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Several missing tricks entries; hope this is faster #140

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Merged
merged 2 commits into from
Oct 24, 2025
Merged

Several missing tricks entries; hope this is faster #140

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Several missing tricks entries; hope this is faster
pavpanchekha Oct 23, 2025
6cf3b4c
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pavpanchekha Oct 23, 2025
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44 changes: 29 additions & 15 deletions eval/tricks.rkt
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Original file line number Diff line number Diff line change
Expand Up @@ -85,6 +85,13 @@
; Output: '( '(upper-ampl-bound lower-ampl-bound) ...) with len(srcs) number of elements
(define (get-bounds op z srcs)
(case (object-name op)
[(ival-neg ival-neg!)
; Γ[*]'x = 1
; ↑ampl[*]'x = 0
; ↓ampl[*]'x = 0
(define x (first srcs))
(list (cons 0 0))] ; bounds per x

[(ival-mult ival-mult!)
; Γ[*]'x = 1
; ↑ampl[*]'x = logspan(y)
Expand All @@ -111,7 +118,7 @@
(list (cons (logspan y) 0) ; bounds per x
(cons (+ (logspan x) (* 2 (logspan y))) 0))] ; bounds per y

[(ival-sqrt ival-cbrt)
[(ival-sqrt ival-cbrt ival-sqrt! ival-cbrt!)
; Γ[sqrt]'x = 0.5
; ↑ampl[sqrt]'x = logspan(x)/2 - 1
; ↓ampl[sqrt]'x = 0
Expand Down Expand Up @@ -180,7 +187,7 @@
y-slack)
0)))] ; bounds per y

[(ival-exp ival-exp2)
[(ival-exp ival-exp2 ival-exp! ival-exp2!)
; Γ[exp & exp2]'x = |x| & |x*ln(2)|
; ↑ampl[exp & exp2]'x = maxlog(x) + logspan(z)
; ↓ampl[exp & exp2]'x = minlog(x)
Expand Down Expand Up @@ -224,7 +231,7 @@
(- (- 2) (maxlog z #:less-slack #t))))
(list (cons (+ (- (maxlog x) (minlog z)) (min (maxlog x) 0)) 0)))]

[(ival-sinh)
[(ival-sinh ival-sinh!)
; Γ[sinh]'x = |x * cosh(x) / sinh(x)|
; ↑ampl[sinh]'x = maxlog(x) + logspan(z) - min(minlog(x), 0)
; ↓ampl[sinh]'x = max(0, minlog(x))
Expand All @@ -234,7 +241,7 @@
(max 0 (minlog x #:less-slack #t))))
(list (cons (- (+ (maxlog x) (logspan z)) (min (minlog x) 0)) 0)))]

[(ival-cosh)
[(ival-cosh ival-cosh!)
; Γ[cosh]'x = |x * sinh(x) / cosh(x)|
; ↑ampl[cosh]'x = maxlog(x) + logspan(z) + min(maxlog(x), 0)
; ↓ampl[cosh]'x = max(0, minlog(x) - 1)
Expand All @@ -244,7 +251,7 @@
(max 0 (- (minlog x #:less-slack #t) 1))))
(list (cons (+ (maxlog x) (logspan z) (min (maxlog x) 0)) 0)))]

[(ival-log ival-log2 ival-log10)
[(ival-log ival-log2 ival-log10 ival-log! ival-log2! ival-log10!)
; Γ[log & log2 & log10]'x = |1 / ln(x)| & |ln(2) / ln(x)| & |ln(10) / ln(x)|
; ↑ampl[log & log2 & log10]'x = logspan(x) - minlog(z) + 1
; ↓ampl[log & log2 & log10]'x = - maxlog(z)
Expand All @@ -253,7 +260,7 @@
(list (cons (+ (- (logspan x) (minlog z)) 1) (- (maxlog z #:less-slack #t))))
(list (cons (+ (- (logspan x) (minlog z)) 1) 0)))]

[(ival-asin)
[(ival-asin ival-asin!)
; Γ[asin]'x = |x / (sqrt(1-x^2) * arcsin(x))|
; ↑ampl[asin]'x = | slack, if maxlog(z) > 1
; | 1 else
Expand All @@ -263,7 +270,7 @@
(cons (get-slack) 0) ; assumes that log[1-x^2]/2 is equal to slack
(cons 1 0)))]

