# The doubles below 2^23 closest to multiples of pi/2: the six closest in each binade from 2 up, found from the continued fraction
# of (pi/2)×2^(52-e). Their sines or cosines are the hardest results to reduce accurately. Each line is an input.
3.141592653589793
4.71238898038469
6.283185307179586
9.42477796076938
10.995574287564276
12.566370614359172
18.84955592153876
21.991148575128552
23.56194490192345
32.98672286269283
39.269908169872416
45.553093477052
51.83627878423159
70.68583470577035
78.53981633974483
91.106186954104
103.67255756846318
116.23892818282235
141.3716694115407
149.22565104551518
174.35839227423352
182.212373908208
232.4778563656447
240.33183799961918
298.45130209103036
331.4380249537232
348.71678454846705
364.424747816416
447.67695313654554
464.9557127312894
513.6503988619312
645.5972903127025
728.849495632832
878.0751466783472
1027.3007977238624
1159.2476891746337
1457.698991265664
1606.9246423111792
1756.1502933566944
2054.601595447725
2335.7741379440113
2634.2254400350416
2915.397982531328
3512.300586713389
3793.4731292096753
4671.5482758880225
5251.172120475339
5268.450880070083
5830.795965062656
7007.322413832034
8166.5701030066675
9343.096551776045
10502.344240950679
11081.968085537996
11661.591930125313
14014.644827664068
15753.516361426018
19845.440792726724
21004.688481901358
22163.93617107599
22743.560015663308
23323.183860250625
31507.032722852036
42009.376963802715
43168.62465297735
44327.87234215198
45487.120031326616
46066.74387591393
46646.36772050125
87496.49699512933
88655.74468430397
89814.9923734786
90974.24006265323
91553.86390724055
92133.48775182787
137040.98393856717
138200.2316277418
181948.48012530647
183107.7278144811
184266.97550365573
229174.47169039503
274081.96787713433
276400.4632554836
321307.9594422229
368533.95100731147
413441.44719405076
458348.94338079006
552800.9265109672
642615.9188844458
687523.4150711851
737067.9020146229
826882.8943881015
916697.8867615801
1240324.3415821523
1285231.8377688916
1375046.8301423702
1653765.788776203
1698673.2849629424
1743580.7811496817
2480648.6831643046
2570463.675537783
2615371.1717245225
3307531.577552406
3397346.5699258847
3487161.5622993633
4269136.960500726
4358951.952874204
5051112.358702088
6794693.139851769
7576668.538053132
7666483.53042661
