Take two. Add the missing file that should have been committed

with r219571 and re-enable building of cbrtl.

Implement the long double version for the cube root function, cbrtl.
The algorithm uses Newton's iterations with a crude estimate of the
cube root to converge to a result.

Reviewed by:    bde
Approved by:    das

1 files changed, 157 insertions, 0 deletions

diff --git a/lib/msun/src/s_cbrtl.c b/lib/msun/src/s_cbrtl.c
new file mode 100644
index 0000000..23c9184
--- /dev/null
+++ b/lib/msun/src/s_cbrtl.c
@@ -0,0 +1,157 @@
+/*-
+ * ====================================================
+ * 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 <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <float.h>
+#include <ieeefp.h>
+
+#include "fpmath.h"    
+#include "math.h"
+#include "math_private.h"
+
+#define	BIAS	(LDBL_MAX_EXP - 1)
+
+static const unsigned
+    B1 = 709958130;	/* B1 = (127-127.0/3-0.03306235651)*2**23 */
+
+long double
+cbrtl(long double x)
+{
+	union IEEEl2bits u, v;
+	long double r, s, t, w;
+	double dr, dt, dx;
+	float ft, fx;
+	uint32_t hx;
+	uint16_t expsign;
+	int k;
+
+	u.e = x;
+	expsign = u.xbits.expsign;
+	k = expsign & 0x7fff;
+
+	/*
+	 * If x = +-Inf, then cbrt(x) = +-Inf.
+	 * If x = NaN, then cbrt(x) = NaN.
+	 */
+	if (k == BIAS + LDBL_MAX_EXP)
+		return (x + x);
+
+#ifdef __i386__
+	fp_prec_t oprec;
+
+	oprec = fpgetprec();
+	if (oprec != FP_PE)
+		fpsetprec(FP_PE);
+#endif
+
+	if (k == 0) {
+		/* If x = +-0, then cbrt(x) = +-0. */
+		if ((u.bits.manh | u.bits.manl) == 0) {
+#ifdef __i386__
+			if (oprec != FP_PE)
+				fpsetprec(oprec);
+#endif
+			return (x);
+	    	}
+		/* Adjust subnormal numbers. */
+		u.e *= 0x1.0p514;
+		k = u.bits.exp;
+		k -= BIAS + 514;
+ 	} else
+		k -= BIAS;
+	u.xbits.expsign = BIAS;
+	v.e = 1; 
+
+	x = u.e;
+	switch (k % 3) {
+	case 1:
+	case -2:
+		x = 2*x;
+		k--;
+		break;
+	case 2:
+	case -1:
+		x = 4*x;
+		k -= 2;
+		break;
+	}
+	v.xbits.expsign = (expsign & 0x8000) | (BIAS + k / 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: */
+	fx = x;
+	GET_FLOAT_WORD(hx, fx);
+	SET_FLOAT_WORD(ft, ((hx & 0x7fffffff) / 3 + B1));
+
+	/* ~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).
+	 */
+	volatile double vd2 = 0x1.0p32;
+	volatile double vd1 = 0x1.0p-31;
+	#define vd ((long double)vd2 + vd1)
+
+	t = dt + vd - 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;
+#else
+#error "Unsupported long double format"
+#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.e;
+#ifdef __i386__
+	if (oprec != FP_PE)
+		fpsetprec(oprec);
+#endif
+	return (t);
+}