{
  "format_version": 1,
  "description": "Legacy adjacent-real packed unitary 1D/2D/3D FFT with operation-ordered IEEE-f32 stages.",
  "operation_order": {
    "butterfly_real": "f32(f32(f32(a.r + f32(cos*b.r)) - f32(sin*b.i)) * f32(1/sqrt(2)))",
    "butterfly_imag": "f32(f32(f32(a.i + f32(cos*b.i)) + f32(sin*b.r)) * f32(1/sqrt(2)))",
    "complex_multiply": "real=f32(f32(ar*br)-f32(ai*bi)); imag=f32(f32(ar*bi)+f32(ai*br))",
    "kernel_scaling": "scale each kernel spectrum component first by f32(sqrt(sample_count)/kernel_sum)"
  },
  "layout": "adjacent x samples become real/imag; spectrum x extent is Nx/2+1; x remains fastest",
  "cases": [
    {
      "shape": [
        8
      ],
      "packed_shape": [
        5
      ],
      "input_f32": {
        "decimal": [
          0.0555555559694767,
          0.4444444477558136,
          0.8333333134651184,
          0.1666666716337204,
          0.5555555820465088,
          0.9444444179534912,
          0.2777777910232544,
          0.6666666865348816
        ],
        "bits": [
          "0x3d638e39",
          "0x3ee38e39",
          "0x3f555555",
          "0x3e2aaaab",
          "0x3f0e38e4",
          "0x3f71c71c",
          "0x3e8e38e4",
          "0x3f2aaaab"
        ]
      },
      "kernel_f32": {
        "decimal": [
          0.35384616255760193,
          0.7384615540504456,
          0.2769230902194977,
          0.6615384817123413,
          0.20000000298023224,
          0.5846154093742371,
          0.9692307710647583,
          0.5076923370361328
        ],
        "bits": [
          "0x3eb52b53",
          "0x3f3d0bd1",
          "0x3e8dc8dd",
          "0x3f295a96",
          "0x3e4ccccd",
          "0x3f15a95b",
          "0x3f781f82",
          "0x3f01f820"
        ]
      },
      "kernel_sum_f64": 4.292307692307693,
      "scales_f32": {
        "unitary_butterfly": {
          "decimal": 0.7071067690849304,
          "bits": "0x3f3504f3"
        },
        "forward_real_conversion": {
          "decimal": 0.3535533845424652,
          "bits": "0x3eb504f3"
        },
        "inverse_real_conversion": {
          "decimal": 0.7071067690849304,
          "bits": "0x3f3504f3"
        },
        "spectral_correction": {
          "decimal": 0.658952534198761,
          "bits": "0x3f28b11d"
        }
      },
      "plans": {
        "x_forward_butterflies": [
          {
            "stage": 1,
            "entries": [
              {
                "output": 0,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    -0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x80000000"
                  ]
                }
              },
              {
                "output": 1,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    -1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0xa50d3132"
                  ]
                }
              },
              {
                "output": 2,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    -0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x80000000"
                  ]
                }
              },
              {
                "output": 3,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    -1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0xa50d3132"
                  ]
                }
              }
            ]
          },
          {
            "stage": 2,
            "entries": [
              {
                "output": 0,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    -0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x80000000"
                  ]
                }
              },
              {
                "output": 1,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    6.123234262925839e-17,
                    -1.0
                  ],
                  "bits": [
                    "0x248d3132",
                    "0xbf800000"
                  ]
                }
              },
              {
                "output": 2,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    -1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0xa50d3132"
                  ]
                }
              },
              {
                "output": 3,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    -1.8369701465288538e-16,
                    1.0
                  ],
                  "bits": [
                    "0xa553c9ca",
                    "0x3f800000"
                  ]
                }
              }
            ]
          }
        ],
        "x_forward_real_conversion": [
          {
            "output": 0,
            "source": [
              0,
              0
            ],
            "twiddle": {
              "decimal": [
                6.123234262925839e-17,
                -1.0
              ],
              "bits": [
                "0x248d3132",
                "0xbf800000"
              ]
            }
          },
          {
            "output": 1,
            "source": [
              1,
              3
            ],
            "twiddle": {
              "decimal": [
                -0.7071067690849304,
                -0.7071067690849304
              ],
              "bits": [
                "0xbf3504f3",
                "0xbf3504f3"
              ]
            }
          },
          {
            "output": 2,
            "source": [
              2,
