/* Copyright (c) 2002,2007 Michael Stumpf Portions of documentation Copyright (c) 1990 - 1994 The Regents of the University of California. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the copyright holders nor the names of contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* $Id: math.h,v 1.21 2007/12/19 13:33:54 dmix Exp $ */ /* math.h - mathematical functions Author : Michael Stumpf Michael.Stumpf@t-online.de __ATTR_CONST__ added by marekm@linux.org.pl for functions that "do not examine any values except their arguments, and have no effects except the return value", for better optimization by gcc. */ #ifndef __MATH_H #define __MATH_H /** \file */ /** \defgroup avr_math : Mathematics \code #include \endcode This header file declares basic mathematics constants and functions. \par Notes: - In order to access the functions delcared herein, it is usually also required to additionally link against the library \c libm.a. See also the related \ref faq_libm "FAQ entry". - Math functions do not raise exceptions and do not change the \c errno variable. Therefore the majority of them are declared with const attribute, for better optimization by GCC. */ /** \ingroup avr_math The constant \c pi. */ #define M_PI 3.141592653589793238462643 /** \ingroup avr_math The square root of 2. */ #define M_SQRT2 1.4142135623730950488016887 /** \ingroup avr_math NAN constant. */ #define NAN __builtin_nan("") /** \ingroup avr_math INFINITY constant. */ #define INFINITY __builtin_inf() #ifndef __ATTR_CONST__ # define __ATTR_CONST__ __attribute__((__const__)) #endif #ifdef __cplusplus extern "C" { #endif /** \ingroup avr_math The cos() function returns the cosine of \a __x, measured in radians. */ extern double cos(double __x) __ATTR_CONST__; /** \ingroup avr_math The fabs() function computes the absolute value of a floating-point number \a __x. */ extern double fabs(double __x) __ATTR_CONST__; #if 0 /* fabs seems to be built in already */ extern inline double fabs( double __x ) { double __res; __asm__ __volatile__ ("andi %D0,0x7F \n\t" : "=d" (__res) : "0" (__x) ); return __res; } #endif /** \ingroup avr_math The function fmod() returns the floating-point remainder of __x / __y. */ extern double fmod(double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The modf() function breaks the argument \a __x into integral and fractional parts, each of which has the same sign as the argument. It stores the integral part as a double in the object pointed to by \a __iptr. The modf() function returns the signed fractional part of \a __x. \note This implementation skips writing by zero pointer. */ extern double modf(double __x, double *__iptr); /** \ingroup avr_math The sin() function returns the sine of \a __x, measured in radians. */ extern double sin(double __x) __ATTR_CONST__; /** \ingroup avr_math The sqrt() function returns the non-negative square root of \a __x. */ extern double sqrt(double __x) __ATTR_CONST__; /** \ingroup avr_math The tan() function returns the tangent of \a __x, measured in radians. */ extern double tan(double __x) __ATTR_CONST__; /** \ingroup avr_math The floor() function returns the largest integral value less than or equal to \a __x, expressed as a floating-point number. */ extern double floor(double __x) __ATTR_CONST__; /** \ingroup avr_math The ceil() function returns the smallest integral value greater than or equal to \a __x, expressed as a floating-point number. */ extern double ceil(double __x) __ATTR_CONST__; /** \ingroup avr_math The frexp() function breaks a floating-point number into a normalized fraction and an integral power of 2. It stores the integer in the \c int object pointed to by \a __pexp. If \a __x is a normal float point number, the frexp() function returns the value \c v, such that \c v has a magnitude in the interval [1/2, 1) or zero, and \a __x equals \c v times 2 raised to the power \a __pexp. If \a __x is zero, both parts of the result are zero. If \a __x is not a finite number, the frexp() returns \a __x as is and stores 0 by \a __pexp. \note This implementation permits a zero pointer as a directive to skip a storing the exponent. */ extern double frexp(double __x, int *__pexp); /** \ingroup avr_math The ldexp() function multiplies a floating-point number by an integral power of 2. The ldexp() function returns the value of \a __x times 2 raised to the power \a __exp. */ extern double ldexp(double __x, int __exp) __ATTR_CONST__; /** \ingroup avr_math The exp() function returns the exponential value of \a __x. */ extern double exp(double __x) __ATTR_CONST__; /** \ingroup avr_math The cosh() function returns the hyperbolic cosine of \a __x. */ extern double cosh(double __x) __ATTR_CONST__; /** \ingroup avr_math The sinh() function returns the hyperbolic sine of \a __x. */ extern double sinh(double __x) __ATTR_CONST__; /** \ingroup avr_math The tanh() function returns the hyperbolic tangent of \a __x. */ extern double tanh(double __x) __ATTR_CONST__; /** \ingroup avr_math The acos() function computes the principal value of the arc cosine of \a __x. The returned value is in the range [0, pi] radians. A domain error occurs for arguments not in the range [-1, +1]. */ extern double acos(double __x) __ATTR_CONST__; /** \ingroup avr_math The asin() function computes the principal value of the arc sine of \a __x. The returned value is in the range [-pi/2, pi/2] radians. A domain error occurs for arguments not in the range [-1, +1]. */ extern