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math.easing: fix bounce family, add tests (#25956)
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4 files changed

+119
-108
lines changed

‎vlib/math/easing/easing.v‎

Lines changed: 6 additions & 12 deletions
Original file line numberDiff line numberDiff line change
@@ -244,26 +244,20 @@ pub fn in_bounce(x f64) f64 {
244244

245245
// out_bounce returns the equivalent of https://easings.net/#easeOutBounce .
246246
pub fn out_bounce(x f64) f64 {
247-
if math.close(x, 1.0) {
248-
return 1.0
249-
}
250247
xd1 := x * d1
251-
return n1 * (if xd1 < 1.0 {
252-
x * x
248+
return if xd1 < 1.0 {
249+
n1 * x * x
253250
} else if xd1 < 2.0 {
254-
pow((x - 1.5 / d1), 2.0) + 0.75
251+
n1 * pow(x - 1.5 / d1, 2.0) + 0.75
255252
} else if xd1 < 2.5 {
256-
pow((x - 2.25 / d1), 2.0) + 0.9375
253+
n1 * pow(x - 2.25 / d1, 2.0) + 0.9375
257254
} else {
258-
pow((x - 2.625 / d1), 2.0) + 0.984375
259-
})
255+
n1 * pow(x - 2.625 / d1, 2.0) + 0.984375
256+
}
260257
}
261258

262259
// in_out_bounce returns the equivalent of https://easings.net/#easeInOutBounce .
263260
pub fn in_out_bounce(x f64) f64 {
264-
if math.close(x, 1.0) {
265-
return 1.0
266-
}
267261
return if x < 0.5 {
268262
(1.0 - out_bounce(1.0 - 2.0 * x)) / 2.0
269263
} else {

‎vlib/math/easing/easing_test.v‎

Lines changed: 17 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -18,3 +18,20 @@ fn test_in_out_back() {
1818
fn test_in_out_expo() {
1919
assert easing.in_out_expo(123).eq_epsilon(1.0)
2020
}
21+
22+
fn test_in_bounce() {
23+
assert easing.in_bounce(0.333).eq_epsilon(0.1382769374999998)
24+
assert easing.in_bounce(33).eq_epsilon(-7743)
25+
}
26+
27+
fn test_in_out_bounce() {
28+
assert easing.in_out_bounce(0.333).eq_epsilon(0.07817887500000009)
29+
assert easing.in_out_bounce(33).eq_epsilon(15511)
30+
}
31+
32+
fn test_out_bounce() {
33+
assert easing.out_bounce(0.200).eq_epsilon(0.30250000000000005)
34+
assert easing.out_bounce(0.600).eq_epsilon(0.7725)
35+
assert easing.out_bounce(0.800).eq_epsilon(0.94)
36+
assert easing.out_bounce(33).eq_epsilon(7767)
37+
}

‎vlib/v/slow_tests/inout/math_easing_tables.out‎

Lines changed: 63 additions & 63 deletions
Original file line numberDiff line numberDiff line change
@@ -2,77 +2,77 @@
22
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
