Piotr Caban : msvcrt: Import asin from musl.

[Alexandre Julliard]

Module: wine
Branch: master
Commit: 2cb6a1780c37ad8f3a261600c3b187a192486b22
URL:    https://source.winehq.org/git/wine.git/?a=commit;h=2cb6a1780c37ad8f3a261600c3b187a192486b22

Author: Piotr Caban <piotr at codeweavers.com>
Date:   Thu Aug  6 16:59:17 2020 +0200

msvcrt: Import asin from musl.

Signed-off-by: Piotr Caban <piotr at codeweavers.com>
Signed-off-by: Alexandre Julliard <julliard at winehq.org>

---

 dlls/msvcrt/math.c | 70 ++++++++++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 66 insertions(+), 4 deletions(-)

diff --git a/dlls/msvcrt/math.c b/dlls/msvcrt/math.c
index daa94c6f7c..723c341c65 100644
--- a/dlls/msvcrt/math.c
+++ b/dlls/msvcrt/math.c
@@ -654,13 +654,75 @@ double CDECL MSVCRT_acos( double x )
 
 /*********************************************************************
  *		MSVCRT_asin (MSVCRT.@)
+ *
+ * Copied from musl: src/math/asin.c
  */
+static double asin_R(double z)
+{
+    /* coefficients for R(x^2) */
+    static const double pS0 =  1.66666666666666657415e-01,
+                 pS1 = -3.25565818622400915405e-01,
+                 pS2 =  2.01212532134862925881e-01,
+                 pS3 = -4.00555345006794114027e-02,
+                 pS4 =  7.91534994289814532176e-04,
+                 pS5 =  3.47933107596021167570e-05,
+                 qS1 = -2.40339491173441421878e+00,
+                 qS2 =  2.02094576023350569471e+00,
+                 qS3 = -6.88283971605453293030e-01,
+                 qS4 =  7.70381505559019352791e-02;
+
+    double p, q;
+    p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+    q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+    return p / q;
+}
+
 double CDECL MSVCRT_asin( double x )
 {
-  double ret = atan2(x, sqrt((1 - x) * (1 + x)));
-  if (x < -1.0 || x > 1.0 || !isfinite(x))
-    return math_error(_DOMAIN, "asin", x, 0, ret);
-  return ret;
+    static const double pio2_hi = 1.57079632679489655800e+00,
+                 pio2_lo = 6.12323399573676603587e-17;
+
+    double z, r, s;
+    unsigned int hx, ix;
+    ULONGLONG llx;
+
+    hx = *(ULONGLONG*)&x >> 32;
+    ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if (ix >= 0x3ff00000) {
+        unsigned int lx;
+        lx = *(ULONGLONG*)&x;
+        if (((ix - 0x3ff00000) | lx) == 0)
+            /* asin(1) = +-pi/2 with inexact */
+            return x * pio2_hi + 7.5231638452626401e-37;
+        if (isnan(x)) return x;
+        return math_error(_DOMAIN, "asin", x, 0, 0 / (x - x));
+    }
+    /* |x| < 0.5 */
+    if (ix < 0x3fe00000) {
+        /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+        if (ix < 0x3e500000 && ix >= 0x00100000)
+            return x;
+        return x + x * asin_R(x * x);
+    }
+    /* 1 > |x| >= 0.5 */
+    z = (1 - fabs(x)) * 0.5;
+    s = sqrt(z);
+    r = asin_R(z);
+    if (ix >= 0x3fef3333) {  /* if |x| > 0.975 */
+        x = pio2_hi - (2 * (s + s * r) - pio2_lo);
+    } else {
+        double f, c;
+        /* f+c = sqrt(z) */
+        f = s;
+        llx = (*(ULONGLONG*)&f >> 32) << 32;
+        f = *(double*)&llx;
+        c = (z - f * f) / (s + f);
+        x = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f));
+    }
+    if (hx >> 31)
+        return -x;
+    return x;
 }
 
 /*********************************************************************