#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)
{
*/
static long double adjust(long double hi, long double lo)
{
- union ld80 uhi, ulo;
+ union ldshape uhi, ulo;
if (lo == 0)
return hi;
- uhi.x = hi;
- if (uhi.bits.m & 0x3ff)
+ uhi.f = hi;
+ if (uhi.i.m & 0x3ff)
return hi;
- ulo.x = lo;
- if (uhi.bits.s == ulo.bits.s)
- uhi.bits.m++;
+ ulo.f = lo;
+ if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
+ uhi.i.m++;
else {
- uhi.bits.m--;
/* handle underflow and take care of ld80 implicit msb */
- if (uhi.bits.m == (uint64_t)-1/2) {
- uhi.bits.m *= 2;
- uhi.bits.e--;
+ if (uhi.i.m << 1 == 0) {
+ uhi.i.m = 0;
+ uhi.i.se--;
}
+ uhi.i.m--;
}
- return uhi.x;
+ return uhi.f;
}
/* adjusted add so the result is correct when rounded to double (or less) precision */
static int getexp(long double x)
{
- union ld80 u;
- u.x = x;
- return u.bits.e;
+ 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;
} 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);
- /* make sure that the sign of 0 is correct */
- return (xy + z) + lo1;
+ z_ = z;
+ return (xy + z_) + lo1;
}
} else {
/*
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)
- return dadd(hi, dadd(lo1, lo2));
- return hi + (lo1 + lo2);
+ 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 */
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 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;
/*
* 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 scalbn(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);
projects / musl / blobdiff