33
| x | linear | sine | quad | cubic | quart | quint | expo | circ | back | elastic | bounce |
44
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
5-
| -0.5 | -0.500 | 0.293 | 0.250 | -0.125 | 0.063 | -0.031 | 0.000 | 0.134 | -0.763 | 0.000 | -8.694 |
6-
| -0.4 | -0.400 | 0.191 | 0.160 | -0.064 | 0.026 | -0.010 | 0.000 | 0.083 | -0.445 | -0.000 | -7.945 |
7-
| -0.3 | -0.300 | 0.109 | 0.090 | -0.027 | 0.008 | -0.002 | 0.000 | 0.046 | -0.226 | -0.000 | -7.347 |
8-
| -0.2 | -0.200 | 0.049 | 0.040 | -0.008 | 0.002 | -0.000 | 0.000 | 0.020 | -0.090 | 0.000 | -6.900 |
9-
| -0.1 | -0.100 | 0.012 | 0.010 | -0.001 | 0.000 | -0.000 | 0.000 | 0.005 | -0.020 | -0.000 | -6.604 |
10-
| -0.0 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
11-
| 0.1 | 0.100 | 0.012 | 0.010 | 0.001 | 0.000 | 0.000 | 0.002 | 0.005 | -0.014 | 0.002 | -6.140 |
12-
| 0.2 | 0.200 | 0.049 | 0.040 | 0.008 | 0.002 | 0.000 | 0.004 | 0.020 | -0.046 | -0.002 | -6.092 |
13-
| 0.3 | 0.300 | 0.109 | 0.090 | 0.027 | 0.008 | 0.002 | 0.008 | 0.046 | -0.080 | -0.004 | -4.853 |
14-
| 0.4 | 0.400 | 0.191 | 0.160 | 0.064 | 0.026 | 0.010 | 0.016 | 0.083 | -0.099 | 0.016 | -4.694 |
15-
| 0.5 | 0.500 | 0.293 | 0.250 | 0.125 | 0.063 | 0.031 | 0.031 | 0.134 | -0.088 | -0.016 | -4.688 |
16-
| 0.6 | 0.600 | 0.412 | 0.360 | 0.216 | 0.130 | 0.078 | 0.063 | 0.200 | -0.029 | -0.031 | -4.832 |
17-
| 0.7 | 0.700 | 0.546 | 0.490 | 0.343 | 0.240 | 0.168 | 0.125 | 0.286 | 0.093 | 0.125 | 0.319 |
18-
| 0.8 | 0.800 | 0.691 | 0.640 | 0.512 | 0.410 | 0.328 | 0.250 | 0.400 | 0.294 | -0.125 | 0.697 |
19-
| 0.9 | 0.900 | 0.844 | 0.810 | 0.729 | 0.656 | 0.590 | 0.500 | 0.564 | 0.591 | -0.250 | 0.924 |
20-
| 1.0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
21-
| 1.1 | 1.100 | 1.156 | 1.210 | 1.331 | 1.464 | 1.611 | 2.000 | nan | 1.537 | -1.000 | 0.924 |
22-
| 1.2 | 1.200 | 1.309 | 1.440 | 1.728 | 2.074 | 2.488 | 4.000 | nan | 2.218 | -2.000 | 0.698 |
23-
| 1.3 | 1.300 | 1.454 | 1.690 | 2.197 | 2.856 | 3.713 | 8.000 | nan | 3.060 | 8.000 | 0.319 |
24-
| 1.4 | 1.400 | 1.588 | 1.960 | 2.744 | 3.842 | 5.378 | 16.000 | nan | 4.078 | -8.000 | -0.210 |
25-
| 1.5 | 1.500 | 1.707 | 2.250 | 3.375 | 5.063 | 7.594 | 32.000 | nan | 5.289 | -16.000 | -0.891 |
5+
| -0.5 | -0.5000 | 0.2929 | 0.2500 | -0.1250 | 0.0625 | -0.0313 | 0.0000 | 0.1340 | -0.7631 | 0.0000 | -2.2344 |
