Add a "fork" of musl as //fusl.

fusl/src/math/cbrtl.c

+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtl.c */
+/*-
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ * The argument reduction and testing for exceptional cases was
+ * written by Steven G. Kargl with input from Bruce D. Evans
+ * and David A. Schultz.
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double cbrtl(long double x)
+{
+        return cbrt(x);
+}
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+static const unsigned B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
+
+long double cbrtl(long double x)
+{
+        union ldshape u = {x}, v;
+        union {float f; uint32_t i;} uft;
+        long double r, s, t, w;
+        double_t dr, dt, dx;
+        float_t ft;
+        int e = u.i.se & 0x7fff;
+        int sign = u.i.se & 0x8000;
+
+        /*
+         * If x = +-Inf, then cbrt(x) = +-Inf.
+         * If x = NaN, then cbrt(x) = NaN.
+         */
+        if (e == 0x7fff)
+                return x + x;
+        if (e == 0) {
+                /* Adjust subnormal numbers. */
+                u.f *= 0x1p120;
+                e = u.i.se & 0x7fff;
+                /* If x = +-0, then cbrt(x) = +-0. */
+                if (e == 0)
+                        return x;
+                e -= 120;
+        }
+        e -= 0x3fff;
+        u.i.se = 0x3fff;
+        x = u.f;
+        switch (e % 3) {
+        case 1:
+        case -2:
+                x *= 2;
+                e--;
+                break;
+        case 2:
+        case -1:
+                x *= 4;
+                e -= 2;
+                break;
+        }
+        v.f = 1.0;
+        v.i.se = sign | (0x3fff + e/3);
+
+        /*
+         * The following is the guts of s_cbrtf, with the handling of
+         * special values removed and extra care for accuracy not taken,
+         * but with most of the extra accuracy not discarded.
+         */
+
+        /* ~5-bit estimate: */
+        uft.f = x;
+        uft.i = (uft.i & 0x7fffffff)/3 + B1;
+        ft = uft.f;
+
+        /* ~16-bit estimate: */
+        dx = x;
+        dt = ft;
+        dr = dt * dt * dt;
+        dt = dt * (dx + dx + dr) / (dx + dr + dr);
+
+        /* ~47-bit estimate: */
+        dr = dt * dt * dt;
+        dt = dt * (dx + dx + dr) / (dx + dr + dr);
+
+#if LDBL_MANT_DIG == 64
+        /*
+         * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8).
+         * Round it away from zero to 32 bits (32 so that t*t is exact, and
+         * away from zero for technical reasons).
+         */
+        t = dt + (0x1.0p32L + 0x1.0p-31L) - 0x1.0p32;
+#elif LDBL_MANT_DIG == 113
+        /*
+         * Round dt away from zero to 47 bits.  Since we don't trust the 47,
+         * add 2 47-bit ulps instead of 1 to round up.  Rounding is slow and
+         * might be avoidable in this case, since on most machines dt will
+         * have been evaluated in 53-bit precision and the technical reasons
+         * for rounding up might not apply to either case in cbrtl() since
+         * dt is much more accurate than needed.
+         */
+        t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60;
+#endif
+
+        /*
+         * Final step Newton iteration to 64 or 113 bits with
+         * error < 0.667 ulps
+         */
+        s = t*t;         /* t*t is exact */
+        r = x/s;         /* error <= 0.5 ulps; |r| < |t| */
+        w = t+t;         /* t+t is exact */
+        r = (r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */
+        t = t+t*r;       /* error <= 0.5 + 0.5/3 + epsilon */
+
+        t *= v.f;
+        return t;
+}
+#endif