15  *	acos(x)  = pi/2 - asin(x)
16  *	acos(-x) = pi/2 + asin(x)
18  *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
20  * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
21  *		= 2asin(sqrt((1-x)/2))  
22  *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
23  *		= 2f + (2c + 2s*z*R(z))
24  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
25  *     for f so that f+c ~ sqrt(z).
26  * For x<-0.5
27  *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
28  *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
47 pio2_lo =  6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
49 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
50 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
51 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
52 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
53 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
54 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
55 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
57 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
58 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
63 	double z,p,q,r,w,s,c,df;  in acos()  local
70 	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */  in acos()
72 		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */  in acos()
74 	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */  in acos()
77 	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/  in acos()
78 	    z = x*x;  in acos()
79 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));  in acos()
80 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));  in acos()
82 	    return pio2_hi - (x - (pio2_lo-x*r));  in acos()
83 	} else  if (hx<0) {		/* x < -0.5 */  in acos()
84 	    z = (one+x)*0.5;  in acos()
85 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));  in acos()
86 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));  in acos()
87 	    s = sqrt(z);  in acos()
89 	    w = r*s-pio2_lo;  in acos()
90 	    return pi - 2.0*(s+w);  in acos()
92 	    z = (one-x)*0.5;  in acos()
93 	    s = sqrt(z);  in acos()
96 	    c  = (z-df*df)/(s+df);  in acos()
97 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));  in acos()
98 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));  in acos()