fpowh.c
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// powh - software implementation of function "half powh(half x, half y)"
#include <stdint.h>
#include "extmath.h"
//#if !(SOFT_FOPS_HALF & EXTMATH_FPOP_MASK_)
// #error NO HW FPOWH implementation
//#endif
extern half scalbnh(half x, int n);
static const half
bp[] = {1.0H, 1.5H,},
dp_h[] = { 0.0, 5.84960938e-01H,}, /* float: 0x3f15c000 */
dp_l[] = { 0.0, 1.56322085e-06H,}, /* float: 0x35d1cfdc */
zero = 0.0H,
one = 1.0H,
two = 2.0H,
two11 = 2048.0H, /* 0x6800 */ /* float: two24 = 16777216.0, 0x4b800000 */
huge = 6.4e4H,
tiny = 6.4e-4H,
/* TODO: vvv correct constants vvv */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01H, /* 0x3f19999a */
L2 = 4.2857143283e-01H, /* 0x3edb6db7 */
L3 = 3.3333334327e-01H, /* 0x3eaaaaab */
L4 = 2.7272811532e-01H, /* 0x3e8ba305 */
L5 = 2.3066075146e-01H, /* 0x3e6c3255 */
L6 = 2.0697501302e-01H, /* 0x3e53f142 */
P1 = 1.6666667163e-01H, /* 0x3e2aaaab */
P2 = -2.7777778450e-03H, /* 0xbb360b61 */
P3 = 6.6137559770e-05H, /* 0x388ab355 */
P4 = -1.6533901999e-06H, /* 0xb5ddea0e */
P5 = 4.1381369442e-08H, /* 0x3331bb4c */
lg2 = 6.9314718246e-01H, /* 0x3f317218 */
lg2_h = 6.93145752e-01H, /* 0x3f317200 */
lg2_l = 1.42860654e-06H, /* 0x35bfbe8c */
ovt = 4.2995665694e-08H, /* -(128-log2(ovfl+.5ulp)) */
cp = 9.6179670095e-01H, /* 0x3f76384f =2/(3ln2) */
cp_h = 9.6191406250e-01H, /* 0x3f764000 =12b cp */
cp_l = -1.1736857402e-04H, /* 0xb8f623c6 =tail of cp_h */
ivln2 = 1.4426950216e+00H, /* 0x3fb8aa3b =1/ln2 */
ivln2_h = 1.4426879883e+00H, /* 0x3fb8aa00 =16b 1/ln2*/
ivln2_l = 7.0526075433e-06H; /* 0x36eca570 =1/ln2 tail*/
half powh(half x, half y)
{
half z,ax,z_h,z_l,p_h,p_l;
half y1,t1,t2,r,s,sn,t,u,v,w;
uint16_t i,j,k,yisint,n;
int16_t hx,hy,ix,iy,is;
GET_HALF_WORD(hx,x);
GET_HALF_WORD(hy,y);
ix = hx&0x7fff; iy = hy&0x7fff;
/* y==zero: x**0 = 1 */
if(iy==0) return one;
/* x==1: 1**y = 1, even if y is NaN */
if (hx==0x3C00) return one;
/* y!=zero: result is NaN if either arg is NaN */
if(ix > 0x7C00 ||
iy > 0x7C00)
return (x+0.0H)+(y+0.0H);
/* 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>=0x6800)
yisint = 2; /* even integer y */
else if(iy>=0x3C00) {
k = (iy>>10)-0xf; /* exponent */
j = iy>>(10-k);
if((j<<(10-k))==iy) yisint = 2-(j&1);
}
}
/* special value of y */
if (iy==0x7C00) { /* y is +-inf */
if (ix==0x3C00)
return one; /* (-1)**+-inf is NaN */
else if (ix > 0x3C00)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3C00) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x4000) return x*x; /* y is 2 */
if(hy==0x4020) return x*x*x; /* y is 3 */
if(hy==0x4040) { /* y is 4 */
u = x*x;
return u*u;
}
if(hy==0x3800) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return sqrth(x);
}
ax = fabsh(x);
/* special value of x */
if(ix==0x7C00||ix==0||ix==0x3C00){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3C00)|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;
}
n = ((uint16_t)hx>>15)-1;
/* (x<0)**(non-int) is NaN */
if((n|yisint)==0) return (x-x)/(x-x);
sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
/* |y| is huge */
if(iy>0x4c00) { /* if |y| > 2**27 */ /* float: 0x4d000000 */
/* over/underflow if x is not close to one */
if(ix<0x3BF7) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
if(ix>0x3C01) return (hy>0)? sn*huge*huge:sn*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)*(0.5H-t*(0.333333333333H-t*0.25H));
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
GET_HALF_WORD(is,t1);
SET_HALF_WORD(t1,is&0xfff0);
t2 = v-(t1-u);
} else {
half s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x0400) {
ax *= two11;
n -= 11;
GET_HALF_WORD(ix,ax);
}
n += ((ix)>>10)-0x0f;
j = ix & 0x03ff;
/* determine interval */
ix = j | 0x3c00; /* normalize ix */
if(j<=0x00e6)
k=0; /* |x|<sqrt(3/2) */
else if(j<0x02ed)
k=1; /* |x|<sqrt(3) */
else {
k=0;n+=1;ix -= 0x0400;
}
SET_HALF_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_HALF_WORD(is,s_h);
SET_HALF_WORD(s_h,is&0xfff0);
/* t_h=ax+bp[k] High */
is = ((ix>>1)&0xfff0)|0x2000;
SET_HALF_WORD(t_h,is+0x0200+(k<<8));
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 = 3.0H+s2+r;
GET_HALF_WORD(is,t_h);
SET_HALF_WORD(t_h,is&0xfff0);
t_l = r-((t_h-3.0H)-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_HALF_WORD(is,p_h);
SET_HALF_WORD(p_h,is&0xfff0);
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 = (half)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
GET_HALF_WORD(is,t1);
SET_HALF_WORD(t1,is&0xfff0);
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
GET_HALF_WORD(is,y);
SET_HALF_WORD(y1,is&0xfff0);
p_l = (y-y1)*t1+y*t2;
p_h = y1*t1;
z = p_l+p_h;
GET_HALF_WORD(j,z);
if (j>0x4C00) /* if z > 16 */ /* float: 0x43000000 = 128 */
return sn*huge*huge; /* overflow */
else if (j==0x4C00) { /* if z == 16 */
if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
} else if ((j&0x7fff)>0x4e40) /* z <= -25 */ /* float : 0x43160000 = 150 */
return sn*tiny*tiny; /* underflow */
else if (j==0xce40){ /* z == -25 */ /* float: 0xc3160000 = -150 */
if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fff;
k = (i>>10)-0x0f;
n = 0;
if(i>0x3800) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x0400>>(k+1));
k = ((n&0x7fff)>>10)-0x0f; /* new k for n */
SET_HALF_WORD(t,n&~(0x03ff>>k));
n = ((n&0x03ff)|0x0400)>>(23-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
GET_HALF_WORD(is,t);
SET_HALF_WORD(t,is&0xfff0);
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_HALF_WORD(j,z);
j += (n<<10);
if((j>>10)<=0) z = scalbnh(z,n); /* subnormal output */
else SET_HALF_WORD(z,j);
return sn*z;
}