/** @file Floating-point Math functions and macros. Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.
This program and the accompanying materials are licensed and made available under the terms and conditions of the BSD License that accompanies this distribution. The full text of the license may be found at http://opensource.org/licenses/bsd-license. THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED. * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== NetBSD: math.h,v 1.44 2006/03/25 16:41:11 xtraeme Exp dlibm.h 5.1 93/09/24 **/ #ifndef _MATH_H_ #define _MATH_H_ #include #include /** @{ @brief These are forward references to unions and macros used internaly by the implementation of the math functions and macros. **/ union __float_u { unsigned char __dummy[sizeof(float)]; float __val; }; union __double_u { unsigned char __dummy[sizeof(double)]; double __val; }; union __long_double_u { unsigned char __dummy[sizeof(long double)]; long double __val; }; #include /* may use __float_u, __double_u, or __long_double_u */ #ifdef __HAVE_LONG_DOUBLE #define __fpmacro_unary_floating(__name, __arg0) \ /* LINTED */ \ ((sizeof (__arg0) == sizeof (float)) \ ? __ ## __name ## f (__arg0) \ : (sizeof (__arg0) == sizeof (double)) \ ? __ ## __name ## d (__arg0) \ : __ ## __name ## l (__arg0)) #else #define __fpmacro_unary_floating(__name, __arg0) \ /* LINTED */ \ ((sizeof (__arg0) == sizeof (float)) \ ? __ ## __name ## f (__arg0) \ : __ ## __name ## d (__arg0)) #endif /* __HAVE_LONG_DOUBLE */ extern const union __double_u __infinity; extern const union __float_u __infinityf; extern const union __long_double_u __infinityl; /* C99 7.12.3.1 int fpclassify(real-floating x) */ #define fpclassify(__x) __fpmacro_unary_floating(fpclassify, __x) /* C99 7.12.3.3 int isinf(real-floating x) */ #ifdef __isinf #define isinf(__x) __isinf(__x) #else #define isinf(__x) __fpmacro_unary_floating(isinf, __x) #endif /* C99 7.12.3.4 int isnan(real-floating x) */ #ifdef __isnan #define isnan(__x) __isnan(__x) #else #define isnan(__x) __fpmacro_unary_floating(isnan, __x) #endif /*@)*/ /*############################################################# * ISO C95 */ /**@{ Double, float, and long double versions, respectively, of HUGE_VAL. */ #define HUGE_VAL __infinity.__val #define HUGE_VALF __infinityf.__val #define HUGE_VALL __infinityl.__val /*@)*/ __BEGIN_DECLS /* * ANSI/POSIX */ /** Compute the principal value of the arc cosine of Arg. @param[in] Arg The value to compute the arc cosine of. @return The computed value of the arc cosine of Arg in the interval [0,pi] radians. If Arg is not in the interval [-1,+1], errno is set to EDOM. **/ double acos(double Arg); /** Compute the principal value of the arc sine of Arg. @param[in] Arg The value to compute the arc sine of. @return The computed value of the arc sine of Arg in the interval [-pi/2,+pi/2] radians. If Arg is not in the interval [-1,+1], errno is set to EDOM. **/ double asin(double Arg); /** Compute the principal value of the arc tangent of Arg. @param[in] Arg The value to compute the arc tangent of. @return The computed value of the arc tangent of Arg in the interval [-pi/2,+pi/2] radians. **/ double atan(double Arg); /** Compute the value of the arc tangent of (Num / Denom). The sign of both arguments is used to determine the quadrant of the return value. @param[in] Num The numerator of the value to compute the arc tangent of. @param[in] Denom The denominator of the value to compute the arc tangent of. @return The computed value of the arc tangent of (Num / Denom) in the interval [-pi,+pi] radians. **/ double atan2(double Num, double Denom); /** Compute the value of the cosine of Arg, measured in radians. @param[in] Arg The value to compute the cosine of. @return The computed value of the cosine of Arg. **/ double cos(double Arg); /** Compute the value of the sine of Arg. @param[in] Arg The value to compute the sine of. @return The computed value of the