Jpeg.jpeg.idct.basis: def of gralha-jpeg-decode@0.1.0.1
Import: import gralha-jpeg-decode@0.1.0.1/jpeg.bend as Jpeg
Lines 617-625 of gralha-jpeg-decode@0.1.0.1/jpeg.bend: https://jend.leeeet.dev/read.txt?path=gralha-jpeg-decode@0.1.0.1/jpeg.bend&start_line=617&end_line=625

import Base
import gralha-text-scan@0.1.0.1/scan.bend as U

# Separable, normalized 8x8 inverse DCT. Coefficients remain quantized until
# every sequential scan has been decoded; each component has a padded plane.
def jpeg.idct.basis(+x: U32, +u: U32) -> F32:
  +k = ((2 * x + 1) * u % 32 : U32)
  +fold = U.choose(U32, U32.is_gt(k, 16), (32 - k : U32), k)
  +negative = U32.is_gt(fold, 8)
  +i = U.choose(U32, negative, (16 - fold : U32), fold)
  +cosine = U.nth(Con{1.0, Con{0.9807852804032304, Con{0.9238795325112867, Con{0.8314696123025452, Con{0.7071067811865476, Con{0.5555702330196023, Con{0.3826834323650898, Con{0.1950903220161283, Con{0.0, Nil{}}}}}}}}}}, U32.to_nat(i), 0.0)
  (0.5 * U.choose(F32, U32.is_eq(u, 0), 0.7071067811865476, 1.0) * U.choose(F32, negative, F32.neg(cosine), cosine) : F32)

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.neg
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_gt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=gralha-text-scan@0.1.0.1/scan.bend&name=choose
  https://jend.leeeet.dev/definition.txt?path=gralha-text-scan@0.1.0.1/scan.bend&name=nth