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