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)]
powf(x: f32, y: f32) -> f3247 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 - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
242 v = 1.0 / (ax + 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 - 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 + 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) + 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) - 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