+#include <fenv.h>
+#include "libm.h"
+
+#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
+/* 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 (or less) precision is correct
+*/
+static long double adjust(long double hi, long double lo)
+{
+ union ldshape uhi, ulo;
+
+ if (lo == 0)
+ return hi;
+ uhi.f = hi;
+ if (uhi.i.m & 0x3ff)
+ return hi;
+ ulo.f = lo;
+ if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
+ uhi.i.m++;
+ else {
+ /* handle underflow and take care of ld80 implicit msb */
+ if (uhi.i.m << 1 == 0) {
+ uhi.i.m = 0;
+ uhi.i.se--;
+ }
+ uhi.i.m--;
+ }
+ return uhi.f;
+}
+
+/* adjusted add so the result is correct when rounded to double (or less) precision */
+static long double dadd(long double x, long double y)
+{
+ add(&x, &y, x, y);
+ return adjust(x, y);
+}
+
+/* adjusted mul so the result is correct when rounded to double (or less) precision */
+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 ldshape u;
+ u.f = x;
+ return u.i.se & 0x7fff;
+}
+
+double fma(double x, double y, double z)
+{
+ #pragma STDC FENV_ACCESS ON
+ 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) {
+ /*
+ xy + z is 0, but it should be calculated with the
+ original rounding mode so the sign is correct, if the
+ compiler does not support FENV_ACCESS ON it does not
+ know about the changed rounding mode and eliminates
+ the xy + z below without the volatile memory access
+ */
+ volatile double z_;
+ fesetround(round);
+ z_ = z;
+ 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;
+ }
+ /*
+ the result is stored before return for correct precision and exceptions
+
+ one corner case is when the underflow flag should be raised because
+ the precise result is an inexact subnormal double, but the calculated
+ long double result is an exact subnormal double
+ (so rounding to double does not raise exceptions)
+
+ in nearest rounding mode dadd takes care of this: the last bit of the
+ result is adjusted so rounding sees an inexact value when it should
+
+ in non-nearest rounding mode fenv is used for the workaround
+ */
+ fesetround(round);
+ if (round == FE_TONEAREST)
+ z = dadd(hi, dadd(lo1, lo2));
+ else {
+#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
+ int e = fetestexcept(FE_INEXACT);
+ feclearexcept(FE_INEXACT);
+#endif
+ z = hi + (lo1 + lo2);
+#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
+ if (getexp(z) < 0x3fff-1022 && fetestexcept(FE_INEXACT))
+ feraiseexcept(FE_UNDERFLOW);
+ else if (e)
+ feraiseexcept(FE_INEXACT);
+#endif
+ }
+ return z;
+}
+#else
/* origin: FreeBSD /usr/src/lib/msun/src/s_fma.c */
/*-
* Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
* 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
static inline double add_adjusted(double a, double b)
{
struct dd sum;
- uint64_t hibits, lobits;
+ union {double f; uint64_t i;} uhi, ulo;
sum = dd_add(a, b);
if (sum.lo != 0) {
- EXTRACT_WORD64(hibits, sum.hi);
- if ((hibits & 1) == 0) {
+ uhi.f = sum.hi;
+ if ((uhi.i & 1) == 0) {
/* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
- EXTRACT_WORD64(lobits, sum.lo);
- hibits += 1 - ((hibits ^ lobits) >> 62);
- INSERT_WORD64(sum.hi, hibits);
+ ulo.f = sum.lo;
+ uhi.i += 1 - ((uhi.i ^ ulo.i) >> 62);
+ sum.hi = uhi.f;
}
}
return (sum.hi);
static inline double add_and_denormalize(double a, double b, int scale)
{
struct dd sum;
- uint64_t hibits, lobits;
+ union {double f; uint64_t i;} uhi, ulo;
int bits_lost;
sum = dd_add(a, b);
* break the ties manually.
*/
if (sum.lo != 0) {
- EXTRACT_WORD64(hibits, sum.hi);
- bits_lost = -((int)(hibits >> 52) & 0x7ff) - scale + 1;
- if (bits_lost != 1 ^ (int)(hibits & 1)) {
+ uhi.f = sum.hi;
+ bits_lost = -((int)(uhi.i >> 52) & 0x7ff) - scale + 1;
+ if ((bits_lost != 1) ^ (int)(uhi.i & 1)) {
/* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
- EXTRACT_WORD64(lobits, sum.lo);
- hibits += 1 - (((hibits ^ lobits) >> 62) & 2);
- INSERT_WORD64(sum.hi, hibits);
+ ulo.f = sum.lo;
+ uhi.i += 1 - (((uhi.i ^ ulo.i) >> 62) & 2);
+ sum.hi = uhi.f;
}
}
- return (ldexp(sum.hi, scale));
+ return scalbn(sum.hi, scale);
}
/*
*/
double fma(double x, double y, double z)
{
+ #pragma STDC FENV_ACCESS ON
double xs, ys, zs, adj;
struct dd xy, r;
int oround;
* 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);
}
}
if (spread <= DBL_MANT_DIG * 2)
- zs = ldexp(zs, -spread);
+ zs = scalbn(zs, -spread);
else
zs = copysign(DBL_MIN, zs);
*/
fesetround(oround);
volatile double vzs = zs; /* XXX gcc CSE bug workaround */
- return (xy.hi + vzs + ldexp(xy.lo, spread));
+ return xy.hi + vzs + scalbn(xy.lo, spread);
}
if (oround != FE_TONEAREST) {
/*
* There is no need to worry about double rounding in directed
* rounding modes.
+ * But underflow may not be raised properly, example in downward rounding:
+ * fma(0x1.000000001p-1000, 0x1.000000001p-30, -0x1p-1066)
*/
+ double ret;
+#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
+ int e = fetestexcept(FE_INEXACT);
+ feclearexcept(FE_INEXACT);
+#endif
fesetround(oround);
adj = r.lo + xy.lo;
- return (ldexp(r.hi + adj, spread));
+ ret = scalbn(r.hi + adj, spread);
+#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
+ if (ilogb(ret) < -1022 && fetestexcept(FE_INEXACT))
+ feraiseexcept(FE_UNDERFLOW);
+ else if (e)
+ feraiseexcept(FE_INEXACT);
+#endif
+ return ret;
}
adj = add_adjusted(r.lo, xy.lo);
if (spread + ilogb(r.hi) > -1023)
- return (ldexp(r.hi + adj, spread));
+ return scalbn(r.hi + adj, spread);
else
- return (add_and_denormalize(r.hi, adj, spread));
+ return add_and_denormalize(r.hi, adj, spread);
}
+#endif
projects / musl / blobdiff