mirror of
https://github.com/allaunthefox/Research-Stack.git
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0cf775c80e
- Prover-Integrated Orchestration Layers (L0-L3): Goedel-Prover-V2 watchdog, BFS-Prover-V2 swarm consensus, bf4prover topology adaptation - FAMM Verilator benchmark: uniform vs preshaped delay comparison (4.4x speedup) - Swarm topological device prober: 11 agents probing traces, caps, delays, errors, vias, PDN - Spec sheet puller: 10 components with key params and topological relevance - Virtual FPGA system tests: 6/6 passed, 134K ops/s throughput - Fixed merge conflicts in AI-Newton test_experiment.ipynb
602 lines
19 KiB
Text
602 lines
19 KiB
Text
import Lean.Data.Json
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import Mathlib.Data.UInt
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import Mathlib.Tactic
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import Mathlib.Data.Int.Basic
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import Mathlib.Data.Nat.Basic
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set_option maxRecDepth 20000
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namespace Semantics.FixedPoint
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open Lean
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/--
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Q0.16 pure fraction representation using UInt16 (range: [-1, 1 - 2^-16])
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- 16-bit unsigned integer interpreted as signed 0.16 fixed point.
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- 0x8000 = 1.0 (max positive value)
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- 0x0000 = 0.0
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- Range: [-1.0, 1.0 - 2^-16] ≈ [-1.0, 0.999985]
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- Resolution: 1/32767 ≈ 0.0000305
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-/
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structure Q0_16 where
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val : UInt16
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deriving Repr, DecidableEq, BEq, Inhabited
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instance : ToJson Q0_16 where
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toJson q := Json.mkObj [("val", toJson q.val.toNat)]
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instance : FromJson Q0_16 where
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fromJson? j := do
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let val ← (← j.getObjVal? "val").getNat?
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pure ⟨val.toUInt16⟩
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namespace Q0_16
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def zero : Q0_16 := ⟨0x0000⟩
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def one : Q0_16 := ⟨0x7FFF⟩ -- Max positive value (represents ~1.0)
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def half : Q0_16 := ⟨0x3FFF⟩
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def neg (x : Q0_16) : Q0_16 := ⟨-x.val⟩
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def add (a b : Q0_16) : Q0_16 := ⟨a.val + b.val⟩
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def sub (a b : Q0_16) : Q0_16 := ⟨a.val - b.val⟩
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def mul (a b : Q0_16) : Q0_16 :=
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let prod : UInt32 := UInt32.ofNat (a.val.toNat * b.val.toNat)
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⟨(prod >>> 15).toUInt16⟩
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def div (a b : Q0_16) : Q0_16 :=
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if b.val = 0 then ⟨0x7FFF⟩
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else ⟨(UInt32.ofNat (a.val.toNat * (1 <<< 15)) / UInt32.ofNat b.val.toNat).toUInt16⟩
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def abs (x : Q0_16) : Q0_16 :=
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if (x.val &&& 0x8000) != 0 then neg x else x
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instance : Add Q0_16 where add := add
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instance : Sub Q0_16 where sub := sub
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instance : Mul Q0_16 where mul := mul
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instance : Div Q0_16 where div := div
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instance : Neg Q0_16 where neg := neg
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def lt (a b : Q0_16) : Bool := a.val < b.val
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def le (a b : Q0_16) : Bool := a.val ≤ b.val
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def gt (a b : Q0_16) : Bool := b.val < a.val
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def ge (a b : Q0_16) : Bool := b.val ≤ a.val
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def toFloat (q : Q0_16) : Float :=
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Float.ofInt (Int.ofNat q.val.toNat) / 32767.0
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def ofFloat (f : Float) : Q0_16 :=
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if f.isNaN then zero
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else if f ≥ 1.0 then one
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else if f ≤ -1.0 then neg one
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else ⟨((f * 32767.0).round).toUInt16⟩
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def log2 (q : Q0_16) : Q0_16 :=
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if q.val == 0 then zero
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else
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let f := toFloat q
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if f ≤ 0.0 then zero
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else ofFloat (Float.log2 f)
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def min (a b : Q0_16) : Q0_16 :=
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if a.val ≤ b.val then a else b
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end Q0_16
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/--
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Q16.16 fixed-point representation.
