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module math
// cbrt returns the cube root of a.
//
// special cases are:
// cbrt(±0) = ±0
// cbrt(±inf) = ±inf
// cbrt(nan) = nan
pub fn cbrt(a f64) f64 {
mut x := a
b1 := 715094163 // (682-0.03306235651)*2**20
b2 := 696219795 // (664-0.03306235651)*2**20
c := 5.42857142857142815906e-01 // 19/35 = 0x3FE15F15F15F15F1
d := -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
e_ := 1.41428571428571436819e+00 // 99/70 = 0x3FF6A0EA0EA0EA0F
f := 1.60714285714285720630e+00 // 45/28 = 0x3FF9B6DB6DB6DB6E
g := 3.57142857142857150787e-01 // 5/14 = 0x3FD6DB6DB6DB6DB7
smallest_normal := 2.22507385850720138309e-308 // 2**-1022 = 0x0010000000000000
if x == 0.0 || is_nan(x) || is_inf(x, 0) {
return x
}
mut sign := false
if x < 0 {
x = -x
sign = true
}
// rough cbrt to 5 bits
mut t := f64_from_bits(f64_bits(x) / u64(3 + (u64(b1) << 32)))
if x < smallest_normal {
// subnormal number
t = f64(u64(1) << 54) // set t= 2**54
t *= x
t = f64_from_bits(f64_bits(t) / u64(3 + (u64(b2) << 32)))
}
// new cbrt to 23 bits
mut r := t * t / x
mut s := c + r * t
t *= g + f / (s + e_ + d / s)
// chop to 22 bits, make larger than cbrt(x)
t = f64_from_bits(f64_bits(t) & (u64(0xffffffffc) << 28) + (u64(1) << 30))
// one step newton iteration to 53 bits with error less than 0.667ulps
s = t * t // t*t is exact
r = x / s
w := t + t
r = (r - t) / (w + r) // r-s is exact
t = t + t * r
// restore the sign bit
if sign {
t = -t
}
return t
}
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