feat: add gzip and new headers

1 files changed, 101 insertions, 0 deletions

diff --git a/lib/libm/acos.c b/lib/libm/acos.c
new file mode 100644
index 00000000..cc798159
--- /dev/null
+++ b/lib/libm/acos.c
@@ -0,0 +1,101 @@
+/* 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 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 */
+
+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 acos(double x)
+{
+	double z, w, s, c, df;
+	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) {
+			/* acos(1)=0, acos(-1)=pi */
+			if (hx >> 31)
+				return 2 * pio2_hi + 0x1p-120f;
+			return 0;
+		}
+		return 0 / (x - x);
+	}
+	/* |x| < 0.5 */
+	if (ix < 0x3fe00000) {
+		if (ix <= 0x3c600000) /* |x| < 2**-57 */
+			return pio2_hi + 0x1p-120f;
+		return pio2_hi - (x - (pio2_lo - x * R(x * x)));
+	}
+	/* x < -0.5 */
+	if (hx >> 31) {
+		z = (1.0 + x) * 0.5;
+		s = sqrt(z);
+		w = R(z) * s - pio2_lo;
+		return 2 * (pio2_hi - (s + w));
+	}
+	/* x > 0.5 */
+	z = (1.0 - x) * 0.5;
+	s = sqrt(z);
+	df = s;
+	SET_LOW_WORD(df, 0);
+	c = (z - df * df) / (s + df);
+	w = R(z) * s + c;
+	return 2 * (df + w);
+}