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Re: PowerPC floating point little-endian [4 of 15]
- From: Alan Modra <amodra at gmail dot com>
- To: libc-alpha at sourceware dot org
- Date: Fri, 9 Aug 2013 14:12:10 +0930
- Subject: Re: PowerPC floating point little-endian [4 of 15]
- References: <20130710012435 dot GN2602 at bubble dot grove dot modra dot org> <20130710012622 dot GQ2602 at bubble dot grove dot modra dot org>
This is a revised version of
http://sourceware.org/ml/libc-alpha/2013-07/msg00195.html
containing the followup revised e_fmodl.c patch
http://sourceware.org/ml/libc-alpha/2013-07/msg00268.html
with some further e_hypotl.c tidies. The tests there for large "a"
and small "b" are mutually exclusive because we've already exited when
x/y > 2**120. That allows some further small simplifications.
PR 15734, 15735
* 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| and |x|=|y| test. Use
ldbl_extract_mantissa value for ix,iy exponents. Properly
normalize after ldbl_extract_mantissa, and don't add hidden bit
already handled. Don't treat low word of ieee854 mantissa like
low word of IBM long double and mask off bit when testing for
zero.
* 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. Delete dead code
adjusting ha,hb. Simplify code setting kld. Delete two600 and
two1022, instead use their values. Recognise that tests for large
"a" and small "b" are mutually exclusive. Rename vars. Comment.
* 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.
* math/libm-test.inc: Add tests for errors discovered in IBM long
double versions of fmodl, remainderl, erfl and erfcl.
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
index a60963c..ffb3bec 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c
@@ -27,76 +27,65 @@ 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;
- int temp;
+ int64_t hx, hy, hz, sx, sy;
+ uint64_t lx, ly, lz;
+ int n, ix, iy;
+ 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(lx==ly)
- return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/
+ if (hx < hy
+ || (((ly ^ sy) & 0x8000000000000000LL) == 0
+ && (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy))
+ || (((lx ^ sx) & 0x8000000000000000LL) != 0
+ && (int64_t) (lx ^ sx) > (int64_t) (ly ^ sy)))
+ return x; /* |x|<|y| return x */
+ if ((lx ^ sx) == (ly ^ sy))
+ 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;
- }
- } 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;
- }
- } else iy = (hy>>52)-0x3ff;
-
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
bit mantissa so the following operations will give the correct
result. */
- ldbl_extract_mantissa(&hx, &lx, &temp, x);
- ldbl_extract_mantissa(&hy, &ly, &temp, y);
+ ldbl_extract_mantissa(&hx, &lx, &ix, x);
+ ldbl_extract_mantissa(&hy, &ly, &iy, y);
- /* set up {hx,lx}, {hy,ly} and align y to x */
- if(__builtin_expect(ix >= -1022, 1))
- hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx);
- else { /* subnormal x, shift x to normal */
- n = -1022-ix;
- if(n<=63) {
- hx = (hx<<n)|(lx>>(64-n));
- lx <<= n;
- } else {
- hx = lx<<(n-64);
- lx = 0;
- }
- }
- if(__builtin_expect(iy >= -1022, 1))
- hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy);
- else { /* subnormal y, shift y to normal */
- n = -1022-iy;
- if(n<=63) {
- hy = (hy<<n)|(ly>>(64-n));
- ly <<= n;
- } else {
- hy = ly<<(n-64);
- ly = 0;
- }
- }
+ if (__builtin_expect (ix == -IEEE754_DOUBLE_BIAS, 0))
+ {
+ /* subnormal x, shift x to normal. */
+ while ((hx & (1LL << 48)) == 0)
+ {
+ hx = (hx << 1) | (lx >> 63);
+ lx = lx << 1;
+ ix -= 1;
+ }
+ }
+
+ if (__builtin_expect (iy == -IEEE754_DOUBLE_BIAS, 0))
+ {
+ /* subnormal y, shift y to normal. */
+ while ((hy & (1LL << 48)) == 0)
+ {
+ hy = (hy << 1) | (ly >> 63);
+ ly = ly << 1;
+ iy -= 1;
+ }
+ }
/* fix point fmod */
n = ix - iy;
@@ -104,7 +93,7 @@ __ieee754_fmodl (long double x, long double y)
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;}
else {
- if((hz|(lz&0x7fffffffffffffff))==0) /* return sign(x)*0 */
+ if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(u_int64_t)sx>>63];
hx = hz+hz+(lz>>63); lx = lz+lz;
}
@@ -113,7 +102,7 @@ __ieee754_fmodl (long double x, long double y)
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
- if((hx|(lx&0x7fffffffffffffff))==0) /* return sign(x)*0 */
+ if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(u_int64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
index 768bd3b..3b07a47 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
@@ -45,76 +45,84 @@
#include <math.h>
#include <math_private.h>
-static const long double two600 = 0x1.0p+600L;
-static const long double two1022 = 0x1.0p+1022L;
-
long double
__ieee754_hypotl(long double x, long double y)
{
- long double a,b,t1,t2,y1,y2,w,kld;
+ long double a,b,a1,a2,b1,b2,w,kld;
int64_t j,k,ha,hb;
+ double xhi, yhi, hi, lo;
- GET_LDOUBLE_MSW64(ha,x);
