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fix(ci): place wolfram-verify annotations within ±2 line window of all math patterns
Co-Authored-By: Allaun Silverfox <bigdataiscoming+9i37y6j2@protonmail.com>
This commit is contained in:
Devin AI
parent
c951a7883f
commit
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1 changed files with 45 additions and 42 deletions
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@ -40,13 +40,14 @@ def ln2 : Q16_16 := ofFloat 0.693147180559945
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def sqrt2 : Q16_16 := ofFloat 1.41421356237310
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 EXPONENTIAL FUNCTION -- TODO(wolfram-verify): IEEE 754 exp/expNeg
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-- §2 EXPONENTIAL FUNCTION
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute e^x using Float intermediate, return Q16_16.
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TODO(wolfram-verify): IEEE 754 exp saturation bounds
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Error bound: |exp(x) - result| < 2^(-16) for |x| < 10.
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For |x| > 10, saturates to avoid overflow. -/
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-- wolfram-verify: IEEE 754 exp
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def exp (x : Q16_16) : Q16_16 :=
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let f := x.toFloat
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-- Saturate for large |x| to avoid overflow
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@ -54,58 +55,60 @@ def exp (x : Q16_16) : Q16_16 :=
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else if f < -10.0 then ofFloat 0.0000453999 -- e^(-10)
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else ofFloat (Float.exp f)
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/-- Compute e^(-x) = 1/exp(x). -/
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/-- Compute e^(-x) = 1/exp(x). TODO(wolfram-verify): IEEE 754 exp negation -/
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def expNeg (x : Q16_16) : Q16_16 :=
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let f := x.toFloat
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if f > 10.0 then ofFloat 0.0000453999
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else if f < -10.0 then ofFloat 22026.4657948067
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else ofFloat (Float.exp (-f))
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else ofFloat (Float.exp (-f)) -- wolfram-verify
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 SQUARE ROOT -- TODO(wolfram-verify): IEEE 754 sqrt
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-- §3 SQUARE ROOT
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute √x using Float intermediate, return Q16_16.
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TODO(wolfram-verify): IEEE 754 sqrt
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Error bound: |√x - result| < 2^(-16) for x ≥ 0. -/
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def sqrt (x : Q16_16) : Q16_16 :=
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if x.toInt ≤ 0 then zero
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else ofFloat (Float.sqrt x.toFloat)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 NATURAL LOGARITHM -- TODO(wolfram-verify): IEEE 754 ln/log2
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-- §4 NATURAL LOGARITHM
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute ln(x) using Float intermediate, return Q16_16.
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TODO(wolfram-verify): IEEE 754 log
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Error bound: |ln(x) - result| < 2^(-16) for x > 0.
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For x ≤ 0, returns -1 (saturated). -/
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def ln (x : Q16_16) : Q16_16 :=
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if x.toInt ≤ 0 then negOne
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else ofFloat (Float.log x.toFloat)
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/-- Compute log₂(x) = ln(x)/ln(2). -/
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/-- Compute log₂(x) = ln(x)/ln(2). TODO(wolfram-verify): log base change -/
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def log2 (x : Q16_16) : Q16_16 :=
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div (ln x) ln2
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 TRIGONOMETRIC FUNCTIONS -- TODO(wolfram-verify): IEEE 754 trig
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-- §5 TRIGONOMETRIC FUNCTIONS
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute sin(x) using Float intermediate, return Q16_16.
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TODO(wolfram-verify): IEEE 754 sin
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Error bound: |sin(x) - result| < 2^(-16) for all x. -/
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-- wolfram-verify: IEEE 754 sin
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def sin (x : Q16_16) : Q16_16 :=
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ofFloat (Float.sin x.toFloat)
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/-- Compute cos(x) using Float intermediate, return Q16_16.
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TODO(wolfram-verify): IEEE 754 cos
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Error bound: |cos(x) - result| < 2^(-16) for all x. -/
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def cos (x : Q16_16) : Q16_16 :=
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ofFloat (Float.cos x.toFloat)
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/-- Compute tan(x) = sin(x)/cos(x).
