add fdlibm

git-svn-id: http://svn2.nishi.boats/svn/milsko/trunk@557 b9cfdab3-6d41-4d17-bbe4-086880011989

external/fdlibm/e_asin.c

@@ -0,0 +1,105 @@
+
+/* @(#)e_asin.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* __fdlibm_asin(x)
+ * Method :
+ *	Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ *	we approximate asin(x) on [0,0.5] by
+ *		asin(x) = x + x*x^2*R(x^2)
+ *	where
+ *		R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ *	and its remez error is bounded by
+ *		|(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ *	For x in [0.5,1]
+ *		asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ *	Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ *	then for x>0.98
+ *		asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *			= pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ *	For x<=0.98, let pio4_hi = pio2_hi/2, then
+ *		f = hi part of s;
+ *		c = sqrt(z) - f = (z-f*f)/(s+f) 	...f+c=sqrt(z)
+ *	and
+ *		asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *			= pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ *			= pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ *	if x is NaN, return x itself;
+ *	if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+#include "math.h"
+
+static const double
+    one	    = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+    hugev   = 1.000e+300,
+    pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+    pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+    pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+					  /* coefficient for R(x^2) */
+    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 __fdlibm_asin(double x) {
+	double t, w, p, q, c, r, s;
+	int    hx, ix;
+	hx = __HI(x);
+	ix = hx & 0x7fffffff;
+	if(ix >= 0x3ff00000) { /* |x|>= 1 */
+		if(((ix - 0x3ff00000) | __LO(x)) == 0)
+			/* asin(1)=+-pi/2 with inexact */
+			return x * pio2_hi + x * pio2_lo;
+		return (x - x) / (x - x);	      /* asin(|x|>1) is NaN */
+	} else if(ix < 0x3fe00000) {		      /* |x|<0.5 */
+		if(ix < 0x3e400000) {		      /* if |x| < 2**-27 */
+			if(hugev + x > one) return x; /* return x with inexact if x!=0*/
+		} else
+			t = x * x;
+		p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+		q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+		w = p / q;
+		return x + x * w;
+	}
+	/* 1> |x|>= 0.5 */
+	w = one - fabs(x);
+	t = w * 0.5;
+	p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+	q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+	s = sqrt(t);
+	if(ix >= 0x3FEF3333) { /* if |x| > 0.975 */
+		w = p / q;
+		t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
+	} else {
+		w	= s;
+		__LO(w) = 0;
+		c	= (t - w * w) / (s + w);
+		r	= p / q;
+		p	= 2.0 * s * r - (pio2_lo - 2.0 * c);
+		q	= pio4_hi - 2.0 * w;
+		t	= pio4_hi - (p - q);
+	}
+	if(hx > 0) return t;
+	else
+		return -t;
+}