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-rw-r--r--libm/double/acos.c58
1 files changed, 58 insertions, 0 deletions
diff --git a/libm/double/acos.c b/libm/double/acos.c
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+++ b/libm/double/acos.c
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+/* acos()
+ *
+ * Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1, 1 50000 3.3e-17 8.2e-18
+ * IEEE -1, 1 10^6 2.2e-16 6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 NAN
+ */
+
+#define __USE_BSD
+#include <math.h>
+
+double acos(double x)
+{
+ if (x < -0.5) {
+ return (M_PI - 2.0 * asin( sqrt((1+x)/2) ));
+ }
+ if (x > 0.5) {
+ return (2.0 * asin( sqrt((1-x)/2) ));
+ }
+
+ return(M_PI_2 - asin(x));
+}