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-rw-r--r--src/math/fma.c146
-rw-r--r--src/math/fmal.c8
-rw-r--r--src/math/scalbn.c76
-rw-r--r--src/math/scalbnf.c70
-rw-r--r--src/math/scalbnl.c71
5 files changed, 208 insertions, 163 deletions
diff --git a/src/math/fma.c b/src/math/fma.c
index f44ecda7..87d450c7 100644
--- a/src/math/fma.c
+++ b/src/math/fma.c
@@ -1,3 +1,137 @@
+#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
diff --git a/src/math/fmal.c b/src/math/fmal.c
index 3944c292..cbaf46eb 100644
--- a/src/math/fmal.c
+++ b/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);
diff --git a/src/math/scalbn.c b/src/math/scalbn.c
index b51551b5..c9c7af80 100644
--- a/src/math/scalbn.c
+++ b/src/math/scalbn.c
@@ -1,62 +1,28 @@
-/* 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;
}
diff --git a/src/math/scalbnf.c b/src/math/scalbnf.c
index 0a6168b0..243dafdf 100644
--- a/src/math/scalbnf.c
+++ b/src/math/scalbnf.c
@@ -1,54 +1,28 @@
-/* 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;
}
diff --git a/src/math/scalbnl.c b/src/math/scalbnl.c
index 0ed5b7fd..a5d0adba 100644
--- a/src/math/scalbnl.c
+++ b/src/math/scalbnl.c
@@ -1,21 +1,3 @@
-/* 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
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