math: fix atanh (overflow and underflow issues)

in atanh exception handling was left to the called log functions,
but the argument to those functions could underflow or overflow.

use double_t and float_t to avoid some useless stores on x86

diff --git a/src/math/atanh.c b/src/math/atanh.c
index 84a84c69278b7ea8350b36292adb2ce9febab12b..63a035d7063ae2d5df2c31728e10e5d471209c79 100644 (file)
--- a/src/math/atanh.c
+++ b/src/math/atanh.c
@@ -6,16 +6,24 @@ double atanh(double x)
        union {double f; uint64_t i;} u = {.f = x};
        unsigned e = u.i >> 52 & 0x7ff;
        unsigned s = u.i >> 63;
+       double_t y;
 
        /* |x| */
        u.i &= (uint64_t)-1/2;
-       x = u.f;
+       y = u.f;
 
        if (e < 0x3ff - 1) {
-               /* |x| < 0.5, up to 1.7ulp error */
-               x = 0.5*log1p(2*x + 2*x*x/(1-x));
+               if (e < 0x3ff - 32) {
+                       /* handle underflow */
+                       if (e == 0)
+                               FORCE_EVAL((float)y);
+               } else {
+                       /* |x| < 0.5, up to 1.7ulp error */
+                       y = 0.5*log1p(2*y + 2*y*y/(1-y));
+               }
        } else {
-               x = 0.5*log1p(2*x/(1-x));
+               /* avoid overflow */
+               y = 0.5*log1p(2*(y/(1-y)));
        }
-       return s ? -x : x;
+       return s ? -y : y;
 }

diff --git a/src/math/atanhf.c b/src/math/atanhf.c
index ca106efcbcba23f1d7219fb787567d315a206644..65f07c0f4f26e302f98ee4cc75b471c4204ee829 100644 (file)
--- a/src/math/atanhf.c
+++ b/src/math/atanhf.c
@@ -5,16 +5,24 @@ float atanhf(float x)
 {
        union {float f; uint32_t i;} u = {.f = x};
        unsigned s = u.i >> 31;
+       float_t y;
 
        /* |x| */
        u.i &= 0x7fffffff;
-       x = u.f;
+       y = u.f;
 
        if (u.i < 0x3f800000 - (1<<23)) {
-               /* |x| < 0.5, up to 1.7ulp error */
-               x = 0.5f*log1pf(2*x + 2*x*x/(1-x));
+               if (u.i < 0x3f800000 - (32<<23)) {
+                       /* handle underflow */
+                       if (u.i < (1<<23))
+                               FORCE_EVAL((float)(y*y));
+               } else {
+                       /* |x| < 0.5, up to 1.7ulp error */
+                       y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
+               }
        } else {
-               x = 0.5f*log1pf(2*x/(1-x));
+               /* avoid overflow */
+               y = 0.5f*log1pf(2*(y/(1-y)));
        }
-       return s ? -x : x;
+       return s ? -y : y;
 }

diff --git a/src/math/atanhl.c b/src/math/atanhl.c
index 72a1e345b88e383824267aefb0e7280e915debc9..f63d60b153faec6881f5ecc7007e5d2a418adbe1 100644 (file)
--- a/src/math/atanhl.c
+++ b/src/math/atanhl.c
@@ -17,11 +17,18 @@ long double atanhl(long double x)
        u.i.se = e;
        x = u.f;
 
-       if (e < 0x3fff - 1) {
-               /* |x| < 0.5, up to 1.7ulp error */
-               x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+       if (e < 0x3ff - 1) {
+               if (e < 0x3ff - LDBL_MANT_DIG/2) {
+                       /* handle underflow */
+                       if (e == 0)
+                               FORCE_EVAL((float)x);
+               } else {
+                       /* |x| < 0.5, up to 1.7ulp error */
+                       x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+               }
        } else {
-               x = 0.5*log1pl(2*x/(1-x));
+               /* avoid overflow */
+               x = 0.5*log1pl(2*(x/(1-x)));
        }
        return s ? -x : x;
 }