From c5c81ebf59d664026ad5295ca22680daddb38c5b Mon Sep 17 00:00:00 2001
From: Sam Lantinga <slouken@libsdl.org>
Date: Mon, 15 Sep 2008 04:31:30 +0000
Subject: [PATCH] http://sources.redhat.com/ml/newlib/2002/msg00230.html

Stephen L Moshier wrote:
>
> pow(x,y) returns 0 when x is very close to -1.0 and y is very large.
> The following test program prints
>
> pow(1.0000000000000002e+00 4.5035996273704970e+15) = 2.7182818284590455e+00
> pow(-1.0000000000000002e+00 4.5035996273704970e+15) =0.0000000000000000e+00
> pow(9.9999999999999978e-01 4.5035996273704970e+15) = 3.6787944117144222e-01
> pow(-9.9999999999999978e-01 4.5035996273704970e+15) = 0.0000000000000000e+00
>
> which is incorrect for the negative arguments raised to an odd integer
> power.
>
> -----
> double pow (double, double);
>
> int
> main ()
> {
>   double x, y, z;
>
>   x = 1.0 + pow (2.0, -52.0);
>   y = 1.0 + pow (2.0, 52.0);
>   z = pow (x, y);
>   printf ("pow(%.16e %.16e) = %.16e\n", x, y, z);
>   x = -x;
>   z = pow (x, y);
>   printf ("pow(%.16e %.16e) = %.16e\n", x, y, z);
>   x = 1.0 - pow (2.0, -52.0);
>   z = pow (x, y);
>   printf ("pow(%.16e %.16e) = %.16e\n", x, y, z);
>   x = -x;
>   z = pow (x, y);
>   printf ("pow(%.16e %.16e) = %.16e\n", x, y, z);
> }
> -----
>
> Here is a patch for newlib/libm/math/epow.c:

Patch checked in and duplicated for ef_pow.c.  Thanks.

-- Jeff J.
---
 src/video/e_pow.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/video/e_pow.h b/src/video/e_pow.h
index d87348d72..62fc989ce 100644
--- a/src/video/e_pow.h
+++ b/src/video/e_pow.h
@@ -208,7 +208,7 @@ __ieee754_pow(x, y)
             return (hy > 0) ? huge * huge : tiny * tiny;
         /* now |1-x| is tiny <= 2**-20, suffice to compute
            log(x) by x-x^2/2+x^3/3-x^4/4 */
-        t = x - 1;              /* t has 20 trailing zeros */
+        t = ax - 1;             /* t has 20 trailing zeros */
         w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
         u = ivln2_h * t;        /* ivln2_h has 21 sig. bits */
         v = t * ivln2_l - w * ivln2;