math: ld80 invtrig cleanups

[musl] / src / math / atanl.c

diff --git a/src/math/atanl.c b/src/math/atanl.c
index 4e99955..33ecff0 100644 (file)
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -23,9 +23,52 @@ long double atanl(long double x)
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 #include "__invtrigl.h"
-static const long double
-one = 1.0,
-huge = 1.0e300;
+
+#define ATAN_CONST      (BIAS + 65)     /* 2**65 */
+#define ATAN_LINEAR     (BIAS - 32)     /* 2**-32 */
+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)
 {
@@ -53,7 +96,7 @@ long double atanl(long double x)
        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 > one)
+                       if (huge+x > 1.0)
                                return x;
                }
                id = -1;
@@ -62,15 +105,15 @@ long double atanl(long double x)
                if (expman < (BIAS << 8) + 0x30) {  /* |x| < 1.1875 */
                        if (expman < ((BIAS - 1) << 8) + 0x60) { /*  7/16 <= |x| < 11/16 */
                                id = 0;
-                               x = (2.0*x-one)/(2.0+x);
+                               x = (2.0*x-1.0)/(2.0+x);
                        } else {                                 /* 11/16 <= |x| < 19/16 */
                                id = 1;
-                               x = (x-one)/(x+one);
+                               x = (x-1.0)/(x+1.0);
                        }
                } else {
                        if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
                                id = 2;
-                               x = (x-1.5)/(one+1.5*x);
+                               x = (x-1.5)/(1.0+1.5*x);
                        } else {                                 /* 2.4375 <= |x| < 2^ATAN_CONST */
                                id = 3;
                                x = -1.0/x;