*
* Special cases:
* 1. (anything) ** 0 is 1
- * 2. (anything) ** 1 is itself
- * 3. (anything except 1) ** NAN is NAN, 1 ** NAN is 1
+ * 2. 1 ** (anything) is 1
+ * 3. (anything except 1) ** 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 1
+ * 9. -1 ** +-INF is 1
* 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
+ * 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
+ * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
+ * 14. -0 ** (+odd integer) is -0
+ * 15. -0 ** (-odd integer) is -INF, raise divbyzero
+ * 16. +INF ** (+anything except 0,NAN) is +INF
+ * 17. +INF ** (-anything except 0,NAN) is +0
+ * 18. -INF ** (+odd integer) is -INF
+ * 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
+ * 20. (anything) ** 1 is (anything)
+ * 21. (anything) ** -1 is 1/(anything)
+ * 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ * 23. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
-zero = 0.0,
-one = 1.0,
-two = 2.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
huge = 1.0e300,
tiny = 1.0e-300,
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
- /* y == zero: x**0 = 1 */
+ /* x**0 = 1, even if x is NaN */
if ((iy|ly) == 0)
- return one;
-
- /* x == 1: 1**y = 1, even if y is NaN */
+ return 1.0;
+ /* 1**y = 1, even if y is NaN */
if (hx == 0x3ff00000 && lx == 0)
- return one;
-
- /* y != zero: result is NaN if either arg is NaN */
+ return 1.0;
+ /* NaN if either arg is NaN */
if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0))
- return (x+0.0) + (y+0.0);
+ return x + y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
if (ly == 0) {
if (iy == 0x7ff00000) { /* y is +-inf */
if (((ix-0x3ff00000)|lx) == 0) /* (-1)**+-inf is 1 */
- return one;
+ return 1.0;
else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
- return hy >= 0 ? y : zero;
+ return hy >= 0 ? y : 0.0;
else /* (|x|<1)**+-inf = 0,inf */
- return hy < 0 ? -y : zero;
- }
- if (iy == 0x3ff00000) { /* y is +-1 */
- if (hy < 0)
- return one/x;
- return x;
+ return hy >= 0 ? 0.0 : -y;
}
+ if (iy == 0x3ff00000) /* y is +-1 */
+ return hy >= 0 ? x : 1.0/x;
if (hy == 0x40000000) /* y is 2 */
return x*x;
if (hy == 0x3fe00000) { /* y is 0.5 */
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { /* x is +-0,+-inf,+-1 */
z = ax;
if (hy < 0) /* z = (1/|x|) */
- z = one/z;
+ z = 1.0/z;
if (hx < 0) {
if (((ix-0x3ff00000)|yisint) == 0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
}
}
- /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
- n = (hx>>31)+1;
- but ANSI C says a right shift of a signed negative quantity is
- implementation defined. */
- n = ((uint32_t)hx>>31) - 1;
-
- /* (x<0)**(non-int) is NaN */
- if ((n|yisint) == 0)
- return (x-x)/(x-x);
-
- s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if ((n|(yisint-1)) == 0)
- s = -one;/* (-ve)**(odd int) */
+ s = 1.0; /* sign of result */
+ if (hx < 0) {
+ if (yisint == 0) /* (x<0)**(non-int) is NaN */
+ return (x-x)/(x-x);
+ if (yisint == 1) /* (x<0)**(odd int) */
+ s = -1.0;
+ }
/* |y| is huge */
if (iy > 0x41e00000) { /* if |y| > 2**31 */
return hy > 0 ? s*huge*huge : s*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 = ax - one; /* t has 20 trailing zeros */
+ t = ax - 1.0; /* 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;
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
+ v = 1.0/(ax+bp[k]);
ss = u*v;
s_h = ss;
SET_LOW_WORD(s_h, 0);
/* t_h=ax+bp[k] High */
- t_h = zero;
+ t_h = 0.0;
SET_HIGH_WORD(t_h, ((ix>>1)|0x20000000) + 0x00080000 + (k<<18));
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j + (0x00100000>>(k+1));
k = ((n&0x7fffffff)>>20) - 0x3ff; /* new k for n */
- t = zero;
+ t = 0.0;
SET_HIGH_WORD(t, n & ~(0x000fffff>>k));
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if (j < 0)
w = v - (z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
- r = (z*t1)/(t1-two) - (w + z*w);
- z = one - (r-z);
+ r = (z*t1)/(t1-2.0) - (w + z*w);
+ z = 1.0 - (r-z);
GET_HIGH_WORD(j, z);
j += n<<20;
if ((j>>20) <= 0) /* subnormal output */
projects / musl / blobdiff