ntdll: Copy atan() implementation from msvcrt.

dlls/ntdll/math.c

@@ -16,6 +16,23 @@
  * You should have received a copy of the GNU Lesser General Public
  * License along with this library; if not, write to the Free Software
  * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
+ *
+ *
+ * For functions copied from musl libc (http://musl.libc.org/):
+ * ====================================================
+ * Copyright 2005-2020 Rich Felker, et al.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ * ====================================================
  */
 
 #include <math.h>
@@ -24,6 +41,15 @@
 #define WIN32_NO_STATUS
 #include "ntdll_misc.h"
 
+/* Copied from musl: src/internal/libm.h */
+static inline float fp_barrierf(float x)
+{
+    volatile float y = x;
+    return y;
+}
+
+
+
 /*********************************************************************
  *                  abs   (NTDLL.@)
  */
@@ -34,10 +60,88 @@ int CDECL abs( int i )
 
 /*********************************************************************
  *                  atan   (NTDLL.@)
+ *
+ * Copied from musl: src/math/atan.c
  */
-double CDECL atan( double d )
+double CDECL atan( double x )
 {
-    return unix_funcs->atan( d );
+    static const double atanhi[] = {
+        4.63647609000806093515e-01,
+        7.85398163397448278999e-01,
+        9.82793723247329054082e-01,
+        1.57079632679489655800e+00,
+    };
+    static const double atanlo[] = {
+        2.26987774529616870924e-17,
+        3.06161699786838301793e-17,
+        1.39033110312309984516e-17,
+        6.12323399573676603587e-17,
+    };
+    static const double aT[] = {
+        3.33333333333329318027e-01,
+        -1.99999999998764832476e-01,
+        1.42857142725034663711e-01,
+        -1.11111104054623557880e-01,
+        9.09088713343650656196e-02,
+        -7.69187620504482999495e-02,
+        6.66107313738753120669e-02,
+        -5.83357013379057348645e-02,
+        4.97687799461593236017e-02,
+        -3.65315727442169155270e-02,
+        1.62858201153657823623e-02,
+    };
+
+    double w, s1, s2, z;
+    unsigned int ix, sign;
+    int id;
+
+    ix = *(ULONGLONG*)&x >> 32;
+    sign = ix >> 31;
+    ix &= 0x7fffffff;
+    if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
+        if (isnan(x))
+            return x;
+        z = atanhi[3] + 7.5231638452626401e-37;
+        return sign ? -z : z;
+    }
+    if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
+        if (ix < 0x3e400000) {  /* |x| < 2^-27 */
+            if (ix < 0x00100000)
+                /* raise underflow for subnormal x */
+                fp_barrierf((float)x);
+            return x;
+        }
+        id = -1;
+    } else {
+        x = fabs(x);
+        if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
+            if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */
+                id = 0;
+                x = (2.0 * x - 1.0) / (2.0 + x);
+            } else {                /* 11/16 <= |x| < 19/16 */
+                id = 1;
+                x = (x - 1.0) / (x + 1.0);
+            }
+        } else {
+            if (ix < 0x40038000) {  /* |x| < 2.4375 */
+                id = 2;
+                x = (x - 1.5) / (1.0 + 1.5 * x);
+            } else {                /* 2.4375 <= |x| < 2^66 */
+                id = 3;
+                x = -1.0 / x;
+            }
+        }
+    }
+    /* end of argument reduction */
+    z = x * x;
+    w = z * z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+    s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
+    s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
+    if (id < 0)
+        return x - x * (s1 + s2);
+    z = atanhi[id] - (x * (s1 + s2) - atanlo[id] - x);
+    return sign ? -z : z;
 }
 
 /*********************************************************************