newlib/libm/machine/amdgcn/v64df_pow.c

   1 /*
   2  * Copyright 2023 Siemens
   3  *
   4  * The authors hereby grant permission to use, copy, modify, distribute,
   5  * and license this software and its documentation for any purpose, provided
   6  * that existing copyright notices are retained in all copies and that this
   7  * notice is included verbatim in any distributions.  No written agreement,
   8  * license, or royalty fee is required for any of the authorized uses.
   9  * Modifications to this software may be copyrighted by their authors
  10  * and need not follow the licensing terms described here, provided that
  11  * the new terms are clearly indicated on the first page of each file where
  12  * they apply.
  13  */
  14
  15 /*
  16  * ====================================================
  17  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  18  *
  19  * Developed at SunPro, a Sun Microsystems, Inc. business.
  20  * Permission to use, copy, modify, and distribute this
  21  * software is freely granted, provided that this notice
  22  * is preserved.
  23  * ====================================================
  24  */
  25
  26 /* Based on newlib/libm/math/e_pow.c in Newlib.  */
  27
  28 #include "amdgcnmach.h"
  29
  30 static const double
  31 bp[] = {1.0, 1.5,},
  32 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
  33 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
  34 zero    =  0.0,
  35 one     =  1.0,
  36 two     =  2.0,
  37 two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
  38         /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
  39 L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
  40 L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
  41 L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
  42 L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
  43 L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
  44 L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
  45 P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
  46 P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
  47 P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
  48 P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
  49 P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
  50 lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  51 lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
  52 lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
  53 ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
  54 cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
  55 cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
  56 cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
  57 ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
  58 ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
  59 ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
  60
  61 v64df v64df_sqrt_aux (v64df, v64di);
  62 v64df v64df_scalbn_aux (v64df, v64si, v64di);
  63
  64 static v64df v64df_math_oflow (v64di sign)
  65 {
  66   errno = ERANGE;
  67   return VECTOR_MERGE (VECTOR_INIT (-0x1p769),
  68                        VECTOR_INIT (0x1p769), sign) * 0x1p769;
  69 }
  70
  71 static v64df v64df_math_uflow (v64di sign)
  72 {
  73   errno = ERANGE;
  74   return VECTOR_MERGE (VECTOR_INIT (-0x1p-767),
  75                        VECTOR_INIT (0x1p-767), sign) * 0x1p-767;
  76 }
  77
  78 static v64si v64df_issignaling_inline (v64df x)
  79 {
  80   v64si __mask = VECTOR_INIT (-1);
  81   v64si ix;
  82   GET_HIGH_WORD (ix, x, NO_COND);
  83   /* Use IEEE-754 2008 encoding - i.e. exponent bits all 1, MSB of
  84      significand is 0 for signalling NaN.  */
