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math: use 0x1p-120f and 0x1p120f for tiny and huge values 

previously 0x1p-1000 and 0x1p1000 was used for raising inexact
exception like x+tiny (when x is big) or x+huge (when x is small)

the rational is that these float consts are large enough
(0x1p-120 + 1 raises inexact even on ld128 which has 113 mant bits)
and float consts maybe smaller or easier to load on some platforms
(on i386 this reduced the object file size by 4bytes in some cases)
This commit is contained in:
Szabolcs Nagy 2012-12-16 20:28:43 +01:00
parent d8a7619e37
commit c6383b7b10
10 changed files with 27 additions and 27 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
src/math/acos.c
View File

@ -72,7 +72,7 @@ double acos(double x)
if ((ix-0x3ff00000 | lx) == 0) {
/* acos(1)=0, acos(-1)=pi */
if (hx >> 31)
return 2*pio2_hi + 0x1p-1000;
return 2*pio2_hi + 0x1p-120f;
return 0;
}
return 0/(x-x);
@ -80,7 +80,7 @@ double acos(double x)
/* |x| < 0.5 */
if (ix < 0x3fe00000) {
if (ix <= 0x3c600000) /* |x| < 2**-57 */
return pio2_hi + 0x1p-1000;
return pio2_hi + 0x1p-120f;
return pio2_hi - (x - (pio2_lo-x*R(x*x)));
}
/* x < -0.5 */

4
src/math/acosl.c
View File

@ -38,14 +38,14 @@ long double acosl(long double x)
((u.bits.manh & ~LDBL_NBIT) | u.bits.manl) == 0) {
if (expsign > 0)
return 0; /* acos(1) = 0 */
return 2*pio2_hi + 0x1p-1000; /* acos(-1)= pi */
return 2*pio2_hi + 0x1p-120f; /* acos(-1)= pi */
}
return 0/(x-x); /* acos(|x|>1) is NaN */
}
/* |x| < 0.5 */
if (expt < 0x3fff - 1) {
if (expt < 0x3fff - 65)
return pio2_hi + 0x1p-1000; /* x < 0x1p-65: acosl(x)=pi/2 */
return pio2_hi + 0x1p-120f; /* x < 0x1p-65: acosl(x)=pi/2 */
return pio2_hi - (x - (pio2_lo - x * __invtrigl_R(x*x)));
}
/* x < -0.5 */

4
src/math/asin.c
View File

@ -77,14 +77,14 @@ double asin(double x)
GET_LOW_WORD(lx, x);
if ((ix-0x3ff00000 | lx) == 0)
/* asin(1) = +-pi/2 with inexact */
return x*pio2_hi + 0x1p-1000;
return x*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
/* |x| < 0.5 */
if (ix < 0x3fe00000) {
if (ix < 0x3e500000) {
/* |x|<0x1p-26, return x with inexact if x!=0*/
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
return x;
}
return x + x*R(x*x);

2
src/math/asinh.c
View File

@ -22,7 +22,7 @@ double asinh(double x)
x = log1p(x + x*x/(sqrt(x*x+1)+1));
} else {
/* |x| < 0x1p-26, raise inexact if x != 0 */
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
}
return s ? -x : x;
}

2
src/math/asinhl.c
View File

@ -31,7 +31,7 @@ long double asinhl(long double x)
x = log1pl(x + x*x/(sqrtl(x*x+1)+1));
} else {
/* |x| < 0x1p-32, raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
}
return s ? -x : x;
}

4
src/math/asinl.c
View File

@ -39,13 +39,13 @@ long double asinl(long double x)
if (expt == 0x3fff &&
((u.bits.manh&~LDBL_NBIT)|u.bits.manl) == 0)
/* asin(+-1)=+-pi/2 with inexact */
return x*pio2_hi + 0x1p-1000;
return x*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
if (expt < 0x3fff - 1) { /* |x| < 0.5 */
if (expt < 0x3fff - 32) { /* |x|<0x1p-32, asinl(x)=x */
/* return x with inexact if x!=0 */
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
return x;
}
return x + x*__invtrigl_R(x*x);

4
src/math/atan.c
View File

@ -72,13 +72,13 @@ double atan(double x)
if (ix >= 0x44100000) { /* if |x| >= 2^66 */
if (isnan(x))
return x;
z = atanhi[3] + 0x1p-1000;
z = atanhi[3] + 0x1p-120f;
return sign ? -z : z;
}
if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
if (ix < 0x3e400000) { /* |x| < 2^-27 */
/* raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
return x;
}
id = -1;

22
src/math/atan2l.c
View File

@ -52,39 +52,39 @@ long double atan2l(long double y, long double x)
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return 2*pio2_hi+0x1p-1000; /* atan(+0,-anything) = pi */
case 3: return -2*pio2_hi-0x1p-1000; /* atan(-0,-anything) =-pi */
case 2: return 2*pio2_hi+0x1p-120f; /* atan(+0,-anything) = pi */
case 3: return -2*pio2_hi-0x1p-120f; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
/* when x is INF */
if (exptx == 0x7fff) {
if (expty == 0x7fff) {
switch(m) {
case 0: return pio2_hi*0.5+0x1p-1000; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-0x1p-1000; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+0x1p-1000; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi-0x1p-1000; /* atan(-INF,-INF) */
case 0: return pio2_hi*0.5+0x1p-120f; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-0x1p-120f; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+0x1p-120f; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi-0x1p-120f; /* atan(-INF,-INF) */
}
} else {
switch(m) {
case 0: return 0.0; /* atan(+...,+INF) */
case 1: return -0.0; /* atan(-...,+INF) */
case 2: return 2*pio2_hi+0x1p-1000; /* atan(+...,-INF) */
case 3: return -2*pio2_hi-0x1p-1000; /* atan(-...,-INF) */
case 2: return 2*pio2_hi+0x1p-120f; /* atan(+...,-INF) */
case 3: return -2*pio2_hi-0x1p-120f; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if (expty == 0x7fff)
return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
/* compute y/x */
k = expty-exptx;
if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
z = pio2_hi+0x1p-1000;
z = pio2_hi+0x1p-120f;
m &= 1;
} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
z = 0.0;

4
src/math/atanl.c
View File

@ -80,7 +80,7 @@ long double atanl(long double x)
if (expt == 0x7fff &&
((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) /* NaN */
return x+x;
z = atanhi[3] + 0x1p-1000;
z = atanhi[3] + 0x1p-120f;
return expsign < 0 ? -z : z;
}
/* Extract the exponent and the first few bits of the mantissa. */
@ -89,7 +89,7 @@ long double atanl(long double x)
if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
if (expt < 0x3fff - 32) { /* if |x| is small, atanl(x)~=x */
/* raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p1000);
FORCE_EVAL(x + 0x1p120f);
return x;
}
id = -1;

4
src/math/exp2f.c
View File

@ -97,11 +97,11 @@ float exp2f(float x)
return x;
}
if (x >= 128) {
STRICT_ASSIGN(float, x, x * 0x1p127);
STRICT_ASSIGN(float, x, x * 0x1p127f);
return x;
}
if (x <= -150) {
STRICT_ASSIGN(float, x, 0x1p-100*0x1p-100);
STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
return x;
}
} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */