Initial import

2025-05-28 00:02:28 +00:00 · 2020-06-15 07:18:57 -07:00 · 2020-06-15 07:18:57 -07:00 · c91b3c5006
commit c91b3c5006
14915 changed files with 590219 additions and 0 deletions
--- a/libc/math/asin.c
+++ b/libc/math/asin.c
@ -0,0 +1,107 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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.
+ * ====================================================
+ */
+/* 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 "libc/math/libm.h"
+
+static const double
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+/* coefficients 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 */
+
+static double R(double z)
+{
+	double_t p, q;
+	p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	return p/q;
+}
+
+double asin(double x)
+{
+	double z,r,s;
+	uint32_t hx,ix;
+
+	GET_HIGH_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	/* |x| >= 1 or nan */
+	if (ix >= 0x3ff00000) {
+		uint32_t lx;
+		GET_LOW_WORD(lx, x);
+		if ((ix-0x3ff00000 | lx) == 0)
+			/* asin(1) = +-pi/2 with inexact */
+			return x*pio2_hi + 0x1p-120f;
+		return 0/(x-x);
+	}
+	/* |x| < 0.5 */
+	if (ix < 0x3fe00000) {
+		/* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+		if (ix < 0x3e500000 && ix >= 0x00100000)
+			return x;
+		return x + x*R(x*x);
+	}
+	/* 1 > |x| >= 0.5 */
+	z = (1 - fabs(x))*0.5;
+	s = sqrt(z);
+	r = R(z);
+	if (ix >= 0x3fef3333) {  /* if |x| > 0.975 */
+		x = pio2_hi-(2*(s+s*r)-pio2_lo);
+	} else {
+		double f,c;
+		/* f+c = sqrt(z) */
+		f = s;
+		SET_LOW_WORD(f,0);
+		c = (z-f*f)/(s+f);
+		x = 0.5*pio2_hi - (2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f));
+	}
+	if (hx >> 31)
+		return -x;
+	return x;
+}