math: fix acoshf for negative inputs

on some negative inputs (e.g. -0x1.1e6ae8p+5) acoshf failed to return
nan. ensure that negative inputs result nan without introducing new
branches. this was tried before in

  commit 101e6012856918440b5d7474739c3fc22a8d3b85
  math: fix acoshf on negative values

but that fix was wrong. there are 3 formulas used:

  log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)))
  log(2*x - 1/(x+sqrt(x*x-1)))
  log(x) + 0.693147180559945309417232121458176568

the first fails on large negative inputs (may compute log1p(0) or
log1p(inf)), the second one fails on some mid range or large negative
inputs (may compute log(large) or log(inf)) and the last one fails on
-0 (returns -inf).

diff --git a/src/math/acoshf.c b/src/math/acoshf.c
index 8a4ec4d..b773d48 100644 (file)
--- a/src/math/acoshf.c
+++ b/src/math/acoshf.c
@@ -15,12 +15,12 @@ float acoshf(float x)
        uint32_t a = u.i & 0x7fffffff;
 
        if (a < 0x3f800000+(1<<23))
-               /* |x| < 2, invalid if x < 1 or nan */
+               /* |x| < 2, invalid if x < 1 */
                /* up to 2ulp error in [1,1.125] */
                return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
-       if (a < 0x3f800000+(12<<23))
-               /* |x| < 0x1p12 */
+       if (u.i < 0x3f800000+(12<<23))
+               /* 2 <= x < 0x1p12 */
                return logf(2*x - 1/(x+sqrtf(x*x-1)));
-       /* x >= 0x1p12 */
+       /* x >= 0x1p12 or x <= -2 or nan */
        return logf(x) + 0.693147180559945309417232121458176568f;
 }