Merge remote branch 'nsz/master'

src/math/fma.c

+#include <fenv.h>
+#include "libm.h"
+
+#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
+union ld80 {
+	long double x;
+	struct {
+		uint64_t m;
+		uint16_t e : 15;
+		uint16_t s : 1;
+		uint16_t pad;
+	} bits;
+};
+
+/* exact add, assumes exponent_x >= exponent_y */
+static void add(long double *hi, long double *lo, long double x, long double y)
+{
+	long double r;
+
+	r = x + y;
+	*hi = r;
+	r -= x;
+	*lo = y - r;
+}
+
+/* exact mul, assumes no over/underflow */
+static void mul(long double *hi, long double *lo, long double x, long double y)
+{
+	static const long double c = 1.0 + 0x1p32L;
+	long double cx, xh, xl, cy, yh, yl;
+
+	cx = c*x;
+	xh = (x - cx) + cx;
+	xl = x - xh;
+	cy = c*y;
+	yh = (y - cy) + cy;
+	yl = y - yh;
+	*hi = x*y;
+	*lo = (xh*yh - *hi) + xh*yl + xl*yh + xl*yl;
+}
+
+/*
+assume (long double)(hi+lo) == hi
+return an adjusted hi so that rounding it to double is correct
+*/
+static long double adjust(long double hi, long double lo)
+{
+	union ld80 uhi, ulo;
+
+	if (lo == 0)
+		return hi;
+	uhi.x = hi;
+	if (uhi.bits.m & 0x3ff)
+		return hi;
+	ulo.x = lo;
+	if (uhi.bits.s == ulo.bits.s)
+		uhi.bits.m++;
+	else
+		uhi.bits.m--;
+	return uhi.x;
+}
+
+static long double dadd(long double x, long double y)
+{
+	add(&x, &y, x, y);
+	return adjust(x, y);
+}
+
+static long double dmul(long double x, long double y)
+{
+	mul(&x, &y, x, y);
+	return adjust(x, y);
+}
+
+static int getexp(long double x)
+{
+	union ld80 u;
+	u.x = x;
+	return u.bits.e;
+}
+
+double fma(double x, double y, double z)
+{
+	long double hi, lo1, lo2, xy;
+	int round, ez, exy;
+
+	/* handle +-inf,nan */
+	if (!isfinite(x) || !isfinite(y))
+		return x*y + z;
+	if (!isfinite(z))
+		return z;
+	/* handle +-0 */
+	if (x == 0.0 || y == 0.0)
+		return x*y + z;
+	round = fegetround();
+	if (z == 0.0) {
+		if (round == FE_TONEAREST)
+			return dmul(x, y);
+		return x*y;
+	}
+
+	/* exact mul and add require nearest rounding */
+	/* spurious inexact exceptions may be raised */
+	fesetround(FE_TONEAREST);
+	mul(&xy, &lo1, x, y);
+	exy = getexp(xy);
+	ez = getexp(z);
+	if (ez > exy) {
+		add(&hi, &lo2, z, xy);
+	} else if (ez > exy - 12) {
+		add(&hi, &lo2, xy, z);
+		if (hi == 0) {
+			fesetround(round);
+			/* make sure that the sign of 0 is correct */
+			return (xy + z) + lo1;
+		}
+	} else {
+		/*
+		ez <= exy - 12
+		the 12 extra bits (1guard, 11round+sticky) are needed so with
+			lo = dadd(lo1, lo2)
+		elo <= ehi - 11, and we use the last 10 bits in adjust so
+			dadd(hi, lo)
+		gives correct result when rounded to double
+		*/
+		hi = xy;
+		lo2 = z;
+	}
+	fesetround(round);
+	if (round == FE_TONEAREST)
+		return dadd(hi, dadd(lo1, lo2));
+	return hi + (lo1 + lo2);
+}
+#else
 /* origin: FreeBSD /usr/src/lib/msun/src/s_fma.c */
 /*-
  * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
@@ -25,9 +159,6 @@
  * SUCH DAMAGE.
  */
 