6+
| -0.4 | -0.4000 | 0.1910 | 0.1600 | -0.0640 | 0.0256 | -0.0102 | 0.0001 | 0.0835 | -0.4452 | -0.0000 | -1.4850 |
7+
| -0.3 | -0.3000 | 0.1090 | 0.0900 | -0.0270 | 0.0081 | -0.0024 | 0.0001 | 0.0461 | -0.2261 | -0.0001 | -0.8869 |
8+
| -0.2 | -0.2000 | 0.0489 | 0.0400 | -0.0080 | 0.0016 | -0.0003 | 0.0002 | 0.0202 | -0.0897 | 0.0002 | -0.4400 |
9+
| -0.1 | -0.1000 | 0.0123 | 0.0100 | -0.0010 | 0.0001 | -0.0000 | 0.0005 | 0.0050 | -0.0197 | -0.0002 | -0.1444 |
10+
| -0.0 | -0.0000 | 0.0000 | 0.0000 | -0.0000 | 0.0000 | -0.0000 | 0.0000 | 0.0000 | -0.0000 | 0.0000 | 0.0000 |
11+
| 0.1 | 0.1000 | 0.0123 | 0.0100 | 0.0010 | 0.0001 | 0.0000 | 0.0020 | 0.0050 | -0.0143 | 0.0020 | 0.0119 |
12+
| 0.2 | 0.2000 | 0.0489 | 0.0400 | 0.0080 | 0.0016 | 0.0003 | 0.0039 | 0.0202 | -0.0465 | -0.0020 | 0.0600 |
13+
| 0.3 | 0.3000 | 0.1090 | 0.0900 | 0.0270 | 0.0081 | 0.0024 | 0.0078 | 0.0461 | -0.0802 | -0.0039 | 0.0694 |
14+
| 0.4 | 0.4000 | 0.1910 | 0.1600 | 0.0640 | 0.0256 | 0.0102 | 0.0156 | 0.0835 | -0.0994 | 0.0156 | 0.2275 |
15+
| 0.5 | 0.5000 | 0.2929 | 0.2500 | 0.1250 | 0.0625 | 0.0313 | 0.0313 | 0.1340 | -0.0877 | -0.0156 | 0.2344 |
16+
| 0.6 | 0.6000 | 0.4122 | 0.3600 | 0.2160 | 0.1296 | 0.0778 | 0.0625 | 0.2000 | -0.0290 | -0.0312 | 0.0900 |
17+
| 0.7 | 0.7000 | 0.5460 | 0.4900 | 0.3430 | 0.2401 | 0.1681 | 0.1250 | 0.2859 | 0.0929 | 0.1250 | 0.3194 |
18+
| 0.8 | 0.8000 | 0.6910 | 0.6400 | 0.5120 | 0.4096 | 0.3277 | 0.2500 | 0.4000 | 0.2942 | -0.1250 | 0.6975 |
19+
| 0.9 | 0.9000 | 0.8436 | 0.8100 | 0.7290 | 0.6561 | 0.5905 | 0.5000 | 0.5641 | 0.5912 | -0.2500 | 0.9244 |
20+
| 1.0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
21+
| 1.1 | 1.1000 | 1.1564 | 1.2100 | 1.3310 | 1.4641 | 1.6105 | 2.0000 | nan | 1.5369 | -1.0000 | 0.9244 |
22+
| 1.2 | 1.2000 | 1.3090 | 1.4400 | 1.7280 | 2.0736 | 2.4883 | 4.0000 | nan | 2.2181 | -2.0000 | 0.6975 |
23+
| 1.3 | 1.3000 | 1.4540 | 1.6900 | 2.1970 | 2.8561 | 3.7129 | 8.0000 | nan | 3.0597 | 8.0000 | 0.3194 |
24+
| 1.4 | 1.4000 | 1.5878 | 1.9600 | 2.7440 | 3.8416 | 5.3782 | 16.0000 | nan | 4.0780 | -8.0000 | -0.2100 |
25+
| 1.5 | 1.5000 | 1.7071 | 2.2500 | 3.3750 | 5.0625 | 7.5938 | 32.0000 | nan | 5.2893 |-16.0000 | -0.8906 |
2626
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
2727
out_ functions, compared to the linear one
2828
