From 650ef4bd7976e36831cba22d838b567d3b5f6e8f Mon Sep 17 00:00:00 2001 From: Alan Modra Date: Sat, 17 Aug 2013 18:25:51 +0930 Subject: PowerPC floating point little-endian [4 of 15] http://sourceware.org/ml/libc-alpha/2013-08/msg00084.html 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. The e_hypotl.c tests 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. [BZ #15734], [BZ #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. --- ChangeLog | 27 +++++++ math/libm-test.inc | 19 +++++ sysdeps/ieee754/ldbl-128ibm/e_fmodl.c | 125 +++++++++++++++-------------- sysdeps/ieee754/ldbl-128ibm/e_hypotl.c | 88 +++++++++++--------- sysdeps/ieee754/ldbl-128ibm/e_remainderl.c | 18 +++-- sysdeps/ieee754/ldbl-128ibm/s_erfl.c | 55 +++++++------ 6 files changed, 198 insertions(+), 134 deletions(-) diff --git a/ChangeLog b/ChangeLog index 829d433..e3647f3 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,5 +1,32 @@ 2013-10-04 Alan Modra + [BZ #15734], [BZ #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. + +2013-10-04 Alan Modra + * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c (__ieee754_atan2l): Rewrite all uses of ieee854 long double macros and unions. Simplify tests for long doubles that are fully specified by the high double. diff --git a/math/libm-test.inc b/math/libm-test.inc index 2cb3d2c..9677052 100644 --- a/math/libm-test.inc +++ b/math/libm-test.inc @@ -7829,6 +7829,11 @@ 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 @@ -7857,6 +7862,10 @@ 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), @@ -9355,6 +9364,13 @@ 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 @@ -12316,6 +12332,9 @@ 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 diff --git a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c index a60963c..a140fb3 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c @@ -27,76 +27,83 @@ 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>63]; /* |x|=|y| return x*0*/ + if (__builtin_expect (hx <= hy, 0)) + { + /* If |x| < |y| return x. */ + if (hx < hy) + return x; + /* At this point the absolute value of the high doubles of + x and y must be equal. */ + /* If the low double of y is the same sign as the high + double of y (ie. the low double increases |y|)... */ + if (((ly ^ sy) & 0x8000000000000000LL) == 0 + /* ... then a different sign low double to high double + for x or same sign but lower magnitude... */ + && (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If the low double of x differs in sign to the high + double of x (ie. the low double decreases |x|)... */ + if (((lx ^ sx) & 0x8000000000000000LL) != 0 + /* ... then a different sign low double to high double + for y with lower magnitude (we've already caught + the same sign for y case above)... */ + && (int64_t) (lx ^ sx) > (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If |x| == |y| return x*0. */ + if ((lx ^ sx) == (ly ^ sy)) + return Zero[(uint64_t) sx >> 63]; } - /* 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<>(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<>(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 +111,7 @@ __ieee754_fmodl (long double x, long double y) hz=hx-hy;lz=lx-ly; if(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 +120,7 @@ __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 #include -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; -- cgit v1.1