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/*
* ====================================================
* 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.
* ====================================================
*/
/* Based on newlib/libm/math/e_pow.c in Newlib. */
#include "amdgcnmach.h"
static const double
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 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
v64df v64df_sqrt_aux (v64df, v64di);
v64df v64df_scalbn_aux (v64df, v64si, v64di);
static v64df v64df_math_oflow (v64di sign)
{
errno = ERANGE;
return VECTOR_MERGE (VECTOR_INIT (-0x1p769),
VECTOR_INIT (0x1p769), sign) * 0x1p769;
}
static v64df v64df_math_uflow (v64di sign)
{
errno = ERANGE;
return VECTOR_MERGE (VECTOR_INIT (-0x1p-767),
VECTOR_INIT (0x1p-767), sign) * 0x1p-767;
}
static v64si v64df_issignaling_inline (v64df x)
{
v64si __mask = VECTOR_INIT (-1);
v64si ix;
GET_HIGH_WORD (ix, x, NO_COND);
/* Use IEEE-754 2008 encoding - i.e. exponent bits all 1, MSB of
significand is 0 for signalling NaN. */
return ((ix & 0x7ff00000) == 0x7ff00000) & ((ix & 0x00080000) == 0);
}
#if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv)
DEF_VD_MATH_FUNC (v64df, pow, v64df x, v64df y)
{
FUNCTION_INIT (v64df);
v64si hx, hy, lx, ly;
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hy,ly,y);
v64si ix = hx&0x7fffffff;
v64si iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 unless x is snan */
VECTOR_IF ((iy|ly)==0, cond)
VECTOR_RETURN (x + y, cond & v64df_issignaling_inline(x));
VECTOR_RETURN (VECTOR_INIT (1.0), cond);
VECTOR_ENDIF
/* x|y==NaN return NaN unless x==1 then return 1 */
VECTOR_IF ((ix > 0x7ff00000) | ((ix==0x7ff00000)&(lx!=0))
| (iy > 0x7ff00000) | ((iy==0x7ff00000)&(ly!=0)), cond)
VECTOR_RETURN (VECTOR_INIT (1.0), cond & ((hx-0x3ff00000)|lx)==0
& ~v64df_issignaling_inline(y));
VECTOR_RETURN (x + y, cond);
VECTOR_ENDIF
/* 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
*/
v64si yisint = VECTOR_INIT (0);
VECTOR_IF (hx < 0, cond)
VECTOR_IF2(iy>=0x43400000, cond2, cond)
VECTOR_COND_MOVE (yisint, VECTOR_INIT (2), cond2); /* even integer y */
VECTOR_ELSEIF2 (iy>=0x3ff00000, cond2, cond)
v64si k = (iy>>20)-0x3ff; /* exponent */
VECTOR_IF2 (k>20, cond3, cond2)
v64si j = ly>>(52-k);
VECTOR_COND_MOVE (yisint, 2-(j&1), cond3 & (j<<(52-k))==ly);
VECTOR_ELSEIF2 (ly==0, cond3, cond2)
v64si j = iy>>(20-k);
VECTOR_COND_MOVE (yisint, 2-(j&1), cond3 & (j<<(20-k))==iy);
VECTOR_ENDIF
VECTOR_ENDIF
VECTOR_ENDIF
/* special value of y */
VECTOR_IF (ly==0, cond)
VECTOR_IF2 (iy==0x7ff00000, cond2, cond) /* y is +-inf */
VECTOR_IF2 (((ix-0x3ff00000)|lx)==0, cond3, cond2)
VECTOR_RETURN (VECTOR_INIT (1.0), cond3); /* +-1**+-inf = 1 */
VECTOR_ELSEIF2 (ix >= 0x3ff00000, cond3, cond2) /* (|x|>1)**+-inf = inf,0 */
VECTOR_RETURN (y, cond3 & hy>=0);
VECTOR_RETURN (VECTOR_INIT (0.0), cond3);
VECTOR_ELSE2 (cond3, cond2) /* (|x|<1)**-,+inf = inf,0 */
VECTOR_RETURN (-y, cond3 & hy<0);
VECTOR_RETURN (VECTOR_INIT (0.0), cond3);
VECTOR_ENDIF
VECTOR_ENDIF
VECTOR_IF2 (iy==0x3ff00000, cond2, cond) /* y is +-1 */
VECTOR_RETURN (VECTOR_INIT (1.0) / x, cond2 & hy<0);
VECTOR_RETURN (x, cond2);
VECTOR_ENDIF