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
2929
| x | linear | sine | quad | cubic | quart | quint | expo | circ | back | elastic | bounce |
3030
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
31-
| -0.5 | -0.500 | -0.707 | -1.250 | -2.375 | -4.063 | -6.594 | -31.000 | nan | -4.289 | 17.000 | 1.891 |
32-
| -0.4 | -0.400 | -0.588 | -0.960 | -1.744 | -2.842 | -4.378 | -15.000 | nan | -3.078 | 9.000 | 1.210 |
33-
| -0.3 | -0.300 | -0.454 | -0.690 | -1.197 | -1.856 | -2.713 | -7.000 | nan | -2.060 | -7.000 | 0.681 |
34-
| -0.2 | -0.200 | -0.309 | -0.440 | -0.728 | -1.074 | -1.488 | -3.000 | nan | -1.218 | 3.000 | 0.303 |
35-
| -0.1 | -0.100 | -0.156 | -0.210 | -0.331 | -0.464 | -0.611 | -1.000 | nan | -0.537 | 2.000 | 0.076 |
36-
| -0.0 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
37-
| 0.1 | 0.100 | 0.156 | 0.190 | 0.271 | 0.344 | 0.410 | 0.500 | 0.436 | 0.409 | 1.250 | 0.076 |
38-
| 0.2 | 0.200 | 0.309 | 0.360 | 0.488 | 0.590 | 0.672 | 0.750 | 0.600 | 0.706 | 1.125 | 0.302 |
39-
| 0.3 | 0.300 | 0.454 | 0.510 | 0.657 | 0.760 | 0.832 | 0.875 | 0.714 | 0.907 | 0.875 | 0.681 |
40-
| 0.4 | 0.400 | 0.588 | 0.640 | 0.784 | 0.870 | 0.922 | 0.938 | 0.800 | 1.029 | 1.031 | 5.832 |
41-
| 0.5 | 0.500 | 0.707 | 0.750 | 0.875 | 0.938 | 0.969 | 0.969 | 0.866 | 1.088 | 1.016 | 5.688 |
42-
| 0.6 | 0.600 | 0.809 | 0.840 | 0.936 | 0.974 | 0.990 | 0.984 | 0.917 | 1.099 | 0.984 | 5.694 |
43-
| 0.7 | 0.700 | 0.891 | 0.910 | 0.973 | 0.992 | 0.998 | 0.992 | 0.954 | 1.080 | 1.004 | 5.853 |
44-
| 0.8 | 0.800 | 0.951 | 0.960 | 0.992 | 0.998 | 1.000 | 0.996 | 0.980 | 1.046 | 1.002 | 7.092 |
45-
| 0.9 | 0.900 | 0.988 | 0.990 | 0.999 | 1.000 | 1.000 | 0.998 | 0.995 | 1.014 | 0.998 | 7.140 |
46-
| 1.0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
47-
| 1.1 | 1.100 | 0.988 | 0.990 | 1.001 | 1.000 | 1.000 | 1.000 | 0.995 | 1.020 | 1.000 | 7.604 |
48-
| 1.2 | 1.200 | 0.951 | 0.960 | 1.008 | 0.998 | 1.000 | 1.000 | 0.980 | 1.090 | 1.000 | 7.900 |
49-
| 1.3 | 1.300 | 0.891 | 0.910 | 1.027 | 0.992 | 1.002 | 1.000 | 0.954 | 1.226 | 1.000 | 8.347 |
50-
| 1.4 | 1.400 | 0.809 | 0.840 | 1.064 | 0.974 | 1.010 | 1.000 | 0.917 | 1.445 | 1.000 | 8.945 |
51-
| 1.5 | 1.500 | 0.707 | 0.750 | 1.125 | 0.937 | 1.031 | 1.000 | 0.866 | 1.763 | 1.000 | 9.694 |
31+
| -0.5 | -0.5000 | -0.7071 | -1.2500 | -2.3750 | -4.0625 | -6.5938 |-31.0000 | nan | -4.2893 | 17.0000 | 1.8906 |
