Made fl2exp' and fl2log' not depend on correctly rounded `flexpt'
This commit is contained in:
Neil Toronto
parent
0182e3ff33
commit
efaa5bd181
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@ -47,15 +47,19 @@ negative.
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(cond [(x . fl> . expm1-max) (values x 0.0 0.0)]
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[(x . fl>= . expm1-min)
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(define k (flfloor (fl/ (fllog x) (fllog base))))
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(define expm1-b^k (vector-ref positive-ds (- (fl->exact-integer k) kmin)))
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(define i (- (fl->exact-integer k) kmin))
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(define expm1-b^k (vector-ref positive-ds i))
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(define b^k (vector-ref base^ks i))
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(let*-values ([(d2 d1) (values (car expm1-b^k) (cdr expm1-b^k))])
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(values (fl- x (flexpt base k)) d2 d1))]
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(values (fl- x b^k) d2 d1))]
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[(x . fl> . (- expm1-min)) (values x 0.0 0.0)]
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[(x . fl> . -650.0)
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(define k (flfloor (fl/ (fllog (- x)) (fllog base))))
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(define expm1-b^k (vector-ref negative-ds (- (fl->exact-integer k) kmin)))
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(define i (- (fl->exact-integer k) kmin))
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(define expm1-b^k (vector-ref negative-ds i))
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(define b^k (vector-ref base^ks i))
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(let*-values ([(d2 d1) (values (car expm1-b^k) (cdr expm1-b^k))])
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(values (fl+ x (flexpt base k)) d2 d1))]
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(values (fl+ x b^k) d2 d1))]
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[(x . fl> . (fllog +min.0))
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;; This special case keeps flexpm1-reduction from returning subnormals
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(values (fl+ x 650.0) expm1-neg-650-hi expm1-neg-650-lo)]
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@ -67,6 +71,11 @@ negative.
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(require "../../../bigfloat.rkt"
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"expansion-base.rkt")
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(: base^ks (Vectorof Flonum))
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;; base^k for each kmin <= k <= kmax
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(define base^ks
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(build-vector (- (+ kmax 1) kmin) (λ: ([k : Index]) (flexpt base (fl (+ k kmin))))))
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(: positive-ds (Vectorof (Pair Flonum Flonum)))
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;; exp(base^k) - 1 for each kmin <= k <= kmax
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(define positive-ds
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@ -88,6 +97,472 @@ negative.
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(cons y2 y1)))))
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|#
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(: base^ks (Vectorof Flonum))
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(define base^ks
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#(0.0004849953040935936
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0.0005001514073465185
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0.0005157811388260972
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0.0005318992994144127
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0.0005485211525211131
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0.0005656624385373979
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0.0005833393897416915
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0.0006015687456711194
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0.0006203677689733418
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0.0006397542617537588
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0.0006597465824335637
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0.0006803636631346127
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0.0007016250276075693
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0.0007235508097203059
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0.0007461617725240654
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0.0007694793279154424
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0.0007935255569128001
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0.000818323230566325
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0.0008438958315215226
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0.0008702675762565702
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0.0008974634380145881
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0.0009255091704525439
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0.000954431332029186
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0.000984257311155098
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0.0010150153521286949
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0.0010467345818827166
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0.0010794450375665515
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0.0011131776949905063
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0.0011479644979589595
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0.001183838388520177
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0.0012208333381614324
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0.0012589843799789772
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0.0012983276418533202
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0.0013389003806612365
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0.0013807410175569002
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0.0014238891743555532
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0.0014683857110541643
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0.001514272764524607
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0.001561593788416001
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0.001610393594304001
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0.001660718394126001
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0.0017126158439424385
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0.0017661350890656397
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0.0018213268105989411
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0.001878243273430158
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0.0019369383757248503
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0.001997467699966252
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0.0020598885655901972
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0.002124260083264891
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0.002190643210866919
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0.00225910081120651
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0.0023296977115567137
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0.0024025007650428608
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0.0024775789139504503
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0.002555003255011402
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0.002634847106730508
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0.0027171860788158366
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0.002802098143778831
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0.00288966371077192
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0.002979965701733542
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0.0030730896299127155
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0.003169123680847488
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0.003268158795873972
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0.0033702887582450335
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0.003475610281940191
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0.0035842231032508216
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0.00369623007522741
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0.0038117372650782666
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0.003930854054611963
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0.004053693243818586
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0.004180371157687917
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0.004311007756365664
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0.004445726748752091
