From c350873c7c977efe5210484f04160be45f84ba7e Mon Sep 17 00:00:00 2001 From: Mike Gabriel Date: Fri, 21 Jul 2017 12:31:09 +0200 Subject: Convert nx-X11/lib/ build flow from imake to autotools. --- nx-X11/lib/X11/cmsTrig.c | 578 ----------------------------------------------- 1 file changed, 578 deletions(-) delete mode 100644 nx-X11/lib/X11/cmsTrig.c (limited to 'nx-X11/lib/X11/cmsTrig.c') diff --git a/nx-X11/lib/X11/cmsTrig.c b/nx-X11/lib/X11/cmsTrig.c deleted file mode 100644 index b23033aa8..000000000 --- a/nx-X11/lib/X11/cmsTrig.c +++ /dev/null @@ -1,578 +0,0 @@ - -/* - * Code and supporting documentation (c) Copyright 1990 1991 Tektronix, Inc. - * All Rights Reserved - * - * This file is a component of an X Window System-specific implementation - * of Xcms based on the TekColor Color Management System. Permission is - * hereby granted to use, copy, modify, sell, and otherwise distribute this - * software and its documentation for any purpose and without fee, provided - * that this copyright, permission, and disclaimer notice is reproduced in - * all copies of this software and in supporting documentation. TekColor - * is a trademark of Tektronix, Inc. - * - * Tektronix makes no representation about the suitability of this software - * for any purpose. It is provided "as is" and with all faults. - * - * TEKTRONIX DISCLAIMS ALL WARRANTIES APPLICABLE TO THIS SOFTWARE, - * INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A - * PARTICULAR PURPOSE. IN NO EVENT SHALL TEKTRONIX BE LIABLE FOR ANY - * SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER - * RESULTING FROM LOSS OF USE, DATA, OR PROFITS, WHETHER IN AN ACTION OF - * CONTRACT, NEGLIGENCE, OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN - * CONNECTION WITH THE USE OR THE PERFORMANCE OF THIS SOFTWARE. - */ - -/* - * It should be pointed out that for simplicity's sake, the - * environment parameters are defined as floating point constants, - * rather than octal or hexadecimal initializations of allocated - * storage areas. This means that the range of allowed numbers - * may not exactly match the hardware's capabilities. For example, - * if the maximum positive double precision floating point number - * is EXACTLY 1.11...E100 and the constant "MAXDOUBLE is - * defined to be 1.11E100 then the numbers between 1.11E100 and - * 1.11...E100 are considered to be undefined. For most - * applications, this will cause no problems. - * - * An alternate method is to allocate a global static "double" variable, - * say "maxdouble", and use a union declaration and initialization - * to initialize it with the proper bits for the EXACT maximum value. - * This was not done because the only compilers available to the - * author did not fully support union initialization features. - * - */ - -#ifdef HAVE_CONFIG_H -#include -#endif -#include "Xcmsint.h" - -/* forward/static */ -static double _XcmsModulo(double value, double base); -static double _XcmsPolynomial( - register int order, - double const *coeffs, - double x); -static double -_XcmsModuloF( - double val, - register double *dp); - -/* - * DEFINES - */ -#define XCMS_MAXERROR 0.000001 -#define XCMS_MAXITER 10000 -#define XCMS_PI 3.14159265358979323846264338327950 -#define XCMS_TWOPI 6.28318530717958620 -#define XCMS_HALFPI 1.57079632679489660 -#define XCMS_FOURTHPI 0.785398163397448280 -#define XCMS_SIXTHPI 0.523598775598298820 -#define XCMS_RADIANS(d) ((d) * XCMS_PI / 180.0) -#define XCMS_DEGREES(r) ((r) * 180.0 / XCMS_PI) -#define XCMS_X6_UNDERFLOWS (4.209340e-52) /* X**6 almost underflows */ -#define XCMS_X16_UNDERFLOWS (5.421010e-20) /* X**16 almost underflows*/ -#define XCMS_CHAR_BIT 8 -#define XCMS_LONG_MAX 0x7FFFFFFF -#define XCMS_DEXPLEN 11 -#define XCMS_NBITS(type) (XCMS_CHAR_BIT * (int)sizeof(type)) -#define XCMS_FABS(x) ((x) < 0.0 ? -(x) : (x)) - -/* XCMS_DMAXPOWTWO - largest