test f* function with one argument

source/himalaya/mh2_eft/ThresholdLoopFunctions.cpp

@@ -458,10 +458,14 @@ double g(double r) noexcept
 
 double f1(double r) noexcept
 {
+   if (r == 0.) {
+      return 0;
+   }
+
    const double r2 = sqr(r);
 
-   if (is_zero(r, 0.01)) {
-      return 18./7.*r2;
+   if (std::fabs(r) < 0.01) {
+      return r2*(18./7 + 6./7*r2*(7 + 5*std::log(r2)));
    }
 
    const double d = r2 - 1;
@@ -478,10 +482,14 @@ double f1(double r) noexcept
 
 double f2(double r) noexcept
 {
+   if (r == 0.) {
+      return 0;
+   }
+
    const double r2 = sqr(r);
 
-   if (is_zero(r, 0.01)) {
-      return 22./9.*r2;
+   if (std::fabs(r) < 0.01) {
+      return r2*(22./9 + 2./9*r2*(23 + 17*std::log(r2)));
    }
 
    const double d = r2 - 1;
@@ -498,11 +506,16 @@ double f2(double r) noexcept
 
 double f3(double r) noexcept
 {
-   if (is_zero(r, 1e-6)) {
-      return 4./3.;
+   if (r == 0.) {
+      return 4./3;
    }
 
    const double r2 = sqr(r);
+
+   if (is_zero(r, 1e-6)) {
+      return 4./3 + 2./3*r2*(13 + 6*std::log(r2));
+   }
+
    const double d = r2 - 1;
 
    if (is_equal(std::fabs(r), 1., 0.01)) {
@@ -518,11 +531,16 @@ double f3(double r) noexcept
 
 double f4(double r) noexcept
 {
-   if (is_zero(r, 1e-6)) {
+   if (r == 0.) {
       return 12./7.;
    }
 
    const double r2 = sqr(r);
+
+   if (is_zero(r, 1e-6)) {
+      return 12./7 + 2./7*r2*(37 + 18*std::log(r2));
+   }
+
    const double d = r2 - 1;
 