double asin(double __x) __ATTR_CONST__; /** \ingroup avr_math The atan() function computes the principal value of the arc tangent of \a __x. The returned value is in the range [-pi/2, pi/2] radians. */ extern double atan(double __x) __ATTR_CONST__; /** \ingroup avr_math The atan2() function computes the principal value of the arc tangent of __y / __x, using the signs of both arguments to determine the quadrant of the return value. The returned value is in the range [-pi, +pi] radians. */ extern double atan2(double __y, double __x) __ATTR_CONST__; /** \ingroup avr_math The log() function returns the natural logarithm of argument \a __x. */ extern double log(double __x) __ATTR_CONST__; /** \ingroup avr_math The log10() function returns the logarithm of argument \a __x to base 10. */ extern double log10(double __x) __ATTR_CONST__; /** \ingroup avr_math The function pow() returns the value of \a __x to the exponent \a __y. */ extern double pow(double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The function isnan() returns 1 if the argument \a __x represents a "not-a-number" (NaN) object, otherwise 0. */ extern int isnan(double __x) __ATTR_CONST__; /** \ingroup avr_math The function isinf() returns 1 if the argument \a __x is positive infinity, -1 if \a __x is negative infinity, and 0 otherwise. */ extern int isinf(double __x) __ATTR_CONST__; /** \ingroup avr_math The function square() returns __x * __x. \note This function does not belong to the C standard definition. */ extern double square(double __x) __ATTR_CONST__; /** \ingroup avr_math The copysign() function returns \a __x but with the sign of \a __y. They work even if \a __x or \a __y are NaN or zero. */ __ATTR_CONST__ extern inline double copysign (double __x, double __y) { asm ( "bst %D2, 7 \n\t" "bld %D0, 7 " : "=r" (__x) : "0" (__x), "r" (__y) ); return __x; } /** \ingroup avr_math The fdim() function returns max(__x - __y, 0). If \a __x or \a __y or both are NaN, NaN is returned. */ extern double fdim (double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The fma() function performs floating-point multiply-add. This is the operation (__x * __y) + __z, but the intermediate result is not rounded to the destination type. This can sometimes improve the precision of a calculation. */ extern double fma (double __x, double __y, double __z) __ATTR_CONST__; /** \ingroup avr_math The fmax() function returns the greater of the two values \a __x and \a __y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned. */ extern double fmax (double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The fmin() function returns the lesser of the two values \a __x and \a __y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned. */ extern double fmin (double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The signbit() function returns a nonzero value if the value of \a __x has its sign bit set. This is not the same as `\a __x < 0.0', because IEEE 754 floating point allows zero to be signed. The comparison `-0.0 < 0.0' is false, but `signbit (-0.0)' will return a nonzero value. \note This implementation returns 1 if sign bit is set. */ extern int signbit (double __x) __ATTR_CONST__; /** \ingroup avr_math The trunc() function rounds \a __x to the nearest integer not larger in absolute value. */ extern double trunc (double __x) __ATTR_CONST__; /** \ingroup avr_math The isfinite() function returns a nonzero value if \a __x is finite: not plus or minus infinity, and not NaN. */ __ATTR_CONST__ extern inline int isfinite (double __x) { unsigned char __exp; asm ( "mov %0, %C1 \n\t" "lsl %0 \n\t" "mov %0, %D1 \n\t" "rol %0 " : "=r" (__exp) : "r" (__x) ); return __exp != 0xff; } /** \ingroup avr_math The hypot() function returns sqrt(__x*__x + __y*__y). This is the length of the hypotenuse of a right triangle with sides of length \a __x and \a __y, or the distance of the point (\a __x, \a __y) from the origin. Using this function instead of the direct formula is wise, since the error is much smaller. No underflow with small \a __x and \a __y. No overflow if result is in range. */ double hypot (double __x, double __y) __ATTR_CONST__; /** \ingroup avr_math The round() function rounds \a __x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). Overflow is impossible. \return The rounded value. If \a __x is an integral or infinite, \a __x itself is returned. If \a __x is \c NaN, then \c NaN is returned. */ double round (double __x) __ATTR_CONST__; /** \ingroup avr_math The lround() function rounds \a __x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). This function is similar to round() function, but it differs in type of return value and in that an overflow is possible. \return The rounded long integer value. If \a __x is not a finite number or an overflow was, this realization returns the \c LONG_MIN value (0x80000000). */ long lround (double __x) __ATTR_CONST__; /** \ingroup avr_math The lrint() function rounds \a __x to the nearest integer, rounding the halfway cases to the even integer direction. (That is both 1.5 and 2.5 values are rounded to 2). This function is similar to rint() function, but it differs in type of return value and in that an overflow is possible. \return The rounded long integer value. If \a __x is not a finite number or an overflow was, this realization returns the \c LONG_MIN value (0x80000000). */ long lrint (double __x) __ATTR_CONST__; #ifdef __cplusplus } #endif #endif /* _MATH_H */