This is the mail archive of the
libc-alpha@sourceware.org
mailing list for the glibc project.
PowerPC floating point little-endian [4 of 15]
- From: Alan Modra <amodra at gmail dot com>
- To: libc-alpha at sourceware dot org
- Date: Wed, 10 Jul 2013 10:56:22 +0930
- Subject: PowerPC floating point little-endian [4 of 15]
- References: <20130710012435 dot GN2602 at bubble dot grove dot modra dot org>
Another batch of ieee854 macros and union replacement. These four
files also have bugs fixed with this patch. The fact that the two
doubles in an IBM long double may have different signs means that
negation and absolute value operations can't just twiddle one sign bit
as you can with ieee864 style extended double. fmodl, remainderl,
erfl and erfcl all had errors of this type. erfl also returned +1 for
large magnitude negative input where it should return -1. The hypotl
error is innocuous since the value adjusted twice is only used as a
flag.
2013-07-10 Alan Modra <amodra@gmail.com>
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c (__ieee754_fmodl): Rewrite
all uses of ieee875 long double macros and unions. Simplify test
for 0.0L. Correct |x|<|y| test. Remove dead code. Replace u_int64_t
with uint64_t.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Rewrite
all uses of ieee875 long double macros and unions. Simplify tests
for 0.0L and inf. Correct double adjustment of k.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c (__ieee754_remainderl):
Rewrite all uses of ieee875 long double macros and unions. Simplify
test for 0.0L and nan. Correct negation.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Rewrite all uses of
ieee875 long double macros and unions. Correct output for large
magnitude x. Correct absolute value calculation.
(__erfcl): Likewise.
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
index a60963c..6fc9a8b 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
@@ -27,43 +27,43 @@ static const long double one = 1.0, Zero[] = {0.0, -0.0,};
long double
__ieee754_fmodl (long double x, long double y)
{
- int64_t n,hx,hy,hz,ix,iy,sx, i;
- u_int64_t lx,ly,lz;
+ int64_t n,hx,hy,hz,ix,iy,sx,sy,i;
+ uint64_t lx,ly,lz;
int temp;
+ double xhi, xlo, yhi, ylo;
- GET_LDOUBLE_WORDS64(hx,lx,x);
- GET_LDOUBLE_WORDS64(hy,ly,y);
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
+ ldbl_unpack (y, &yhi, &ylo);
+ EXTRACT_WORDS64 (hy, yhi);
+ EXTRACT_WORDS64 (ly, ylo);
sx = hx&0x8000000000000000ULL; /* sign of x */
- hx ^=sx; /* |x| */
- hy &= 0x7fffffffffffffffLL; /* |y| */
+ hx ^= sx; /* |x| */
+ sy = hy&0x8000000000000000ULL; /* sign of y */
+ hy ^= sy; /* |y| */
/* purge off exception values */
- if(__builtin_expect((hy|(ly&0x7fffffffffffffff))==0 ||
+ if(__builtin_expect(hy==0 ||
(hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */
(hy>0x7ff0000000000000LL),0)) /* or y is NaN */
return (x*y)/(x*y);
if(__builtin_expect(hx<=hy,0)) {
- if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
+ if (hx < hy
+ || (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy))
+ return x; /* |x|<|y| return x */
if(lx==ly)
- return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/
+ return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(__builtin_expect(hx<0x0010000000000000LL,0)) { /* subnormal x */
- if(hx==0) {