              2
            ],
            "twiddle": {
              "decimal": [
                -1.0,
                -1.2246468525851679e-16
              ],
              "bits": [
                "0xbf800000",
                "0xa50d3132"
              ]
            }
          },
          {
            "output": 3,
            "source": [
              3,
              1
            ],
            "twiddle": {
              "decimal": [
                -0.7071067690849304,
                0.7071067690849304
              ],
              "bits": [
                "0xbf3504f3",
                "0x3f3504f3"
              ]
            }
          },
          {
            "output": 4,
            "source": [
              0,
              0
            ],
            "twiddle": {
              "decimal": [
                -1.8369701465288538e-16,
                1.0
              ],
              "bits": [
                "0xa553c9ca",
                "0x3f800000"
              ]
            }
          }
        ],
        "x_inverse_real_conversion": [
          {
            "output": 0,
            "source": [
              0,
              4
            ],
            "twiddle": {
              "decimal": [
                6.123234262925839e-17,
                1.0
              ],
              "bits": [
                "0x248d3132",
                "0x3f800000"
              ]
            }
          },
          {
            "output": 1,
            "source": [
              1,
              3
            ],
            "twiddle": {
              "decimal": [
                -0.7071067690849304,
                0.7071067690849304
              ],
              "bits": [
                "0xbf3504f3",
                "0x3f3504f3"
              ]
            }
          },
          {
            "output": 2,
            "source": [
              2,
              2
            ],
            "twiddle": {
              "decimal": [
                -1.0,
                1.2246468525851679e-16
              ],
              "bits": [
                "0xbf800000",
                "0x250d3132"
              ]
            }
          },
          {
            "output": 3,
            "source": [
              3,
              1
            ],
            "twiddle": {
              "decimal": [
                -0.7071067690849304,
                -0.7071067690849304
              ],
              "bits": [
                "0xbf3504f3",
                "0xbf3504f3"
              ]
            }
          },
          {
            "output": 4,
            "source": [
              4,
              0
            ],
            "twiddle": {
              "decimal": [
                -1.8369701465288538e-16,
                -1.0
              ],
              "bits": [
                "0xa553c9ca",
                "0xbf800000"
              ]
            }
          }
        ],
        "x_inverse_butterflies": [
          {
            "stage": 1,
            "entries": [
              {
                "output": 0,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x00000000"
                  ]
                }
              },
              {
                "output": 1,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0x250d3132"
                  ]
                }
              },
              {
                "output": 2,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x00000000"
                  ]
                }
              },
              {
                "output": 3,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0x250d3132"
                  ]
                }
              }
            ]
          },
          {
            "stage": 2,
            "entries": [
              {
                "output": 0,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    1.0,
                    0.0
                  ],
                  "bits": [
                    "0x3f800000",
                    "0x00000000"
                  ]
                }
              },
              {
                "output": 1,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    6.123234262925839e-17,
                    1.0
                  ],
                  "bits": [
                    "0x248d3132",
                    "0x3f800000"
                  ]
                }
              },
              {
                "output": 2,
                "source": [
                  0,
                  2
                ],
                "twiddle": {
                  "decimal": [
                    -1.0,
                    1.2246468525851679e-16
                  ],
                  "bits": [
                    "0xbf800000",
                    "0x250d3132"
                  ]
                }
              },
              {
                "output": 3,
                "source": [
                  1,
                  3
                ],
                "twiddle": {
                  "decimal": [
                    -1.8369701465288538e-16,
                    -1.0
                  ],
                  "bits": [
                    "0xa553c9ca",
                    "0xbf800000"
                  ]
                }
              }
            ]
          }
        ]
      },
      "forward_field_stages": [
        {
          "name": "adjacent_real_pack",