32+
| -0.4 | -0.4000 | -0.5878 | -0.9600 | -1.7440 | -2.8416 | -4.3782 |-15.0000 | nan | -3.0780 | 9.0000 | 1.2100 |
33+
| -0.3 | -0.3000 | -0.4540 | -0.6900 | -1.1970 | -1.8561 | -2.7129 | -7.0000 | nan | -2.0597 | -7.0000 | 0.6806 |
34+
| -0.2 | -0.2000 | -0.3090 | -0.4400 | -0.7280 | -1.0736 | -1.4883 | -3.0000 | nan | -1.2181 | 3.0000 | 0.3025 |
35+
| -0.1 | -0.1000 | -0.1564 | -0.2100 | -0.3310 | -0.4641 | -0.6105 | -1.0000 | nan | -0.5369 | 2.0000 | 0.0756 |
36+
| -0.0 | -0.0000 | -0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | -0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
37+
| 0.1 | 0.1000 | 0.1564 | 0.1900 | 0.2710 | 0.3439 | 0.4095 | 0.5000 | 0.4359 | 0.4088 | 1.2500 | 0.0756 |
38+
| 0.2 | 0.2000 | 0.3090 | 0.3600 | 0.4880 | 0.5904 | 0.6723 | 0.7500 | 0.6000 | 0.7058 | 1.1250 | 0.3025 |
39+
| 0.3 | 0.3000 | 0.4540 | 0.5100 | 0.6570 | 0.7599 | 0.8319 | 0.8750 | 0.7141 | 0.9071 | 0.8750 | 0.6806 |
40+
| 0.4 | 0.4000 | 0.5878 | 0.6400 | 0.7840 | 0.8704 | 0.9222 | 0.9375 | 0.8000 | 1.0290 | 1.0313 | 0.9100 |
41+
| 0.5 | 0.5000 | 0.7071 | 0.7500 | 0.8750 | 0.9375 | 0.9688 | 0.9688 | 0.8660 | 1.0877 | 1.0156 | 0.7656 |
42+
| 0.6 | 0.6000 | 0.8090 | 0.8400 | 0.9360 | 0.9744 | 0.9898 | 0.9844 | 0.9165 | 1.0994 | 0.9844 | 0.7725 |
43+
| 0.7 | 0.7000 | 0.8910 | 0.9100 | 0.9730 | 0.9919 | 0.9976 | 0.9922 | 0.9539 | 1.0802 | 1.0039 | 0.9306 |
44+
| 0.8 | 0.8000 | 0.9511 | 0.9600 | 0.9920 | 0.9984 | 0.9997 | 0.9961 | 0.9798 | 1.0465 | 1.0020 | 0.9400 |
45+
| 0.9 | 0.9000 | 0.9877 | 0.9900 | 0.9990 | 0.9999 | 1.0000 | 0.9980 | 0.9950 | 1.0143 | 0.9980 | 0.9881 |
46+
| 1.0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
47+
| 1.1 | 1.1000 | 0.9877 | 0.9900 | 1.0010 | 0.9999 | 1.0000 | 0.9995 | 0.9950 | 1.0197 | 1.0002 | 1.1444 |
48+
| 1.2 | 1.2000 | 0.9511 | 0.9600 | 1.0080 | 0.9984 | 1.0003 | 0.9998 | 0.9798 | 1.0897 | 0.9998 | 1.4400 |
49+
| 1.3 | 1.3000 | 0.8910 | 0.9100 | 1.0270 | 0.9919 | 1.0024 | 0.9999 | 0.9539 | 1.2261 | 1.0001 | 1.8869 |
50+
| 1.4 | 1.4000 | 0.8090 | 0.8400 | 1.0640 | 0.9744 | 1.0102 | 0.9999 | 0.9165 | 1.4452 | 1.0000 | 2.4850 |
51+
| 1.5 | 1.5000 | 0.7071 | 0.7500 | 1.1250 | 0.9375 | 1.0313 | 1.0000 | 0.8660 | 1.7631 | 1.0000 | 3.2344 |
5252
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
5353