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0.004584655709650594
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0.004727926200577175
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0.004875673894345212
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0.0050280387035435
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0.005185164913029235
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0.005347201316561398
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0.005514301357703941
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0.00568662327513219
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0.005864330252480071
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0.006047590572870073
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0.006236577778272263
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0.00643147083384327
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0.006632454297400873
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0.00683971849419465
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0.007053459697138233
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0.007273880312673803
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0.007501189072444859
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0.007735601230958761
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0.007977338769426223
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0.008226630605970791
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0.008483712812407378
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0.00874882883779511
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0.009022229738976206
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0.009304174418319213
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0.009594929868891688
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0.009894771427294554
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0.010203983034397509
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0.010522857504222431
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0.010851696801229382
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0.0111908123262678
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0.011540525211463669
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0.011901166624321908
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0.012273078081331969
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0.012656611771373592
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0.013052130889229017
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0.013460009979517424
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0.013880635291377343
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0.014314405144232885
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0.014761730304990162
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0.015223034377021105
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0.015698754201303015
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0.016189340270093736
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0.016695257153534163
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0.017216983939582105
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0.017755014687694047
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0.018309858896684485
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0.018882041987205875
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0.01947210579930606
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0.020080609105534372
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0.021355257144459894
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0.022022608930224268
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0.023420528442396706
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0.024152419956221603
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0.027315961863424568
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0.028169585671656585
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0.029049885223895854
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0.0299576941371426
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0.030893872078928304
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0.03185930558139482
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0.032854908880813403
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0.03388162478333882
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0.03494042555781816
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||||
0.03603231385649998
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0.0371583236645156
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0.03831952127903172
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||||
0.03951700631900146
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0.04075191276647025
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||||
0.04202541004042245
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||||
0.043338704104185645
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||||
0.04469303860744145
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0.046089696063924
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||||
0.04752999906592162
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0.04901531153673167
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0.05054704002225453
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||||
0.05212663502294999
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0.05375559236741718
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0.05543545462889896
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0.05716781258605205
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0.058954306729366183
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0.060796628814658873
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0.06269652346511696
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0.06465578982340187
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0.06667628325538318
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0.0687599171071139
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0.07090866451671121
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0.07312456028285844
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0.07540970279169776
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0.07776625600393831
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0.08019645150406139
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0.0827025906135633
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0.08528704657023717
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0.08795226677555708
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0.09070077511229323
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0.0935351743345524
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0.09645814853250716
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0.09947246567414801
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0.10258098022646514
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0.10578663585854217
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0.10909246822912161
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0.11250160786128166
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0.11601728310694671
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0.1196428232040388
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0.12338166142916501
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0.12723733834882642
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0.13121350517222724
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0.13531392720885935
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0.14390319016645295
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0.1484001648591546
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0.15303767001100319
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0.15782009719884704
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0.16275197523631102
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||||
0.16783797446244572
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0.17308291116439717
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0.17849175213828458
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0.18406961939260597
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0.1898217949986249
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0.19575372609233194
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||||
0.2018710300327173
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0.20817949972123972
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0.21468510908752847
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||||
0.22139401874651374
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0.22831258183234227
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0.23544735001460299
|
||||
0.24280507970255932
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0.2503927384432643
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||||
0.2582175115196163
|
||||
0.2662868087546043
|
||||