- for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
- } else {
- for (ix = -1022, i=(hx<<11); i>0; i<<=1) ix -=1;
- }
+ for (ix = -1022, i=(hx<<11); i>0; i<<=1) ix -=1;
} else ix = (hx>>52)-0x3ff;
/* determine iy = ilogb(y) */
if(__builtin_expect(hy<0x0010000000000000LL,0)) { /* subnormal y */
- if(hy==0) {
- for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
- } else {
- for (iy = -1022, i=(hy<<11); i>0; i<<=1) iy -=1;
- }
+ for (iy = -1022, i=(hy<<11); i>0; i<<=1) iy -=1;
} else iy = (hy>>52)-0x3ff;
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
index 768bd3b..92db3f3 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
@@ -53,10 +53,13 @@ __ieee754_hypotl(long double x, long double y)
{
long double a,b,t1,t2,y1,y2,w,kld;
int64_t j,k,ha,hb;
+ double xhi, yhi;
- GET_LDOUBLE_MSW64(ha,x);
+ xhi = (double) x;
+ EXTRACT_WORDS64 (ha, xhi);
+ yhi = (double) y;
+ EXTRACT_WORDS64 (hb, yhi);
ha &= 0x7fffffffffffffffLL;
- GET_LDOUBLE_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsl(a); /* a <- |a| */
@@ -66,18 +69,16 @@ __ieee754_hypotl(long double x, long double y)
kld = 1.0L;
if(ha > 0x5f30000000000000LL) { /* a>2**500 */
if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */
- u_int64_t low;
w = a+b; /* for sNaN */
- GET_LDOUBLE_LSW64(low,a);
- if(((ha&0xfffffffffffffLL)|(low&0x7fffffffffffffffLL))==0)
+ if(ha == 0x7ff0000000000000LL)
w = a;
- GET_LDOUBLE_LSW64(low,b);
- if(((hb^0x7ff0000000000000LL)|(low&0x7fffffffffffffffLL))==0)
+ if(hb == 0x7ff0000000000000LL)
w = b;
return w;
}
/* scale a and b by 2**-600 */
- ha -= 0x2580000000000000LL; hb -= 0x2580000000000000LL; k += 600;
+ ha -= 0x2580000000000000LL;
+ hb -= 0x2580000000000000LL;
a /= two600;
b /= two600;
k += 600;
@@ -85,9 +86,7 @@ __ieee754_hypotl(long double x, long double y)
}
if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */
if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */
- u_int64_t low;
- GET_LDOUBLE_LSW64(low,b);
- if((hb|(low&0x7fffffffffffffffLL))==0) return a;
+ if(hb==0) return a;
t1=two1022; /* t1=2^1022 */
b *= t1;
a *= t1;
@@ -105,14 +104,14 @@ __ieee754_hypotl(long double x, long double y)
/* medium size a and b */
w = a-b;
if (w>b) {
- SET_LDOUBLE_WORDS64(t1,ha,0);
+ t1 = (double) a;
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
- SET_LDOUBLE_WORDS64(y1,hb,0);
+ y1 = (double) b;
y2 = b - y1;
- SET_LDOUBLE_WORDS64(t1,ha+0x0010000000000000LL,0);
+ t1 = (double) a;
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c b/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c
index 67d7db7..800416f 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c
@@ -33,18 +33,22 @@ __ieee754_remainderl(long double x, long double p)
int64_t hx,hp;
u_int64_t sx,lx,lp;
long double p_half;
+ double xhi, xlo, phi, plo;
- GET_LDOUBLE_WORDS64(hx,lx,x);
- GET_LDOUBLE_WORDS64(hp,lp,p);
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
+ ldbl_unpack (p, &phi, &plo);
+ EXTRACT_WORDS64 (hp, phi);
+ EXTRACT_WORDS64 (lp, plo);
sx = hx&0x8000000000000000ULL;
hp &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* purge off exception values */
- if((hp|(lp&0x7fffffffffffffff))==0) return (x*p)/(x*p); /* p = 0 */
+ if(hp==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff0000000000000LL)|| /* x not finite */
- ((hp>=0x7ff0000000000000LL)&& /* p is NaN */
