math: use the rounding idiom consistently

the idiomatic rounding of x is

  n = x + toint - toint;

where toint is either 1/EPSILON (x is non-negative) or 1.5/EPSILON
(x may be negative and nearest rounding mode is assumed) and EPSILON is
according to the evaluation precision (the type of toint is not very
important, because single precision float can represent the 1/EPSILON of
ieee binary128).

in case of FLT_EVAL_METHOD!=0 this avoids a useless store to double or
float precision, and the long double code became cleaner with
1/LDBL_EPSILON instead of ifdefs for toint.

__rem_pio2f and __rem_pio2 functions slightly changed semantics:
on i386 a double-rounding is avoided so close to half-way cases may
get evaluated differently eg. as sin(pi/4-eps) instead of cos(pi/4+eps)
This commit is contained in:
Szabolcs Nagy
2014-10-29 00:34:37 +01:00
committed by Rich Felker
parent 79ca86094d
commit 0ce946cf80
13 changed files with 89 additions and 58 deletions

View File

@ -6,11 +6,9 @@ long double rintl(long double x)
return rint(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
#define TOINT 0x1p63
#elif LDBL_MANT_DIG == 113
#define TOINT 0x1p112
#endif
static const long double toint = 1/LDBL_EPSILON;
long double rintl(long double x)
{
union ldshape u = {x};
@ -21,9 +19,9 @@ long double rintl(long double x)
if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x;
if (s)
y = x - TOINT + TOINT;
y = x - toint + toint;
else
y = x + TOINT - TOINT;
y = x + toint - toint;
if (y == 0)
return 0*x;
return y;