VECTOR_RETURN (x*x, cond & hy==0x40000000); /* y is 2 */
/* y is 0.5 */
/* x >= +0 */
VECTOR_RETURN (v64df_sqrt_aux (x, __mask), cond & (hy==0x3fe00000) & (hx>=0));
VECTOR_ENDIF
v64df ax = __builtin_gcn_fabsv(x);
/* special value of x */
VECTOR_IF (lx==0, cond)
VECTOR_IF2 ((ix==0x7ff00000)|(ix==0)|(ix==0x3ff00000), cond2, cond)
v64df z = ax; /*x is +-0,+-inf,+-1*/
VECTOR_COND_MOVE (z, VECTOR_INIT (1.0) / z, cond2 & (hy<0)); /* z = (1/|x|) */
VECTOR_IF2 (hx<0, cond3, cond2)
VECTOR_IF2 (((ix-0x3ff00000)|yisint)==0, cond4, cond3)
VECTOR_COND_MOVE (z, (z-z)/(z-z), cond4); /* (-1)**non-int is NaN */
VECTOR_ELSEIF2 (yisint==1, cond4, cond3)
VECTOR_COND_MOVE (z, -z, cond4); /* (x<0)**odd = -(|x|**odd) */
VECTOR_ENDIF
VECTOR_ENDIF
VECTOR_RETURN (z, cond2);
VECTOR_ENDIF
VECTOR_ENDIF
/* (x<0)**(non-int) is NaN */
VECTOR_RETURN ((x-x)/(x-x), ((((hx >> 31) & 1) - 1)|yisint)==0);
v64df t1, t2;
/* |y| is huge */
VECTOR_IF(iy>0x41e00000, cond) /* if |y| > 2**31 */
VECTOR_IF2 (iy>0x43f00000, cond2, cond) /* if |y| > 2**64, must o/uflow */
VECTOR_IF2 (ix<=0x3fefffff, cond3, cond2)
VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond3 & (hy<0));
VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond3);
VECTOR_ENDIF
VECTOR_IF2 (ix>=0x3ff00000, cond3, cond2)
VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond3 & (hy>0));
VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond3);
VECTOR_ENDIF
VECTOR_ENDIF
/* over/underflow if x is not close to one */
VECTOR_IF2 (ix<0x3fefffff, cond2, cond)
VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond2 & (hy<0));
VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond2);
VECTOR_ENDIF
VECTOR_IF2 (ix>0x3ff00000, cond2, cond)
VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond2 & (hy>0));
VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond2);
VECTOR_ENDIF
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
v64df t = ax-1; /* t has 20 trailing zeros */
v64df w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
v64df u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v64df v = t*ivln2_l-w*ivln2;
VECTOR_COND_MOVE (t1, u+v, cond);
SET_LOW_WORD (t1, VECTOR_INIT (0), cond);
VECTOR_COND_MOVE (t2, v-(t1-u), cond);
VECTOR_ELSE (cond)
v64si n = VECTOR_INIT (0);
/* take care subnormal number */
VECTOR_IF2 (ix<0x00100000, cond2, cond)
VECTOR_COND_MOVE (ax, ax * two53, cond2);
VECTOR_COND_MOVE (n, n - 53, cond2);
GET_HIGH_WORD (ix, ax, cond2);
VECTOR_ENDIF
n += ((ix)>>20)-0x3ff;
v64si j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
v64si k;
VECTOR_IF2 (j<=0x3988E, cond2, cond)
VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2); /* |x|<sqrt(3/2) */
VECTOR_ELSEIF2 (j<0xBB67A, cond2, cond)
VECTOR_COND_MOVE (k, VECTOR_INIT (1), cond2); /* |x|<sqrt(3) */
VECTOR_ELSE2 (cond2, cond)
VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2);
VECTOR_COND_MOVE (n, n + 1, cond2);
VECTOR_COND_MOVE (ix, ix - 0x00100000, cond2);
VECTOR_ENDIF
SET_HIGH_WORD (ax, ix, cond);
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
v64df bp_k = VECTOR_MERGE (VECTOR_INIT (bp[1]), VECTOR_INIT (bp[0]), k == 1);
v64df u = ax-bp_k; /* bp[0]=1.0, bp[1]=1.5 */
v64df v = 1.0/(ax+bp_k);
v64df s = u*v;
v64df s_h = s;