    if (is_equal(std::fabs(r), 1., 0.01)) {

test/data/f1_.txt

@@ -0,0 +1,146 @@
+0	0
+0.05	0.00630460475817347
+0.1	0.0242938547018057
+0.15	0.0522313029319074
+0.2	0.0883469368623725
+0.25	0.131038854842681
+0.3	0.178924759803624
+0.35	0.230840307182088
+0.4	0.285818157821581
+0.45	0.343061485563424
+0.5	0.401917686943558
+0.55	0.461854557849988
+0.6	0.522439636897915
+0.65	0.58332271999505
+0.7	0.644221263069468
+0.75	0.704908294859515
+0.8	0.765202455328139
+0.85	0.824959807004785
+0.9	0.884067111710167
+0.95	0.942436311990352
+1.	1.
+1.05	1.05670769460087
+1.1	1.11252277972501
+1.15	1.16741998395255
+1.2	1.22138330341281
+1.25	1.27440428823995
+1.3	1.32648062757347
+1.35	1.37761498008385
+1.4	1.42781400673457
+1.45	1.47708757038713
+1.5	1.52544807326572
+1.55	1.5729099085065
+1.6	1.61948900625463
+1.65	1.66520245822531
+1.7	1.71006820746416
+1.75	1.75410479234749
+1.8	1.79733113575135
+1.85	1.83976637186859
+1.9	1.88142970442821
+1.95	1.92234029112154
+2.	1.96251714990736
+2.05	2.00197908358546
+2.1	2.04074461962238
+2.15	2.07883196270673
+2.2	2.11625895792183
+2.25	2.15304306276514
+2.3	2.18920132652905
+2.35	2.22475037579607
+2.4	2.25970640500067
+2.45	2.29408517117707
+2.5	2.32790199215267
+2.55	2.36117174756423
+2.6	2.39390888217343
+2.65	2.4261274110413
+2.7	2.45784092619167
+2.75	2.48906260445299
+2.8	2.51980521621781
+2.85	2.55008113490149
+2.9	2.57990234691764
+2.95	2.60928046201766
+3.	2.63822672386764
+3.05	2.66675202075718
+3.1	2.69486689635334
+3.15	2.72258156042789
+3.2	2.7499058994997
+3.25	2.77684948734469
+3.3	2.80342159533524
+3.35	2.82963120257901
+3.4	2.85548700583347
+3.45	2.88099742917825
+3.5	2.90617063343189
+3.55	2.93101452530378
+3.6	2.95553676627511
+3.65	2.97974478120547
+3.7	3.00364576666399
+3.75	3.02724669898588
+3.8	3.05055434205653
+3.85	3.0735752548268
+3.9	3.09631579856398
+3.95	3.11878214384382
+4.	3.14098027728945
+4.05	3.16291600806374
+4.1	3.18459497412175
+4.15	3.20602264823045
+4.2	3.22720434376263
+4.25	3.24814522027253
+4.3	3.26885028886027
+4.35	3.28932441733245
+4.4	3.30957233516611
+4.45	3.32959863828305
+4.5	3.34940779364169
+4.55	3.36900414365306
+4.6	3.38839191042774
+4.65	3.40757519986027
+4.7	3.42655800555719
+4.75	3.44534421261499
+4.8	3.46393760125379
+4.85	3.48234185031255
+4.9	3.50056054061129
+4.95	3.51859715818566
+5.	3.53645509739909
+0.9	0.884067111710167
+0.99	0.988554343782905
+0.999	0.998856971485806
+0.9999	0.999885712571486
+0.99999	0.999988571411429
+0.999999	0.999998857142686
+0.9999999	0.999999885714284
+0.99999999	0.999999988571429
+0.999999999	0.999999998857143
+0.9999999999	0.99999999988571
+0.99999999999	0.99999999998857
+0.999999999999	0.99999999999886
+0.9999999999999	0.99999999999989
+0.99999999999999	0.99999999999999
+1.	1.
+1.1	1.11252277972501
+1.01	1.01141137233964
+1.001	1.00114268565723
+1.0001	1.00011428399994
+1.00001	1.00001142855429
+1.000001	1.00000114285697
+1.0000001	1.00000011428571
+1.00000001	1.00000001142857
+1.000000001	1.00000000114286
+1.0000000001	1.00000000011429
+1.00000000001	1.00000000001143
+1.000000000001	1.00000000000114
+1.0000000000001	1.00000000000011
+1.00000000000001	1.00000000000001
+1.	1.
+0.1	0.0242938547018057
+0.01	0.000256808027154226
+0.001	2.57137536194125e-6
+0.0001	2.5714278419708e-8
+1.e-5	2.57142856216035e-10
+1.e-6	2.57142857131615e-12
+1.e-7	2.57142857142725e-14
+1.e-8	2.57142857142856e-16
+1.e-9	2.57142857142857e-18
+1.e-10	2.57142857142857e-20
+1.e-11	2.57142857142857e-22
+1.e-12	2.57142857142857e-24
+1.e-13	2.57142857142857e-26
+1.e-14	2.57142857142857e-28
+1.e-15	2.57142857142857e-30

