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glibc/sysdeps/ieee754/flt-32/e_powf.c
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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) 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,}, | |
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ | |
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ | |
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 */ | |
lg2 = 6.9314718246e-01, /* 0x3f317218 */ | |
lg2_h = 6.93145752e-01, /* 0x3f317200 */ | |
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ | |
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ | |
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ | |
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ | |
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ | |
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ | |
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ | |
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ | |
float | |
__ieee754_powf(float x, float y) | |
{ | |
float z,ax,z_h,z_l,p_h,p_l; | |
float y1,t1,t2,r,s,t,u,v,w; | |
int32_t i,j,k,yisint,n; | |
int32_t hx,hy,ix,iy,is; | |
GET_FLOAT_WORD(hx,x); | |
GET_FLOAT_WORD(hy,y); | |
ix = hx&0x7fffffff; iy = hy&0x7fffffff; | |
/* y==zero: x**0 = 1 */ | |
if(iy==0) return one; | |
/* x==+-1 */ | |
if(x == 1.0) return one; | |
if(x == -1.0 && isinf(y)) return one; | |
/* +-NaN return x+y */ | |
if(__builtin_expect(ix > 0x7f800000 || | |
iy > 0x7f800000, 0)) | |
return x+y; | |
/* 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); | |
} | |
} | |
/* 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); | |
} | |
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(((((u_int32_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 */ | |
t = ax-1; /* t has 20 trailing zeros */ | |
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); | |
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ | |
v = t*ivln2_l-w*ivln2; | |
t1 = u+v; | |
GET_FLOAT_WORD(is,t1); | |
SET_FLOAT_WORD(t1,is&0xfffff000); | |
t2 = v-(t1-u); | |
} else { | |
float s2,s_h,s_l,t_h,t_l; | |
/* 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 s = 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]); | |
s = u*v; | |
s_h = s; | |
GET_FLOAT_WORD(is,s_h); | |
SET_FLOAT_WORD(s_h,is&0xfffff000); | |
/* t_h=ax+bp[k] High */ | |
SET_FLOAT_WORD (t_h, | |
((((ix>>1)|0x20000000)+0x00400000+(k<<21)) | |
& 0xfffff000)); | |
t_l = ax - (t_h-bp[k]); | |
s_l = v*((u-s_h*t_h)-s_h*t_l); | |
/* compute log(ax) */ | |
s2 = s*s; | |
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); | |
r += s_l*(s_h+s); | |
s2 = s_h*s_h; | |
t_h = (float)3.0+s2+r; | |
GET_FLOAT_WORD(is,t_h); | |
SET_FLOAT_WORD(t_h,is&0xfffff000); | |
t_l = r-((t_h-(float)3.0)-s2); | |
/* u+v = s*(1+...) */ | |
u = s_h*t_h; | |
v = s_l*t_h+t_l*s; | |
/* 2/(3log2)*(s+...) */ | |
p_h = u+v; | |
GET_FLOAT_WORD(is,p_h); | |
SET_FLOAT_WORD(p_h,is&0xfffff000); | |
p_l = v-(p_h-u); | |
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | |
z_l = cp_l*p_h+p_l*cp+dp_l[k]; | |
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
t = (float)n; | |
t1 = (((z_h+z_l)+dp_h[k])+t); | |
GET_FLOAT_WORD(is,t1); | |
SET_FLOAT_WORD(t1,is&0xfffff000); | |
t2 = z_l-(((t1-t)-dp_h[k])-z_h); | |
} | |
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | |
if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) | |
s = -one; /* (-ve)**(odd int) */ | |
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | |
GET_FLOAT_WORD(is,y); | |
SET_FLOAT_WORD(y1,is&0xfffff000); | |
p_l = (y-y1)*t1+y*t2; | |
p_h = y1*t1; | |
z = p_l+p_h; | |
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(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ | |
} | |
else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */ | |
return s*tiny*tiny; /* underflow */ | |
else if (__builtin_expect((u_int32_t) j==0xc3160000, 0)){/* z == -150*/ | |
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | |
} | |
/* | |
* compute 2**(p_h+p_l) | |
*/ | |
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(t,n&~(0x007fffff>>k)); | |
n = ((n&0x007fffff)|0x00800000)>>(23-k); | |
if(j<0) n = -n; | |
p_h -= t; | |
} | |
t = p_l+p_h; | |
GET_FLOAT_WORD(is,t); | |
SET_FLOAT_WORD(t,is&0xfffff000); | |
u = t*lg2_h; | |
v = (p_l-(t-p_h))*lg2+t*lg2_l; | |
z = u+v; | |
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); | |
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) |