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devctl.h: update for POSIX-1.2024
[newlib-cygwin.git] / newlib / libm / machine / amdgcn / v64sf_pow.c
blob9cb1cc231dc45d9a6a5cdaa08efeef86b220336a
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/ef_pow.c in Newlib. */
27
28 #include "amdgcnmach.h"
29
30 static const float
31 bp[] = {1.0, 1.5,},
32 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
33 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
34 zero = 0.0,
35 one = 1.0,
36 two = 2.0,
37 two24 = 16777216.0, /* 0x4b800000 */
38 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
39 L1 = 6.0000002384e-01, /* 0x3f19999a */
40 L2 = 4.2857143283e-01, /* 0x3edb6db7 */
41 L3 = 3.3333334327e-01, /* 0x3eaaaaab */
42 L4 = 2.7272811532e-01, /* 0x3e8ba305 */
43 L5 = 2.3066075146e-01, /* 0x3e6c3255 */
44 L6 = 2.0697501302e-01, /* 0x3e53f142 */
45 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
46 P2 = -2.7777778450e-03, /* 0xbb360b61 */
47 P3 = 6.6137559770e-05, /* 0x388ab355 */
48 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
49 P5 = 4.1381369442e-08, /* 0x3331bb4c */
50 lg2 = 6.9314718246e-01, /* 0x3f317218 */
51 lg2_h = 6.93145752e-01, /* 0x3f317200 */
52 lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
53 ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
54 cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
55 cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
56 cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
57 ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
58 ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
59 ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
60
61 v64sf v64sf_sqrtf_aux (v64sf, v64si);
62 v64sf v64sf_scalbnf_aux (v64sf, v64si, v64si);
63
64 #if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsvf)
65
66 DEF_VS_MATH_FUNC (v64sf, powf, v64sf x, v64sf y)
67 {
68 FUNCTION_INIT (v64sf);
69
70 v64si hx, hy;
71 GET_FLOAT_WORD (hx,x, NO_COND);
72 GET_FLOAT_WORD (hy,y, NO_COND);
73 v64si ix = hx&0x7fffffff;
74 v64si iy = hy&0x7fffffff;
75
76 /* y==zero: x**0 = 1 */
77 VECTOR_IF (FLT_UWORD_IS_ZERO(iy), cond)
78 VECTOR_RETURN (x + y, cond & v64sf_issignalingf_inline(x));
79 VECTOR_RETURN (VECTOR_INIT (1.0f), cond);
80 VECTOR_ENDIF
81
82 /* x|y==NaN return NaN unless x==1 then return 1 */
83 VECTOR_IF (FLT_UWORD_IS_NAN(ix) | FLT_UWORD_IS_NAN(iy), cond)
84 VECTOR_IF2 (hx==0x3f800000 & ~v64sf_issignalingf_inline(y), cond2, cond)
85 VECTOR_RETURN (VECTOR_INIT (1.0f), cond2);
86 VECTOR_ELSE2 (cond2, cond)
87 VECTOR_RETURN (x + y, cond2);
88 VECTOR_ENDIF
89 VECTOR_ENDIF
90
91 /* determine if y is an odd int when x < 0
92 * yisint = 0 ... y is not an integer
