dos -> unix

1 files changed, 593 insertions, 593 deletions

diff --git a/libX11/src/xcms/cmsTrig.c b/libX11/src/xcms/cmsTrig.c
index 26ae05f75..5a01a56c8 100644
--- a/libX11/src/xcms/cmsTrig.c
+++ b/libX11/src/xcms/cmsTrig.c
@@ -1,593 +1,593 @@
-

-/*

- * 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 <config.h>

-#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 */

-#ifdef _CRAY

-#define XCMS_DMAXPOWTWO	((double)(1 < 47))

-#else

-#define XCMS_DMAXPOWTWO	((double)(XCMS_LONG_MAX) * \

-	    (1L << ((XCMS_NBITS(double)-XCMS_DEXPLEN) - XCMS_NBITS(int) + 1)))

-#endif

-

-/*

- *	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;

-

-#if 0

-    auto double curr_coeff;

-    if (order <= 0) {

-	rtn_value = *coeffs;

-    } else {

-	curr_coeff = *coeffs;	/* Bug in Unisoft's compiler.  Does not */

-	coeffs++;		/* generate good code for *coeffs++ */

-	rtn_value = curr_coeff + x * _XcmsPolynomial (--order, coeffs, x);

-    }

-#else /* ++jrb -- removed tail recursion */

-    coeffs += order;

-    rtn_value = *coeffs--;

-    while(order-- > 0)

-	rtn_value = *coeffs-- + (x * rtn_value);

-#endif

-

-    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));

-}

+
+/*
+ * 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 <config.h>
+#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 */
+#ifdef _CRAY
+#define XCMS_DMAXPOWTWO	((double)(1 < 47))
+#else
+#define XCMS_DMAXPOWTWO	((double)(XCMS_LONG_MAX) * \
+	    (1L << ((XCMS_NBITS(double)-XCMS_DEXPLEN) - XCMS_NBITS(int) + 1)))
+#endif
+
+/*
+ *	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;
+
+#if 0
+    auto double curr_coeff;
+    if (order <= 0) {
+	rtn_value = *coeffs;
+    } else {
+	curr_coeff = *coeffs;	/* Bug in Unisoft's compiler.  Does not */
+	coeffs++;		/* generate good code for *coeffs++ */
+	rtn_value = curr_coeff + x * _XcmsPolynomial (--order, coeffs, x);
+    }
+#else /* ++jrb -- removed tail recursion */
+    coeffs += order;
+    rtn_value = *coeffs--;
+    while(order-- > 0)
+	rtn_value = *coeffs-- + (x * rtn_value);
+#endif
+
+    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));
+}