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+/* @(#)e_acos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
+ for performance improvement on pipelined processors.
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
+#endif
+
+/* __ieee754_acos(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
+ * For x>0.5
+ * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ * = 2asin(sqrt((1-x)/2))
+ * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
+ * = 2f + (2c + 2s*z*R(z))
+ * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ * for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: __ieee754_sqrt
+ */
+
+#include "math.h"
+#include "math_private.h"
+#define one qS[0]
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+ -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+ 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+ -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+ 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+ 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */
+qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+ 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+ -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+ 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+ double __ieee754_acos(double x)
+#else
+ double __ieee754_acos(x)
+ double x;
+#endif
+{
+ double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,z2,z4,z6;
+ int32_t hx,ix;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x3ff00000) { /* |x| >= 1 */
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
+ if(hx>0) return 0.0; /* acos(1) = 0 */
+ else return pi+2.0*pio2_lo; /* acos(-1)= pi */
+ }
+ return (x-x)/(x-x); /* acos(|x|>1) is NaN */
+ }
+ if(ix<0x3fe00000) { /* |x| < 0.5 */
+ if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+ z = x*x;
+#ifdef DO_NOT_USE_THIS
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+#else
+ p1 = z*pS[0]; z2=z*z;
+ p2 = pS[1]+z*pS[2]; z4=z2*z2;
+ p3 = pS[3]+z*pS[4]; z6=z4*z2;
+ q1 = one+z*qS[1];
+ q2 = qS[2]+z*qS[3];
+ p = p1 + z2*p2 + z4*p3 + z6*pS[5];
+ q = q1 + z2*q2 + z4*qS[4];
+#endif
+ r = p/q;
+ return pio2_hi - (x - (pio2_lo-x*r));
+ } else if (hx<0) { /* x < -0.5 */
+ z = (one+x)*0.5;
+#ifdef DO_NOT_USE_THIS
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+#else
+ p1 = z*pS[0]; z2=z*z;
+ p2 = pS[1]+z*pS[2]; z4=z2*z2;
+ p3 = pS[3]+z*pS[4]; z6=z4*z2;
+ q1 = one+z*qS[1];
+ q2 = qS[2]+z*qS[3];
+ p = p1 + z2*p2 + z4*p3 + z6*pS[5];
+ q = q1 + z2*q2 + z4*qS[4];
+#endif
+ s = __ieee754_sqrt(z);
+ r = p/q;
+ w = r*s-pio2_lo;
+ return pi - 2.0*(s+w);
+ } else { /* x > 0.5 */
+ z = (one-x)*0.5;
+ s = __ieee754_sqrt(z);
+ df = s;
+ SET_LOW_WORD(df,0);
+ c = (z-df*df)/(s+df);
+#ifdef DO_NOT_USE_THIS
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+#else
+ p1 = z*pS[0]; z2=z*z;
+ p2 = pS[1]+z*pS[2]; z4=z2*z2;
+ p3 = pS[3]+z*pS[4]; z6=z4*z2;
+ q1 = one+z*qS[1];
+ q2 = qS[2]+z*qS[3];
+ p = p1 + z2*p2 + z4*p3 + z6*pS[5];
+ q = q1 + z2*q2 + z4*qS[4];
+#endif
+ r = p/q;
+ w = r*s+c;
+ return 2.0*(df+w);
+ }
+}