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+/* @(#)e_acos.c 1.2 95/01/04 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* __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: sqrt
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+ pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+ pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+ pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+ pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+ pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+ pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+ pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+ qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+ qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+ qS4 = 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;
+ _INT32 hx, ix;
+ hx = __HI(x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x| >= 1 */
+ if (((ix - 0x3ff00000) | __LO(x)) == 0) { /* |x|==1 */
+ if (hx > 0)
+ return 0.0; /* acos(1) = 0 */
+ else
+ return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
+ }
+ return NAN; /* 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;
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ r = p / q;
+ return pio2_hi - (x - (pio2_lo - x * r));
+ } else if (hx < 0) { /* x < -0.5 */
+ z = (one + x) * 0.5;
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ s = 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 = sqrt(z);
+ df = s;
+ __LO(df) = 0;
+ c = (z - df * df) / (s + df);
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ r = p / q;
+ w = r * s + c;
+ return 2.0 * (df + w);
+ }
+}