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- 32-bit unsigned integer interpreted as signed 16.16 fixed point.
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- 0x00010000 = 1.0
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- 0xFFFFFFFF = -0.000015 (or used as sentinel for infinity/illegal)
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- Range: [-32768.0, 32767.999985]
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- Resolution: 1/65536 ≈ 0.000015
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All arithmetic uses saturating logic for hardware parity.
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-/
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structure Q16_16 where
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val : UInt32
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deriving Repr, DecidableEq, BEq, Inhabited
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instance : ToJson Q16_16 where
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toJson q := Json.mkObj [("val", toJson q.val.toNat)]
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instance : FromJson Q16_16 where
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fromJson? j := do
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let val ← (← j.getObjVal? "val").getNat?
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pure ⟨val.toUInt32⟩
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namespace Q16_16
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@[ext]
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theorem ext {a b : Q16_16} (h : a.val = b.val) : a = b := by
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cases a; cases b; simp at h; simp [h]
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def ofNat (n : Nat) : Q16_16 := ⟨(n * 65536).toUInt32⟩
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def satFromNat (n : Nat) : Q16_16 :=
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if n ≥ 32768 then ⟨0x7FFFFFFF⟩
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else ⟨(n * 65536).toUInt32⟩
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/-- Rational constructor: numerator/denominator → Q16_16.
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No Float used. Intermediate in Nat to avoid overflow.
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Returns zero literal if den=0 to avoid forward reference. -/
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def ofRatio (num : Nat) (den : Nat) : Q16_16 :=
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if den = 0 then ⟨0x00000000⟩
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else ⟨(num * 65536 / den).toUInt32⟩
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instance : OfNat Q16_16 n where
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ofNat := ofNat n
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def zero : Q16_16 := ⟨0x00000000⟩
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def one : Q16_16 := ⟨0x00010000⟩
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def negOne : Q16_16 := ⟨0xFFFF0000⟩
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def epsilon : Q16_16 := ⟨0x00000001⟩
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def two : Q16_16 := ⟨0x00020000⟩
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def infinity : Q16_16 := ⟨0xFFFFFFFF⟩
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def maxVal : Q16_16 := ⟨0x7FFFFFFF⟩
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def minVal : Q16_16 := ⟨0x80000000⟩
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@[inline]
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def toInt (q : Q16_16) : Int :=
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Int.ofNat (q.val.toUInt64 : UInt64).toNat - (if q.val ≥ 0x80000000 then 0x100000000 else 0)
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/-- Signed raw Q16.16 constructor with saturation at the representable bounds. -/
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@[inline]
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def ofRawInt (raw : Int) : Q16_16 :=
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if raw > 0x7FFFFFFF then maxVal
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else if raw < -0x80000000 then minVal
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else ⟨UInt32.ofInt raw⟩
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/-- Boundary conversion from external float -/
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@[inline]
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def ofFloat (f : Float) : Q16_16 :=
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if f.isNaN || f ≥ 32768.0 then infinity
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else if f ≤ -32768.0 then ⟨0x80000000⟩
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else ⟨(f * 65536.0).floor.toUInt32⟩
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@[inline]
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def toFloat (q : Q16_16) : Float :=
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Float.ofInt (toInt q) / 65536.0
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def scale : Nat := 65536
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@[inline]
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def ofInt (n : Int) : Q16_16 :=
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ofRawInt (n * 65536)
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/-- Saturating addition (matches hardware add_sat) -/
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@[inline]
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def add (a b : Q16_16) : Q16_16 :=
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let a_s := Int.ofNat a.val.toNat
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let b_s := Int.ofNat b.val.toNat
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let res := a_s + b_s
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if res > 0x7FFFFFFF then ⟨0x7FFFFFFF⟩
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else if res < -0x80000000 then ⟨0x80000000⟩