- (((hp-0x7ff0000000000000LL)|lp)!=0)))
+ (hp>0x7ff0000000000000LL)) /* p is NaN */
return (x*p)/(x*p);
@@ -64,8 +68,8 @@ __ieee754_remainderl(long double x, long double p)
if(x>=p_half) x -= p;
}
}
- GET_LDOUBLE_MSW64(hx,x);
- SET_LDOUBLE_MSW64(x,hx^sx);
+ if (sx)
+ x = -x;
return x;
}
strong_alias (__ieee754_remainderl, __remainderl_finite)
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
index 6a4475e..553c5ca 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
@@ -760,16 +760,16 @@ long double
__erfl (long double x)
{
long double a, y, z;
- int32_t i, ix, sign;
- ieee854_long_double_shape_type u;
+ int32_t i, ix, hx;
+ double xhi;
- u.value = x;
- sign = u.parts32.w0;
- ix = sign & 0x7fffffff;
+ xhi = (double) x;
+ GET_HIGH_WORD (hx, xhi);
+ ix = hx & 0x7fffffff;
if (ix >= 0x7ff00000)
{ /* erf(nan)=nan */
- i = ((sign & 0xfff00000) >> 31) << 1;
+ i = ((uint32_t) hx >> 31) << 1;
return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */
}
@@ -778,7 +778,7 @@ __erfl (long double x)
if (ix >= 0x4039A0DE)
{
/* __erfcl (x) underflows if x > 25.6283 */
- if (sign)
+ if ((hx & 0x80000000) == 0)
return one-tiny;
else
return tiny-one;
@@ -789,8 +789,9 @@ __erfl (long double x)
return (one - y);
}
}
- u.parts32.w0 = ix;
- a = u.value;
+ a = x;
+ if ((hx & 0x80000000) != 0)
+ a = -a;
z = x * x;
if (ix < 0x3fec0000) /* a < 0.875 */
{
@@ -814,7 +815,7 @@ __erfl (long double x)
y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2);
}
- if (sign & 0x80000000) /* x < 0 */
+ if (hx & 0x80000000) /* x < 0 */
y = -y;
return( y );
}
@@ -824,18 +825,18 @@ long double
__erfcl (long double x)
{
long double y, z, p, r;
- int32_t i, ix, sign;
- ieee854_long_double_shape_type u;
+ int32_t i, ix;
+ uint32_t hx;
+ double xhi;
- u.value = x;
- sign = u.parts32.w0;
- ix = sign & 0x7fffffff;
- u.parts32.w0 = ix;
+ xhi = (double) x;
+ GET_HIGH_WORD (hx, xhi);
+ ix = hx & 0x7fffffff;
if (ix >= 0x7ff00000)
{ /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
- return (long double) (((u_int32_t) sign >> 31) << 1) + one / x;
+ return (long double) ((hx >> 31) << 1) + one / x;
}
if (ix < 0x3fd00000) /* |x| <1/4 */
@@ -846,7 +847,8 @@ __erfcl (long double x)
}
if (ix < 0x3ff40000) /* 1.25 */
{
- x = u.value;
+ if ((hx & 0x80000000) != 0)
+ x = -x;
i = 8.0 * x;
switch (i)
{
@@ -891,7 +893,7 @@ __erfcl (long double x)
y += C20a;
break;
}
- if (sign & 0x80000000)
+ if (hx & 0x80000000)
y = 2.0L - y;
return y;
}
@@ -899,10 +901,11 @@ __erfcl (long double x)
if (ix < 0x405ac000)
{
/* x < -9 */
- if ((ix >= 0x40220000) && (sign & 0x80000000))
+ if (hx >= 0xc0220000)
return two - tiny;
- x = fabsl (x);
+ if ((hx & 0x80000000) != 0)
+ x = -x;
z = one / (x * x);
i = 8.0 / x;
switch (i)
@@ -933,21 +936,17 @@ __erfcl (long double x)
p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8);
break;
}
- u.value = x;
- u.parts32.w3 = 0;
- u.parts32.w2 = 0;
- u.parts32.w1 &= 0xf8000000;
- z = u.value;
+ z = (float) x;
r = __ieee754_expl (-z * z - 0.5625) *
__ieee754_expl ((z - x) * (z + x) + p);
- if ((sign & 0x80000000) == 0)
+ if ((hx & 0x80000000) == 0)
return r / x;
else
return two - r / x;
}
else
{
- if ((sign & 0x80000000) == 0)
+ if ((hx & 0x80000000) == 0)
return tiny * tiny;
else
return two - tiny;
--
Alan Modra
Australia Development Lab, IBM