sine of Arg. **/ double sin(double Arg); /** Compute the value of the tangent of Arg. @param[in] Arg The value to compute the tangent of. @return The computed value of the tangent of Arg. **/ double tan(double Arg); /** Compute the value of the hyperbolic cosine of Arg. @param[in] Arg The value to compute the hyperbolic cosine of. @return The computed value of the hyperbolic cosine of Arg. If the magnitude of Arg is too large, errno is set to ERANGE. **/ double cosh(double Arg); /** Compute the value of the hyperbolic sine of Arg. @param[in] Arg The value to compute the hyperbolic sine of. @return The computed value of the hyperbolic sine of Arg. If the magnitude of Arg is too large, errno is set to ERANGE. **/ double sinh(double Arg); /** Compute the value of the hyperbolic tangent of Arg. @param[in] Arg The value to compute the hyperbolic tangent of. @return The computed value of the hyperbolic tangent of Arg. **/ double tanh(double Arg); /** Compute the base-e exponential of Arg. @param[in] Arg The value to compute the base-e exponential of. @return The computed value of e**Arg. If the magnitude of Arg is too large, errno is set to ERANGE. **/ double exp(double Arg); /** Break a floating-point number into a normalized fraction and an integral power of 2. @param[in] Value The floating-point value to be broken down. @param[out] Exp A pointer to an integer object to receive the integral power of 2 exponent. @return The frexp function returns a value R, such that Value == R**Exp. If Value is zero, both parts of the result are zero. **/ double frexp(double Value, int *Exp); /** Multiply a floating-point number, Value, by an integral power of 2, Exp. @param[in] Value The floating-point value to be multiplied. @param[out] Exp The integral power of 2 to multiply Value by. @return The ldexp function returns a value R, such that R = Value x 2**Exp. If a range error occurs, errno will be set to ERANGE. **/ double ldexp(double Value, int Exp); /** Compute the natural logarithm of Arg. @param[in] Arg The value to compute the natural logarithm of. @return The log function returns log base-e of Arg. If Arg is negative, errno is set to EDOM. Otherwise, errno will be set to ERANGE if a range error occurs. **/ double log(double Arg); /** Compute the common (base-10) logarithm of Arg. @param[in] Arg The value to compute the common logarithm of. @return The log10 function returns log base-10 of Arg. If Arg is negative, errno is set to EDOM. Otherwise, errno will be set to ERANGE if Arg is 0. **/ double log10(double Arg); /** Compute the base-2 logarithm of Arg. @param[in] Arg The value to compute the base-2 logarithm of. @return The log function returns log base-2 of Arg. If Arg is negative, errno is set to EDOM. Otherwise, errno will be set to ERANGE if Arg is 0. **/ double log2(double Arg); /** Break Value into integral and fractional parts, each of which has the same type and sign as Value. Store the integral part in the object pointed to by Integ and return the fractional part. @param[in] Value The value to compute the arc cosine of. @param[out] Integ Pointer to where the integral component is to be stored. @return The fractional part of Value is returned directly while the integral part is returned in the location pointed to by Integ. **/ double modf(double Value, double *Integ); /** Compute Value raised to the power Exp. @param[in] Value The value to be raised. @param[in] Exp The power Value is to be raised to. @return The pow function returns Value**Exp. If an error occurs, errno will be set as follows: - EDOM: Value is finite and negative and Exp is finite and not an integer. - EDOM: Both Value and Exp are zero. - EDOM: Value is zero and Exp is less than zero. **/ double pow(double Value, double Exp); /** Compute the non-negative square root of Arg. @param[in] Arg The value to compute the square root of. @return The square root of Arg. If Arg is less than zero, errno is set to EDOM. **/ double