-#include <fenv.h>
-#include "libm.h"
-
 /*
  * A struct dd represents a floating-point number with twice the precision
  * of a double.  We maintain the invariant that "hi" stores the 53 high-order
@@ -178,14 +309,14 @@ double fma(double x, double y, double z)
 	 * return values here are crucial in handling special cases involving
 	 * infinities, NaNs, overflows, and signed zeroes correctly.
 	 */
-	if (x == 0.0 || y == 0.0)
-		return (x * y + z);
-	if (z == 0.0)
-		return (x * y);
 	if (!isfinite(x) || !isfinite(y))
 		return (x * y + z);
 	if (!isfinite(z))
 		return (z);
+	if (x == 0.0 || y == 0.0)
+		return (x * y + z);
+	if (z == 0.0)
+		return (x * y);
 
 	xs = frexp(x, &ex);
 	ys = frexp(y, &ey);
@@ -278,3 +409,4 @@ double fma(double x, double y, double z)
 	else
 		return (add_and_denormalize(r.hi, adj, spread));
 }
+#endif

src/math/fmal.c

@@ -173,14 +173,14 @@ long double fmal(long double x, long double y, long double z)
 	 * return values here are crucial in handling special cases involving
 	 * infinities, NaNs, overflows, and signed zeroes correctly.
 	 */
-	if (x == 0.0 || y == 0.0)
-		return (x * y + z);
-	if (z == 0.0)
-		return (x * y);
 	if (!isfinite(x) || !isfinite(y))
 		return (x * y + z);
 	if (!isfinite(z))
 		return (z);
+	if (x == 0.0 || y == 0.0)
+		return (x * y + z);
+	if (z == 0.0)
+		return (x * y);
 
 	xs = frexpl(x, &ex);
 	ys = frexpl(y, &ey);

src/math/scalbn.c

-/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbn.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * 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.
- * ====================================================
- */
-/*
- * scalbn (double x, int n)
- * scalbn(x,n) returns x* 2**n  computed by  exponent
- * manipulation rather than by actually performing an
- * exponentiation or a multiplication.
- */
-
 #include "libm.h"
 
-static const double
-two54  = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
-twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
-huge   = 1.0e+300,
-tiny   = 1.0e-300;
-
 double scalbn(double x, int n)
 {
-// FIXME: k+n check depends on signed int overflow.. use unsigned hx
-// TODO: when long != int:
-//       scalbln(x,long n) { if(n>9999)n=9999; else if(n<-9999)n=-9999; return scalbn(x,n); }
-// TODO: n < -50000 ...
-	int32_t k,hx,lx;
+	double scale;
 
-	EXTRACT_WORDS(hx, lx, x);
-	k = (hx&0x7ff00000)>>20;                /* extract exponent */
-	if (k == 0) {                           /* 0 or subnormal x */
-		if ((lx|(hx&0x7fffffff)) == 0)  /* +-0 */
-			return x;
-		x *= two54;
-		GET_HIGH_WORD(hx, x);
-		k = ((hx&0x7ff00000)>>20) - 54;
-		if (n < -50000)
-			return tiny*x;          /*underflow*/
-	}
-	if (k == 0x7ff)                         /* NaN or Inf */
-		return x + x;
-	k = k + n;
-	if (k > 0x7fe)
-		return huge*copysign(huge, x);  /* overflow  */
-	if (k > 0) {                            /* normal result */
-		SET_HIGH_WORD(x, (hx&0x800fffff)|(k<<20));
-		return x;
+	if (n > 1023) {
+		x *= 0x1p1023;
+		n -= 1023;
+		if (n > 1023) {
+			x *= 0x1p1023;
+			n -= 1023;
+			if (n > 1023)
+				return x * 0x1p1023;
+		}
+	} else if (n < -1022) {
+		x *= 0x1p-1022;
+		n += 1022;
+		if (n < -1022) {
+			x *= 0x1p-1022;
+			n += 1022;
+			if (n < -1022)
+				return x * 0x1p-1022;
+		}
 	}
-	if (k <= -54)
-		if (n > 50000)      /* in case integer overflow in n+k */
-			return huge*copysign(huge, x);  /*overflow*/
-		return tiny*copysign(tiny, x);  /*underflow*/
-	k += 54;                                /* subnormal result */
-	SET_HIGH_WORD(x, (hx&0x800fffff)|(k<<20));
-	return x*twom54;
+	INSERT_WORDS(scale, (uint32_t)(0x3ff+n)<<20, 0);
+	return x * scale;
 }

src/math/scalbnf.c

-/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbnf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * 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.
- * ====================================================
- */
-
 #include "libm.h"
 
