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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
47pub 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}
libm/math/powf.rs

libm/math/
powf.rs