93 * yisint = 1 ... y is an odd int
94 * yisint = 2 ... y is an even int
95 */
96 v64si yisint = VECTOR_INIT (0);
97
98 VECTOR_IF (hx < 0, cond)
99 VECTOR_IF2 (iy >= 0x4b800000, cond2, cond)
100 VECTOR_COND_MOVE (yisint, VECTOR_INIT (2), cond2); /* even integer y */
101 VECTOR_ELSEIF2 (iy >= 0x3f800000, cond2, cond)
102 v64si k = (iy>>23)-0x7f; /* exponent */
103 v64si j = iy>>(23-k);
104 VECTOR_COND_MOVE (yisint, 2-(j&1), cond2 & (j<<(23-k))==iy);
105 VECTOR_ENDIF
106 VECTOR_ENDIF
107
108 /* special value of y */
109 VECTOR_IF (FLT_UWORD_IS_INFINITE(iy), cond) /* y is +-inf */
110 VECTOR_IF2 (ix==0x3f800000, cond2, cond)
111 VECTOR_RETURN (VECTOR_INIT (1.0f), cond2); /* +-1**+-inf = 1 */
112 VECTOR_ELSEIF2 (ix > 0x3f800000, cond2, cond) /* (|x|>1)**+-inf = inf,0 */
113 VECTOR_RETURN (y, cond2 & (hy >= 0));
114 VECTOR_RETURN (VECTOR_INIT (0.0f), cond2);
115 VECTOR_ELSE2 (cond2, cond) /* (|x|<1)**-,+inf = inf,0 */
116 VECTOR_RETURN (-y, cond2 & (hy<0));
117 VECTOR_RETURN (VECTOR_INIT (0.0f), cond2);
118 VECTOR_ENDIF
119 VECTOR_ENDIF
120 VECTOR_IF (iy==0x3f800000, cond) /* y is +-1 */
121 VECTOR_RETURN (VECTOR_INIT (1.0f) / x, cond & (hy<0));
122 VECTOR_RETURN (x, cond);
123 VECTOR_ENDIF
124
125 VECTOR_RETURN (x*x, hy==0x40000000); /* y is 2 */
126 /* y is 0.5 */
127 /* x >= +0 */
128 VECTOR_RETURN (v64sf_sqrtf_aux (x, __mask), (hy==0x3f000000) & (hx >= 0));
129
130 v64sf ax = __builtin_gcn_fabsvf(x);
131 /* special value of x */
132 VECTOR_IF (FLT_UWORD_IS_INFINITE(ix)|FLT_UWORD_IS_ZERO(ix)|ix==0x3f800000, cond)
133 v64sf z = ax; /*x is +-0,+-inf,+-1*/
134 VECTOR_COND_MOVE (z, VECTOR_INIT (1.0f) / z, cond & (hy < 0)); /* z = (1/|x|) */
135 VECTOR_IF2 (hx<0, cond2, cond)
136 VECTOR_IF2 (((ix-0x3f800000)|yisint)==0, cond3, cond2)
137 /* (-1)**non-int is NaN */
138 VECTOR_COND_MOVE (z, (z-z)/(z-z), cond3);
139 VECTOR_ELSEIF2 (yisint==1, cond3, cond2)
140 /* (x<0)**odd = -(|x|**odd) */
141 VECTOR_COND_MOVE (z, -z, cond3);
142 VECTOR_ENDIF
143 VECTOR_ENDIF
144 VECTOR_RETURN (z, cond);
145 VECTOR_ENDIF
146
147 /* (x<0)**(non-int) is NaN */
148 VECTOR_RETURN ((x-x)/(x-x), ((((hx >> 31) & 1) - 1)|yisint)==0);
149
150 v64sf t1, t2;
151
152 /* |y| is huge */
153 VECTOR_IF (iy>0x4d000000, cond) /* if |y| > 2**27 */
154 /* over/underflow if x is not close to one */
155 VECTOR_IF2(ix<0x3f7ffff4, cond2, cond)
156 VECTOR_RETURN (v64sf_math_oflowf(VECTOR_INIT (0)), cond2 & (hy < 0));
157 VECTOR_RETURN (v64sf_math_uflowf(VECTOR_INIT (0)), cond2);
158 VECTOR_ENDIF
159 VECTOR_IF2(ix>0x3f800007, cond2, cond)
160 VECTOR_RETURN (v64sf_math_oflowf(VECTOR_INIT (0)), cond2 & (hy > 0));
161 VECTOR_RETURN (v64sf_math_uflowf(VECTOR_INIT (0)), cond2);
