BSD 4.4 Lite Lib Sources

4 files changed, 668 insertions, 0 deletions

diff --git a/lib/libm/common/atan2.c b/lib/libm/common/atan2.c
new file mode 100644
index 0000000..958a154
--- /dev/null
+++ b/lib/libm/common/atan2.c
@@ -0,0 +1,281 @@
+/*
+ * Copyright (c) 1985, 1993
+ *	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:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. 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.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)atan2.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* ATAN2(Y,X)
+ * RETURN ARG (X+iY)
+ * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
+ * CODED IN C BY K.C. NG, 1/8/85; 
+ * REVISED BY K.C. NG on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85.
+ *
+ * Required system supported functions :
+ *	copysign(x,y)
+ *	scalb(x,y)
+ *	logb(x)
+ *	
+ * Method :
+ *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ *	2. Reduce x to positive by (if x and y are unexceptional): 
+ *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
+ *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
+ *	3. According to the integer k=4t+0.25 truncated , t=y/x, the argument 
+ *	   is further reduced to one of the following intervals and the 
+ *	   arctangent of y/x is evaluated by the corresponding formula:
+ *
+ *         [0,7/16]	   atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ *	   [7/16,11/16]    atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) )
+ *	   [11/16.19/16]   atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) )
+ *	   [19/16,39/16]   atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) )
+ *	   [39/16,INF]     atan(y/x) = atan(INF) + atan( -x/y )
+ *
+ * Special cases:
+ * Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
+ *
+ *	ARG( NAN , (anything) ) is NaN;
+ *	ARG( (anything), NaN ) is NaN;
+ *	ARG(+(anything but NaN), +-0) is +-0  ;
+ *	ARG(-(anything but NaN), +-0) is +-PI ;
+ *	ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2;
+ *	ARG( +INF,+-(anything but INF and NaN) ) is +-0 ;
+ *	ARG( -INF,+-(anything but INF and NaN) ) is +-PI;
+ *	ARG( +INF,+-INF ) is +-PI/4 ;
+ *	ARG( -INF,+-INF ) is +-3PI/4;
+ *	ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2;
+ *
+ * Accuracy:
+ *	atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded, 
+ *	where
+ *
+ *	in decimal:
+ *		pi = 3.141592653589793 23846264338327 ..... 
+ *    53 bits   PI = 3.141592653589793 115997963 ..... ,
+ *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
+ *
+ *	in hexadecimal:
+ *		pi = 3.243F6A8885A308D313198A2E....
+ *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18	error=.276ulps
+ *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
+ *	
+ *	In a test run with 356,000 random argument on [-1,1] * [-1,1] on a
+ *	VAX, the maximum observed error was 1.41 ulps (units of the last place)
+ *	compared with (PI/pi)*(the exact ARG(x+iy)).
+ *
+ * Note:
+ *	We use machine PI (the true pi rounded) in place of the actual
+ *	value of pi for all the trig and inverse trig functions. In general, 
+ *	if trig is one of sin, cos, tan, then computed trig(y) returns the 
+ *	exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig 
+ *	returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the 
+ *	trig functions have period PI, and trig(arctrig(x)) returns x for
+ *	all critical values x.