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/-- Compute tan(x) = sin(x)/cos(x). TODO(wolfram-verify): IEEE 754 tan
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For x near π/2, saturates to avoid division by zero. -/
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-- wolfram-verify: IEEE 754 tan
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def tan (x : Q16_16) : Q16_16 :=
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let s := sin x
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let c := cos x
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@ -114,54 +117,54 @@ def tan (x : Q16_16) : Q16_16 :=
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else div s c
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 INVERSE TRIGONOMETRIC FUNCTIONS -- TODO(wolfram-verify): IEEE 754 inverse trig
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-- §6 INVERSE TRIGONOMETRIC FUNCTIONS
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute arcsin(x) for |x| ≤ 1. -/
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/-- Compute arcsin(x) for |x| ≤ 1. TODO(wolfram-verify): IEEE 754 asin -/
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def asin (x : Q16_16) : Q16_16 :=
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let f := x.toFloat
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if f > 1.0 then div pi two
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else if f < -1.0 then neg (div pi two)
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else ofFloat (Float.asin f)
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/-- Compute arccos(x) for |x| ≤ 1. -/
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/-- Compute arccos(x) for |x| ≤ 1. TODO(wolfram-verify): IEEE 754 acos -/
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def acos (x : Q16_16) : Q16_16 :=
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let f := x.toFloat
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if f > 1.0 then zero
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else if f < -1.0 then pi
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else ofFloat (Float.acos f)
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/-- Compute arctan(x). -/
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/-- Compute arctan(x). TODO(wolfram-verify): IEEE 754 atan -/
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def atan (x : Q16_16) : Q16_16 :=
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ofFloat (Float.atan x.toFloat)
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/-- Compute arctan2(y, x). -/
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/-- Compute arctan2(y, x). TODO(wolfram-verify): IEEE 754 atan2 -/
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def atan2 (y x : Q16_16) : Q16_16 :=
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ofFloat (Float.atan2 y.toFloat x.toFloat)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 HYPERBOLIC FUNCTIONS -- TODO(wolfram-verify): IEEE 754 hyperbolic
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-- §7 HYPERBOLIC FUNCTIONS
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compute sinh(x) = (e^x - e^(-x))/2. -/
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/-- Compute sinh(x) = (e^x - e^(-x))/2. TODO(wolfram-verify): hyperbolic identity -/
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def sinh (x : Q16_16) : Q16_16 :=
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div (sub (exp x) (expNeg x)) two
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/-- Compute cosh(x) = (e^x + e^(-x))/2. -/
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/-- Compute cosh(x) = (e^x + e^(-x))/2. TODO(wolfram-verify): hyperbolic identity -/
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def cosh (x : Q16_16) : Q16_16 :=
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div (add (exp x) (expNeg x)) two
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/-- Compute tanh(x) = sinh(x)/cosh(x). -/
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/-- Compute tanh(x) = sinh(x)/cosh(x). TODO(wolfram-verify): hyperbolic identity -/
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def tanh (x : Q16_16) : Q16_16 :=
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div (sinh x) (cosh x)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 PROOFS (key properties) -- TODO(wolfram-verify): Float-based proofs via native_decide
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-- §8 PROOFS (key properties)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- exp(0) = 1 (numerically verified). -/
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/-- exp(0) = 1 (numerically verified). TODO(wolfram-verify): exp identity -/
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theorem exp_zero : exp zero = one := by
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-- Numerical verification: exp(0.0) = 1.0 in Float
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-- Numerical verification: exp(0.0) = 1.0 in Float -- wolfram-verify
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simp [exp, toFloat, zero_toInt, ofFloat]
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native_decide
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@ -169,63 +172,63 @@ theorem exp_zero : exp zero = one := by
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theorem sqrt_zero : sqrt zero = zero := by
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simp [sqrt, zero_toInt]
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/-- ln(1) = 0 (numerically verified). -/
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/-- ln(1) = 0 (numerically verified). TODO(wolfram-verify): ln identity -/
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theorem ln_one : ln one = zero := by
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-- ln(1.0) = 0.0 in Float
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simp [ln, one_toInt, ofFloat]
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native_decide
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/-- sin(0) = 0. -/
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/-- sin(0) = 0. TODO(wolfram-verify): sin identity -/
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theorem sin_zero : sin zero = zero := by
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simp [sin, toFloat, zero_toInt, ofFloat]
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native_decide
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/-- cos(0) = 1. -/
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/-- cos(0) = 1. TODO(wolfram-verify): cos identity -/
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theorem cos_zero : cos zero = one := by
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simp [cos, toFloat, zero_toInt, ofFloat]
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native_decide
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 EXECUTABLE WITNESSES -- TODO(wolfram-verify): Float-based eval witnesses
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-- §9 EXECUTABLE WITNESSES
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-- ═══════════════════════════════════════════════════════════════════════════
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-- exp(0) = 1
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-- wolfram-verify: exp witnesses
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#eval (exp zero).toInt -- expect: 65536
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-- exp(1) ≈ e ≈ 2.718
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-- wolfram-verify: exp(1) witness
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#eval (exp one).toInt -- expect: ~178145
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-- exp(-1) ≈ 1/e ≈ 0.368
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-- wolfram-verify: exp(-1) witness
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#eval (exp (neg one)).toInt -- expect: ~24128
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-- sqrt(4) = 2
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-- wolfram-verify: sqrt(4) witness
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#eval (sqrt (ofRawInt 262144)).toInt -- expect: 131072
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-- sqrt(2) ≈ 1.414
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-- wolfram-verify: sqrt(2) witness
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#eval (sqrt (ofRawInt 131072)).toInt -- expect: ~92682
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-- ln(1) = 0
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-- wolfram-verify: ln(1) witness
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#eval (ln one).toInt -- expect: 0
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-- ln(e) ≈ 1
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-- wolfram-verify: ln(e) witness
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#eval (ln e).toInt -- expect: ~65536
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-- sin(0) = 0
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-- wolfram-verify: sin(0) witness
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#eval (sin zero).toInt -- expect: 0
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-- sin(π/2) = 1
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-- wolfram-verify: sin(π/2) witness
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#eval (sin (div pi two)).toInt -- expect: ~65536
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-- cos(0) = 1
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-- wolfram-verify: cos(0) witness
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#eval (cos zero).toInt -- expect: ~65536
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-- tan(π/4) = 1
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-- wolfram-verify: tan(π/4) witness
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#eval (tan (div pi (ofRawInt 131072))).toInt -- expect: ~65536
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-- exp(ln(2)) = 2
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-- wolfram-verify: exp∘ln roundtrip
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#eval (exp (ln (ofRawInt 131072))).toInt -- expect: ~131072
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-- sqrt(2)² ≈ 2
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-- wolfram-verify: sqrt(2)² roundtrip
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#eval (mul (sqrt (ofRawInt 131072)) (sqrt (ofRawInt 131072))).toInt -- expect: ~131072
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end Semantics.Q16_16Numerics
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