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-rw-r--r--v_windows/v/vlib/math/cbrt.v52
1 files changed, 52 insertions, 0 deletions
diff --git a/v_windows/v/vlib/math/cbrt.v b/v_windows/v/vlib/math/cbrt.v
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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
+}