  85   return ((ix & 0x7ff00000) == 0x7ff00000) & ((ix & 0x00080000) == 0);
  86 }
  87
  88 #if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv)
  89
  90 DEF_VD_MATH_FUNC (v64df, pow, v64df x, v64df y)
  91 {
  92   FUNCTION_INIT (v64df);
  93
  94   v64si hx, hy, lx, ly;
  95   EXTRACT_WORDS(hx,lx,x);
  96   EXTRACT_WORDS(hy,ly,y);
  97   v64si ix = hx&0x7fffffff;
  98   v64si iy = hy&0x7fffffff;
  99
 100   /* y==zero: x**0 = 1 unless x is snan */
 101   VECTOR_IF ((iy|ly)==0, cond)
 102     VECTOR_RETURN (x + y, cond & v64df_issignaling_inline(x));
 103     VECTOR_RETURN (VECTOR_INIT (1.0), cond);
 104   VECTOR_ENDIF
 105
 106   /* x|y==NaN return NaN unless x==1 then return 1 */
 107   VECTOR_IF ((ix > 0x7ff00000) | ((ix==0x7ff00000)&(lx!=0))
 108              | (iy > 0x7ff00000) | ((iy==0x7ff00000)&(ly!=0)), cond)
 109     VECTOR_RETURN (VECTOR_INIT (1.0), cond & ((hx-0x3ff00000)|lx)==0
 110                                       & ~v64df_issignaling_inline(y));
 111     VECTOR_RETURN (x + y, cond);
 112   VECTOR_ENDIF
 113
 114   /* determine if y is an odd int when x < 0
 115     * yisint = 0        ... y is not an integer
 116     * yisint = 1        ... y is an odd int
 117     * yisint = 2        ... y is an even int
 118     */
 119   v64si yisint = VECTOR_INIT (0);
 120
 121   VECTOR_IF (hx < 0, cond)
 122     VECTOR_IF2(iy>=0x43400000, cond2, cond)
 123       VECTOR_COND_MOVE (yisint, VECTOR_INIT (2), cond2); /* even integer y */
 124     VECTOR_ELSEIF2 (iy>=0x3ff00000, cond2, cond)
 125       v64si k = (iy>>20)-0x3ff;    /* exponent */
 126       VECTOR_IF2 (k>20, cond3, cond2)
 127         v64si j = ly>>(52-k);
 128         VECTOR_COND_MOVE (yisint, 2-(j&1), cond3 & (j<<(52-k))==ly);
 129       VECTOR_ELSEIF2 (ly==0, cond3, cond2)
 130         v64si j = iy>>(20-k);
 131         VECTOR_COND_MOVE (yisint, 2-(j&1), cond3 & (j<<(20-k))==iy);
 132       VECTOR_ENDIF
 133     VECTOR_ENDIF
 134   VECTOR_ENDIF
 135
 136   /* special value of y */
 137         VECTOR_IF (ly==0, cond)
 138     VECTOR_IF2 (iy==0x7ff00000, cond2, cond)    /* y is +-inf */
 139       VECTOR_IF2 (((ix-0x3ff00000)|lx)==0, cond3, cond2)
 140         VECTOR_RETURN (VECTOR_INIT (1.0), cond3);               /* +-1**+-inf = 1 */
 141       VECTOR_ELSEIF2 (ix >= 0x3ff00000, cond3, cond2) /* (|x|>1)**+-inf = inf,0 */
 142         VECTOR_RETURN (y, cond3 & hy>=0);
 143         VECTOR_RETURN (VECTOR_INIT (0.0), cond3);
 144       VECTOR_ELSE2 (cond3, cond2) /* (|x|<1)**-,+inf = inf,0 */
 145         VECTOR_RETURN (-y, cond3 & hy<0);
 146         VECTOR_RETURN (VECTOR_INIT (0.0), cond3);
 147       VECTOR_ENDIF
 148     VECTOR_ENDIF
 149     VECTOR_IF2 (iy==0x3ff00000, cond2, cond)  /* y is  +-1 */
 150       VECTOR_RETURN (VECTOR_INIT (1.0) / x, cond2 & hy<0);
 151                   VECTOR_RETURN (x, cond2);
 152     VECTOR_ENDIF
 153     VECTOR_RETURN (x*x, cond & hy==0x40000000); /* y is  2 */
 154     /* y is  0.5 */
 155     /* x >= +0 */
 156     VECTOR_RETURN (v64df_sqrt_aux (x, __mask), cond & (hy==0x3fe00000) & (hx>=0));
 157   VECTOR_ENDIF
 158
 159   v64df ax = __builtin_gcn_fabsv(x);
 160     /* special value of x */
 161   VECTOR_IF (lx==0, cond)
 162     VECTOR_IF2 ((ix==0x7ff00000)|(ix==0)|(ix==0x3ff00000), cond2, cond)
 163       v64df z = ax;                     /*x is +-0,+-inf,+-1*/
 164       VECTOR_COND_MOVE (z, VECTOR_INIT (1.0) / z, cond2 & (hy<0));  /* z = (1/|x|) */
 165       VECTOR_IF2 (hx<0, cond3, cond2)
 166         VECTOR_IF2 (((ix-0x3ff00000)|yisint)==0, cond4, cond3)
 167           VECTOR_COND_MOVE (z, (z-z)/(z-z), cond4); /* (-1)**non-int is NaN */
 168         VECTOR_ELSEIF2 (yisint==1, cond4, cond3)
