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)

diff --git a/src/math/acos.c b/src/math/acos.c
index be95d25..cd5d06a 100644 (file)
--- a/src/math/acos.c
+++ b/src/math/acos.c
@@ -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 */

diff --git a/src/math/acosl.c b/src/math/acosl.c
index 9e9b01e..9e7b7fb 100644 (file)
--- a/src/math/acosl.c
+++ b/src/math/acosl.c
@@ -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 */

diff --git a/src/math/asin.c b/src/math/asin.c
index a1906b0..d61c04b 100644 (file)
--- a/src/math/asin.c
+++ b/src/math/asin.c
@@ -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);

diff --git a/src/math/asinh.c b/src/math/asinh.c
index 4152dc3..0829f22 100644 (file)
--- a/src/math/asinh.c
+++ b/src/math/asinh.c
@@ -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;
 }

diff --git a/src/math/asinhl.c b/src/math/asinhl.c
index db96624..3ea8874 100644 (file)
--- a/src/math/asinhl.c
+++ b/src/math/asinhl.c
@@ -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;
 }

diff --git a/src/math/asinl.c b/src/math/asinl.c
index 0ef9853..8799341 100644 (file)
--- a/src/math/asinl.c
+++ b/src/math/asinl.c
@@ -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);

diff --git a/src/math/atan.c b/src/math/atan.c
index 7fd8a3b..3c9a59f 100644 (file)
--- a/src/math/atan.c
+++ b/src/math/atan.c
@@ -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;

diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index e86dbff..7cb42c2 100644 (file)
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -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;

diff --git a/src/math/atanl.c b/src/math/atanl.c
index 6a480a7..e76693e 100644 (file)
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -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;

diff --git a/src/math/exp2f.c b/src/math/exp2f.c
index 279f32d..ea50db4 100644 (file)
--- a/src/math/exp2f.c
+++ b/src/math/exp2f.c
@@ -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 */