1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */ |
2 | /* |
3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
4 | */ |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | use super::{fabsf, scalbnf, sqrtf}; |
17 | |
18 | const BP: [f32; 2] = [1.0, 1.5]; |
19 | const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */ |
20 | const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */ |
21 | const TWO24: f32 = 16777216.0; /* 0x4b800000 */ |
22 | const HUGE: f32 = 1.0e30; |
23 | const TINY: f32 = 1.0e-30; |
24 | const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */ |
25 | const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */ |
26 | const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */ |
27 | const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */ |
28 | const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */ |
29 | const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */ |
30 | const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */ |
31 | const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */ |
32 | const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */ |
33 | const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */ |
34 | const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */ |
35 | const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */ |
36 | const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */ |
37 | const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */ |
38 | const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */ |
39 | const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */ |
40 | const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */ |
41 | const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */ |
42 | const IVLN2: f32 = 1.4426950216e+00; |
43 | const IVLN2_H: f32 = 1.4426879883e+00; |
44 | const IVLN2_L: f32 = 7.0526075433e-06; |
45 | |
46 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
47 | pub fn powf(x: f32, y: f32) -> f32 { |
48 | let mut z: f32; |
49 | let mut ax: f32; |
50 | let z_h: f32; |
51 | let z_l: f32; |
52 | let mut p_h: f32; |
53 | let mut p_l: f32; |
54 | let y1: f32; |
55 | let mut t1: f32; |
56 | let t2: f32; |
57 | let mut r: f32; |
58 | let s: f32; |
59 | let mut sn: f32; |
60 | let mut t: f32; |
61 | let mut u: f32; |
62 | let mut v: f32; |
63 | let mut w: f32; |
64 | let i: i32; |
65 | let mut j: i32; |
66 | let mut k: i32; |
67 | let mut yisint: i32; |
68 | let mut n: i32; |
69 | let hx: i32; |
70 | let hy: i32; |
71 | let mut ix: i32; |
72 | let iy: i32; |
73 | let mut is: i32; |
74 | |
75 | hx = x.to_bits() as i32; |
76 | hy = y.to_bits() as i32; |
77 | |
78 | ix = hx & 0x7fffffff; |
79 | iy = hy & 0x7fffffff; |
80 | |
81 | /* x**0 = 1, even if x is NaN */ |
82 | if iy == 0 { |
83 | return 1.0; |
84 | } |
85 | |
86 | /* 1**y = 1, even if y is NaN */ |
87 | if hx == 0x3f800000 { |
88 | return 1.0; |
89 | } |
90 | |
91 | /* NaN if either arg is NaN */ |
92 | if ix > 0x7f800000 || iy > 0x7f800000 { |
93 | return x + y; |
94 | } |
95 | |
96 | /* determine if y is an odd int when x < 0 |
97 | * yisint = 0 ... y is not an integer |
98 | * yisint = 1 ... y is an odd int |
99 | * yisint = 2 ... y is an even int |
100 | */ |
101 | yisint = 0; |
102 | if hx < 0 { |
103 | if iy >= 0x4b800000 { |
104 | yisint = 2; /* even integer y */ |
105 | } else if iy >= 0x3f800000 { |
106 | k = (iy >> 23) - 0x7f; /* exponent */ |
107 | j = iy >> (23 - k); |
108 | if (j << (23 - k)) == iy { |
109 | yisint = 2 - (j & 1); |
110 | } |
111 | } |
112 | } |
113 | |
114 | /* special value of y */ |
115 | if iy == 0x7f800000 { |
116 | /* y is +-inf */ |
117 | if ix == 0x3f800000 { |
118 | /* (-1)**+-inf is 1 */ |
119 | return 1.0; |
120 | } else if ix > 0x3f800000 { |
121 | /* (|x|>1)**+-inf = inf,0 */ |
122 | return if hy >= 0 { y } else { 0.0 }; |
123 | } else { |
124 | /* (|x|<1)**+-inf = 0,inf */ |
125 | return if hy >= 0 { 0.0 } else { -y }; |
126 | } |
127 | } |
128 | if iy == 0x3f800000 { |
129 | /* y is +-1 */ |
130 | return if hy >= 0 { x } else { 1.0 / x }; |
131 | } |
132 | |
133 | if hy == 0x40000000 { |
134 | /* y is 2 */ |
135 | return x * x; |
136 | } |
137 | |
138 | if hy == 0x3f000000 |
139 | /* y is 0.5 */ |
140 | && hx >= 0 |
141 | { |
142 | /* x >= +0 */ |
143 | return sqrtf(x); |
144 | } |
145 | |
146 | ax = fabsf(x); |
147 | /* special value of x */ |
148 | if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 { |
149 | /* x is +-0,+-inf,+-1 */ |
150 | z = ax; |
151 | if hy < 0 { |
152 | /* z = (1/|x|) */ |
153 | z = 1.0 / z; |
154 | } |
155 | |
156 | if hx < 0 { |
157 | if ((ix - 0x3f800000) | yisint) == 0 { |
158 | z = (z - z) / (z - z); /* (-1)**non-int is NaN */ |
159 | } else if yisint == 1 { |
160 | z = -z; /* (x<0)**odd = -(|x|**odd) */ |
161 | } |
162 | } |
163 | return z; |
164 | } |
165 | |
166 | sn = 1.0; /* sign of result */ |
167 | if hx < 0 { |
168 | if yisint == 0 { |
169 | /* (x<0)**(non-int) is NaN */ |
170 | return (x - x) / (x - x); |
171 | } |
172 | |
173 | if yisint == 1 { |
174 | /* (x<0)**(odd int) */ |
175 | sn = -1.0; |
176 | } |
177 | } |
178 | |
179 | /* |y| is HUGE */ |
180 | if iy > 0x4d000000 { |
181 | /* if |y| > 2**27 */ |
182 | /* over/underflow if x is not close to one */ |
183 | if ix < 0x3f7ffff8 { |
184 | return if hy < 0 { |
185 | sn * HUGE * HUGE |
186 | } else { |
187 | sn * TINY * TINY |
188 | }; |
189 | } |
190 | |
191 | if ix > 0x3f800007 { |
192 | return if hy > 0 { |
193 | sn * HUGE * HUGE |
194 | } else { |
195 | sn * TINY * TINY |
196 | }; |
197 | } |
198 | |
199 | /* now |1-x| is TINY <= 2**-20, suffice to compute |
200 | log(x) by x-x^2/2+x^3/3-x^4/4 */ |
201 | t = ax - 1.; /* t has 20 trailing zeros */ |
202 | w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25)); |
203 | u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */ |
204 | v = t * IVLN2_L - w * IVLN2; |
205 | t1 = u + v; |
206 | is = t1.to_bits() as i32; |
207 | t1 = f32::from_bits(is as u32 & 0xfffff000); |
208 | t2 = v - (t1 - u); |
209 | } else { |
210 | let mut s2: f32; |
211 | let mut s_h: f32; |
212 | let s_l: f32; |
213 | let mut t_h: f32; |
214 | let mut t_l: f32; |
215 | |
216 | n = 0; |
217 | /* take care subnormal number */ |
218 | if ix < 0x00800000 { |
219 | ax *= TWO24; |
220 | n -= 24; |
221 | ix = ax.to_bits() as i32; |
222 | } |
223 | n += ((ix) >> 23) - 0x7f; |
224 | j = ix & 0x007fffff; |
225 | /* determine interval */ |
226 | ix = j | 0x3f800000; /* normalize ix */ |
227 | if j <= 0x1cc471 { |
228 | /* |x|<sqrt(3/2) */ |
229 | k = 0; |
230 | } else if j < 0x5db3d7 { |
231 | /* |x|<sqrt(3) */ |
232 | k = 1; |
233 | } else { |
234 | k = 0; |
235 | n += 1; |
236 | ix -= 0x00800000; |
237 | } |
238 | ax = f32::from_bits(ix as u32); |
239 | |
240 | /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
241 | u = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */ |
242 | v = 1.0 / (ax + i!(BP, k as usize)); |
243 | s = u * v; |
244 | s_h = s; |
245 | is = s_h.to_bits() as i32; |
246 | s_h = f32::from_bits(is as u32 & 0xfffff000); |
247 | /* t_h=ax+bp[k] High */ |
248 | is = (((ix as u32 >> 1) & 0xfffff000) | 0x20000000) as i32; |
249 | t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21)); |
250 | t_l = ax - (t_h - i!(BP, k as usize)); |
251 | s_l = v * ((u - s_h * t_h) - s_h * t_l); |
252 | /* compute log(ax) */ |
253 | s2 = s * s; |
254 | r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); |
255 | r += s_l * (s_h + s); |
256 | s2 = s_h * s_h; |
257 | t_h = 3.0 + s2 + r; |
258 | is = t_h.to_bits() as i32; |
259 | t_h = f32::from_bits(is as u32 & 0xfffff000); |
260 | t_l = r - ((t_h - 3.0) - s2); |
261 | /* u+v = s*(1+...) */ |
262 | u = s_h * t_h; |
263 | v = s_l * t_h + t_l * s; |
264 | /* 2/(3log2)*(s+...) */ |
265 | p_h = u + v; |
266 | is = p_h.to_bits() as i32; |
267 | p_h = f32::from_bits(is as u32 & 0xfffff000); |
268 | p_l = v - (p_h - u); |
269 | z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */ |
270 | z_l = CP_L * p_h + p_l * CP + i!(DP_L, k as usize); |
271 | /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
272 | t = n as f32; |
273 | t1 = ((z_h + z_l) + i!(DP_H, k as usize)) + t; |
274 | is = t1.to_bits() as i32; |
275 | t1 = f32::from_bits(is as u32 & 0xfffff000); |
276 | t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h); |
277 | }; |
278 | |
279 | /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
280 | is = y.to_bits() as i32; |
281 | y1 = f32::from_bits(is as u32 & 0xfffff000); |
282 | p_l = (y - y1) * t1 + y * t2; |
283 | p_h = y1 * t1; |
284 | z = p_l + p_h; |
285 | j = z.to_bits() as i32; |
286 | if j > 0x43000000 { |
287 | /* if z > 128 */ |
288 | return sn * HUGE * HUGE; /* overflow */ |
289 | } else if j == 0x43000000 { |
290 | /* if z == 128 */ |
291 | if p_l + OVT > z - p_h { |
292 | return sn * HUGE * HUGE; /* overflow */ |
293 | } |
294 | } else if (j & 0x7fffffff) > 0x43160000 { |
295 | /* z < -150 */ |
296 | // FIXME: check should be (uint32_t)j > 0xc3160000 |
297 | return sn * TINY * TINY; /* underflow */ |
298 | } else if j as u32 == 0xc3160000 |
299 | /* z == -150 */ |
300 | && p_l <= z - p_h |
301 | { |
302 | return sn * TINY * TINY; /* underflow */ |
303 | } |
304 | |
305 | /* |
306 | * compute 2**(p_h+p_l) |
307 | */ |
308 | i = j & 0x7fffffff; |
309 | k = (i >> 23) - 0x7f; |
310 | n = 0; |
311 | if i > 0x3f000000 { |
312 | /* if |z| > 0.5, set n = [z+0.5] */ |
313 | n = j + (0x00800000 >> (k + 1)); |
314 | k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */ |
315 | t = f32::from_bits(n as u32 & !(0x007fffff >> k)); |
316 | n = ((n & 0x007fffff) | 0x00800000) >> (23 - k); |
317 | if j < 0 { |
318 | n = -n; |
319 | } |
320 | p_h -= t; |
321 | } |
322 | t = p_l + p_h; |
323 | is = t.to_bits() as i32; |
324 | t = f32::from_bits(is as u32 & 0xffff8000); |
325 | u = t * LG2_H; |
326 | v = (p_l - (t - p_h)) * LG2 + t * LG2_L; |
327 | z = u + v; |
328 | w = v - (z - u); |
329 | t = z * z; |
330 | t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); |
331 | r = (z * t1) / (t1 - 2.0) - (w + z * w); |
332 | z = 1.0 - (r - z); |
333 | j = z.to_bits() as i32; |
334 | j += n << 23; |
335 | if (j >> 23) <= 0 { |
336 | /* subnormal output */ |
337 | z = scalbnf(z, n); |
338 | } else { |
339 | z = f32::from_bits(j as u32); |
340 | } |
341 | sn * z |
342 | } |
343 | |