          "values": {
            "decimal": [
              [
                0.0555555559694767,
                0.4444444477558136
              ],
              [
                0.8333333134651184,
                0.1666666716337204
              ],
              [
                0.5555555820465088,
                0.9444444179534912
              ],
              [
                0.2777777910232544,
                0.6666666865348816
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3d638e39",
                "0x3ee38e39"
              ],
              [
                "0x3f555555",
                "0x3e2aaaab"
              ],
              [
                "0x3f0e38e4",
                "0x3f71c71c"
              ],
              [
                "0x3e8e38e4",
                "0x3f2aaaab"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "x_butterfly_1",
          "values": {
            "decimal": [
              [
                0.43212082982063293,
                0.9820926785469055
              ],
              [
                -0.3535533845424652,
                -0.3535533547401428
              ],
              [
                0.7856742143630981,
                0.589255690574646
              ],
              [
                0.3928370773792267,
                -0.3535533845424652
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3edd3ef1",
                "0x3f7b6a6d"
              ],
              [
                "0xbeb504f3",
                "0xbeb504f2"
              ],
              [
                "0x3f4921f2",
                "0x3f16d976"
              ],
              [
                "0x3ec921f1",
                "0xbeb504f3"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "x_butterfly_2",
          "values": {
            "decimal": [
              [
                0.8611111044883728,
                1.1111111640930176
              ],
              [
                -0.4999999701976776,
                -0.5277777314186096
              ],
              [
                -0.2499999850988388,
                0.27777770161628723
              ],
              [
                0.0,
                0.027777785435318947
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3f5c71c7",
                "0x3f8e38e4"
              ],
              [
                "0xbeffffff",
                "0xbf071c71"
              ],
              [
                "0xbe7fffff",
                "0x3e8e38e1"
              ],
              [
                "0x00000000",
                "0x3ce38e3d"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "x_real_to_half_complex",
          "values": {
            "decimal": [
              [
                1.3945717811584473,
                4.810867222485138e-17
              ],
              [
                -0.1767766773700714,
                0.05358143523335457
              ],
              [
                -0.1767766773700714,
                -0.19641849398612976
              ],
              [
                -0.1767766773700714,
                0.44641849398612976
              ],
              [
                -0.1767767369747162,
                -1.4432601005710924e-16
              ]
            ],
            "bits": [
              [
                "0x3fb28154",
                "0x245ddcb2"
              ],
              [
                "0xbe3504f2",
                "0x3d5b7835"
              ],
              [
                "0xbe3504f2",
                "0xbe4921ee"
              ],
              [
                "0xbe3504f2",
                "0x3ee490f7"
              ],
              [
                "0xbe3504f6",
                "0xa5266585"
              ]
            ]
          }
        }
      ],
      "field_spectrum": {
        "decimal": [
          [
            1.3945717811584473,
            4.810867222485138e-17
          ],
          [
            -0.1767766773700714,
            0.05358143523335457
          ],
          [
            -0.1767766773700714,
            -0.19641849398612976
          ],
          [
            -0.1767766773700714,
            0.44641849398612976
          ],
          [
            -0.1767767369747162,
            -1.4432601005710924e-16
          ]
        ],
        "bits": [
          [
            "0x3fb28154",
            "0x245ddcb2"
          ],
          [
            "0xbe3504f2",
            "0x3d5b7835"
          ],
          [
            "0xbe3504f2",
            "0xbe4921ee"
          ],
          [
            "0xbe3504f2",
            "0x3ee490f7"
          ],
          [
            "0xbe3504f6",
            "0xa5266585"
          ]
        ]
      },
      "kernel_spectrum": {
        "decimal": [
          [
            1.5175600051879883,
            5.3955724116135564e-17
          ],
          [
            0.054392825812101364,
            0.16784465312957764
          ],
          [
            -0.2447677105665207,
            -0.05439281463623047
          ],
          [
            0.054392825812101364,
            -0.32169079780578613
          ],
          [
            -0.24476774036884308,
            -1.6186714918734954e-16
          ]
        ],
        "bits": [
          [
            "0x3fc23f68",
            "0x2478d3ad"
          ],
          [
            "0x3d5ecb03",
            "0x3e2bdf78"
