Implement fmal.

lib/msun/src/s_fmal.c

@@ -0,0 +1,170 @@
+/*-
+ * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+
+/*
+ * Fused multiply-add: Compute x * y + z with a single rounding error.
+ *
+ * We use scaling to avoid overflow/underflow, along with the
+ * canonical precision-doubling technique adapted from:
+ *
+ *	Dekker, T.  A Floating-Point Technique for Extending the
+ *	Available Precision.  Numer. Math. 18, 224-242 (1971).
+ *
+ * XXX May incur a small error for subnormal results due to double
+ *     rounding induced by the final scaling operation.
+ */
+long double
+fmal(long double x, long double y, long double z)
+{
+#if LDBL_MANT_DIG == 64
+	static const long double split = 0x1p32L + 1.0;
+#elif LDBL_MANT_DIG == 113
+	static const long double split = 0x1p57L + 1.0;
+#endif
+	long double xs, ys, zs;
+	long double c, cc, hx, hy, p, q, tx, ty;
+	long double r, rr, s;
+	int oround;
+	int ex, ey, ez;
+	int spread;
+
+	if (z == 0.0)
+		return (x * y);
+	if (x == 0.0 || y == 0.0)
+		return (x * y + z);
+
+	/* Results of frexp() are undefined for these cases. */
+	if (!isfinite(x) || !isfinite(y) || !isfinite(z))
+		return (x * y + z);
+
+	xs = frexpl(x, &ex);
+	ys = frexpl(y, &ey);
+	zs = frexpl(z, &ez);
+	oround = fegetround();
+	spread = ex + ey - ez;
+
+	/*
+	 * If x * y and z are many orders of magnitude apart, the scaling
+	 * will overflow, so we handle these cases specially.  Rounding
+	 * modes other than FE_TONEAREST are painful.
+	 */
+	if (spread > LDBL_MANT_DIG * 2) {
+		fenv_t env;
+		feraiseexcept(FE_INEXACT);
+		switch(oround) {
+		case FE_TONEAREST:
+			return (x * y);
+		case FE_TOWARDZERO:
+			if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
+				return (x * y);
+			feholdexcept(&env);
+			r = x * y;
+			if (!fetestexcept(FE_INEXACT))
+				r = nextafterl(r, 0);
+			feupdateenv(&env);
+			return (r);
+		case FE_DOWNWARD:
+			if (z > 0.0)
+				return (x * y);
+			feholdexcept(&env);
+			r = x * y;
+			if (!fetestexcept(FE_INEXACT))
+				r = nextafterl(r, -INFINITY);
+			feupdateenv(&env);
+			return (r);
+		default:	/* FE_UPWARD */
+			if (z < 0.0)
+				return (x * y);
+			feholdexcept(&env);
+			r = x * y;
+			if (!fetestexcept(FE_INEXACT))
+				r = nextafterl(r, INFINITY);
+			feupdateenv(&env);
+			return (r);
+		}
+	}
+	if (spread < -LDBL_MANT_DIG) {
+		feraiseexcept(FE_INEXACT);
+		if (!isnormal(z))
+			feraiseexcept(FE_UNDERFLOW);
+		switch (oround) {
+		case FE_TONEAREST:
+			return (z);
+		case FE_TOWARDZERO:
+			if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
+				return (z);
+			else
+				return (nextafterl(z, 0));
+		case FE_DOWNWARD:
+			if (x > 0.0 ^ y < 0.0)
+				return (z);
+			else
+				return (nextafterl(z, -INFINITY));
+		default:	/* FE_UPWARD */
+			if (x > 0.0 ^ y < 0.0)
+				return (nextafterl(z, INFINITY));
+			else
+				return (z);
+		}
+	}
+
+	/*
+	 * Use Dekker's algorithm to perform the multiplication and
+	 * subsequent addition in twice the machine precision.
+	 * Arrange so that x * y = c + cc, and x * y + z = r + rr.
+	 */
+	fesetround(FE_TONEAREST);
+
+	p = xs * split;
+	hx = xs - p;
+	hx += p;
+	tx = xs - hx;
+
+	p = ys * split;
+	hy = ys - p;
+	hy += p;
+	ty = ys - hy;
+
+	p = hx * hy;
+	q = hx * ty + tx * hy;
+	c = p + q;
+	cc = p - c + q + tx * ty;
+
+	zs = ldexpl(zs, -spread);
+	r = c + zs;
+	s = r - c;
+	rr = (c - (r - s)) + (zs - s) + cc;
+
+	fesetround(oround);
+	return (ldexpl(r + rr, ex + ey));
+}