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else ⟨UInt32.ofNat res.toNat⟩
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/-- Saturating subtraction (matches hardware sub_sat) -/
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@[inline]
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def sub (a b : Q16_16) : Q16_16 :=
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let a_s := Int.ofNat a.val.toNat
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let b_s := Int.ofNat b.val.toNat
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let res := a_s - b_s
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if res > 0x7FFFFFFF then ⟨0x7FFFFFFF⟩
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else if res < -0x80000000 then ⟨0x80000000⟩
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else ⟨UInt32.ofNat res.toNat⟩
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@[inline]
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def mul (a b : Q16_16) : Q16_16 :=
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⟨((a.val.toUInt64 * b.val.toUInt64) >>> 16).toUInt32⟩
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@[inline]
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def div (a b : Q16_16) : Q16_16 :=
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if b.val == 0 then infinity
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else ⟨(a.val.toUInt64 <<< 16 / b.val.toUInt64).toUInt32⟩
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@[inline]
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def abs (q : Q16_16) : Q16_16 :=
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if q.val == 0x80000000 then ⟨0x80000000⟩
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else ⟨(if q.val ≥ 0x80000000 then UInt32.ofInt (-q.toInt) else q.val)⟩
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@[inline]
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def neg (q : Q16_16) : Q16_16 := ⟨UInt32.ofInt (-q.toInt)⟩
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@[inline]
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def sqrt (q : Q16_16) : Q16_16 :=
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if q.val == 0 then zero
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else
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let f := toFloat q
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if f ≤ 0.0 then zero
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else ofFloat (Float.sqrt f)
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/-- Natural logarithm approximation (Taylor series) -/
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def ln (q : Q16_16) : Q16_16 :=
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let x := q.toInt
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if x ≤ 0 then zero
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else
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let y := x - 65536
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let y2 := (y * y) / 65536
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let y3 := (y * y2) / 65536
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let raw := y - y2 / 2 + y3 / 3
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⟨UInt32.ofInt raw⟩
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def log2 (q : Q16_16) : Q16_16 :=
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let ln2 : Q16_16 := ⟨45426⟩ -- ln(2) ≈ 0.6931
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div (ln q) ln2
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def expNeg (x : Q16_16) : Q16_16 :=
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if x.val ≥ 0x00030000 then zero
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else if x.val ≥ 0x00020000 then ⟨0x00004D29⟩
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else if x.val ≥ 0x00010000 then ⟨0x0000C5C0⟩
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else ⟨0x0001C5C0⟩
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instance : Add Q16_16 := ⟨add⟩
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instance : Sub Q16_16 := ⟨sub⟩
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instance : Mul Q16_16 := ⟨mul⟩
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instance : Div Q16_16 := ⟨div⟩
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instance : Neg Q16_16 := ⟨neg⟩
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-- Comparison
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instance : LE Q16_16 where
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le a b := a.toInt ≤ b.toInt
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instance : LT Q16_16 where
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lt a b := a.toInt < b.toInt
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instance : DecidableRel (fun a b : Q16_16 => a ≤ b) :=
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fun a b => inferInstanceAs (Decidable (a.toInt ≤ b.toInt))
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instance : DecidableRel (fun a b : Q16_16 => a < b) :=
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fun a b => inferInstanceAs (Decidable (a.toInt < b.toInt))
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@[inline]
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def ge (a b : Q16_16) : Bool := b.toInt ≤ a.toInt
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@[inline]
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def gt (a b : Q16_16) : Bool := b.toInt < a.toInt
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def lt (a b : Q16_16) : Bool := a.toInt < b.toInt
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def isNeg (q : Q16_16) : Bool := q.val ≥ 0x80000000
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def clip (x lo hi : Q16_16) : Q16_16 :=
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if x.toInt < lo.toInt then lo
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else if x.toInt > hi.toInt then hi
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else x
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Algebraic Lemmas (for theorem proving)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- zero.toInt = 0 -/
