v
Зеркало из https://github.com/vlang/v
1module math
2
3// The vlang code is a modified version of the original C code from
4// http://www.netlib.org/fdlibm/s_cbrt.c and came with this notice.
5//
6// ====================================================
7// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8//
9// Developed at SunSoft, 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// cbrt returns the cube root of a.
16//
17// special cases are:
18// cbrt(±0) = ±0
19// cbrt(±inf) = ±inf
20// cbrt(nan) = nan
21pub fn cbrt(a f64) f64 {
22mut x := a
23b1 := 715094163 // (682-0.03306235651)*2**20
24b2 := 696219795 // (664-0.03306235651)*2**20
25c := 5.42857142857142815906e-01 // 19/35 = 0x3FE15F15F15F15F1
26d := -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
27e_ := 1.41428571428571436819e+00 // 99/70 = 0x3FF6A0EA0EA0EA0F
28f := 1.60714285714285720630e+00 // 45/28 = 0x3FF9B6DB6DB6DB6E
29g := 3.57142857142857150787e-01 // 5/14 = 0x3FD6DB6DB6DB6DB7
30smallest_normal := 2.22507385850720138309e-308 // 2**-1022 = 0x0010000000000000
31if x == 0.0 || is_nan(x) || is_inf(x, 0) {
32return x
33}
34mut sign := false
35if x < 0 {
36x = -x
37sign = true
38}
39// rough cbrt to 5 bits
40mut t := f64_from_bits(f64_bits(x) / u64(3) + (u64(b1) << 32))
41if x < smallest_normal {
42// subnormal number
43t = f64(u64(1) << 54) // set t= 2**54
44t *= x
45t = f64_from_bits(f64_bits(t) / u64(3) + (u64(b2) << 32))
46}
47// new cbrt to 23 bits
48mut r := t * t / x
49mut s := c + r * t
50t *= g + f / (s + e_ + d / s)
51// chop to 22 bits, make larger than cbrt(x)
52t = f64_from_bits(f64_bits(t) & (u64(0xffffffffc) << 28) + (u64(1) << 30))
53// one step newton iteration to 53 bits with error less than 0.667ulps
54s = t * t // t*t is exact
55r = x / s
56w := t + t
57r = (r - t) / (w + r) // r-s is exact
58t = t + t * r
59// restore the sign bit
60if sign {
61t = -t
62}
63return t
64}
65