newlib/libm/machine/amdgcn/v64df_lgamma_r.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
  27 /* Based on newlib/libm/math/er_lgamma.c in Newlib.  */
  28
  29 #include "amdgcnmach.h"
  30
  31 static const double two52=  4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
  32 half=  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  33 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  34 pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  35 a0  =  7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
  36 a1  =  3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
  37 a2  =  6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
  38 a3  =  2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
  39 a4  =  7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
  40 a5  =  2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
  41 a6  =  1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
  42 a7  =  5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
  43 a8  =  2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
  44 a9  =  1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
  45 a10 =  2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
  46 a11 =  4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
  47 tc  =  1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
  48 tf  = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
  49 /* tt = -(tail of tf) */
  50 tt  = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
  51 t0  =  4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
  52 t1  = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
  53 t2  =  6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
  54 t3  = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
  55 t4  =  1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
  56 t5  = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
  57 t6  =  6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
  58 t7  = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
  59 t8  =  2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
  60 t9  = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
  61 t10 =  8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
  62 t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
  63 t12 =  3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
  64 t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
  65 t14 =  3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
  66 u0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
  67 u1  =  6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
  68 u2  =  1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
  69 u3  =  9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
  70 u4  =  2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
  71 u5  =  1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
  72 v1  =  2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
  73 v2  =  2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
  74 v3  =  7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
  75 v4  =  1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
  76 v5  =  3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
  77 s0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
  78 s1  =  2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
  79 s2  =  3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
  80 s3  =  1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
  81 s4  =  2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
  82 s5  =  1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
  83 s6  =  3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
  84 r1  =  1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
  85 r2  =  7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
  86 r3  =  1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
  87 r4  =  1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
  88 r5  =  7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
  89 r6  =  7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
  90 w0  =  4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
  91 w1  =  8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
  92 w2  = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
  93 w3  =  7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
  94 w4  = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
  95 w5  =  8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