in_out_ functions, compared to the linear one
5454
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
5555
| x | linear | sine | quad | cubic | quart | quint | expo | circ | back | elastic | bounce |
5656
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
57-
| -0.5 | -0.500 | 0.500 | 0.500 | -0.500 | 0.500 | -0.500 | 0.000 | 0.500 | -3.095 | -0.000 | -7.355 |
58-
| -0.4 | -0.400 | 0.345 | 0.320 | -0.256 | 0.205 | -0.164 | 0.000 | 0.200 | -1.751 | 0.000 | -5.925 |
59-
| -0.3 | -0.300 | 0.206 | 0.180 | -0.108 | 0.065 | -0.039 | 0.000 | 0.100 | -0.855 | -0.000 | -4.797 |
60-
| -0.2 | -0.200 | 0.095 | 0.080 | -0.032 | 0.013 | -0.005 | 0.000 | 0.042 | -0.323 | 0.000 | -3.972 |
61-
| -0.1 | -0.100 | 0.024 | 0.020 | -0.004 | 0.001 | -0.000 | 0.000 | 0.010 | -0.066 | -0.000 | -3.450 |
62-
| -0.0 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
63-
| 0.1 | 0.100 | 0.024 | 0.020 | 0.004 | 0.001 | 0.000 | 0.002 | 0.010 | -0.038 | 0.000 | -3.046 |
64-
| 0.2 | 0.200 | 0.095 | 0.080 | 0.032 | 0.013 | 0.005 | 0.008 | 0.042 | -0.093 | -0.004 | -2.347 |
65-
| 0.3 | 0.300 | 0.206 | 0.180 | 0.108 | 0.065 | 0.039 | 0.031 | 0.100 | -0.079 | 0.024 | -2.416 |
66-
| 0.4 | 0.400 | 0.345 | 0.320 | 0.256 | 0.205 | 0.164 | 0.125 | 0.200 | 0.090 | -0.117 | 0.349 |
67-
| 0.5 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 |
68-
| 0.6 | 0.600 | 0.655 | 0.680 | 0.744 | 0.795 | 0.836 | 0.875 | 0.800 | 0.910 | 1.117 | 0.651 |
69-
| 0.7 | 0.700 | 0.794 | 0.820 | 0.892 | 0.935 | 0.961 | 0.969 | 0.900 | 1.079 | 0.976 | 3.416 |
70-
| 0.8 | 0.800 | 0.905 | 0.920 | 0.968 | 0.987 | 0.995 | 0.992 | 0.958 | 1.093 | 1.004 | 3.347 |
71-
| 0.9 | 0.900 | 0.976 | 0.980 | 0.996 | 0.999 | 1.000 | 0.998 | 0.990 | 1.038 | 1.000 | 4.046 |
72-
| 1.0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
73-
| 1.1 | 1.100 | 0.976 | 0.980 | 1.004 | 0.999 | 1.000 | 1.000 | 0.990 | 1.066 | 1.000 | 4.450 |
74-
| 1.2 | 1.200 | 0.905 | 0.920 | 1.032 | 0.987 | 1.005 | 1.000 | 0.958 | 1.323 | 1.000 | 4.972 |
75-
| 1.3 | 1.300 | 0.794 | 0.820 | 1.108 | 0.935 | 1.039 | 1.000 | 0.900 | 1.855 | 1.000 | 5.797 |
76-
| 1.4 | 1.400 | 0.655 | 0.680 | 1.256 | 0.795 | 1.164 | 1.000 | 0.800 | 2.751 | 1.000 | 6.925 |
77-
| 1.5 | 1.500 | 0.500 | 0.500 | 1.500 | 0.500 | 1.500 | 1.000 | nan | 4.095 | 1.000 | 8.355 |
57+