[(ival-acos)
[(ival-acos ival-acos!)
; Γ[acos]'x = |-x / (sqrt(1-x^2) * arccos(x))|
; ↑ampl[acos]'x = | slack, if maxlog(x) >= 0
; | 0 else
Expand All @@ -273,7 +280,7 @@
(cons (get-slack) 0) ; assumes that log[1-x^2]/2 is equal to slack
(cons 0 0)))]

[(ival-atan)
[(ival-atan ival-atan!)
; Γ[atan]'x = | x / ((1+x^2) * arctan(x))|
; ↑ampl[atan]'x = - min(|minlog(x)|, |maxlog(x)|) - minlog(z) + logspan(x)
; ↓ampl[atan]'x = - max(|minlog(x)|, |maxlog(x)|) - maxlog(z) - 2
Expand Down Expand Up @@ -306,7 +313,7 @@
(cons (+ (- (maxlog x) (minlog z)) slack) 0))] ; bounds per y

; Currently log1p has a very poor approximation
[(ival-log1p)
[(ival-log1p ival-log1p!)
; Γ[log1p]'x ~ |x * log1p(x) / (1+x)|
; ↑ampl[log1p]'x = | maxlog(x) - minlog(z) + slack, if x is negative
; | maxlog(x) - minlog(z), else
Expand All @@ -320,7 +327,7 @@
(cons (- (maxlog x) (minlog z)) 0)))]

; Currently expm1 has a very poor solution for negative values
[(ival-expm1)
[(ival-expm1 ival-expm1!)
; Γ[expm1]'x = |x * e^x / expm1|
; ↑ampl[expm1]'x = max(1 + maxlog(x), 1 + maxlog(x) - minlog(z))
; ↓ampl[expm1]'x = 0
Expand All @@ -344,14 +351,14 @@
(cons (- (+ (maxlog x) (maxlog y)) (* 2 (min (minlog x) (minlog y))) (minlog z))
0)))]

[(ival-tanh)
[(ival-tanh ival-tanh!)
; Γ[tanh]'x = |x / (sinh(x) * cosh(x))|
; ↑ampl[tanh]'x = logspan(z) + logspan(x)
; ↓ampl[tanh]'x = 0
(define x (first srcs))
(list (cons (+ (logspan z) (logspan x)) 0))]

[(ival-atanh)
[(ival-atanh ival-atanh!)
; Γ[atanh]'x = |x / (log(1-x^2) * atanh(x))|
; ↑ampl[atanh]'x = | 1, if x < 0.5
; | slack
Expand All @@ -361,7 +368,7 @@
(cons (get-slack) 0)
(cons 1 0)))]

[(ival-acosh)
[(ival-acosh ival-acosh!)
; Γ[acosh]'x = |x / (sqrt(x-1) * sqrt(x+1) * acosh)|
; ↑ampl[acosh]'x = | -minlog(z) + slack, if minlog(z) < 2
; | 0
Expand Down Expand Up @@ -399,14 +406,21 @@
(define n (cdr srcs)) ; n is already a floor(log(n))
(list (cons (- (maxlog x) n (- (max (abs (maxlog z)) (abs (minlog z)))) -3) 0))]

; TODO
[(ival-asinh ival-asinh!) (list (cons (get-slack) 0))]

; TODO
[(ival-hypot ival-hypot!) (list (cons (get-slack) 0) (cons (get-slack) 0))]

; TODO
; ↑ampl[...] = slack
; ↓ampl[...] = 0
[(ival-erfc ival-erf ival-lgamma ival-tgamma ival-asinh ival-logb) (list (cons (get-slack) 0))]
[(ival-erfc ival-erf ival-erfc! ival-erf! ival-lgamma ival-tgamma ival-logb)
(list (cons (get-slack) 0))]

; TODO
; ↑ampl[...] = slack
; ↓ampl[...] = 0
[(ival-ceil ival-floor ival-rint ival-round ival-trunc) (list (cons (get-slack) 0))]
[(ival-ceil ival-floor ival-rint ival-rint! ival-round ival-trunc) (list (cons (get-slack) 0))]

[else (map (λ (_) (cons 0 0)) srcs)])) ; exponents for arguments