long double acoshl(long double);
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long double acosl(long double);
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double asin(double);
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float asinf(float);
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double asinh(double);
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float asinhf(float);
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long double asinhl(long double);
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long double asinl(long double);
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double atan(double);
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double atan2(double, double);
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float atan2f(float, float);
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long double atan2l(long double, long double);
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float atanf(float);
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double atanh(double);
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float atanhf(float);
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long double atanhl(long double);
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long double atanl(long double);
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double cbrt(double);
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float cbrtf(float);
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long double cbrtl(long double);
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double ceil(double);
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float ceilf(float);
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long double ceill(long double);
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double copysign(double, double);
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float copysignf(float, float);
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long double copysignl(long double, long double);
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double cos(double);
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float cosf(float);
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double cosh(double);
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float coshf(float);
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long double coshl(long double);
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long double cosl(long double);
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double erf(double);
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double erfc(double);
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float erfcf(float);
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long double erfcl(long double);
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float erff(float);
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long double erfl(long double);
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double exp(double);
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double exp2(double);
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float exp2f(float);
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long double exp2l(long double);
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float expf(float);
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long double expl(long double);
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double expm1(double);
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float expm1f(float);
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long double expm1l(long double);
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double fabs(double);
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float fabsf(float);
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long double fabsl(long double);
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double fdim(double, double);
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float fdimf(float, float);
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long double fdiml(long double, long double);
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double floor(double);
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float floorf(float);
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long double floorl(long double);
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double fma(double, double, double);
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float fmaf(float, float, float);
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long double fmal(long double, long double, long double);
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double fmax(double, double);
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float fmaxf(float, float);
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long double fmaxl(long double, long double);
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double fmin(double, double);
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float fminf(float, float);
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long double fminl(long double, long double);
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double fmod(double, double);
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float fmodf(float, float);
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long double fmodl(long double, long double);
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double frexp(double, int *);
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float frexpf(float value, int *);
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long double frexpl(long double value, int *);
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double hypot(double, double);
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float hypotf(float, float);
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long double hypotl(long double, long double);
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int ilogb(double);
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int ilogbf(float);
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int ilogbl(long double);
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double j0(double);
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double j1(double);
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double jn(int, double);
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double ldexp(double, int);
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float ldexpf(float, int);
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long double ldexpl(long double, int);
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double lgamma(double);
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float lgammaf(float);
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long double lgammal(long double);
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long long llrint(double);
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long long llrintf(float);
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long long llrintl(long double);
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long long llround(double);
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long long llroundf(float);
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long long llroundl(long double);
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double log(double);
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double log10(double);
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float log10f(float);
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long double log10l(long double);
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double log1p(double);
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float log1pf(float);
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long double log1pl(long double);
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double log2(double);
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float log2f(float);
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long double log2l(long double);
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double logb(double);
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float logbf(float);
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long double logbl(long double);
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float logf(float);
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long double logl(long double);
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long lrint(double);
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long lrintf(float);
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long lrintl(long double);
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long lround(double);
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long lroundf(float);
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long lroundl(long double);
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double modf(double, double *);
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float modff(float, float *);
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long double modfl(long double, long double *);
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double nan(const char *);
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float nanf(const char *);
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long double nanl(const char *);
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double nearbyint(double);
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float nearbyintf(float);
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long double nearbyintl(long double);
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double nextafter(double, double);
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float nextafterf(float, float);
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long double nextafterl(long double, long double);
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double nexttoward(double, long double);
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float nexttowardf(float, long double);
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long double nexttowardl(long double, long double);
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double pow(double, double);
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float powf(float, float);
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long double powl(long double, long double);
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double remainder(double, double);
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float remainderf(float, float);
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long double remainderl(long double, long double);
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double remquo(double, double, int *);
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float remquof(float, float, int *);
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long double remquol(long double, long double, int *);
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double rint(double);
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float rintf(float);
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long double rintl(long double);
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double round(double);
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float roundf(float);
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long double roundl(long double);
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double scalb(double, double);
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double scalbln(double, long);
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float scalblnf(float, long);
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long double scalblnl(long double, long);
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double scalbn(double, int);
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float scalbnf(float, int);
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long double scalbnl(long double, int);
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double sin(double);
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float sinf(float);
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double sinh(double);
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float sinhf(float);
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long double sinhl(long double);
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long double sinl(long double);
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double sqrt(double);
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float sqrtf(float);
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long double sqrtl(long double);
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double tan(double);
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float tanf(float);
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double tanh(double);
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float tanhf(float);
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long double tanhl(long double);
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long double tanl(long double);
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double tgamma(double);
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float tgammaf(float);
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long double tgammal(long double);
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double trunc(double);
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float truncf(float);
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long double truncl(long double);
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double y0(double);
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double y1(double);
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double yn(int, double);
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\fP
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.fi
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.RE
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.LP
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The following external variable shall be defined:
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.sp
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.RS
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.nf
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\fB
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extern int signgam;
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\fP
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.fi
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.RE
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.LP
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The behavior of each of the functions defined in \fI<math.h>\fP is
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specified in the System Interfaces volume of
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IEEE\ Std\ 1003.1-2001 for all representable values of its input arguments,
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except where stated otherwise. Each function
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shall execute as if it were a single operation without generating
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any externally visible exceptional conditions.