power of two exactly representable as a double */ -#define XCMS_DMAXPOWTWO ((double)(XCMS_LONG_MAX) * \ - (1L << ((XCMS_NBITS(double)-XCMS_DEXPLEN) - XCMS_NBITS(int) + 1))) - -/* - * LOCAL VARIABLES - */ - -static double const cos_pcoeffs[] = { - 0.12905394659037374438e7, - -0.37456703915723204710e6, - 0.13432300986539084285e5, - -0.11231450823340933092e3 -}; - -static double const cos_qcoeffs[] = { - 0.12905394659037373590e7, - 0.23467773107245835052e5, - 0.20969518196726306286e3, - 1.0 -}; - -static double const sin_pcoeffs[] = { - 0.20664343336995858240e7, - -0.18160398797407332550e6, - 0.35999306949636188317e4, - -0.20107483294588615719e2 -}; - -static double const sin_qcoeffs[] = { - 0.26310659102647698963e7, - 0.39270242774649000308e5, - 0.27811919481083844087e3, - 1.0 -}; - -/* - * - * FUNCTION - * - * _XcmsCosine double precision cosine - * - * KEY WORDS - * - * cos - * machine independent routines - * trigonometric functions - * math libraries - * - * DESCRIPTION - * - * Returns double precision cosine of double precision - * floating point argument. - * - * USAGE - * - * double _XcmsCosine (x) - * double x; - * - * REFERENCES - * - * Computer Approximations, J.F. Hart et al, John Wiley & Sons, - * 1968, pp. 112-120. - * - * RESTRICTIONS - * - * The sin and cos routines are interactive in the sense that - * in the process of reducing the argument to the range -PI/4 - * to PI/4, each may call the other. Ultimately one or the - * other uses a polynomial approximation on the reduced - * argument. The sin approximation has a maximum relative error - * of 10**(-17.59) and the cos approximation has a maximum - * relative error of 10**(-16.18). - * - * These error bounds assume exact arithmetic - * in the polynomial evaluation. Additional rounding and - * truncation errors may occur as the argument is reduced - * to the range over which the polynomial approximation - * is valid, and as the polynomial is evaluated using - * finite-precision arithmetic. - * - * PROGRAMMER - * - * Fred Fish - * - * INTERNALS - * - * Computes cos(x) from: - * - * (1) Reduce argument x to range -PI to PI. - * - * (2) If x > PI/2 then call cos recursively - * using relation cos(x) = -cos(x - PI). - * - * (3) If x < -PI/2 then call cos recursively - * using relation cos(x) = -cos(x + PI). - * - * (4) If x > PI/4 then call sin using - * relation cos(x) = sin(PI/2 - x). - * - * (5) If x < -PI/4 then call cos using - * relation cos(x) = sin(PI/2 + x). - * - * (6) If x would cause underflow in approx - * evaluation arithmetic then return - * sqrt(1.0 - x**2). - * - * (7) By now x has been reduced to range - * -PI/4 to PI/4 and the approximation - * from HART pg. 119 can be used: - * - * cos(x) = ( p(y) / q(y) ) - * Where: - * - * y = x * (4/PI) - * - * p(y) = SUM [ Pj * (y**(2*j)) ] - * over j = {0,1,2,3} - * - * q(y) = SUM [ Qj * (y**(2*j)) ] - * over j = {0,1,2,3} - * - * P0 = 0.12905394659037374438571854e+7 - * P1 = -0.3745670391572320471032359e+6 - * P2 = 0.134323009865390842853673e+5 - * P3 = -0.112314508233409330923e+3 - * Q0 = 0.12905394659037373590295914e+7 - * Q1 = 0.234677731072458350524124e+5 - * Q2 = 0.2096951819672630628621e+3 - * Q3 = 1.0000... - * (coefficients from HART table #3843 pg 244) - * - * - * **** NOTE **** The range reduction relations used in - * this routine depend on the final approximation being valid - * over the negative argument range in addition to the positive - * argument range. The particular approximation chosen from - * HART satisfies this requirement, although not explicitly - * stated in the text. This may not be true of other - * approximations given in the reference. - * - */ - -double _XcmsCosine(double x) -{ - auto double y; - auto double yt2; - double retval; - - if (x < -XCMS_PI || x > XCMS_PI) { - x = _XcmsModulo (x, XCMS_TWOPI); - if (x > XCMS_PI) { - x = x - XCMS_TWOPI; - } else if (x < -XCMS_PI) { - x = x + XCMS_TWOPI; - } - } - if (x > XCMS_HALFPI) { - retval = -(_XcmsCosine (x - XCMS_PI)); - } else if (x < -XCMS_HALFPI) { - retval = -(_XcmsCosine (x + XCMS_PI)); - } else if (x > XCMS_FOURTHPI) { - retval = _XcmsSine (XCMS_HALFPI - x); - } else if (x < -XCMS_FOURTHPI) { - retval = _XcmsSine (XCMS_HALFPI + x); - } else if (x < XCMS_X6_UNDERFLOWS && x > -XCMS_X6_UNDERFLOWS) { - retval = _XcmsSquareRoot (1.0 - (x * x)); - } else { - y = x / XCMS_FOURTHPI; - yt2 = y * y; - retval = _XcmsPolynomial (3, cos_pcoeffs, yt2) / _XcmsPolynomial (3, cos_qcoeffs, yt2); - } - return (retval); -} - - -/* - * FUNCTION - * - * _XcmsModulo double precision modulo - * - * KEY WORDS - * - * _XcmsModulo - * machine independent routines - * math libraries - * - * DESCRIPTION - * - * Returns double precision modulo of two double - * precision arguments. - * - * USAGE - * - * double _XcmsModulo (value, base) - * double value; - * double base; - * - * PROGRAMMER - * - * Fred Fish - * - */ -static double _XcmsModulo(double value, double base) -{ - auto double intpart; - - value /= base; - value = _XcmsModuloF (value, &intpart); - value *= base; - return(value); -} - - -/* - * frac = (double) _XcmsModuloF(double val, double *dp) - * return fractional part of 'val' - * set *dp to integer part of 'val' - * - * Note -> only compiled for the CA or KA. For the KB/MC, - * "math.c" instantiates a copy of the inline function - * defined in "math.h". - */ -static double -_XcmsModuloF( - double val, - register double *dp) -{ - register double abs; - /* - * Don't use a register for this. The extra precision this results - * in on some systems causes problems. - */ - double ip; - - /* should check for illegal values here - nan, inf, etc */ - abs = XCMS_FABS(val); - if (abs >= XCMS_DMAXPOWTWO) { - ip = val; - } else { - ip = abs + XCMS_DMAXPOWTWO; /* dump fraction */ - ip -= XCMS_DMAXPOWTWO; /* restore w/o frac */ - if (ip > abs) /* if it rounds up */ - ip -= 1.0; /* fix it */ - ip = XCMS_FABS(ip); - } - *dp = ip; - return (val - ip); /* signed fractional part */ -} - - -/* - * FUNCTION - * - * _XcmsPolynomial double precision polynomial evaluation - * - * KEY WORDS - * - * poly - * machine independent routines - * math libraries - * - * DESCRIPTION - * - * Evaluates a polynomial and returns double precision - * result. Is passed a the order of the polynomial, - * a pointer to an array of double precision polynomial - * coefficients (in ascending order), and the independent - * variable. - * - * USAGE - * - * double _XcmsPolynomial (order, coeffs, x) - * int order; - * double *coeffs; - * double x; - * - * PROGRAMMER - * - * Fred Fish - * - * INTERNALS - * - * Evalates the polynomial using recursion and the form: - * - * P(x) = P0 + x(P1 + x(P2 +...x(Pn))) - * - */ - -static double _XcmsPolynomial( - register int order, - double const *coeffs, - double x) -{ - auto double rtn_value; - - coeffs += order; - rtn_value = *coeffs--; - while(order-- > 0) - rtn_value = *coeffs-- + (x * rtn_value); - - return(rtn_value); -} - - -/* - * FUNCTION - * - * _XcmsSine double precision sine - * - * KEY WORDS - * - * sin - * machine independent routines - * trigonometric functions - * math libraries - * - * DESCRIPTION - * - * Returns double precision sine of double precision - * floating point argument. - * - * USAGE - * - * double _XcmsSine (x) - * double x; - * - * REFERENCES - * - * Computer Approximations, J.F. Hart et al, John Wiley & Sons, - * 1968, pp. 112-120. - * - * RESTRICTIONS - * - * The sin and cos routines are interactive in the sense that - * in the process of reducing the argument to the range -PI/4 - * to PI/4, each may call the other. Ultimately one or the - * other uses a polynomial approximation on the reduced - * argument. The sin approximation has a maximum relative error - * of 