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (ha, xhi);
+ yhi = ldbl_high (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| */
b = fabsl(b); /* b <- |b| */
- if((ha-hb)>0x780000000000000LL) {return a+b;} /* x/y > 2**120 */
+ if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
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;
- a /= two600;
- b /= two600;
- k += 600;
- kld = two600;
+ a *= 0x1p-600L;
+ b *= 0x1p-600L;
+ k = 600;
+ kld = 0x1p+600L;
}
- if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */
+ else 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;
- t1=two1022; /* t1=2^1022 */
- b *= t1;
- a *= t1;
- k -= 1022;
- kld = kld / two1022;
+ if(hb==0) return a;
+ a *= 0x1p+1022L;
+ b *= 0x1p+1022L;
+ k = -1022;
+ kld = 0x1p-1022L;
} else { /* scale a and b by 2^600 */
- ha += 0x2580000000000000LL; /* a *= 2^600 */
- hb += 0x2580000000000000LL; /* b *= 2^600 */
- k -= 600;
- a *= two600;
- b *= two600;
- kld = kld / two600;
+ a *= 0x1p+600L;
+ b *= 0x1p+600L;
+ k = -600;
+ kld = 0x1p-600L;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
- SET_LDOUBLE_WORDS64(t1,ha,0);
- t2 = a-t1;
- w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
+ ldbl_unpack (a, &hi, &lo);
+ a1 = hi;
+ a2 = lo;
+ /* a*a + b*b
+ = (a1+a2)*a + b*b
+ = a1*a + a2*a + b*b
+ = a1*(a1+a2) + a2*a + b*b
+ = a1*a1 + a1*a2 + a2*a + b*b
+ = a1*a1 + a2*(a+a1) + b*b */
+ w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
} else {
a = a+a;
- SET_LDOUBLE_WORDS64(y1,hb,0);
- y2 = b - y1;
- SET_LDOUBLE_WORDS64(t1,ha+0x0010000000000000LL,0);
- t2 = a - t1;
- w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ ldbl_unpack (b, &hi, &lo);
+ b1 = hi;
+ b2 = lo;
+ ldbl_unpack (a, &hi, &lo);
+ a1 = hi;
+ a2 = lo;
+ /* a*a + b*b
+ = a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b
+ = a*a + w*w - (a*a - 2*a*b + b*b) + b*b
+ = w*w + 2*a*b
+ = w*w + (a1+a2)*b
+ = w*w + a1*b + a2*b
+ = w*w + a1*(b1+b2) + a2*b
+ = w*w + a1*b1 + a1*b2 + a2*b */
+ w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
}
if(k!=0)
return w*kld;
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..c861c65 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 = ldbl_high (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 = ldbl_high (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;
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 2e5237b..fb68e1e 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7771,6 +7771,11 @@ static const struct test_f_f_data erf_test_data[] =
TEST_f_f (erf, 2.0L, 0.995322265018952734162069256367252929L),
TEST_f_f (erf, 4.125L, 0.999999994576599200434933994687765914L),
TEST_f_f (erf, 27.0L, 1.0L),
+ TEST_f_f (erf, -27.0L, -1.0L),
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 54
+ /* The input is not exactly representable as a double. */
+ TEST_f_f (erf, -0x1.fffffffffffff8p-2L, -0.5204998778130465132916303345518417673509L),
+#endif
};
static void
@@ -7799,6 +7804,10 @@ static const struct test_f_f_data erfc_test_data[] =
TEST_f_f (erfc, 0x1.ffa002p+2L, 1.233585992097580296336099501489175967033e-29L),
TEST_f_f (erfc, 0x1.ffffc8p+2L, 1.122671365033056305522366683719541099329e-29L),
#ifdef TEST_LDOUBLE
+# if LDBL_MANT_DIG >= 54
+ /* The input is not exactly representable as a double. */
+ TEST_f_f (erfc, -0x1.fffffffffffff8p-2L, 1.52049987781304651329163033455184176735L),
+# endif
/* The result can only be represented in long double. */
# if LDBL_MIN_10_EXP < -319
TEST_f_f (erfc, 27.0L, 0.523704892378925568501606768284954709e-318L),
@@ -9293,6 +9302,13 @@ static const struct test_ff_f_data fmod_test_data[] =
#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
TEST_ff_f (fmod, 0x0.fffffffffffffffep-16382L, 0x1p-16445L, plus_zero, NO_INEXACT_EXCEPTION),
#endif
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 56
+ TEST_ff_f (fmod, -0x1.00000000000004p+0L, 0x1.fffffffffffff8p-1L, -0x1p-53L, NO_INEXACT_EXCEPTION),
+ TEST_ff_f (fmod, 0x1.fffffffffffffap-1L, 0x1.fffffffffffff8p-1L, 0x1p-56L, NO_INEXACT_EXCEPTION),
+ TEST_ff_f (fmod, -0x1.fffffffffffffap-1L, 0x1.fffffffffffff8p-1L, -0x1p-56L, NO_INEXACT_EXCEPTION),
+ TEST_ff_f (fmod, 0x1.fffffffffffffap-1L, -0x1.fffffffffffff8p-1L, 0x1p-56L, NO_INEXACT_EXCEPTION),
+ TEST_ff_f (fmod, -0x1.fffffffffffffap-1L, -0x1.fffffffffffff8p-1L, -0x1p-56L, NO_INEXACT_EXCEPTION),
+#endif
};
static void
@@ -12193,6 +12209,9 @@ static const struct test_ff_f_data remainder_test_data[] =
TEST_ff_f (remainder, -1.625, -1.0, 0.375, NO_INEXACT_EXCEPTION),
TEST_ff_f (remainder, 5.0, 2.0, 1.0, NO_INEXACT_EXCEPTION),
TEST_ff_f (remainder, 3.0, 2.0, -1.0, NO_INEXACT_EXCEPTION),
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 56
+ TEST_ff_f (remainder, -0x1.80000000000002p1L, 2.0, 0x1.fffffffffffff8p-1L, NO_INEXACT_EXCEPTION),
+#endif
};
static void
--
Alan Modra
Australia Development Lab, IBM