diff options
Diffstat (limited to 'libm')
| -rw-r--r-- | libm/e_pow.c | 63 |
1 files changed, 35 insertions, 28 deletions
diff --git a/libm/e_pow.c b/libm/e_pow.c index 137f600c3..3be900389 100644 --- a/libm/e_pow.c +++ b/libm/e_pow.c @@ -21,25 +21,26 @@ * 3. Return x**y = 2**n*exp(y'*log2) * * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * 1. +-1 ** anything is 1.0 + * 2. +-1 ** +-INF is 1.0 + * 3. (anything) ** 0 is 1 + * 4. (anything) ** 1 is itself + * 5. (anything) ** NAN is NAN + * 6. NAN ** (anything except 0) is NAN + * 7. +-(|x| > 1) ** +INF is +INF + * 8. +-(|x| > 1) ** -INF is +0 + * 9. +-(|x| < 1) ** +INF is +0 + * 10 +-(|x| < 1) ** -INF is +INF + * 11. +0 ** (+anything except 0, NAN) is +0 + * 12. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 13. +0 ** (-anything except 0, NAN) is +INF + * 14. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 15. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 16. +INF ** (+anything except 0,NAN) is +INF + * 17. +INF ** (-anything except 0,NAN) is +0 + * 18. -INF ** (anything) = -0 ** (-anything) + * 19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 20. (-anything except 0 and inf) ** (non-integer) is NAN * * Accuracy: * pow(x,y) returns x**y nearly rounded. In particular @@ -99,8 +100,14 @@ double attribute_hidden __ieee754_pow(double x, double y) u_int32_t lx,ly; EXTRACT_WORDS(hx,lx,x); + /* x==1: 1**y = 1 (even if y is NaN) */ + if (hx==0x3ff00000 && lx==0) { + return x; + } + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); - ix = hx&0x7fffffff; iy = hy&0x7fffffff; + iy = hy&0x7fffffff; /* y==zero: x**0 = 1 */ if((iy|ly)==0) return one; @@ -132,13 +139,13 @@ double attribute_hidden __ieee754_pow(double x, double y) /* special value of y */ if(ly==0) { - if (iy==0x7ff00000) { /* y is +-inf */ - if(((ix-0x3ff00000)|lx)==0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ - return (hy>=0)? y: zero; - else /* (|x|<1)**-,+inf = inf,0 */ - return (hy<0)?-y: zero; + if (iy==0x7ff00000) { /* y is +-inf */ + if (((ix-0x3ff00000)|lx)==0) + return one; /* +-1**+-inf is 1 (yes, weird rule) */ + if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ + return (hy>=0) ? y : zero; + /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0) ? -y : zero; } if(iy==0x3ff00000) { /* y is +-1 */ if(hy<0) return one/x; else return x; @@ -146,7 +153,7 @@ double attribute_hidden __ieee754_pow(double x, double y) if(hy==0x40000000) return x*x; /* y is 2 */ if(hy==0x3fe00000) { /* y is 0.5 */ if(hx>=0) /* x >= +0 */ - return __ieee754_sqrt(x); + return __ieee754_sqrt(x); } } |