F64.sq_root_s: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F64
Lines 472-477 of bend-collections-laws-math@1.0.0.0/src/math/f64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&start_line=472&end_line=477

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X

# one step of Zimmermann's SqrtRem (Karatsuba square root) from s = isqrt(nh):
# r = nh - s^2, (q, u) = divmod(r 2^32, 2 s) give S0 = s 2^32 + q with
# N - S0^2 = u 2^32 - q^2 for N = nh 2^64; S0 - 2 <= isqrt(N) <= S0 and the
# exact remainder decides the root and its sticky bit without squaring S0
def sq_root_s(+e: Nat, +nh: W.U64, +s: U32) -> F64:
  sq_div(e, s, X.div32(W.U64{0, X.lo(X.sub(nh, X.mul32(s, s)))}, U32.add(s, s)))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=F64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=sq_div
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=div32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=lo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=mul32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=sub