sqrt(double Arg); /** Compute the smallest integer value not less than Arg. @param[in] Arg The value to compute the ceiling of. @return The ceiling of Arg expressed as a floating-point number. **/ double ceil(double Arg); /** Compute the absolute value of Arg. @param[in] Arg The value to compute the absolute value of. @return The absolute value of Arg. **/ double fabs(double Arg); /** Compute the largest integer value not greater than Arg. @param[in] Arg The value to compute the floor of. @return The largest integer value not greater than Arg, expressed as a floating-point number. **/ double floor(double); /** Compute the floating-point remainder of A1 / A2. @param[in] A1 The dividend. @param[in] A2 The divisor. @return The remainder of A1 / A2 with the same sign as A1. If A2 is zero, the fmod function returns 0. **/ double fmod(double A1, double A2); int finite(double); double expm1(double); /**@{ C99, Posix, or NetBSD functions that are not part of the C95 specification. **/ /* * Functions callable from C, intended to support IEEE arithmetic. */ double copysign(double, double); double scalbn(double, int); /* * Library implementation */ int __fpclassifyf(float); int __fpclassifyd(double); int __isinff(float); int __isinfd(double); int __isnanf(float); int __isnand(double); #ifdef __HAVE_LONG_DOUBLE int __fpclassifyl(long double); int __isinfl(long double); int __isnanl(long double); #endif /* __HAVE_LONG_DOUBLE */ /*@}*/ __END_DECLS /**@{ Extensions provided by NetBSD but not required by the C95 standard. **/ extern int signgam; enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix}; #define _LIB_VERSION_TYPE enum fdversion #define _LIB_VERSION _fdlib_version /** If global variable _LIB_VERSION is not desirable, one may * change the following to be a constant by: * #define _LIB_VERSION_TYPE const enum version * In that case, after one initializes the value _LIB_VERSION (see * s_lib_version.c) during compile time, it cannot be modified * in the middle of a program */ extern _LIB_VERSION_TYPE _LIB_VERSION; #define _IEEE_ fdlibm_ieee #define _SVID_ fdlibm_svid #define _XOPEN_ fdlibm_xopen #define _POSIX_ fdlibm_posix #ifndef __cplusplus struct exception { int type; char *name; double arg1; double arg2; double retval; }; #endif #define HUGE MAXFLOAT /** set X_TLOSS = pi*2**52 **/ #define X_TLOSS 1.41484755040568800000e+16 #define DOMAIN 1 #define SING 2 #define OVERFLOW 3 #define UNDERFLOW 4 #define TLOSS 5 #define PLOSS 6 /*@}*/ /* 7.12#4 INFINITY */ #ifdef __INFINITY #define INFINITY __INFINITY /**< float constant which overflows */ #else #define INFINITY HUGE_VALF /**< positive infinity */ #endif /* __INFINITY */ /* 7.12#5 NAN: a quiet NaN, if supported */ #ifdef __HAVE_NANF extern const union __float_u __nanf; #define NAN __nanf.__val #endif /* __HAVE_NANF */ /**@{ C99 7.12#6 Number classification macros represent mutually exclusive kinds of floating-point values. **/ #define FP_INFINITE 0x00 #define FP_NAN 0x01 #define FP_NORMAL 0x02 #define FP_SUBNORMAL 0x03 #define FP_ZERO 0x04 /* NetBSD extensions */ #define _FP_LOMD 0x80 /**< range for machine-specific classes */ #define _FP_HIMD 0xff /*@)*/ /**@{ * Constants ala XOPEN/SVID. */ #define M_E 2.7182818284590452354 /**< e */ #define M_LOG2E 1.4426950408889634074 /**< log 2e */ #define M_LOG10E 0.43429448190325182765 /**< log 10e */ #define M_LN2 0.69314718055994530942 /**< log e2 */ #define M_LN10 2.30258509299404568402 /**< log e10 */ #define M_PI 3.14159265358979323846 /**< pi */ #define M_PI_2 1.57079632679489661923 /**< pi/2 */ #define M_PI_4 0.78539816339744830962 /**< pi/4 */ #define M_1_PI 0.31830988618379067154 /**< 1/pi */ #define M_2_PI 0.63661977236758134308 /**< 2/pi */ #define M_2_SQRTPI 1.12837916709551257390 /**< 2/sqrt(pi) */ #define M_SQRT2 1.41421356237309504880 /**< sqrt(2) */ #define M_SQRT1_2 0.70710678118654752440 /**< 1/sqrt(2) */ #define MAXFLOAT ((float)3.40282346638528860e+38) /*@}*/ #endif /* _MATH_H_ */