          ],
          [
            "0xbe7aa463",
            "0xbd5ecb00"
          ],
          [
            "0x3d5ecb03",
            "0xbea4b4a8"
          ],
          [
            "0xbe7aa465",
            "0xa53a9ec0"
          ]
        ]
      },
      "spectral_product": {
        "decimal": [
          [
            1.3945717811584473,
            9.769164499906827e-17
          ],
          [
            -0.01226227730512619,
            -0.01763131096959114
          ],
          [
            0.021472277119755745,
            0.03801647573709488
          ],
          [
            0.08829525858163834,
            0.05347359925508499
          ],
          [
            0.02851237542927265,
            4.2133883794654307e-17
          ]
        ],
        "bits": [
          [
            "0x3fb28154",
            "0x24e142f8"
          ],
          [
            "0xbc48e7b8",
            "0xbc906f8a"
          ],
          [
            "0x3cafe6a1",
            "0x3d1bb72a"
          ],
          [
            "0x3db4d425",
            "0x3d5b0722"
          ],
          [
            "0x3ce992c9",
            "0x24424ee9"
          ]
        ]
      },
      "inverse_product_stages": [
        {
          "name": "x_half_complex_to_packed_real",
          "values": {
            "decimal": [
              [
                1.0062724351882935,
                0.9659498929977417
              ],
              [
                0.08612105995416641,
                -0.1184786781668663
              ],
              [
                0.030366385355591774,
                -0.05376341566443443
              ],
              [
                0.021405814215540886,
                -0.017921146005392075
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3f80cd89",
                "0x3f77487e"
              ],
              [
                "0x3db0603d",
                "0xbdf2a4f3"
              ],
              [
                "0x3cf8c2ed",
                "0xbd5c3707"
              ],
              [
                "0x3caf5b3f",
                "0xbc92cf5e"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "x_inverse_butterfly_1",
          "values": {
            "decimal": [
              [
                0.7330143451690674,
                0.6450132727622986
              ],
              [
                0.6900697946548462,
                0.7210461497306824
              ],
              [
                0.07603298127651215,
                -0.09644923359155655
              ],
              [
                0.045760586857795715,
                -0.07110491394996643
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3f3ba6d4",
                "0x3f251f97"
              ],
              [
                "0x3f30a86a",
                "0x3f38967b"
              ],
              [
                "0x3d9bb72e",
                "0xbdc5872d"
              ],
              [
                "0x3d3b6f74",
                "0xbd919f74"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "x_inverse_butterfly_2",
          "values": {
            "decimal": [
              [
                0.5720828771591187,
                0.38789331912994385
              ],
              [
                0.5382317900657654,
                0.5422142148017883
              ],
              [
                0.464555948972702,
                0.5242931842803955
              ],
              [
                0.43767428398132324,
                0.47749900817871094
              ],
              [
                0.0,
                0.0
              ]
            ],
            "bits": [
              [
                "0x3f127406",
                "0x3ec699f4"
              ],
              [
                "0x3f09c98f",
                "0x3f0ace8d"
              ],
              [
                "0x3eedda47",
                "0x3f063814"
              ],
              [
                "0x3ee016d8",
                "0x3ef47ac0"
              ],
              [
                "0x00000000",
                "0x00000000"
              ]
            ]
          }
        },
        {
          "name": "adjacent_real_unpack",
          "values": {
            "decimal": [
              0.5720828771591187,
              0.38789331912994385,
              0.5382317900657654,
              0.5422142148017883,
              0.464555948972702,
              0.5242931842803955,
              0.43767428398132324,
              0.47749900817871094
            ],
            "bits": [
              "0x3f127406",
              "0x3ec699f4",
              "0x3f09c98f",
              "0x3f0ace8d",
              "0x3eedda47",
              "0x3f063814",
              "0x3ee016d8",
              "0x3ef47ac0"
            ]
          }
        }
      ],
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                "0x3eec8c74",
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                "0x3f0102ae",
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                "0x3ee4b7b5",
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        {
          "name": "adjacent_real_unpack",
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      "direct_normalized_f64": [
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      "max_abs_error_to_direct": 8.430757625355056e-08
    }
  ]
}