 169           VECTOR_COND_MOVE (z, -z, cond4); /* (x<0)**odd = -(|x|**odd) */
 170         VECTOR_ENDIF
 171       VECTOR_ENDIF
 172       VECTOR_RETURN (z, cond2);
 173     VECTOR_ENDIF
 174   VECTOR_ENDIF
 175
 176   /* (x<0)**(non-int) is NaN */
 177   VECTOR_RETURN ((x-x)/(x-x), ((((hx >> 31) & 1) - 1)|yisint)==0);
 178
 179   v64df t1, t2;
 180
 181     /* |y| is huge */
 182   VECTOR_IF(iy>0x41e00000, cond) /* if |y| > 2**31 */
 183     VECTOR_IF2 (iy>0x43f00000, cond2, cond)     /* if |y| > 2**64, must o/uflow */
 184       VECTOR_IF2 (ix<=0x3fefffff, cond3, cond2)
 185         VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond3 & (hy<0));
 186         VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond3);
 187       VECTOR_ENDIF
 188       VECTOR_IF2 (ix>=0x3ff00000, cond3, cond2)
 189         VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond3 & (hy>0));
 190         VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond3);
 191       VECTOR_ENDIF
 192     VECTOR_ENDIF
 193     /* over/underflow if x is not close to one */
 194     VECTOR_IF2 (ix<0x3fefffff, cond2, cond)
 195       VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond2 & (hy<0));
 196       VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond2);
 197     VECTOR_ENDIF
 198     VECTOR_IF2 (ix>0x3ff00000, cond2, cond)
 199       VECTOR_RETURN (v64df_math_oflow (VECTOR_INIT (0L)), cond2 & (hy>0));
 200       VECTOR_RETURN (v64df_math_uflow (VECTOR_INIT (0L)), cond2);
 201     VECTOR_ENDIF
 202     /* now |1-x| is tiny <= 2**-20, suffice to compute
 203        log(x) by x-x^2/2+x^3/3-x^4/4 */
 204     v64df t = ax-1;             /* t has 20 trailing zeros */
 205     v64df w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
 206     v64df u = ivln2_h*t;        /* ivln2_h has 21 sig. bits */
 207     v64df v = t*ivln2_l-w*ivln2;
 208     VECTOR_COND_MOVE (t1, u+v, cond);
 209     SET_LOW_WORD (t1, VECTOR_INIT (0), cond);
 210     VECTOR_COND_MOVE (t2, v-(t1-u), cond);
 211   VECTOR_ELSE (cond)
 212     v64si n = VECTOR_INIT (0);
 213     /* take care subnormal number */
 214     VECTOR_IF2 (ix<0x00100000, cond2, cond)
 215       VECTOR_COND_MOVE (ax, ax * two53, cond2);
 216       VECTOR_COND_MOVE (n, n - 53, cond2);
 217       GET_HIGH_WORD (ix, ax, cond2);
 218     VECTOR_ENDIF
 219     n  += ((ix)>>20)-0x3ff;
 220     v64si j  = ix&0x000fffff;
 221     /* determine interval */
 222     ix = j|0x3ff00000;          /* normalize ix */
 223     v64si k;
 224     VECTOR_IF2 (j<=0x3988E, cond2, cond)
 225       VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2); /* |x|<sqrt(3/2) */
 226     VECTOR_ELSEIF2 (j<0xBB67A, cond2, cond)
 227       VECTOR_COND_MOVE (k, VECTOR_INIT (1), cond2); /* |x|<sqrt(3)   */
 228     VECTOR_ELSE2 (cond2, cond)
 229       VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2);
 230       VECTOR_COND_MOVE (n, n + 1, cond2);
 231       VECTOR_COND_MOVE (ix, ix - 0x00100000, cond2);
 232     VECTOR_ENDIF
 233     SET_HIGH_WORD (ax, ix, cond);
 234
 235     /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
 236     v64df bp_k = VECTOR_MERGE (VECTOR_INIT (bp[1]), VECTOR_INIT (bp[0]), k == 1);
 237     v64df u = ax-bp_k;          /* bp[0]=1.0, bp[1]=1.5 */
 238     v64df v = 1.0/(ax+bp_k);
 239     v64df s = u*v;
 240     v64df s_h = s;
 241     SET_LOW_WORD (s_h, VECTOR_INIT (0), cond);
 242     /* t_h=ax+bp[k] High */
 243     v64df t_h = VECTOR_INIT (0.0);
 244     SET_HIGH_WORD (t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18), cond);
 245     v64df t_l = ax - (t_h-bp_k);
 246     v64df s_l = v*((u-s_h*t_h)-s_h*t_l);
 247     /* compute log(ax) */