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theorem zero_toInt : toInt zero = 0 := rfl
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/-- one.toInt = 65536 -/
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theorem one_toInt : toInt one = 65536 := rfl
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/-- epsilon.toInt = 1 -/
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theorem epsilon_toInt : toInt epsilon = 1 := rfl
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/-- epsilon.toInt > 0 -/
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theorem epsilon_toInt_pos : toInt epsilon > 0 := by decide
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private theorem u64_zero_mul (x : UInt64) : UInt64.mul 0 x = 0 := by
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cases x
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simp [UInt64.mul, BitVec.zero_mul]
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private theorem u64_mul_zero (x : UInt64) : UInt64.mul x 0 = 0 := by
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cases x
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simp [UInt64.mul, BitVec.mul_zero]
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private theorem u64_scale_left_toNat (x : UInt32) :
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(UInt64.mul 65536 x.toUInt64).toNat = 65536 * x.toNat := by
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simp [UInt64.mul, UInt64.toNat_ofNat]
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have hlt := UInt32.toNat_lt x
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omega
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private theorem u64_scale_right_toNat (x : UInt32) :
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(UInt64.mul x.toUInt64 65536).toNat = x.toNat * 65536 := by
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simp [UInt64.mul, UInt64.toNat_ofNat]
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have hlt := UInt32.toNat_lt x
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omega
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/-- zero * a = zero -/
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theorem zero_mul (a : Q16_16) : zero * a = zero := by
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cases a with
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| mk av =>
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apply congrArg Q16_16.mk
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cases av
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simp [HMul.hMul, Mul.mul, zero, u64_zero_mul]
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/-- a * zero = zero -/
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theorem mul_zero (a : Q16_16) : a * zero = zero := by
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cases a with
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| mk av =>
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apply congrArg Q16_16.mk
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cases av
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simp [HMul.hMul, Mul.mul, zero, u64_mul_zero]
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/-- one * a = a -/
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theorem one_mul (a : Q16_16) : one * a = a := by
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cases a with
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| mk av =>
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apply congrArg Q16_16.mk
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apply UInt32.ext
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have hlt := UInt32.toNat_lt av
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change (Q16_16.mul one { val := av }).val.toNat = av.toNat
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simp [Q16_16.mul, one, UInt64.toNat_toUInt32, UInt64.toNat_shiftRight,
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UInt64.toNat_ofNat, Nat.shiftRight_eq_div_pow]
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omega
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/-- a * one = a -/
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theorem mul_one (a : Q16_16) : a * one = a := by
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cases a with
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| mk av =>
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apply congrArg Q16_16.mk
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apply UInt32.ext
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have hlt := UInt32.toNat_lt av
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change (Q16_16.mul { val := av } one).val.toNat = av.toNat
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simp [Q16_16.mul, one, UInt64.toNat_toUInt32, UInt64.toNat_shiftRight,
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UInt64.toNat_ofNat, Nat.shiftRight_eq_div_pow]
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omega
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/-- toInt = 0 iff the value is zero -/
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theorem toInt_eq_zero_iff {a : Q16_16} : a.toInt = 0 ↔ a = zero := by
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constructor
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· intro h
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cases a with
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| mk av =>
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apply congrArg Q16_16.mk
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apply UInt32.ext
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have hlt := UInt32.toNat_lt av
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simp [toInt] at h ⊢
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split at h
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· omega
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· omega
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· intro h; subst h; rfl