+ *	
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include "mathimpl.h"
+
+vc(athfhi, 4.6364760900080611433E-1  ,6338,3fed,da7b,2b0d,  -1, .ED63382B0DDA7B)
+vc(athflo, 1.9338828231967579916E-19 ,5005,2164,92c0,9cfe, -62, .E450059CFE92C0)
+vc(PIo4,   7.8539816339744830676E-1  ,0fda,4049,68c2,a221,   0, .C90FDAA22168C2)
+vc(at1fhi, 9.8279372324732906796E-1  ,985e,407b,b4d9,940f,   0, .FB985E940FB4D9)
+vc(at1flo,-3.5540295636764633916E-18 ,1edc,a383,eaea,34d6, -57,-.831EDC34D6EAEA)
+vc(PIo2,   1.5707963267948966135E0   ,0fda,40c9,68c2,a221,   1, .C90FDAA22168C2)
+vc(PI,     3.1415926535897932270E0   ,0fda,4149,68c2,a221,   2, .C90FDAA22168C2)
+vc(a1,     3.3333333333333473730E-1  ,aaaa,3faa,ab75,aaaa,  -1, .AAAAAAAAAAAB75)
+vc(a2,    -2.0000000000017730678E-1  ,cccc,bf4c,946e,cccd,  -2,-.CCCCCCCCCD946E)
+vc(a3,     1.4285714286694640301E-1  ,4924,3f12,4262,9274,  -2, .92492492744262)
+vc(a4,    -1.1111111135032672795E-1  ,8e38,bee3,6292,ebc6,  -3,-.E38E38EBC66292)
+vc(a5,     9.0909091380563043783E-2  ,2e8b,3eba,d70c,b31b,  -3, .BA2E8BB31BD70C)
+vc(a6,    -7.6922954286089459397E-2  ,89c8,be9d,7f18,27c3,  -3,-.9D89C827C37F18)
+vc(a7,     6.6663180891693915586E-2  ,86b4,3e88,9e58,ae37,  -3, .8886B4AE379E58)
+vc(a8,    -5.8772703698290408927E-2  ,bba5,be70,a942,8481,  -4,-.F0BBA58481A942)
+vc(a9,     5.2170707402812969804E-2  ,b0f3,3e55,13ab,a1ab,  -4, .D5B0F3A1AB13AB)
+vc(a10,   -4.4895863157820361210E-2  ,e4b9,be37,048f,7fd1,  -4,-.B7E4B97FD1048F)
+vc(a11,    3.3006147437343875094E-2  ,3174,3e07,2d87,3cf7,  -4, .8731743CF72D87)
+vc(a12,   -1.4614844866464185439E-2  ,731a,bd6f,76d9,2f34,  -6,-.EF731A2F3476D9)
+
+ic(athfhi, 4.6364760900080609352E-1  ,  -2,  1.DAC670561BB4F)
+ic(athflo, 4.6249969567426939759E-18 , -58,  1.5543B8F253271)
+ic(PIo4,   7.8539816339744827900E-1  ,  -1,  1.921FB54442D18)
+ic(at1fhi, 9.8279372324732905408E-1  ,  -1,  1.F730BD281F69B)
+ic(at1flo,-2.4407677060164810007E-17 , -56, -1.C23DFEFEAE6B5)
+ic(PIo2,   1.5707963267948965580E0   ,   0,  1.921FB54442D18)
+ic(PI,     3.1415926535897931160E0   ,   1,  1.921FB54442D18)
+ic(a1,     3.3333333333333942106E-1  ,  -2,  1.55555555555C3)
+ic(a2,    -1.9999999999979536924E-1  ,  -3, -1.9999999997CCD)
+ic(a3,     1.4285714278004377209E-1  ,  -3,  1.24924921EC1D7)
+ic(a4,    -1.1111110579344973814E-1  ,  -4, -1.C71C7059AF280)
+ic(a5,     9.0908906105474668324E-2  ,  -4,  1.745CE5AA35DB2)
+ic(a6,    -7.6919217767468239799E-2  ,  -4, -1.3B0FA54BEC400)
+ic(a7,     6.6614695906082474486E-2  ,  -4,  1.10DA924597FFF)
+ic(a8,    -5.8358371008508623523E-2  ,  -5, -1.DE125FDDBD793)
+ic(a9,     4.9850617156082015213E-2  ,  -5,  1.9860524BDD807)
+ic(a10,   -3.6700606902093604877E-2  ,  -5, -1.2CA6C04C6937A)
+ic(a11,    1.6438029044759730479E-2  ,  -6,  1.0D52174A1BB54)
+
+#ifdef vccast
+#define	athfhi	vccast(athfhi)
+#define	athflo	vccast(athflo)
+#define	PIo4	vccast(PIo4)
+#define	at1fhi	vccast(at1fhi)
+#define	at1flo	vccast(at1flo)
+#define	PIo2	vccast(PIo2)
+#define	PI	vccast(PI)
+#define	a1	vccast(a1)
+#define	a2	vccast(a2)