  96 w6  = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
  97
  98 static const double zero=  0.00000000000000000000e+00;
  99
 100 v64df v64df_cos_aux (v64df x, v64di __mask);
 101 v64df v64df_log_aux (v64df x, v64di __mask);
 102 v64df v64df_sin_aux (v64df x, v64di __mask);
 103
 104 #if defined (__has_builtin) \
 105         && __has_builtin (__builtin_gcn_floorv) \
 106         && __has_builtin (__builtin_gcn_fabsv)
 107
 108 static v64df
 109 v64df_sin_pi (v64df x)
 110 {
 111   // Explicitly create mask for internal function.
 112   v64di __mask = VECTOR_INIT (-1L);
 113   FUNCTION_INIT (v64df);
 114
 115   v64df y, z;
 116   v64si n, ix;
 117
 118   GET_HIGH_WORD (ix, x, NO_COND);
 119   ix &= 0x7fffffff;
 120
 121   VECTOR_IF (ix < 0x3fd00000, cond)
 122     VECTOR_RETURN (v64df_sin_aux (pi * x, __mask), cond);
 123   VECTOR_ENDIF
 124   y = -x; /* x is assume negative */
 125
 126   /*
 127    * argument reduction, make sure inexact flag not raised if input
 128    * is an integer
 129    */
 130   z = __builtin_gcn_floorv (y);
 131   VECTOR_IF (z != y, cond)
 132     /* inexact anyway */
 133     VECTOR_COND_MOVE(y, y * 0.5, cond);
 134     VECTOR_COND_MOVE(y, 2.0 * (y - __builtin_gcn_floorv (y)), cond); /* y = |x| mod 2.0 */
 135     VECTOR_COND_MOVE(n, __builtin_convertvector(y * 4.0, v64si), cond);
 136   VECTOR_ELSE (cond)
 137     VECTOR_IF2 (__builtin_convertvector(ix >= 0x43400000, v64di), cond2, cond)
 138       VECTOR_COND_MOVE(y, VECTOR_INIT(zero), cond2);
 139       VECTOR_COND_MOVE(n, VECTOR_INIT(0), cond2); /* y must be even */
 140     VECTOR_ELSE2 (cond2, cond)
 141       VECTOR_COND_MOVE(z, y + two52 /* exact */, cond2 & __builtin_convertvector(ix < 0x43300000, v64di));
 142       GET_LOW_WORD (n, z, cond2);
 143       VECTOR_COND_MOVE(n, n & 1, cond2);
 144       VECTOR_COND_MOVE(y, __builtin_convertvector(n, v64df), cond2);
 145       VECTOR_COND_MOVE(n, n << 2, cond2);
 146     VECTOR_ENDIF
 147   VECTOR_ENDIF
 148
 149   VECTOR_IF (n == 0, cond)
 150     VECTOR_COND_MOVE(y, v64df_sin_aux (pi * y, __mask), cond);
 151   VECTOR_ELSEIF (n == 1 | n == 2, cond)
 152     VECTOR_COND_MOVE(y, v64df_cos_aux (pi * (0.5 - y), __mask), cond);
 153   VECTOR_ELSEIF (n == 3 | n == 4, cond)
 154     VECTOR_COND_MOVE(y, v64df_sin_aux (pi * (VECTOR_INIT(one) - y), __mask), cond);
 155   VECTOR_ELSEIF (n == 5 | n == 6, cond)
 156     VECTOR_COND_MOVE(y, -v64df_cos_aux (pi * (y - 1.5), __mask), cond);
 157   VECTOR_ELSE (cond)
 158     VECTOR_COND_MOVE(y, v64df_sin_aux (pi * (y - 2.0), __mask), cond);
 159   VECTOR_ENDIF
 160
 161   VECTOR_RETURN(-y, NO_COND);
 162   FUNCTION_RETURN;
 163 }
 164
 165 DEF_VD_MATH_FUNC (v64df, lgamma_r, v64df x, v64si *signgamp)
 166 {
 167   FUNCTION_INIT (v64df);
 168
 169   v64df t,y,z,nadj = VECTOR_INIT(0.0),p,p1,p2,p3,q,r,w;
 170   v64si i,hx,lx,ix;
 171
 172   EXTRACT_WORDS(hx,lx,x);
 173
 174   /* purge off +-inf, NaN, +-0, and negative arguments */
 175   *signgamp = VECTOR_INIT(1);
 176   ix = hx&0x7fffffff;
 177   VECTOR_IF(ix>=0x7ff00000, cond)
 178     VECTOR_RETURN (x*x, cond);
 179   VECTOR_ENDIF
 180   VECTOR_IF((ix|lx)==0, cond)
 181     VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond & (hx<0));
 182     VECTOR_RETURN(one/(x-x), cond);
 183   VECTOR_ENDIF
 184   VECTOR_IF (ix < 0x3b900000, cond) /* |x|<2**-70, return -log(|x|) */
 185     VECTOR_IF2(hx<0, cond2, cond)
 186       VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond);
 187       VECTOR_RETURN (-v64df_log_aux(-x, __mask), cond2);
 188     VECTOR_ELSE2(cond2, cond)
 189       VECTOR_RETURN (-v64df_log_aux(x, __mask), cond2);
 190     VECTOR_ENDIF
 191   VECTOR_ENDIF
 192   VECTOR_IF (hx < 0, cond)
 193     VECTOR_IF2(ix>=0x43300000, cond2, cond) /* |x|>=2**52, must be -integer */
 194       VECTOR_RETURN(one/(x-x), cond2); /* -integer */
 195     VECTOR_ENDIF
 196     VECTOR_COND_MOVE (t, v64df_sin_pi (x), cond);
 197     VECTOR_IF2(__builtin_convertvector(t==zero, v64si), cond2, cond)
 198       VECTOR_RETURN(one/(x-x), cond2); /* -integer */
 199     VECTOR_ENDIF
 200     VECTOR_COND_MOVE(nadj, v64df_log_aux(VECTOR_INIT(pi)/__builtin_gcn_fabsv(t*x), __mask), cond);
 201     VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond & __builtin_convertvector(t < zero, v64si));
 202     VECTOR_COND_MOVE(x, -x, cond);
 203   VECTOR_ENDIF
 204
 205   /* purge off 1 and 2 */
 206   VECTOR_IF((((ix-0x3ff00000)|lx)==0)|(((ix-0x40000000)|lx)==0), cond)
 207     VECTOR_COND_MOVE(r, VECTOR_INIT(0.0), cond);