 248     v64df s2 = s*s;
 249     v64df r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 250     r += s_l*(s_h+s);
 251     s2  = s_h*s_h;
 252     t_h = 3.0+s2+r;
 253     SET_LOW_WORD (t_h, VECTOR_INIT (0), cond);
 254     t_l = r-((t_h-3.0)-s2);
 255     /* u+v = s*(1+...) */
 256     u = s_h*t_h;
 257     v = s_l*t_h+t_l*s;
 258     /* 2/(3log2)*(s+...) */
 259     v64df p_h = u+v;
 260     SET_LOW_WORD (p_h, VECTOR_INIT (0), cond);
 261     v64df p_l = v-(p_h-u);
 262     v64df z_h = cp_h*p_h;               /* cp_h+cp_l = 2/(3*log2) */
 263     v64df dp_l_k = VECTOR_MERGE (VECTOR_INIT (dp_l[1]), VECTOR_INIT (dp_l[0]), k == 1);
 264     v64df z_l = cp_l*p_h+p_l*cp+dp_l_k;
 265     /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 266     v64df t = __builtin_convertvector (n, v64df);
 267     v64df dp_h_k = VECTOR_MERGE (VECTOR_INIT (dp_h[1]), VECTOR_INIT (dp_h[0]), k == 1);
 268     VECTOR_COND_MOVE (t1, ((z_h+z_l)+dp_h_k)+t, cond);
 269     SET_LOW_WORD (t1, VECTOR_INIT (0), cond);
 270     VECTOR_COND_MOVE (t2, z_l-(((t1-t)-dp_h_k)-z_h), cond);
 271   VECTOR_ENDIF
 272
 273   v64df s = VECTOR_INIT (1.0); /* s (sign of result -ve**odd) = -1 else = 1 */
 274   VECTOR_COND_MOVE (s, VECTOR_INIT (-1.0),  /* (-ve)**(odd int) */
 275                     ((hx>>31) != 0)&(yisint == 1));
 276
 277   /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 278   v64df y1 = y;
 279   SET_LOW_WORD (y1, VECTOR_INIT (0), NO_COND);
 280   v64df p_l = (y-y1)*t1+y*t2;
 281   v64df p_h = y1*t1;
 282   v64df z = p_l+p_h;
 283   v64si i, j;
 284   EXTRACT_WORDS(j, i, z);
 285   VECTOR_IF (j>=0x40900000, cond) /* z >= 1024 */
 286     /* if z > 1024 */
 287     v64di cond_di = __builtin_convertvector (cond, v64di);
 288     VECTOR_RETURN (v64df_math_oflow(s<0), cond & (((j-0x40900000)|i)!=0)); /* overflow */
 289     VECTOR_RETURN (v64df_math_oflow(s<0), cond_di & (p_l+ovt>z-p_h));   /* overflow */
 290   VECTOR_ELSEIF ((j&0x7fffffff)>=0x4090cc00, cond)  /* z <= -1075 */
 291     /* z < -1075 */
 292     v64di cond_di = __builtin_convertvector (cond, v64di);
 293     VECTOR_RETURN (v64df_math_uflow(s<0), cond & (((j-0xc090cc00)|i)!=0));  /* underflow */
 294     VECTOR_RETURN (v64df_math_uflow(s<0), cond_di & (p_l<=z-p_h)); /* underflow */
 295   VECTOR_ENDIF
 296
 297   /*
 298    * compute 2**(p_h+p_l)
 299    */
 300   i = j&0x7fffffff;
 301   v64si k = (i>>20)-0x3ff;
 302   v64si n = VECTOR_INIT (0);
 303   VECTOR_IF (i>0x3fe00000, cond)  /* if |z| > 0.5, set n = [z+0.5] */
 304     VECTOR_COND_MOVE (n, j+(0x00100000>>(k+1)), cond);
 305     k = ((n&0x7fffffff)>>20)-0x3ff;     /* new k for n */
 306     v64df t = VECTOR_INIT (0.0);
 307     SET_HIGH_WORD(t, n&~(0x000fffff>>k), cond);
 308     VECTOR_COND_MOVE (n, ((n&0x000fffff)|0x00100000)>>(20-k), cond);
 309     VECTOR_COND_MOVE (n, -n, cond & (j<0));
 310     VECTOR_COND_MOVE (p_h, p_h - t, cond);
 311   VECTOR_ENDIF
 312   v64df t = p_l+p_h;
 313   SET_LOW_WORD(t, VECTOR_INIT (0), NO_COND);
 314   v64df u = t*lg2_h;
 315   v64df v = (p_l-(t-p_h))*lg2+t*lg2_l;
 316   z = u+v;
 317   v64df w = v-(z-u);
 318   t  = z*z;
 319   t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 320   v64df r  = (z*t1)/(t1-two)-(w+z*w);
 321   z  = VECTOR_INIT (1.0)-(r-z);
 322   GET_HIGH_WORD(j,z, NO_COND);
 323   j += (n<<20);
 324   VECTOR_IF ((j>>20)<=0, cond)
 325     VECTOR_COND_MOVE (z, v64df_scalbn_aux (z, n, __mask), cond); /* subnormal output */
 326         VECTOR_ELSE (cond)
 327     SET_HIGH_WORD(z,j, cond);
 328   VECTOR_ENDIF
 329   VECTOR_RETURN (s*z, NO_COND);
 330
 331   FUNCTION_RETURN;
 332 }
 333
 334 DEF_VARIANTS2 (pow, df, df)
 335
 336 #endif