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/-- Non-negative addition: adding epsilon to a non-negative value yields a positive result. -/
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theorem epsilon_add_pos {r : Q16_16} (hr : r.toInt ≥ 0) :
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(r + epsilon).toInt > 0 := by
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change toInt (add r epsilon) > 0
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cases r with
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| mk rv =>
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have hlt := UInt32.toNat_lt rv
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simp [add, epsilon, toInt] at hr ⊢
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split
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· native_decide
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· rename_i hhi
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split
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· rename_i hlo
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omega
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· rename_i hlo
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have hrvadd : (rv + 1).toNat = rv.toNat + 1 := by
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rw [UInt32.toNat_add, UInt32.toNat_ofNat]
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norm_num
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omega
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have hpos : 0 < (rv + 1).toNat := by
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rw [hrvadd]
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omega
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have hnosign : ¬2147483648 ≤ rv + 1 := by
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change ¬(2147483648 : UInt32).toNat ≤ (rv + 1).toNat
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simp [UInt32.toNat_ofNat, hrvadd]
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omega
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simp [hnosign]
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exact_mod_cast hpos
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def sat01 (q : Q16_16) : Q16_16 :=
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if q.toInt < 0 then zero
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else if q.toInt > 65536 then one
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else q
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def max (a b : Q16_16) : Q16_16 :=
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if a.toInt ≥ b.toInt then a else b
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def le (a b : Q16_16) : Bool := a.toInt ≤ b.toInt
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def recip (x : Q16_16) : Q16_16 :=
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let xInt := x.toInt
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if xInt == 0 then maxVal
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else
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let numer : Nat := 0x100000000
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let denom := (if xInt < 0 then -xInt else xInt).toNat
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let r := numer / denom
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let y := if r > 0x7FFFFFFF then maxVal else ⟨r.toUInt32⟩
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if xInt < 0 then neg y else y
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def ofRaw (n : Nat) : Q16_16 := ⟨n.toUInt32⟩
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def min (a b : Q16_16) : Q16_16 :=
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if a.toInt ≤ b.toInt then a else b
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end Q16_16
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/--
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Q0.64 pure fraction representation using UInt64 (range: [-1, 1 - 2^-64])
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- 64-bit unsigned integer interpreted as signed 0.64 fixed point.
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- 0x7FFFFFFFFFFFFFFF = 1.0 (max positive value)
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- 0x0000000000000000 = 0.0
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- Range: [-1.0, 1.0 - 2^-64] ≈ [-1.0, 0.99999999999999999999]
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- Resolution: 1/2^63 ≈ 1.08e-19
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Used for maximum-precision information-theoretic coding calculations
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where dimensionless quantities require highest resolution.
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-/
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structure Q0_64 where
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val : UInt64
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deriving Repr, DecidableEq, BEq, Inhabited
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instance : ToJson Q0_64 where
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toJson q := Json.mkObj [("val", toJson q.val.toNat)]
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instance : FromJson Q0_64 where
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fromJson? j := do
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let val ← (← j.getObjVal? "val").getNat?
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pure ⟨val.toUInt64⟩
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namespace Q0_64
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/-- Maximum positive value (represents ~1.0) -/
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def one : Q0_64 := ⟨0x7FFFFFFFFFFFFFFF⟩
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|
|
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/-- Zero -/
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|
def zero : Q0_64 := ⟨0x0000000000000000⟩
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|
|
|
/-- Rational constructor: numerator/denominator → Q0_64.