 208     /* for x < 2.0 */
 209   VECTOR_ELSEIF(ix<0x40000000, cond)
 210     VECTOR_IF2(ix<=0x3feccccc, cond2, cond)
 211       /* lgamma(x) = lgamma(x+1)-log(x) */
 212       r = -v64df_log_aux(x, __mask);
 213       VECTOR_IF2(ix>=0x3FE76944, cond3, cond2)
 214         VECTOR_COND_MOVE(y, one-x, cond3);
 215         VECTOR_COND_MOVE(i, VECTOR_INIT(0), cond3);
 216       VECTOR_ELSEIF2(ix>=0x3FCDA661, cond3, cond2)
 217         VECTOR_COND_MOVE(y, x-(tc-one), cond3);
 218         VECTOR_COND_MOVE(i, VECTOR_INIT(1), cond3);
 219       VECTOR_ELSE2(cond3, cond2)
 220         VECTOR_COND_MOVE(y, x, cond3);
 221         VECTOR_COND_MOVE(i, VECTOR_INIT(2), cond3);
 222       VECTOR_ENDIF
 223     VECTOR_ELSE2(cond2, cond)
 224       VECTOR_COND_MOVE(r, VECTOR_INIT(zero), cond2);
 225       VECTOR_IF2(ix>=0x3FFBB4C3, cond3, cond2) /* [1.7316,2] */
 226         VECTOR_COND_MOVE(y, VECTOR_INIT(2.0)-x, cond3);
 227         VECTOR_COND_MOVE(i, VECTOR_INIT(0), cond3);
 228       VECTOR_ELSEIF2(ix>=0x3FF3B4C4, cond3, cond2) /* [1.23,1.73] */
 229         VECTOR_COND_MOVE(y, x-tc, cond3);
 230         VECTOR_COND_MOVE(i, VECTOR_INIT(1), cond3);
 231       VECTOR_ELSE2(cond3, cond2)
 232         VECTOR_COND_MOVE(y, x-one, cond3);
 233         VECTOR_COND_MOVE(i, VECTOR_INIT(2), cond3);
 234       VECTOR_ENDIF
 235     VECTOR_ENDIF
 236
 237     VECTOR_IF2(i==0, cond2, cond)
 238       VECTOR_COND_MOVE(z, y*y, cond2);
 239       VECTOR_COND_MOVE(p1, a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))), cond2);
 240       VECTOR_COND_MOVE(p2, z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))), cond2);
 241       VECTOR_COND_MOVE(p, y*p1+p2, cond2);
 242       VECTOR_COND_MOVE(r, r + (p-0.5*y), cond2);
 243     VECTOR_ELSEIF2(i==1, cond2, cond)
 244       VECTOR_COND_MOVE(z, y*y, cond2);
 245       VECTOR_COND_MOVE(w, z*y, cond2);
 246       VECTOR_COND_MOVE(p1, t0+w*(t3+w*(t6+w*(t9 +w*t12))), cond2); /* parallel comp */
 247       VECTOR_COND_MOVE(p2, t1+w*(t4+w*(t7+w*(t10+w*t13))), cond2);
 248       VECTOR_COND_MOVE(p3, t2+w*(t5+w*(t8+w*(t11+w*t14))), cond2);
 249       VECTOR_COND_MOVE(p, z*p1-(tt-w*(p2+y*p3)), cond2);
 250       VECTOR_COND_MOVE(r, r + (tf + p), cond2);
 251     VECTOR_ELSEIF2(i==2, cond2, cond)
 252       VECTOR_COND_MOVE(p1, y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))), cond2);
 253       VECTOR_COND_MOVE(p2, one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))), cond2);
 254       VECTOR_COND_MOVE(r, r + (-0.5*y + p1/p2), cond2);
 255     VECTOR_ENDIF
 256   VECTOR_ELSEIF(ix<0x40200000, cond)
 257   /* x < 8.0 */
 258     VECTOR_COND_MOVE(i, __builtin_convertvector(x, v64si), cond);
 259     VECTOR_COND_MOVE(t, VECTOR_INIT(zero), cond);
 260     VECTOR_COND_MOVE(y, x-__builtin_convertvector(i, v64df), cond);
 261     VECTOR_COND_MOVE(p, y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))), cond);
 262     VECTOR_COND_MOVE(q, one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))), cond);
 263     VECTOR_COND_MOVE(r, half*y+p/q, cond);
 264     VECTOR_COND_MOVE(z, VECTOR_INIT(one), cond); /* lgamma(1+s) = log(s) + lgamma(s) */
 265     VECTOR_IF2(i==7, cond2, cond)
 266       VECTOR_COND_MOVE(z, z * (y+6.0), cond2);
 267     VECTOR_ENDIF
 268     VECTOR_IF2(i==7 | i==6, cond2, cond)
 269       VECTOR_COND_MOVE(z, z * (y+5.0), cond2);
 270     VECTOR_ENDIF
 271     VECTOR_IF2(i<=7 & i>=5, cond2, cond)
 272       VECTOR_COND_MOVE(z, z * (y+4.0), cond2);
 273     VECTOR_ENDIF
 274     VECTOR_IF2(i<=7 & i>=4, cond2, cond)
 275       VECTOR_COND_MOVE(z, z * (y+3.0), cond2);
 276     VECTOR_ENDIF
 277     VECTOR_IF2(i<=7 & i>=3, cond2, cond)
 278       VECTOR_COND_MOVE(z, z * (y+2.0), cond2);
 279       VECTOR_COND_MOVE(r, r + v64df_log_aux(z, __mask), cond2);
 280     VECTOR_ENDIF
 281     /* 8.0 <= x < 2**58 */
 282   VECTOR_ELSEIF(ix < 0x43900000, cond)
 283     VECTOR_COND_MOVE(t, v64df_log_aux(x, __mask), cond);
 284     VECTOR_COND_MOVE(z, one/x, cond);
 285     VECTOR_COND_MOVE(y, z*z, cond);
 286     VECTOR_COND_MOVE(w, w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))), cond);
 287     VECTOR_COND_MOVE(r, (x-half)*(t-one)+w, cond);
 288   VECTOR_ELSE(cond)
 289     /* 2**58 <= x <= inf */
 290     VECTOR_COND_MOVE(r, x*(v64df_log_aux(x, __mask)-one), cond);
 291   VECTOR_ENDIF
 292   VECTOR_IF(hx<0, cond)
 293     VECTOR_COND_MOVE(r, nadj - r, cond);
 294   VECTOR_ENDIF
 295
 296   VECTOR_RETURN(r, NO_COND);
 297   FUNCTION_RETURN;
 298 }
 299
 300 #endif