+#define	a3	vccast(a3)
+#define	a4	vccast(a4)
+#define	a5	vccast(a5)
+#define	a6	vccast(a6)
+#define	a7	vccast(a7)
+#define	a8	vccast(a8)
+#define	a9	vccast(a9)
+#define	a10	vccast(a10)
+#define	a11	vccast(a11)
+#define	a12	vccast(a12)
+#endif
+
+double atan2(y,x)
+double  y,x;
+{  
+	static const double zero=0, one=1, small=1.0E-9, big=1.0E18;
+	double t,z,signy,signx,hi,lo;
+	int k,m;
+
+#if !defined(vax)&&!defined(tahoe)
+    /* if x or y is NAN */
+	if(x!=x) return(x); if(y!=y) return(y);
+#endif	/* !defined(vax)&&!defined(tahoe) */
+
+    /* copy down the sign of y and x */
+	signy = copysign(one,y) ;  
+	signx = copysign(one,x) ;  
+
+    /* if x is 1.0, goto begin */
+	if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;}
+
+    /* when y = 0 */
+	if(y==zero) return((signx==one)?y:copysign(PI,signy));
+
+    /* when x = 0 */
+	if(x==zero) return(copysign(PIo2,signy));
+	    
+    /* when x is INF */
+	if(!finite(x))
+	    if(!finite(y)) 
+		return(copysign((signx==one)?PIo4:3*PIo4,signy));
+	    else
+		return(copysign((signx==one)?zero:PI,signy));
+
+    /* when y is INF */
+	if(!finite(y)) return(copysign(PIo2,signy));
+
+    /* compute y/x */
+	x=copysign(x,one); 
+	y=copysign(y,one); 
+	if((m=(k=logb(y))-logb(x)) > 60) t=big+big; 
+	    else if(m < -80 ) t=y/x;
+	    else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); }
+
+    /* begin argument reduction */
+begin:
+	if (t < 2.4375) {		 
+
+	/* truncate 4(t+1/16) to integer for branching */
+	    k = 4 * (t+0.0625);
+	    switch (k) {
+
+	    /* t is in [0,7/16] */
+	    case 0:                    
+	    case 1:
+		if (t < small) 
+		    { big + small ;  /* raise inexact flag */
+		      return (copysign((signx>zero)?t:PI-t,signy)); }
+
+		hi = zero;  lo = zero;  break;
+
+	    /* t is in [7/16,11/16] */
+	    case 2:                    
+		hi = athfhi; lo = athflo;
+		z = x+x;
+		t = ( (y+y) - x ) / ( z +  y ); break;
+
+	    /* t is in [11/16,19/16] */
+	    case 3:                    
+	    case 4:
+		hi = PIo4; lo = zero;
+		t = ( y - x ) / ( x + y ); break;
+
+	    /* t is in [19/16,39/16] */
+	    default:                   
+		hi = at1fhi; lo = at1flo;
+		z = y-x; y=y+y+y; t = x+x;
+		t = ( (z+z)-x ) / ( t + y ); break;
+	    }
+	}
+	/* end of if (t < 2.4375) */
+
+	else                           
+	{
+	    hi = PIo2; lo = zero;
+
+	    /* t is in [2.4375, big] */
+	    if (t <= big)  t = - x / y;
+
+	    /* t is in [big, INF] */
+	    else          
+	      { big+small;	/* raise inexact flag */
+		t = zero; }
+	}
+    /* end of argument reduction */
+
+    /* compute atan(t) for t in [-.4375, .4375] */
+	z = t*t;
+#if defined(vax)||defined(tahoe)
+	z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
+			z*(a9+z*(a10+z*(a11+z*a12))))))))))));
+#else	/* defined(vax)||defined(tahoe) */
+	z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
+			z*(a9+z*(a10+z*a11)))))))))));
+#endif	/* defined(vax)||defined(tahoe) */
+	z = lo - z; z += t; z += hi;
+
+	return(copysign((signx>zero)?z:PI-z,signy));
+}
