bug in fdlibm e_pow.c

[J. Johnston]

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.


> 
> *** e_pow.c     1999/07/13 23:49:20     1.1
> --- e_pow.c     2002/06/13 17:06:57
> ***************
> *** 224,230 ****
>             if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5];
>         /* 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 */
>             w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
>             u = C[25]*t;        /* ivln2_h has 21 sig. bits */
>             v = t*C[26]-w*C[24];
> --- 224,230 ----
>             if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5];
>         /* now |1-x| is tiny <= 2**-20, suffice to compute
>            log(x) by x-x^2/2+x^3/3-x^4/4 */
> !           t = ax-1;           /* t has 20 trailing zeros */
>             w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
>             u = C[25]*t;        /* ivln2_h has 21 sig. bits */
>             v = t*C[26]-w*C[24];