|
|
Scale = 2^63. No Float used. Intermediate in Nat. -/
|
|
def ofRatio (num : Nat) (den : Nat) : Q0_64 :=
|
|
if den = 0 then zero
|
|
else ⟨(num * (1 <<< 63 : Nat) / den).toUInt64⟩
|
|
|
|
/-- Half -/
|
|
def half : Q0_64 := ⟨0x3FFFFFFFFFFFFFFF⟩
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|
|
|
/-- Negation -/
|
|
def neg (x : Q0_64) : Q0_64 := ⟨-x.val⟩
|
|
|
|
/-- Saturating addition -/
|
|
def add (a b : Q0_64) : Q0_64 :=
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|
let a_s := Int.ofNat a.val.toNat
|
|
let b_s := Int.ofNat b.val.toNat
|
|
let res := a_s + b_s
|
|
if res > 0x7FFFFFFFFFFFFFFF then ⟨0x7FFFFFFFFFFFFFFF⟩
|
|
else if res < -0x8000000000000000 then ⟨0x8000000000000000⟩
|
|
else ⟨UInt64.ofNat res.toNat⟩
|
|
|
|
/-- Saturating subtraction -/
|
|
def sub (a b : Q0_64) : Q0_64 :=
|
|
let a_s := Int.ofNat a.val.toNat
|
|
let b_s := Int.ofNat b.val.toNat
|
|
let res := a_s - b_s
|
|
if res > 0x7FFFFFFFFFFFFFFF then ⟨0x7FFFFFFFFFFFFFFF⟩
|
|
else if res < -0x8000000000000000 then ⟨0x8000000000000000⟩
|
|
else ⟨UInt64.ofNat res.toNat⟩
|
|
|
|
/-- Multiplication with 63-bit right shift -/
|
|
def mul (a b : Q0_64) : Q0_64 :=
|
|
let prod := (a.val.toNat * b.val.toNat : Nat)
|
|
⟨(prod >>> 63).toUInt64⟩
|
|
|
|
/-- Division with 63-bit left shift using Nat for 128-bit intermediate -/
|
|
def div (a b : Q0_64) : Q0_64 :=
|
|
if b.val = 0 then one
|
|
else
|
|
let num := a.val.toNat * (1 <<< 63 : Nat)
|
|
let den := b.val.toNat
|
|
⟨(num / den).toUInt64⟩
|
|
|
|
/-- Absolute value -/
|
|
def abs (x : Q0_64) : Q0_64 :=
|
|
if (x.val &&& 0x8000000000000000) != 0 then neg x else x
|
|
|
|
/-- Convert to Int for comparison -/
|
|
@[inline]
|
|
def toInt (q : Q0_64) : Int :=
|
|
Int.ofNat q.val.toNat - (if q.val ≥ 0x8000000000000000 then 0x10000000000000000 else 0)
|
|
|
|
/-- Boundary conversion from external Float.
|
|
Do not use in canonical hot-path coding. Prefer ofRatio or raw receipts. -/
|
|
def ofFloat (f : Float) : Q0_64 :=
|
|
if f.isNaN || f ≥ 1.0 then one
|
|
else if f ≤ -1.0 then ⟨0x8000000000000000⟩
|
|
else ⟨(f * (2^63 : Float)).floor.toUInt64⟩
|
|
|
|
/-- Convert to Float -/
|
|
def toFloat (q : Q0_64) : Float :=
|
|
Float.ofInt (toInt q) / (2^63 : Float)
|
|
|
|
instance : Add Q0_64 := ⟨add⟩
|
|
instance : Sub Q0_64 := ⟨sub⟩
|
|
instance : Mul Q0_64 := ⟨mul⟩
|
|
instance : Div Q0_64 := ⟨div⟩
|
|
instance : Neg Q0_64 := ⟨neg⟩
|
|
|
|
/--
|
|
Ordering for Q0_64 is signed representation order over canonical normalized
|
|
coding atoms and residual/perturbation atoms.
|
|
|
|
This is valid for:
|
|
- thresholds
|
|
- normalized scores
|
|
- audit pass/fail comparisons
|
|
- bounded coding coordinates
|
|
- signed residual comparisons within the same declared projection domain
|
|
|
|
This is not a physical dimensional order unless the value was produced by an
|
|
explicit source-to-coding projection receipt.
|
|
|
|
Do not compare raw source measurements such as helical diameter, rigidity,
|
|
temperature, charge, or energy directly in Q0_64 unless each value has passed
|
|
through the same declared normalization/projection map.
|
|
-/
|
|
instance : LE Q0_64 where
|
|
le a b := a.toInt ≤ b.toInt
|
|
|
|
instance : LT Q0_64 where
|
|
lt a b := a.toInt < b.toInt
|
|
|
|
instance : DecidableRel (fun a b : Q0_64 => a ≤ b) :=
|
|
fun a b => inferInstanceAs (Decidable (a.toInt ≤ b.toInt))
|
|
|
|
instance : DecidableRel (fun a b : Q0_64 => a < b) :=
|
|
fun a b => inferInstanceAs (Decidable (a.toInt < b.toInt))
|
|
|
|
end Q0_64
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- Pandigital π Approximation (Space-Efficient Construction)
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
namespace PandigitalPi
|
|
|
|
-- Pandigital pi construction using each digit 0-9 exactly once.