diff --git a/lib/libm/common/sincos.c b/lib/libm/common/sincos.c
new file mode 100644
index 0000000..ab88560
--- /dev/null
+++ b/lib/libm/common/sincos.c
@@ -0,0 +1,98 @@
+/*
+ * Copyright (c) 1987, 1993
+ *	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:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. 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.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)sincos.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+#include "trig.h"
+double
+sin(x)
+double x;
+{
+	double a,c,z;
+
+        if(!finite(x))		/* sin(NaN) and sin(INF) must be NaN */
+		return x-x;
+	x=drem(x,PI2);		/* reduce x into [-PI,PI] */
+	a=copysign(x,one);
+	if (a >= PIo4) {
+		if(a >= PI3o4)		/* ... in [3PI/4,PI] */
+			x = copysign((a = PI-a),x);
+		else {			/* ... in [PI/4,3PI/4]  */
+			a = PIo2-a;		/* rtn. sign(x)*C(PI/2-|x|) */
+			z = a*a;
+			c = cos__C(z);
+			z *= half;
+			a = (z >= thresh ? half-((z-half)-c) : one-(z-c));
+			return copysign(a,x);
+		}
+	}
+
+	if (a < small) {		/* rtn. S(x) */
+		big+a;
+		return x;
+	}
+	return x+x*sin__S(x*x);
+}
+
+double
+cos(x) 
+double x;
+{
+	double a,c,z,s = 1.0;
+
+	if(!finite(x))		/* cos(NaN) and cos(INF) must be NaN */
+		return x-x;
+	x=drem(x,PI2);		/* reduce x into [-PI,PI] */
+	a=copysign(x,one);
+	if (a >= PIo4) {
+		if (a >= PI3o4) {	/* ... in [3PI/4,PI] */
+			a = PI-a;
+			s = negone;
+		}
+		else {			/* ... in [PI/4,3PI/4] */
+			a = PIo2-a;
+			return a+a*sin__S(a*a);	/* rtn. S(PI/2-|x|) */ 
+		}
+	}
+	if (a < small) {
+		big+a;
+		return s;		/* rtn. s*C(a) */
+	}
+	z = a*a;
+	c = cos__C(z);
+	z *= half;
+	a = (z >= thresh ? half-((z-half)-c) : one-(z-c));
+	return copysign(a,s);
+}
diff --git a/lib/libm/common/tan.c b/lib/libm/common/tan.c
new file mode 100644
index 0000000..61ed5c5
--- /dev/null
+++ b/lib/libm/common/tan.c
@@ -0,0 +1,74 @@
+/*
+ * Copyright (c) 1987, 1993
+ *	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:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. 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.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)tan.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+#include "trig.h"
+double
+tan(x) 
+double x;
+{
+	double a,z,ss,cc,c;
+	int k;
+
+	if(!finite(x))		/* tan(NaN) and tan(INF) must be NaN */
+		return x-x;
+	x = drem(x,PI);			/* reduce x into [-PI/2, PI/2] */
+	a = copysign(x,one);		/* ... = abs(x) */
+	if (a >= PIo4) {
+		k = 1;
+		x = copysign(PIo2-a,x);
+	}
+	else {
+		k = 0;
+		if (a < small) {
+			big+a;
+			return x;
+		}
+	}
+	z = x*x;
+	cc = cos__C(z);
+	ss = sin__S(z);
+	z *= half;			/* Next get c = cos(x) accurately */
+	c = (z >= thresh ? half-((z-half)-cc) : one-(z-cc));
+	if (k == 0)
+		return x+(x*(z-(cc-ss)))/c;	/* ... sin/cos */
+#ifdef national
+	else if (x == zero)
+		return copysign(fmax,x);	/* no inf on 32k */
+#endif	/* national */
+	else
+		return c/(x+x*ss);		/* ... cos/sin */
+}
diff --git a/lib/libm/common/trig.h b/lib/libm/common/trig.h
new file mode 100644
index 0000000..9e05b0e