SET_LOW_WORD (s_h, VECTOR_INIT (0), cond);
/* t_h=ax+bp[k] High */
v64df t_h = VECTOR_INIT (0.0);
SET_HIGH_WORD (t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18), cond);
v64df t_l = ax - (t_h-bp_k);
v64df s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
v64df s2 = s*s;
v64df 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 = 3.0+s2+r;
SET_LOW_WORD (t_h, VECTOR_INIT (0), cond);
t_l = r-((t_h-3.0)-s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
v64df p_h = u+v;
SET_LOW_WORD (p_h, VECTOR_INIT (0), cond);
v64df p_l = v-(p_h-u);
v64df z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
v64df dp_l_k = VECTOR_MERGE (VECTOR_INIT (dp_l[1]), VECTOR_INIT (dp_l[0]), k == 1);
v64df 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 */
v64df t = __builtin_convertvector (n, v64df);
v64df dp_h_k = VECTOR_MERGE (VECTOR_INIT (dp_h[1]), VECTOR_INIT (dp_h[0]), k == 1);
VECTOR_COND_MOVE (t1, ((z_h+z_l)+dp_h_k)+t, cond);
SET_LOW_WORD (t1, VECTOR_INIT (0), cond);
VECTOR_COND_MOVE (t2, z_l-(((t1-t)-dp_h_k)-z_h), cond);
VECTOR_ENDIF
v64df s = VECTOR_INIT (1.0); /* s (sign of result -ve**odd) = -1 else = 1 */
VECTOR_COND_MOVE (s, VECTOR_INIT (-1.0), /* (-ve)**(odd int) */
((hx>>31) != 0)&(yisint == 1));
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
v64df y1 = y;
SET_LOW_WORD (y1, VECTOR_INIT (0), NO_COND);
v64df p_l = (y-y1)*t1+y*t2;
v64df p_h = y1*t1;
v64df z = p_l+p_h;
v64si i, j;
EXTRACT_WORDS(j, i, z);
VECTOR_IF (j>=0x40900000, cond) /* z >= 1024 */
/* if z > 1024 */
v64di cond_di = __builtin_convertvector (cond, v64di);
VECTOR_RETURN (v64df_math_oflow(s<0), cond & (((j-0x40900000)|i)!=0)); /* overflow */
VECTOR_RETURN (v64df_math_oflow(s<0), cond_di & (p_l+ovt>z-p_h)); /* overflow */
VECTOR_ELSEIF ((j&0x7fffffff)>=0x4090cc00, cond) /* z <= -1075 */
/* z < -1075 */
v64di cond_di = __builtin_convertvector (cond, v64di);
VECTOR_RETURN (v64df_math_uflow(s<0), cond & (((j-0xc090cc00)|i)!=0)); /* underflow */
VECTOR_RETURN (v64df_math_uflow(s<0), cond_di & (p_l<=z-p_h)); /* underflow */
VECTOR_ENDIF
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
v64si k = (i>>20)-0x3ff;
v64si n = VECTOR_INIT (0);
VECTOR_IF (i>0x3fe00000, cond) /* if |z| > 0.5, set n = [z+0.5] */
VECTOR_COND_MOVE (n, j+(0x00100000>>(k+1)), cond);
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
v64df t = VECTOR_INIT (0.0);
SET_HIGH_WORD(t, n&~(0x000fffff>>k), cond);
VECTOR_COND_MOVE (n, ((n&0x000fffff)|0x00100000)>>(20-k), cond);
VECTOR_COND_MOVE (n, -n, cond & (j<0));
VECTOR_COND_MOVE (p_h, p_h - t, cond);
VECTOR_ENDIF
v64df t = p_l+p_h;
SET_LOW_WORD(t, VECTOR_INIT (0), NO_COND);
v64df u = t*lg2_h;
v64df v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
v64df w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
v64df r = (z*t1)/(t1-two)-(w+z*w);
z = VECTOR_INIT (1.0)-(r-z);
GET_HIGH_WORD(j,z, NO_COND);
j += (n<<20);
VECTOR_IF ((j>>20)<=0, cond)
VECTOR_COND_MOVE (z, v64df_scalbn_aux (z, n, __mask), cond); /* subnormal output */
VECTOR_ELSE (cond)
SET_HIGH_WORD(z,j, cond);
VECTOR_ENDIF
VECTOR_RETURN (s*z, NO_COND);
FUNCTION_RETURN;
}
DEF_VARIANTS2 (pow, df, df)
#endif
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