162 VECTOR_ENDIF
163 /* now |1-x| is tiny <= 2**-20, suffice to compute
164 log(x) by x-x^2/2+x^3/3-x^4/4 */
165 v64sf t = ax-1; /* t has 20 trailing zeros */
166 v64sf w = (t*t)*(0.5f-t*(0.333333333333f-t*0.25f));
167 v64sf u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
168 v64sf v = t*ivln2_l-w*ivln2;
169 VECTOR_COND_MOVE (t1, u+v, cond);
170 v64si is;
171 GET_FLOAT_WORD(is,t1, cond);
172 SET_FLOAT_WORD(t1,is&0xfffff000, cond);
173 VECTOR_COND_MOVE (t2, v-(t1-u), cond);
174 VECTOR_RETURN (VECTOR_INIT (0.123456f), cond);
175 VECTOR_ELSE (cond)
176 v64si n = VECTOR_INIT (0);
177 /* take care subnormal number */
178 VECTOR_IF2 (FLT_UWORD_IS_SUBNORMAL(ix), cond2, cond)
179 VECTOR_COND_MOVE (ax, ax * two24, cond);
180 VECTOR_COND_MOVE (n, n - 24, cond2);
181 GET_FLOAT_WORD(ix,ax, cond2);
182 VECTOR_ENDIF
183 n += (ix>>23)-0x7f;
184 v64si j = ix&0x007fffff;
185 /* determine interval */
186 v64si ix = j|0x3f800000; /* normalize ix */
187 v64si k;
188 VECTOR_IF2 (j<=0x1cc471, cond2, cond)
189 VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2); /* |x|<sqrt(3/2) */
190 VECTOR_ELSEIF2 (j<0x5db3d7, cond2, cond)
191 VECTOR_COND_MOVE (k, VECTOR_INIT (1), cond2); /* |x|<sqrt(3) */
192 VECTOR_ELSE2 (cond2, cond)
193 VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2);
194 VECTOR_COND_MOVE (n, n + 1, cond2);
195 VECTOR_COND_MOVE (ix, ix - 0x00800000, cond2);
196 VECTOR_ENDIF
197 SET_FLOAT_WORD(ax,ix, cond);
198
199 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
200 /* bp[0]=1.0, bp[1]=1.5 */
201 v64sf bp_k = VECTOR_MERGE (VECTOR_INIT (bp[1]), VECTOR_INIT (bp[0]), k == 1);
202 v64sf u = ax-bp_k;
203 v64sf v = 1.0f/(ax+bp_k);
204 v64sf s = u*v;
205 v64sf s_h = s;
206 v64si is;
207 GET_FLOAT_WORD(is,s_h, cond);
208 SET_FLOAT_WORD(s_h,is&0xfffff000, cond);
209 /* t_h=ax+bp[k] High */
210 v64sf t_h;
211 SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21), cond);
212 v64sf t_l = ax - (t_h-bp_k);
213 v64sf s_l = v*((u-s_h*t_h)-s_h*t_l);
214 /* compute log(ax) */
215 v64sf s2 = s*s;
216 v64sf r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
217 r += s_l*(s_h+s);
218 s2 = s_h*s_h;
219 t_h = __builtin_convertvector(3.0f+s2+r, v64sf);
220 GET_FLOAT_WORD(is,t_h, cond);
221 SET_FLOAT_WORD(t_h,is&0xfffff000, cond);
222 t_l = r-((t_h-3.0f)-s2);
223 /* u+v = s*(1+...) */
224 u = s_h*t_h;
225 v = s_l*t_h+t_l*s;
226 /* 2/(3log2)*(s+...) */
227 v64sf p_h = u+v;
228 GET_FLOAT_WORD(is,p_h, cond);
229 SET_FLOAT_WORD(p_h,is&0xfffff000, cond);
230 v64sf p_l = v-(p_h-u);
231 v64sf z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
232 v64sf dp_l_k = VECTOR_MERGE (VECTOR_INIT (dp_l[1]), VECTOR_INIT (dp_l[0]), k == 1);