-static const float
-two25  = 3.355443200e+07,  /* 0x4c000000 */
-twom25 = 2.9802322388e-08, /* 0x33000000 */
-huge   = 1.0e+30,
-tiny   = 1.0e-30;
-
 float scalbnf(float x, int n)
 {
-	int32_t k, ix;
-	GET_FLOAT_WORD(ix, x);
-	k = (ix&0x7f800000)>>23;           /* extract exponent */
-	if (k == 0) {                      /* 0 or subnormal x */
-		if ((ix&0x7fffffff) == 0)  /* +-0 */
-			return x;
-		x *= two25;
-		GET_FLOAT_WORD(ix, x);
-		k = ((ix&0x7f800000)>>23) - 25;
-		if (n < -50000)
-			return tiny*x;  /*underflow*/
-	}
-	if (k == 0xff)                     /* NaN or Inf */
-		return x + x;
-	k = k + n;
-	if (k > 0xfe)
-		return huge*copysignf(huge, x);  /* overflow  */
-	if (k > 0) {                       /* normal result */
-		SET_FLOAT_WORD(x, (ix&0x807fffff)|(k<<23));
-		return x;
+	float scale;
+
+	if (n > 127) {
+		x *= 0x1p127f;
+		n -= 127;
+		if (n > 127) {
+			x *= 0x1p127f;
+			n -= 127;
+			if (n > 127)
+				return x * 0x1p127f;
+		}
+	} else if (n < -126) {
+		x *= 0x1p-126f;
+		n += 126;
+		if (n < -126) {
+			x *= 0x1p-126f;
+			n += 126;
+			if (n < -126)
+				return x * 0x1p-126f;
+		}
 	}
-	if (k <= -25)
-		if (n > 50000)  /* in case integer overflow in n+k */
-			return huge*copysignf(huge,x);  /*overflow*/
-		return tiny*copysignf(tiny, x);  /*underflow*/
-	k += 25;                           /* subnormal result */
-	SET_FLOAT_WORD(x, (ix&0x807fffff)|(k<<23));
-	return x*twom25;
+	SET_FLOAT_WORD(scale, (uint32_t)(0x7f+n)<<23);
+	return x * scale;
 }

src/math/scalbnl.c

-/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbnl.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * 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.
- * ====================================================
- */
-/*
- * scalbnl (long double x, int n)
- * scalbnl(x,n) returns x* 2**n  computed by  exponent
- * manipulation rather than by actually performing an
- * exponentiation or a multiplication.
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -24,40 +6,31 @@ long double scalbnl(long double x, int n)
 	return scalbn(x, n);
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-static const long double
-huge = 0x1p16000L,
-tiny = 0x1p-16000L;
-
 long double scalbnl(long double x, int n)
 {
-	union IEEEl2bits u;
-	int k;
+	union IEEEl2bits scale;
 
-	u.e = x;
-	k = u.bits.exp;                    /* extract exponent */
-	if (k == 0) {                      /* 0 or subnormal x */
-		if ((u.bits.manh|u.bits.manl) == 0)  /* +-0 */
-			return x;
-		u.e *= 0x1p128;
-		k = u.bits.exp - 128;
-		if (n < -50000)
-			return tiny*x;  /*underflow*/
-	}
-	if (k == 0x7fff)                   /* NaN or Inf */
-		return x + x;
-	k = k + n;
-	if (k >= 0x7fff)
-		return huge*copysignl(huge, x);  /* overflow  */
-	if (k > 0) {                       /* normal result */
-		u.bits.exp = k;
-		return u.e;
+	if (n > 16383) {
+		x *= 0x1p16383L;
+		n -= 16383;
+		if (n > 16383) {
+			x *= 0x1p16383L;
+			n -= 16383;
+			if (n > 16383)
+				return x * 0x1p16383L;
+		}
+	} else if (n < -16382) {
+		x *= 0x1p-16382L;
+		n += 16382;
+		if (n < -16382) {
+			x *= 0x1p-16382L;
+			n += 16382;
+			if (n < -16382)
+				return x * 0x1p-16382L;
+		}
 	}
-	if (k <= -128)
-		if (n > 50000)  /* in case integer overflow in n+k */
-			return huge*copysign(huge, x);  /*overflow*/
-		return tiny*copysign(tiny, x);  /*underflow*/
-	k += 128;                          /* subnormal result */
-	u.bits.exp = k;
-	return u.e*0x1p-128;
+	scale.e = 1.0L;
+	scale.bits.exp = 0x3fff + n;
+	return x * scale.e;
 }
 #endif