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.LP
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\fIThe following sections are informative.\fP
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.SH APPLICATION USAGE
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.LP
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The FP_CONTRACT pragma can be used to allow (if the state is on) or
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disallow (if the state is off) the implementation to
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contract expressions. Each pragma can occur either outside external
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declarations or preceding all explicit declarations and
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statements inside a compound statement. When outside external declarations,
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the pragma takes effect from its occurrence until
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another FP_CONTRACT pragma is encountered, or until the end of the
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translation unit. When inside a compound statement, the pragma
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takes effect from its occurrence until another FP_CONTRACT pragma
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is encountered (including within a nested compound statement), or
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until the end of the compound statement; at the end of a compound
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statement the state for the pragma is restored to its condition
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just before the compound statement. If this pragma is used in any
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other context, the behavior is undefined. The default state (on
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or off) for the pragma is implementation-defined.
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.SH RATIONALE
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.LP
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Before the ISO/IEC\ 9899:1999 standard, the math library was defined
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only for the floating type \fBdouble\fP. All the names
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formed by appending \fB'f'\fP or \fB'l'\fP to a name in \fI<math.h>\fP
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were reserved to allow for the definition of
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\fBfloat\fP and \fBlong double\fP libraries; and the ISO/IEC\ 9899:1999
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standard provides for all three versions of math
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functions.
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.LP
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The functions \fIecvt\fP(), \fIfcvt\fP(), and \fIgcvt\fP() have been
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dropped from the ISO\ C standard since their capability is available
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through \fIsprintf\fP(). These are provided on XSI-conformant systems
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supporting the
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Legacy Option Group.
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.SH FUTURE DIRECTIONS
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.LP
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None.
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.SH SEE ALSO
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.LP
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\fI<stddef.h>\fP , \fI<sys/types.h>\fP , the System
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Interfaces volume of IEEE\ Std\ 1003.1-2001, \fIacos\fP(), \fIacosh\fP(),
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\fIasin\fP(), \fIatan\fP(), \fIatan2\fP(), \fIcbrt\fP(), \fIceil\fP(),
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\fIcos\fP(), \fIcosh\fP(), \fIerf\fP(), \fIexp\fP(), \fIexpm1\fP(),
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\fIfabs\fP(), \fIfloor\fP(), \fIfmod\fP(), \fIfrexp\fP(), \fIhypot\fP(),
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\fIilogb\fP(), \fIisnan\fP(), \fIj0\fP(), \fIldexp\fP(), \fIlgamma\fP(),
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\fIlog\fP(), \fIlog10\fP(), \fIlog1p\fP(), \fIlogb\fP(), \fImodf\fP(),
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\fInextafter\fP(), \fIpow\fP(), \fIremainder\fP(), \fIrint\fP(), \fIscalb\fP(),
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\fIsin\fP(), \fIsinh\fP(), \fIsqrt\fP(), \fItan\fP(), \fItanh\fP(),
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\fIy0\fP()
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.SH COPYRIGHT
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Portions of this text are reprinted and reproduced in electronic form
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from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
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-- Portable Operating System Interface (POSIX), The Open Group Base
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Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
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Electrical and Electronics Engineers, Inc and The Open Group. In the
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event of any discrepancy between this version and the original IEEE and
|
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The Open Group Standard, the original IEEE and The Open Group Standard
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is the referee document. The original Standard can be obtained online at
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http://www.opengroup.org/unix/online.html .
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