feat: add gzip and new headers

1 files changed, 62 insertions, 0 deletions

diff --git a/lib/libm/csqrtl.c b/lib/libm/csqrtl.c
new file mode 100644
index 00000000..335e51d6
--- /dev/null
+++ b/lib/libm/csqrtl.c
@@ -0,0 +1,62 @@
+#include <stdbool.h>
+#include <float.h>
+#include "__complex.h"
+
+#define THRESH	     (LDBL_MAX / 2.414213562373095048801688724209698L)
+#define cpackl(r, i) ((r) + (i) * (long double complex)I)
+
+long double complex csqrtl(long double complex z)
+{
+	long double complex result;
+	long double a, b;
+	long double t;
+	bool scale;
+	a = creall(z);
+	b = cimagl(z);
+	/* Handle special cases. */
+	if (z == 0.0L)
+		return (cpackl((long double)0.0L, b));
+	if (isinf(b))
+		return (cpackl((long double)INFINITY, b));
+	if (isnan(a)) {
+		t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
+		return (cpackl(a, t)); /* return NaN + NaN i */
+	}
+	if (isinf(a)) {
+		/*
+		 * csqrt(inf + NaN i)  = inf +  NaN i
+		 * csqrt(inf + y i)    = inf +  0 i
+		 * csqrt(-inf + NaN i) = NaN +- inf i
+		 * csqrt(-inf + y i)   = 0   +  inf i
+		 */
+		if (signbit(a))
+			return (cpackl(fabsl(b - b), copysignl(a, b)));
+		else
+			return (cpackl(a, copysignl(b - b, b)));
+	}
+	/*
+	 * The remaining special case (b is NaN) is handled just fine by
+	 * the normal code path below.
+	 */
+	/* Scale to avoid overflow. */
+	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
+		a *= 0.25L;
+		b *= 0.25L;
+		scale = true;
+	} else {
+		scale = false;
+	}
+	/* Algorithm 312, CACM vol 10, Oct 1967. */
+	if (a >= 0L) {
+		t = sqrtl((a + hypotl(a, b)) * 0.5L);
+		result = cpackl(t, b / (2.0L * t));
+	} else {
+		t = sqrtl((-a + hypotl(a, b)) * 0.5L);
+		result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
+	}
+	/* Rescale. */
+	if (scale)
+		return (result * 2.0L);
+	else
+		return (result);
+}