date and time created 85/09/06 17:52:38 by zliu

SCCS-vsn: lib/libm/common_source/asincos.c 1.1

diff --git a/usr/src/lib/libm/common_source/asincos.c b/usr/src/lib/libm/common_source/asincos.c
new file mode 100644 (file)
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--- /dev/null
+++ b/usr/src/lib/libm/common_source/asincos.c
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+/* 
+ * Copyright (c) 1985 Regents of the University of California.
+ * 
+ * Use and reproduction of this software are granted  in  accordance  with
+ * the terms and conditions specified in  the  Berkeley  Software  License
+ * Agreement (in particular, this entails acknowledgement of the programs'
+ * source, and inclusion of this notice) with the additional understanding
+ * that  all  recipients  should regard themselves as participants  in  an
+ * ongoing  research  project and hence should  feel  obligated  to report
+ * their  experiences (good or bad) with these elementary function  codes,
+ * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)asincos.c  1.1 (ELEFUNT) %G%";
+#endif not lint
+
+/* ASIN(X)
+ * RETURNS ARC SINE OF X
+ * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
+ * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
+ *
+ * Required system supported functions:
+ *     copysign(x,y)
+ *     sqrt(x)
+ *
+ * Required kernel function:
+ *     atan2(y,x) 
+ *
+ * Method :                  
+ *     asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is 
+ *               computed as follows
+ *                     1-x*x                     if x <  0.5, 
+ *                     2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
+ *
+ * Special cases:
+ *     if x is NaN, return x itself;
+ *     if |x|>1, return NaN.
+ *
+ * Accuracy:
+ * 1)  If atan2() uses machine PI, then
+ * 
+ *     asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded;
+ *     and PI is the exact pi rounded to machine precision (see atan2 for
+ *      details):
+ *
+ *     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 more than 200,000 random arguments on a VAX, the 
+ *     maximum observed error in ulps (units in the last place) was
+ *     2.06 ulps.      (comparing against (PI/pi)*(exact asin(x)));
+ *
+ * 2)  If atan2() uses true pi, then
+ *
+ *     asin(x) returns the exact asin(x) with error below about 2 ulps.
+ *
+ *     In a test run with more than 1,024,000 random arguments on a VAX, the 
+ *     maximum observed error in ulps (units in the last place) was
+ *      1.99 ulps.
+ */
+
+double asin(x)
+double x;
+{
+       double s,t,copysign(),atan2(),sqrt(),one=1.0;
+#ifndef VAX
+       if(x!=x) return(x);     /* x is NaN */
+#endif
+       s=copysign(x,one);
+       if(s <= 0.5)
+           return(atan2(x,sqrt(one-x*x)));
+       else 
+           { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); }
+
+}
+
+/* ACOS(X)
+ * RETURNS ARC COS OF X
+ * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
+ * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
+ *
+ * Required system supported functions:
+ *     copysign(x,y)
+ *     sqrt(x)
+ *
+ * Required kernel function:
+ *     atan2(y,x) 
+ *
+ * Method :                  
+ *                           ________
+ *                           / 1 - x
+ *     acos(x) = 2*atan2(  / -------- , 1 ) .
+ *                        \/   1 + x
+ *
+ * Special cases:
+ *     if x is NaN, return x itself;
+ *     if |x|>1, return NaN.
+ *
+ * Accuracy:
+ * 1)  If atan2() uses machine PI, then
+ * 
+ *     acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded;
+ *     and PI is the exact pi rounded to machine precision (see atan2 for
+ *      details):
+ *
+ *     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 more than 200,000 random arguments on a VAX, the 
+ *     maximum observed error in ulps (units in the last place) was
+ *     2.07 ulps.      (comparing against (PI/pi)*(exact acos(x)));
+ *
+ * 2)  If atan2() uses true pi, then
+ *
+ *     acos(x) returns the exact acos(x) with error below about 2 ulps.
+ *
+ *     In a test run with more than 1,024,000 random arguments on a VAX, the 
+ *     maximum observed error in ulps (units in the last place) was
+ *     2.15 ulps.
+ */
+
+double acos(x)
+double x;
+{
+       double t,copysign(),atan2(),sqrt(),one=1.0;
+#ifndef VAX
+       if(x!=x) return(x);
+#endif
+       if( x != -1.0)
+           t=atan2(sqrt((one-x)/(one+x)),one);
+       else
+           t=atan2(one,0.0);   /* t = PI/2 */
+       return(t+t);
+}