--- /dev/null
+++ b/lib/libm/common/trig.h
@@ -0,0 +1,215 @@
+/*
+ * Copyright (c) 1987, 1993
+ *	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:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. 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.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
+ *
+ *	@(#)trig.h	8.1 (Berkeley) 6/4/93
+ */
+
+#include "mathimpl.h"
+
+vc(thresh, 2.6117239648121182150E-1 ,b863,3f85,6ea0,6b02, -1, .85B8636B026EA0)
+vc(PIo4,   7.8539816339744830676E-1 ,0fda,4049,68c2,a221,  0, .C90FDAA22168C2)
+vc(PIo2,   1.5707963267948966135E0  ,0fda,40c9,68c2,a221,  1, .C90FDAA22168C2)
+vc(PI3o4,  2.3561944901923449203E0  ,cbe3,4116,0e92,f999,  2, .96CBE3F9990E92)
+vc(PI,     3.1415926535897932270E0  ,0fda,4149,68c2,a221,  2, .C90FDAA22168C2)
+vc(PI2,    6.2831853071795864540E0  ,0fda,41c9,68c2,a221,  3, .C90FDAA22168C2)
+
+ic(thresh, 2.6117239648121182150E-1 , -2, 1.0B70C6D604DD4)
+ic(PIo4,   7.8539816339744827900E-1 , -1, 1.921FB54442D18)
+ic(PIo2,   1.5707963267948965580E0  ,  0, 1.921FB54442D18)
+ic(PI3o4,  2.3561944901923448370E0  ,  1, 1.2D97C7F3321D2)
+ic(PI,     3.1415926535897931160E0  ,  1, 1.921FB54442D18)
+ic(PI2,    6.2831853071795862320E0  ,  2, 1.921FB54442D18)
+
+#ifdef vccast
+#define	thresh	vccast(thresh)
+#define	PIo4	vccast(PIo4)
+#define	PIo2	vccast(PIo2)
+#define	PI3o4	vccast(PI3o4)
+#define	PI	vccast(PI)
+#define	PI2	vccast(PI2)
+#endif
+
+#ifdef national
+static long fmaxx[]	= { 0xffffffff, 0x7fefffff};
+#define   fmax    (*(double*)fmaxx)
+#endif	/* national */
+
+static const double
+	zero = 0,
+	one = 1,
+	negone = -1,
+	half = 1.0/2.0, 
+	small = 1E-10,	/* 1+small**2 == 1; better values for small:
+			 *		small	= 1.5E-9 for VAX D
+			 *			= 1.2E-8 for IEEE Double
+			 *			= 2.8E-10 for IEEE Extended
+			 */
+	big = 1E20;	/* big := 1/(small**2) */
+
+/* sin__S(x*x) ... re-implemented as a macro
+ * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
+ * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) 
+ * CODED IN C BY K.C. NG, 1/21/85; 
+ * REVISED BY K.C. NG on 8/13/85.
+ *
+ *	    sin(x*k) - x
+ * RETURN  --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded
+ *	            x	
+ * value of pi in machine precision:
+ *
+ *	Decimal:
+ *		pi = 3.141592653589793 23846264338327 ..... 
+ *    53 bits   PI = 3.141592653589793 115997963 ..... ,
+ *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
+ *
+ *	Hexadecimal:
+ *		pi = 3.243F6A8885A308D313198A2E....
+ *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18
+ *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    
+ *
+ * Method:
+ *	1. Let z=x*x. Create a polynomial approximation to 
+ *	    (sin(k*x)-x)/x  =  z*(S0 + S1*z^1 + ... + S5*z^5).
+ *	Then
+ *      sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5)
+ *
+ *	The coefficient S's are obtained by a special Remez algorithm.
+ *
+ * Accuracy:
+ *	In the absence of rounding error, the approximation has absolute error 
+ *	less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. 