233 v64sf z_l = cp_l*p_h+p_l*cp+dp_l_k;
234 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
235 v64sf t = __builtin_convertvector (n, v64sf);
236 v64sf dp_h_k = VECTOR_MERGE (VECTOR_INIT (dp_h[1]), VECTOR_INIT (dp_h[0]), k == 1);
237 VECTOR_COND_MOVE (t1, (((z_h+z_l)+dp_h_k)+t), cond);
238 GET_FLOAT_WORD(is,t1, cond);
239 SET_FLOAT_WORD(t1,is&0xfffff000, cond);
240 VECTOR_COND_MOVE (t2, z_l-(((t1-t)-dp_h_k)-z_h), cond);
241 VECTOR_ENDIF
242
243 v64sf s = VECTOR_INIT (1.0f); /* s (sign of result -ve**odd) = -1 else = 1 */
244 VECTOR_COND_MOVE (s, VECTOR_INIT (-1.0f), /* (-ve)**(odd int) */
245 ((hx>>31) != 0)&(yisint == 1));
246
247 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
248 v64si is;
249 GET_FLOAT_WORD(is,y, NO_COND);
250 v64sf y1;
251 SET_FLOAT_WORD(y1,is&0xfffff000, NO_COND);
252 v64sf p_l = (y-y1)*t1+y*t2;
253 v64sf p_h = y1*t1;
254 v64sf z = p_l+p_h;
255 v64si j;
256 GET_FLOAT_WORD(j,z, NO_COND);
257 v64si i = j&0x7fffffff;
258 VECTOR_IF (j>0, cond)
259 VECTOR_RETURN (v64sf_math_oflowf(s<0), cond & i>FLT_UWORD_EXP_MAX); /* overflow */
260 VECTOR_RETURN (v64sf_math_oflowf(s<0), cond & (i==FLT_UWORD_EXP_MAX)
261 & (p_l+ovt>z-p_h)); /* overflow */
262 VECTOR_ELSE (cond)
263 VECTOR_RETURN (v64sf_math_uflowf(s<0), cond & (i>FLT_UWORD_EXP_MIN)); /* underflow */
264 VECTOR_RETURN (v64sf_math_uflowf(s<0), cond & (i==FLT_UWORD_EXP_MIN)
265 & (p_l<=z-p_h)); /* underflow */
266 VECTOR_ENDIF
267 /*
268 * compute 2**(p_h+p_l)
269 */
270 v64si k = (i>>23)-0x7f;
271 v64si n = VECTOR_INIT (0);
272 VECTOR_IF (i>0x3f000000, cond) /* if |z| > 0.5, set n = [z+0.5] */
273 VECTOR_COND_MOVE (n, j+(0x00800000>>(k+1)), cond);
274 k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
275 v64sf t;
276 SET_FLOAT_WORD(t,n&~(0x007fffff>>k), cond);
277 VECTOR_COND_MOVE (n, ((n&0x007fffff)|0x00800000)>>(23-k), cond);
278 VECTOR_COND_MOVE (n, -n, cond & (j<0));
279 VECTOR_COND_MOVE (p_h, p_h - t, cond);
280 VECTOR_ENDIF
281 v64sf t = p_l+p_h;
282 GET_FLOAT_WORD(is,t, NO_COND);
283 SET_FLOAT_WORD(t,is&0xfffff000, NO_COND);
284 v64sf u = t*lg2_h;
285 v64sf v = (p_l-(t-p_h))*lg2+t*lg2_l;
286 z = u+v;
287 v64sf w = v-(z-u);
288 t = z*z;
289 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
290 v64sf r = (z*t1)/(t1-2.0f)-(w+z*w);
291 z = VECTOR_INIT (1.0f)-(r-z);
292 GET_FLOAT_WORD(j,z, NO_COND);
293 j += (n<<23);
294 VECTOR_IF ((j>>23)<=0, cond)
295 VECTOR_COND_MOVE (z, v64sf_scalbnf_aux(z, n, __mask), cond); /* subnormal output */
296 VECTOR_ELSE (cond)
297 SET_FLOAT_WORD(z, j, cond);
298 VECTOR_ENDIF
299 VECTOR_RETURN (s*z, NO_COND);
300
301 FUNCTION_RETURN;
302 }
303
304 DEF_VARIANTS2 (powf, sf, sf)
305
306 #endif