|
|
-- Standard storage: pi ~ 3.1415926 requires 9 ASCII bytes.
|
|
-- Pandigital construction: 3.8415926 - 0.7 = 3.1415926
|
|
-- Uses only 10 nibbles (5 bytes packed) + 1 byte operation = 6 bytes total.
|
|
|
|
/-- High term: 3.8415926 (uses digits 3,8,4,1,5,9,2,6) -/
|
|
def highTerm : Q16_16 := ⟨251819⟩ -- 3.8415926 * 65536 ≈ 251819
|
|
|
|
/-- Low term: 0.7 (uses digits 0,7) -/
|
|
def lowTerm : Q16_16 := ⟨45875⟩ -- 0.7 * 65536 ≈ 45875
|
|
|
|
-- Pandigital pi = highTerm - lowTerm = 3.1415926...
|
|
def piPandigital : Q16_16 := highTerm - lowTerm
|
|
|
|
-- pi reference for comparison (direct Q16.16 encoding)
|
|
def piDirect : Q16_16 := ⟨205944⟩ -- 3.1415926535... * 65536
|
|
|
|
-- Pandigital construction matches direct encoding within 1 LSB
|
|
theorem piPandigitalCorrect : (piPandigital.toInt - piDirect.toInt).natAbs ≤ 1 := by
|
|
native_decide
|
|
|
|
-- Space savings analysis:
|
|
-- - Naive ASCII: "3.1415926" = 9 bytes
|
|
-- - Direct Q16.16: 4 bytes
|
|
-- - Pandigital construction: 2x4 = 8 bytes for terms, but reconstructs pi without storing it
|
|
-- - Packed nibble encoding of digits 0-9: 10 nibbles = 5 bytes + 1 byte op = 6 bytes
|
|
-- - True savings when construction is shared across multiple constants
|
|
def spaceAnalysis : String :=
|
|
"Pandigital pi: 6 bytes packed vs 4 bytes direct Q16.16 (trade-off for mathematical elegance)"
|
|
|
|
-- Verification witnesses
|
|
#eval piPandigital.toFloat -- Expected: ~3.1415925
|
|
#eval piDirect.toFloat -- Expected: ~3.1415925
|
|
#eval (piPandigital.toInt - piDirect.toInt).natAbs -- Expected: 0 or 1
|
|
|
|
end PandigitalPi
|
|
|
|
end Semantics.FixedPoint
|
|
|
|
namespace Semantics
|
|
export FixedPoint (Q0_16 Q16_16 Q0_64)
|
|
namespace Q16_16
|
|
export FixedPoint.Q16_16 (mk zero one negOne epsilon two infinity maxVal minVal ofNat satFromNat ofRatio toInt ofRawInt ofFloat toFloat scale ofInt add sub mul div abs neg sqrt ln log2 expNeg sat01 max min le ge gt lt recip ofRaw clip isNeg zero_mul mul_zero one_mul mul_one zero_toInt one_toInt epsilon_toInt epsilon_toInt_pos toInt_eq_zero_iff epsilon_add_pos)
|
|
end Q16_16
|
|
namespace Q0_16
|
|
export FixedPoint.Q0_16 (zero one half neg add sub mul div abs lt le gt ge toFloat ofFloat log2 min)
|
|
end Q0_16
|
|
namespace Q0_64
|
|
export FixedPoint.Q0_64 (one zero ofRatio half neg add sub mul div abs toInt ofFloat toFloat)
|
|
end Q0_64
|
|
namespace PandigitalPi
|
|
export FixedPoint.PandigitalPi (highTerm lowTerm piPandigital piDirect piPandigitalCorrect spaceAnalysis)
|
|
end PandigitalPi
|
|
end Semantics
|