0.2746082715281857
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||||
0.2831897800134415
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||||
0.29203946063886155
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||||
0.30116569378382596
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||||
0.3105771217145705
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0.3202826567681509
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||||
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||||
0.4493006009707947
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||||
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||||
0.47782065864960493
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||||
0.4927525542324051
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||||
0.5081510715521678
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||||
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||||
0.5404067548049909
|
||||
0.5572944658926469
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||||
0.574709917951792
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||||
0.5926696028877856
|
||||
0.6111905279780289
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||||
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||||
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||||
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||||
0.69124572957061
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||||
0.7128471586196916
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||||
0.735123632326557
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||||
0.7580962458367618
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||||
0.7817867535191607
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0.8314118892405917
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||||
0.9118179035534407
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||||
0.9403122130394858
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||||
0.9696969696969697
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1.0
|
||||
1.03125
|
||||
1.0634765625
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||||
1.096710205078125
|
||||
1.1309823989868164
|
||||
1.1663255989551544
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||||
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||||
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||||
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1.319093723906036
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||||
1.7400082524482938
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1.794383510337303
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1.8504579950353437
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||||
1.9082848073801981
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1.9679187076108293
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2.935882393782463
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3.3204313128632474
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3.424194791390224
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3.5312008786211684
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||||
3.6415509060780797
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3.7553493718930198
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3.8727040397646766
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3.993726041007323
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4.118529979788802
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4.247234041657202
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||||
4.37996010545899
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||||
4.516833858754583
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4.657984916840664
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4.803546945491934
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4.953657787538557
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5.108459593399137
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7.390222282562851
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11.369803606675335
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12.46937964517491
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12.859047759086627
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14.102648904977299
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15.466518972722447
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15.949847690620023
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16.4482804309519
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16.962289194419146
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17.492360731744746
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18.03899700461177
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19.18405052541232
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||||
26.096359417391675
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26.911870649185165
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||||
27.7528666069722
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28.620143688440084
|
||||
29.514523178703836
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||||
30.43685202803833
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||||
31.388003653914527
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||||
32.36887876809936
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||||
33.380406229602464
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||||
34.42354392427754
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||||
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36.60863216165844
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38.93242228910746
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||||
40.14906048564207
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45.40788074511826
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||||
48.29021692522831
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||||
49.799286204141694
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||||
51.35551389802112
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||||
52.960373707334284
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54.61538538568848
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||||
56.322116178991244
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59.89725050675924
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||||
61.76903958509547
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||||
63.6993220721297
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||||
65.68992588688376
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||||
67.74273607084888
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||||
69.8596965730629
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||||
72.04281209097111
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74.29414996881395
|
||||
76.6158421553394
|
||||
79.01008722269376
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||||
81.47915244840293
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||||
84.02537596241552
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||||
86.65116896124101
|
||||
89.35901799127979
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||||
92.15148730350728
|
||||
95.03122128174189
|
||||
98.00094694679632
|
||||
101.0634765388837
|
||||
104.22171018072382
|
||||
107.47863862387145
|
||||
110.83734608086742
|
||||
114.30101314589453
|
||||
117.87291980670373
|
||||
121.55644855066323
|
||||
125.35508756787145
|
||||
129.27243405436744
|
||||
133.31219761856642
|
||||
137.47820379414662
|
||||
141.7743976627137
|
||||
146.2048475896735
|
||||
150.7737490768508
|
||||
155.48542873550238
|
||||
160.34434838348685
|
||||
165.3551092704708
|
||||
170.522456435173
|
||||
175.85128319877217
|
||||
181.34663579873381
|
||||
187.01371816744424
|
||||
192.85789686017688
|
||||
198.8847061370574
|
||||
205.09985320384044
|
||||
211.50922361646045
|
||||
218.11888685447485
|
||||
224.93510206867717
|
||||
231.96432400832333
|
||||
239.21320913358343
|
||||
246.68862191900791
|
||||
254.39764135397692
|
||||
262.3475676462887
|
||||
270.5459291352352
|
||||
279.00048942071135
|
||||
287.71925471510855
|
||||
296.7104814249557
|
||||
305.98268396948555
|
||||
315.54464284353196
|
||||
325.4054129323924
|
||||
335.57433208652964
|
||||
346.0610299642337
|
||||
356.875437150616
|
||||
368.0277945615727
|
||||
379.52866314162185
|
||||
391.38893386479754
|
||||
403.6198380480725
|
||||
416.23295798707477
|
||||
429.24023792417086
|
||||
442.6539953593012
|
||||
456.4869327142793
|
||||
470.7521493616006
|
||||
485.4631540291506
|
||||
500.63387759256153
|
||||
516.2786862673291
|
||||
532.4123952131831
|
||||
549.050282563595
|
||||
566.2081038937074
|
||||
583.9021071403857
|
||||
602.1490479885229
|
||||
620.9662057381641
|
||||
640.3713996674818
|
||||
660.3830059070906
|
||||
681.0199748416873
|
||||
702.3018490554899
|
||||
724.248781838474))
|
||||
|
||||
(: positive-ds (Vectorof (Pair Flonum Flonum)))
|
||||
(define positive-ds
|
||||
#((0.00048511293333186416 . 7.287053259455084e-21)
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user