10**(-17.59) and the cos approximation has a maximum - * relative error of 10**(-16.18). - * - * These error bounds assume exact arithmetic - * in the polynomial evaluation. Additional rounding and - * truncation errors may occur as the argument is reduced - * to the range over which the polynomial approximation - * is valid, and as the polynomial is evaluated using - * finite-precision arithmetic. - * - * PROGRAMMER - * - * Fred Fish - * - * INTERNALS - * - * Computes sin(x) from: - * - * (1) Reduce argument x to range -PI to PI. - * - * (2) If x > PI/2 then call sin recursively - * using relation sin(x) = -sin(x - PI). - * - * (3) If x < -PI/2 then call sin recursively - * using relation sin(x) = -sin(x + PI). - * - * (4) If x > PI/4 then call cos using - * relation sin(x) = cos(PI/2 - x). - * - * (5) If x < -PI/4 then call cos using - * relation sin(x) = -cos(PI/2 + x). - * - * (6) If x is small enough that polynomial - * evaluation would cause underflow - * then return x, since sin(x) - * approaches x as x approaches zero. - * - * (7) By now x has been reduced to range - * -PI/4 to PI/4 and the approximation - * from HART pg. 118 can be used: - * - * sin(x) = y * ( p(y) / q(y) ) - * Where: - * - * y = x * (4/PI) - * - * p(y) = SUM [ Pj * (y**(2*j)) ] - * over j = {0,1,2,3} - * - * q(y) = SUM [ Qj * (y**(2*j)) ] - * over j = {0,1,2,3} - * - * P0 = 0.206643433369958582409167054e+7 - * P1 = -0.18160398797407332550219213e+6 - * P2 = 0.359993069496361883172836e+4 - * P3 = -0.2010748329458861571949e+2 - * Q0 = 0.263106591026476989637710307e+7 - * Q1 = 0.3927024277464900030883986e+5 - * Q2 = 0.27811919481083844087953e+3 - * Q3 = 1.0000... - * (coefficients from HART table #3063 pg 234) - * - * - * **** NOTE **** The range reduction relations used in - * this routine depend on the final approximation being valid - * over the negative argument range in addition to the positive - * argument range. The particular approximation chosen from - * HART satisfies this requirement, although not explicitly - * stated in the text. This may not be true of other - * approximations given in the reference. - * - */ - -double -_XcmsSine (double x) -{ - double y; - double yt2; - double retval; - - if (x < -XCMS_PI || x > XCMS_PI) { - x = _XcmsModulo (x, XCMS_TWOPI); - if (x > XCMS_PI) { - x = x - XCMS_TWOPI; - } else if (x < -XCMS_PI) { - x = x + XCMS_TWOPI; - } - } - if (x > XCMS_HALFPI) { - retval = -(_XcmsSine (x - XCMS_PI)); - } else if (x < -XCMS_HALFPI) { - retval = -(_XcmsSine (x + XCMS_PI)); - } else if (x > XCMS_FOURTHPI) { - retval = _XcmsCosine (XCMS_HALFPI - x); - } else if (x < -XCMS_FOURTHPI) { - retval = -(_XcmsCosine (XCMS_HALFPI + x)); - } else if (x < XCMS_X6_UNDERFLOWS && x > -XCMS_X6_UNDERFLOWS) { - retval = x; - } else { - y = x / XCMS_FOURTHPI; - yt2 = y * y; - retval = y * (_XcmsPolynomial (3, sin_pcoeffs, yt2) / _XcmsPolynomial(3, sin_qcoeffs, yt2)); - } - return(retval); -} - - -/* - * NAME - * _XcmsArcTangent - * - * SYNOPSIS - */ -double -_XcmsArcTangent(double x) -/* - * DESCRIPTION - * Computes the arctangent. - * This is an implementation of the Gauss algorithm as - * described in: - * Forman S. Acton, Numerical Methods That Work, - * New York, NY, Harper & Row, 1970. - * - * RETURNS - * Returns the arctangent - */ -{ - double ai, a1 = 0.0, bi, b1 = 0.0, l, d; - double maxerror; - int i; - - if (x == 0.0) { - return (0.0); - } - if (x < 1.0) { - maxerror = x * XCMS_MAXERROR; - } else { - maxerror = XCMS_MAXERROR; - } - ai = _XcmsSquareRoot( 1.0 / (1.0 + (x * x)) ); - bi = 1.0; - for (i = 0; i < XCMS_MAXITER; i++) { - a1 = (ai + bi) / 2.0; - b1 = _XcmsSquareRoot((a1 * bi)); - if (a1 == b1) - break; - d = XCMS_FABS(a1 - b1); - if (d < maxerror) - break; - ai = a1; - bi = b1; - } - - l = ((a1 > b1) ? b1 : a1); - - a1 = _XcmsSquareRoot(1 + (x * x)); - return (x / (a1 * l)); -} -- cgit v1.2.3