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/* e_powf.c -- float version of e_pow.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/* Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <math.h>
#include <math_private.h>
static const float huge = 1.0e+30, tiny = 1.0e-30;
static const float
bp[] = {1.0, 1.5,},
zero = 0.0,
one = 1.0,
two = 2.0,
two24 = 16777216.0, /* 0x4b800000 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01, /* 0x3f19999a */
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
L6 = 2.0697501302e-01, /* 0x3e53f142 */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08, /* 0x3331bb4c */
ovt = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
static const double
dp[] = { 0.0, 0x1.2b803473f7ad1p-1, }, /* log2(1.5) */
lg2 = M_LN2,
cp = 2.0/3.0/M_LN2,
invln2 = 1.0/M_LN2;
float
__ieee754_powf(float x, float y)
{
float z, ax, s;
double d1, d2;
int32_t i,j,k,yisint,n;
int32_t hx,hy,ix,iy;
GET_FLOAT_WORD(hy,y);
iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if(iy==0 && !issignaling (x)) return one;
/* x==+-1 */
if(x == 1.0 && !issignaling (y)) return one;
if(x == -1.0 && isinf(y)) return one;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
/* +-NaN return x+y */
if(__builtin_expect(ix > 0x7f800000 ||
iy > 0x7f800000, 0))
return x+y;
/* special value of y */
if (__builtin_expect(iy==0x7f800000, 0)) { /* y is +-inf */
if (ix==0x3f800000)
return y - y; /* inf**+-1 is NaN */
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3f800000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3f000000) { /* y is 0.5 */
if(__builtin_expect(hx>=0, 1)) /* x >= +0 */
return __ieee754_sqrtf(x);
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x4b800000) yisint = 2; /* even integer y */
else if(iy>=0x3f800000) {
k = (iy>>23)-0x7f; /* exponent */
j = iy>>(23-k);
if((j<<(23-k))==iy) yisint = 2-(j&1);
}
}
ax = fabsf(x);
/* special value of x */
if(__builtin_expect(ix==0x7f800000||ix==0||ix==0x3f800000, 0)){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3f800000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
/* (x<0)**(non-int) is NaN */
if(__builtin_expect(((((uint32_t)hx>>31)-1)|yisint)==0, 0))
return (x-x)/(x-x);
/* |y| is huge */
if(__builtin_expect(iy>0x4d000000, 0)) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3f800007) 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 */
d2 = ax-1; /* d2 has 20 trailing zeros. */
d2 = d2 * invln2 -
(d2 * d2) * (0.5 - d2 * (0.333333333333 - d2 * 0.25)) * invln2;
} else {
/* Avoid internal underflow for tiny y. The exact value
of y does not matter if |y| <= 2**-32. */
if (iy < 0x2f800000)
SET_FLOAT_WORD (y, (hy & 0x80000000) | 0x2f800000);
n = 0;
/* take care subnormal number */
if(ix<0x00800000)
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
n += ((ix)>>23)-0x7f;
j = ix&0x007fffff;
/* determine interval */
ix = j|0x3f800000; /* normalize ix */
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00800000;}
SET_FLOAT_WORD(ax,ix);
/* compute d1 = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
d1 = (ax-(double)bp[k])/(ax+(double)bp[k]);
/* compute d2 = log(ax) */
d2 = d1 * d1;
d2 = 3.0 + d2 + d2*d2*(L1+d2*(L2+d2*(L3+d2*(L4+d2*(L5+d2*L6)))));
/* 2/(3log2)*(d2+...) */
d2 = d1*d2*cp;
/* log2(ax) = (d2+..)*2/(3*log2) */
d2 = d2+dp[k]+(double)n;
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if(((((uint32_t)hx>>31)-1)|(yisint-1))==0)
s = -one; /* (-ve)**(odd int) */
/* compute y * d2 */
d1 = y * d2;
z = d1;
GET_FLOAT_WORD(j,z);
if (__builtin_expect(j>0x43000000, 0)) /* if z > 128 */
return s*huge*huge; /* overflow */
else if (__builtin_expect(j==0x43000000, 0)) { /* if z == 128 */
if(ovt>(z-d1)) return s*huge*huge; /* overflow */
}
else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */
return s*tiny*tiny; /* underflow */
else if (__builtin_expect((uint32_t) j==0xc3160000, 0)){/* z == -150*/
if(0.0<=(z-d1)) return s*tiny*tiny; /* underflow */
}
/*
* compute 2**d1
*/
i = j&0x7fffffff;
k = (i>>23)-0x7f;
n = 0;
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00800000>>(k+1));
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
SET_FLOAT_WORD(z,n&~(0x007fffff>>k));
n = ((n&0x007fffff)|0x00800000)>>(23-k);
if(j<0) n = -n;
d1 -= z;
}
d1 = d1 * lg2;
d2 = d1*d1;
d2 = d1 - d2*(P1+d2*(P2+d2*(P3+d2*(P4+d2*P5))));
d2 = (d1*d2)/(d2-two);
z = one - (d2-d1);
GET_FLOAT_WORD(j,z);
j += (n<<23);
if((j>>23)<=0) /* subnormal output */
{
z = __scalbnf (z, n);
float force_underflow = z * z;
math_force_eval (force_underflow);
}
else SET_FLOAT_WORD(z,j);
return s*z;
}
strong_alias (__ieee754_powf, __powf_finite)
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