libm/math/
powf.rs

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

libm/math/
powf.rs