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ *
+ */
+
+vc(S0, -1.6666666666666646660E-1  ,aaaa,bf2a,aa71,aaaa,  -2, -.AAAAAAAAAAAA71)
+vc(S1,  8.3333333333297230413E-3  ,8888,3d08,477f,8888,  -6,  .8888888888477F)
+vc(S2, -1.9841269838362403710E-4  ,0d00,ba50,1057,cf8a, -12, -.D00D00CF8A1057)
+vc(S3,  2.7557318019967078930E-6  ,ef1c,3738,bedc,a326, -18,  .B8EF1CA326BEDC)
+vc(S4, -2.5051841873876551398E-8  ,3195,b3d7,e1d3,374c, -25, -.D73195374CE1D3)
+vc(S5,  1.6028995389845827653E-10 ,3d9c,3030,cccc,6d26, -32,  .B03D9C6D26CCCC)
+vc(S6, -6.2723499671769283121E-13 ,8d0b,ac30,ea82,7561, -40, -.B08D0B7561EA82)
+
+ic(S0, -1.6666666666666463126E-1  ,  -3, -1.555555555550C)
+ic(S1,  8.3333333332992771264E-3  ,  -7,  1.111111110C461)
+ic(S2, -1.9841269816180999116E-4  , -13, -1.A01A019746345)
+ic(S3,  2.7557309793219876880E-6  , -19,  1.71DE3209CDCD9)
+ic(S4, -2.5050225177523807003E-8  , -26, -1.AE5C0E319A4EF)
+ic(S5,  1.5868926979889205164E-10 , -33,  1.5CF61DF672B13)
+
+#ifdef vccast
+#define	S0	vccast(S0)
+#define	S1	vccast(S1)
+#define	S2	vccast(S2)
+#define	S3	vccast(S3)
+#define	S4	vccast(S4)
+#define	S5	vccast(S5)
+#define	S6	vccast(S6)
+#endif
+
+#if defined(vax)||defined(tahoe)
+#  define	sin__S(z)	(z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6)))))))
+#else 	/* defined(vax)||defined(tahoe) */
+#  define	sin__S(z)	(z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5))))))
+#endif 	/* defined(vax)||defined(tahoe) */
+
+/* cos__C(x*x) ... re-implemented as a macro
+ * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
+ * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) 
+ * CODED IN C BY K.C. NG, 1/21/85; 
+ * REVISED BY K.C. NG on 8/13/85.
+ *
+ *	   		    x*x	
+ * RETURN   cos(k*x) - 1 + ----- on [-PI/4,PI/4],  where k = pi/PI,
+ *	  		     2	
+ * PI is the rounded value of pi in machine precision :
+ *
+ *	Decimal:
+ *		pi = 3.141592653589793 23846264338327 ..... 
+ *    53 bits   PI = 3.141592653589793 115997963 ..... ,
+ *    56 bits   PI = 3.141592653589793 227020265 ..... ,  
+ *
+ *	Hexadecimal:
+ *		pi = 3.243F6A8885A308D313198A2E....
+ *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18
+ *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    
+ *
+ *
+ * Method:
+ *	1. Let z=x*x. Create a polynomial approximation to 
+ *	    cos(k*x)-1+z/2  =  z*z*(C0 + C1*z^1 + ... + C5*z^5)
+ *	then
+ *      cos__C(z) =  z*z*(C0 + C1*z^1 + ... + C5*z^5)
+ *
+ *	The coefficient C's are obtained by a special Remez algorithm.
+ *
+ * Accuracy:
+ *	In the absence of rounding error, the approximation has absolute error 
+ *	less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. 
+ *	
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+vc(C0,  4.1666666666666504759E-2  ,aaaa,3e2a,a9f0,aaaa,  -4,  .AAAAAAAAAAA9F0)
+vc(C1, -1.3888888888865302059E-3  ,0b60,bbb6,0cca,b60a,  -9, -.B60B60B60A0CCA)
+vc(C2,  2.4801587285601038265E-5  ,0d00,38d0,098f,cdcd, -15,  .D00D00CDCD098F)
+vc(C3, -2.7557313470902390219E-7  ,f27b,b593,e805,b593, -21, -.93F27BB593E805)
+vc(C4,  2.0875623401082232009E-9  ,74c8,320f,3ff0,fa1e, -28,  .8F74C8FA1E3FF0)
+vc(C5, -1.1355178117642986178E-11 ,c32d,ae47,5a63,0a5c, -36, -.C7C32D0A5C5A63)
+
+ic(C0,  4.1666666666666504759E-2  ,  -5,  1.555555555553E)
+ic(C1, -1.3888888888865301516E-3  , -10, -1.6C16C16C14199)
+ic(C2,  2.4801587269650015769E-5  , -16,  1.A01A01971CAEB)
+ic(C3, -2.7557304623183959811E-7  , -22, -1.27E4F1314AD1A)
+ic(C4,  2.0873958177697780076E-9  , -29,  1.1EE3B60DDDC8C)
+ic(C5, -1.1250289076471311557E-11 , -37, -1.8BD5986B2A52E)
+
+#ifdef vccast
+#define	C0	vccast(C0)
+#define	C1	vccast(C1)
+#define	C2	vccast(C2)
+#define	C3	vccast(C3)
+#define	C4	vccast(C4)
+#define	C5	vccast(C5)
+#endif
+
+#define cos__C(z)	(z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5))))))