first commit of the new libm!

[musl] / src / math / acos.c

diff --git a/src/math/acos.c b/src/math/acos.c
new file mode 100644 (file)
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--- /dev/null
+++ b/src/math/acos.c
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+/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* 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 "libm.h"
+
+static const double
+one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+static volatile double
+pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+static const double
+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 */
+
+double acos(double x)
+{
+       double z,p,q,r,w,s,c,df;
+       int32_t hx,ix;
+
+       GET_HIGH_WORD(hx, x);
+       ix = hx & 0x7fffffff;
+       if (ix >= 0x3ff00000) {  /* |x| >= 1 */
+               uint32_t lx;
+
+               GET_LOW_WORD(lx,x);
+               if ((ix-0x3ff00000 | lx) == 0) {  /* |x|==1 */
+                       if (hx > 0) return 0.0;  /* acos(1) = 0  */
+                       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)  /* |x| < 2**-57 */
+                       return pio2_hi + pio2_lo;
+               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;
+               SET_LOW_WORD(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);
+       }
+}