| -0.5 | -0.5000 | 0.5000 | 0.5000 | -0.5000 | 0.5000 | -0.5000 | 0.0000 | 0.5000 | -3.0949 | -0.0000 | -4.1250 |
58+
| -0.4 | -0.4000 | 0.3455 | 0.3200 | -0.2560 | 0.2048 | -0.1638 | 0.0000 | 0.2000 | -1.7507 | 0.0000 | -2.6950 |
59+
| -0.3 | -0.3000 | 0.2061 | 0.1800 | -0.1080 | 0.0648 | -0.0389 | 0.0000 | 0.1000 | -0.8553 | -0.0000 | -1.5675 |
60+
| -0.2 | -0.2000 | 0.0955 | 0.0800 | -0.0320 | 0.0128 | -0.0051 | 0.0000 | 0.0417 | -0.3226 | 0.0000 | -0.7425 |
61+
| -0.1 | -0.1000 | 0.0245 | 0.0200 | -0.0040 | 0.0008 | -0.0002 | 0.0001 | 0.0101 | -0.0663 | -0.0001 | -0.2200 |
62+
| -0.0 | -0.0000 | -0.0000 | 0.0000 | -0.0000 | 0.0000 | -0.0000 | 0.0000 | 0.0000 | -0.0000 | 0.0000 | 0.0000 |
63+
| 0.1 | 0.1000 | 0.0245 | 0.0200 | 0.0040 | 0.0008 | 0.0002 | 0.0020 | 0.0101 | -0.0375 | 0.0003 | 0.0300 |
64+
| 0.2 | 0.2000 | 0.0955 | 0.0800 | 0.0320 | 0.0128 | 0.0051 | 0.0078 | 0.0417 | -0.0926 | -0.0039 | 0.1137 |
65+
| 0.3 | 0.3000 | 0.2061 | 0.1800 | 0.1080 | 0.0648 | 0.0389 | 0.0313 | 0.1000 | -0.0788 | 0.0239 | 0.0450 |
66+
| 0.4 | 0.4000 | 0.3455 | 0.3200 | 0.2560 | 0.2048 | 0.1638 | 0.1250 | 0.2000 | 0.0899 | -0.1175 | 0.3488 |
67+
| 0.5 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 |
68+
| 0.6 | 0.6000 | 0.6545 | 0.6800 | 0.7440 | 0.7952 | 0.8362 | 0.8750 | 0.8000 | 0.9101 | 1.1175 | 0.6512 |
69+
| 0.7 | 0.7000 | 0.7939 | 0.8200 | 0.8920 | 0.9352 | 0.9611 | 0.9688 | 0.9000 | 1.0788 | 0.9761 | 0.9550 |
70+
| 0.8 | 0.8000 | 0.9045 | 0.9200 | 0.9680 | 0.9872 | 0.9949 | 0.9922 | 0.9583 | 1.0926 | 1.0039 | 0.8863 |
71+
| 0.9 | 0.9000 | 0.9755 | 0.9800 | 0.9960 | 0.9992 | 0.9998 | 0.9980 | 0.9899 | 1.0375 | 0.9997 | 0.9700 |
72+
| 1.0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
73+
| 1.1 | 1.1000 | 0.9755 | 0.9800 | 1.0040 | 0.9992 | 1.0002 | 0.9999 | 0.9899 | 1.0663 | 1.0001 | 1.2200 |
74+
| 1.2 | 1.2000 | 0.9045 | 0.9200 | 1.0320 | 0.9872 | 1.0051 | 1.0000 | 0.9583 | 1.3226 | 1.0000 | 1.7425 |
75+
| 1.3 | 1.3000 | 0.7939 | 0.8200 | 1.1080 | 0.9352 | 1.0389 | 1.0000 | 0.9000 | 1.8553 | 1.0000 | 2.5675 |
76+
| 1.4 | 1.4000 | 0.6545 | 0.6800 | 1.2560 | 0.7952 | 1.1638 | 1.0000 | 0.8000 | 2.7507 | 1.0000 | 3.6950 |
77+
| 1.5 | 1.5000 | 0.5000 | 0.5000 | 1.5000 | 0.5000 | 1.5000 | 1.0000 | nan | 4.0949 | 1.0000 | 5.1250 |
7878
+------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+

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