test/data/f2_.txt

@@ -0,0 +1,146 @@
+0	0
+0.05	0.00600075084435775
+0.1	0.0231757281998757
+0.15	0.0499610684959213
+0.2	0.0847491022626568
+0.25	0.126072020488032
+0.3	0.172651681551255
+0.35	0.223401247129679
+0.4	0.277408777907616
+0.45	0.33391518347223
+0.5	0.392291812752649
+0.55	0.452019847065317
+0.6	0.512672233125305
+0.65	0.573898245908807
+0.7	0.63541049226924
+0.75	0.696974063918502
+0.8	0.758397529601582
+0.85	0.819525474935047
+0.9	0.880232331623147
+0.95	0.940417274506647
+1.	1.
+1.05	1.05891723081836
+1.1	1.11711981887933
+1.15	1.17457034099403
+1.2	1.23124110085434
+1.25	1.28711246639657
+1.3	1.34217148439378
+1.35	1.39641072457242
+1.4	1.44982731407678
+1.45	1.50242213006367
+1.5	1.55419912389152
+1.55	1.60516475500992
+1.6	1.65532751645243
+1.65	1.70469753694626
+1.7	1.75328624720441
+1.75	1.80110610006413
+1.8	1.84817033586295
+1.85	1.89449278586966
+1.9	1.94008770776586
+1.95	1.98496964815048
+2.	2.02915332784983
+2.05	2.07265354648988
+2.1	2.11548510334896
+2.15	2.15766273197801
+2.2	2.19920104646749
+2.25	2.24011449756849
+2.3	2.28041733715156
+2.35	2.32012358971829
+2.4	2.35924702987599
+2.45	2.39780116485053
+2.5	2.43579922125121
+2.55	2.4732541354195
+2.6	2.51017854679284
+2.65	2.54658479379936
+2.7	2.58248491187118
+2.75	2.61789063322486
+2.8	2.65281338810964
+2.85	2.68726430726839
+2.9	2.72125422539381
+2.95	2.75479368539478
+3.	2.78789294331534
+3.05	2.82056197377214
+3.1	2.85281047579656
+3.15	2.88464787898487
+3.2	2.91608334987439
+3.25	2.94712579847671
+3.3	2.97778388490934
+3.35	3.00806602607681
+3.4	3.03798040236021
+3.45	3.0675349642807
+3.5	3.0967374391087
+3.55	3.12559533739526
+3.6	3.15411595940654
+3.65	3.18230640144586
+3.7	3.21017356205104
+3.75	3.23772414805739
+3.8	3.26496468051885
+3.85	3.29190150048196
+3.9	3.31854077460885
+3.95	3.34488850064677
+4.	3.37095051274293
+4.05	3.39673248660448
+4.1	3.42223994450417
+4.15	3.44747826013284
+4.2	3.4724526633008
+4.25	3.49716824449012
+4.3	3.52162995926078
+4.35	3.54584263251333
+4.4	3.56981096261165
+4.45	3.59353952536877
+4.5	3.61703277789967
+4.55	3.64029506234439
+4.6	3.66333060946526
+4.65	3.68614354212192
+4.7	3.70873787862782
+4.75	3.73111753599202
+4.8	3.75328633304971
+4.85	3.7752479934854
+4.9	3.79700614875203
+4.95	3.81856434088973
+5.	3.83992602524761
+0.9	0.880232331623147
+0.99	0.988134889832425
+0.999	0.998814681555649
+0.9999	0.999881480148222
+0.99999	0.999988148134815
+0.999999	0.999998814814681
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+0.999999999	0.999999998814815
+0.9999999999	0.99999999988148
+0.99999999999	0.99999999998815
+0.999999999999	0.99999999999881
+0.9999999999999	0.99999999999988
+0.99999999999999	0.99999999999999
+1.	1.
+1.1	1.11711981887933
+1.01	1.01183844537401
+1.001	1.00118505177787
+1.0001	1.00011851718511
+1.00001	1.00001185183852
+1.000001	1.00000118518505
+1.0000001	1.00000011851852
+1.00000001	1.00000001185185
+1.000000001	1.00000000118519
+1.0000000001	1.00000000011852
+1.00000000001	1.00000000001185
+1.000000000001	1.00000000000119
+1.0000000000001	1.00000000000012
+1.00000000000001	1.00000000000001
+1.	1.
+0.1	0.0231757281998757
+0.01	0.000244147522974592
+0.001	2.44439736349333e-6
+0.0001	2.44444379966315e-8
+1.e-5	2.4444444362569e-10
+1.e-6	2.44444444434517e-12
+1.e-7	2.44444444444328e-14
+1.e-8	2.44444444444443e-16
+1.e-9	2.44444444444444e-18
+1.e-10	2.44444444444444e-20
+1.e-11	2.44444444444444e-22
+1.e-12	2.44444444444444e-24
+1.e-13	2.44444444444444e-26
+1.e-14	2.44444444444444e-28
+1.e-15	2.44444444444444e-30