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

[musl] / src / math / atanl.c

diff --git a/src/math/atanl.c b/src/math/atanl.c
index 36072c1..e76693e 100644 (file)
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -22,8 +22,48 @@ long double atanl(long double x)
        return atan(x);
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__invtrigl.h"
-static const long double huge = 1.0e300;
+
+static const long double atanhi[] = {
+        4.63647609000806116202e-01L,
+        7.85398163397448309628e-01L,
+        9.82793723247329067960e-01L,
+        1.57079632679489661926e+00L,
+};
+
+static const long double atanlo[] = {
+        1.18469937025062860669e-20L,
+       -1.25413940316708300586e-20L,
+        2.55232234165405176172e-20L,
+       -2.50827880633416601173e-20L,
+};
+
+static const long double aT[] = {
+        3.33333333333333333017e-01L,
+       -1.99999999999999632011e-01L,
+        1.42857142857046531280e-01L,
+       -1.11111111100562372733e-01L,
+        9.09090902935647302252e-02L,
+       -7.69230552476207730353e-02L,
+        6.66661718042406260546e-02L,
+       -5.88158892835030888692e-02L,
+        5.25499891539726639379e-02L,
+       -4.70119845393155721494e-02L,
+        4.03539201366454414072e-02L,
+       -2.91303858419364158725e-02L,
+        1.24822046299269234080e-02L,
+};
+
+static long double T_even(long double x)
+{
+       return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
+               x * (aT[8] + x * (aT[10] + x * aT[12])))));
+}
+
+static long double T_odd(long double x)
+{
+       return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
+               x * (aT[9] + x * aT[11]))));
+}
 
 long double atanl(long double x)
 {
@@ -36,29 +76,27 @@ long double atanl(long double x)
        u.e = x;
        expsign = u.xbits.expsign;
        expt = expsign & 0x7fff;
-       if (expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
-               if (expt == BIAS + LDBL_MAX_EXP &&
+       if (expt >= 0x3fff + 65) { /* if |x| is large, atan(x)~=pi/2 */
+               if (expt == 0x7fff &&
                    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)  /* NaN */
                        return x+x;
-               if (expsign > 0)
-                       return  atanhi[3]+atanlo[3];
-               else
-                       return -atanhi[3]-atanlo[3];
+               z = atanhi[3] + 0x1p-120f;
+               return expsign < 0 ? -z : z;
        }
        /* Extract the exponent and the first few bits of the mantissa. */
        /* XXX There should be a more convenient way to do this. */
-       expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
-       if (expman < ((BIAS - 2) << 8) + 0xc0) {  /* |x| < 0.4375 */
-               if (expt < ATAN_LINEAR) {   /* if |x| is small, atanl(x)~=x */
-                       /* raise inexact */
-                       if (huge+x > 1.0)
-                               return x;
+       expman = (expt << 8) | ((u.bits.manh >> (LDBL_MANH_SIZE - 9)) & 0xff);
+       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 + 0x1p120f);
+                       return x;
                }
                id = -1;
        } else {
                x = fabsl(x);
-               if (expman < (BIAS << 8) + 0x30) {  /* |x| < 1.1875 */
-                       if (expman < ((BIAS - 1) << 8) + 0x60) { /*  7/16 <= |x| < 11/16 */
+               if (expman < (0x3fff << 8) + 0x30) {  /* |x| < 1.1875 */
+                       if (expman < ((0x3fff - 1) << 8) + 0x60) { /*  7/16 <= |x| < 11/16 */
                                id = 0;
                                x = (2.0*x-1.0)/(2.0+x);
                        } else {                                 /* 11/16 <= |x| < 19/16 */
@@ -66,7 +104,7 @@ long double atanl(long double x)
                                x = (x-1.0)/(x+1.0);
                        }
                } else {
-                       if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
+                       if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
                                id = 2;
                                x = (x-1.5)/(1.0+1.5*x);
                        } else {                                 /* 2.4375 <= |x| < 2^ATAN_CONST */