math: fix acoshf on negative values

acosh(x) is invalid for x<1, acoshf tried to be clever using
signed comparisions to handle all x<2 the same way, but the
formula was wrong on large negative values.

diff --git a/src/math/acoshf.c b/src/math/acoshf.c
index 4596085..16550f1 100644 (file)
--- a/src/math/acoshf.c
+++ b/src/math/acoshf.c
@@ -3,14 +3,15 @@
 /* acosh(x) = log(x + sqrt(x*x-1)) */
 float acoshf(float x)
 {
-       union {float f; int32_t i;} u = {.f = x};
+       union {float f; uint32_t i;} u = {x};
+       uint32_t a = u.i & 0x7fffffff;
 
-       if (u.i < 0x3f800000+(1<<23))
-               /* x < 2, invalid if x < 1 or nan */
+       if (a < 0x3f800000+(1<<23))
+               /* |x| < 2, invalid if x < 1 or nan */
                /* up to 2ulp error in [1,1.125] */
                return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
-       if (u.i < 0x3f800000+(12<<23))
-               /* x < 0x1p12 */
+       if (a < 0x3f800000+(12<<23))
+               /* |x| < 0x1p12 */
                return logf(2*x - 1/(x+sqrtf(x*x-1)));
        /* x >= 0x1p12 */
        return logf(x) + 0.693147180559945309417232121458176568f;

diff --git a/src/math/acoshl.c b/src/math/acoshl.c
index de31fb7..4aa84ac 100644 (file)
--- a/src/math/acoshl.c
+++ b/src/math/acoshl.c
@@ -13,10 +13,10 @@ long double acoshl(long double x)
        int e = u.i.se & 0x7fff;
 
        if (e < 0x3fff + 1)
-               /* x < 2, invalid if x < 1 or nan */
+               /* |x| < 2, invalid if x < 1 or nan */
                return log1pl(x-1 + sqrtl((x-1)*(x-1)+2*(x-1)));
        if (e < 0x3fff + 32)
-               /* x < 0x1p32 */
+               /* |x| < 0x1p32 */
                return logl(2*x - 1/(x+sqrtl(x*x-1)));
        return logl(x) + 0.693147180559945309417232121458176568L;
 }