math: add math.easing module, ported from the functions, described in

https://nicmulvaney.com/easing and https://easings.net/ (vlang#23251)

vlib/math/easing/easing.v

@@ -0,0 +1,272 @@
+module easing
+
+// Easing functions specify the value of a property, given a level of completeness from 0.0 to 1.0 .
+// The names of the easing functions here, are based on the ones from https://easings.net/ and
+// https://nicmulvaney.com/easing .
+import math { cos, pow, sin, sqrt }
+
+const pi = math.pi
+const pi_half = pi / 2.0
+const pi_double = pi * 2.0
+const c1 = 1.70158
+const c2 = c1 * 1.525
+const c3 = c1 + 1.0
+const c4 = pi_double / 3.0
+const c5 = pi_double / 4.5
+const n1 = 7.5625
+const d1 = 2.75
+
+// EasingFN defines the common shape of an easing function, so that you can define your own, and pass them everywhere,
+// that expects easing.EasingFN . It is just a function that accepts a floating point number and returns one too.
+pub type EasingFN = fn (x f64) f64
+
+// linear just returns the parameter x, without changes .
+@[inline]
+pub fn linear(x f64) f64 {
+	return x
+}
+
+// in_sine returns the equivalent of https://easings.net/#easeInSine .
+@[inline]
+pub fn in_sine(x f64) f64 {
+	return 1.0 - cos(x * pi_half)
+}
+
+// out_sine returns the equivalent of https://easings.net/#easeOutSine .
+@[inline]
+pub fn out_sine(x f64) f64 {
+	return sin(x * pi_half)
+}
+
+// in_out_sine returns the equivalent of https://easings.net/#easeInOutSine .
+@[inline]
+pub fn in_out_sine(x f64) f64 {
+	return -(cos(pi * x) - 1.0) / 2.0
+}
+
+// in_quad returns the equivalent of https://easings.net/#easeInQuad .
+@[inline]
+pub fn in_quad(x f64) f64 {
+	return x * x
+}
+
+// out_quad returns the equivalent of https://easings.net/#easeOutQuad .
+@[inline]
+pub fn out_quad(x f64) f64 {
+	return 1.0 - (1.0 - x) * (1.0 - x)
+}
+
+// in_out_quad returns the equivalent of https://easings.net/#easeInOutQuad .
+@[inline]
+pub fn in_out_quad(x f64) f64 {
+	return if x < 0.5 { 2.0 * x * x } else { 1.0 - (2.0 - 2.0 * x) * (2.0 - 2.0 * x) / 2.0 }
+}
+
+// in_cubic returns the equivalent of https://easings.net/#easeInCubic .
+@[inline]
+pub fn in_cubic(x f64) f64 {
+	return x * x * x
+}
+
+// out_cubic returns the equivalent of https://easings.net/#easeOutCubic .
+@[inline]
+pub fn out_cubic(x f64) f64 {
+	return 1.0 - (1.0 - x) * (1.0 - x) * (1.0 - x)
+}
+
+// in_out_cubic returns the equivalent of https://easings.net/#easeInOutCubic .
+@[inline]
+pub fn in_out_cubic(x f64) f64 {
+	return if x < .5 {
+		4.0 * x * x * x
+	} else {
+		1.0 - (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) / 2.0
+	}
+}
+
+// in_quart returns the equivalent of https://easings.net/#easeInQuart .
+@[inline]
+pub fn in_quart(x f64) f64 {
+	return x * x * x * x
+}
+
+// out_quart returns the equivalent of https://easings.net/#easeOutQuart .
+@[inline]
+pub fn out_quart(x f64) f64 {
+	return 1.0 - (1.0 - x) * (1.0 - x) * (1.0 - x) * (1.0 - x)
+}
+
+// in_out_quart returns the equivalent of https://easings.net/#easeInOutQuart .
+@[inline]
+pub fn in_out_quart(x f64) f64 {
+	return if x < 0.5 {
+		8.0 * x * x * x * x
+	} else {
+		1.0 - (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) / 2.0
+	}
+}
+
+// in_quint returns the equivalent of https://easings.net/#easeInQuint .
+@[inline]
+pub fn in_quint(x f64) f64 {
+	return x * x * x * x * x
+}
+
+// out_quint returns the equivalent of https://easings.net/#easeOutQuint .
+@[inline]
+pub fn out_quint(x f64) f64 {
+	return 1.0 - (1.0 - x) * (1.0 - x) * (1.0 - x) * (1.0 - x) * (1.0 - x)
+}
+
+// in_out_quint returns the equivalent of https://easings.net/#easeInOutQuint .
+@[inline]
+pub fn in_out_quint(x f64) f64 {
+	return if x < 0.5 {
+		16.0 * x * x * x * x * x
+	} else {
+		1.0 - (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) * (2.0 - 2.0 * x) / 2.0
+	}
+}
+
+// in_expo returns the equivalent of https://easings.net/#easeInExpo .
+@[inline]
+pub fn in_expo(x f64) f64 {
+	return if math.close(x, 0.0) { 0.0 } else { pow(2.0, 10.0 * x - 10.0) }
+}
+
+// out_expo returns the equivalent of https://easings.net/#easeOutExpo .
+@[inline]
+pub fn out_expo(x f64) f64 {
+	return if math.close(x, 1.0) { 1.0 } else { 1.0 - pow(2, -10.0 * x) }
+}
+
+// in_out_expo returns the equivalent of https://easings.net/#easeInOutExpo .
+@[inline]
+pub fn in_out_expo(x f64) f64 {
+	return if math.close(x, 0.0) {
+		0.0
+	} else if math.close(x, 1.0) {
+		1.0
+	} else if x < 0.5 {
+		pow(2.0, 20.0 * x - 10.0) / 2.0
+	} else {
+		2.0 - pow(2.0, 10.0 - 20.0 * x) / 2.0
+	}
+}
+
+// in_circ returns the equivalent of https://easings.net/#easeInCirc .
+@[inline]
+pub fn in_circ(x f64) f64 {
+	return 1.0 - sqrt(1.0 - x * x)
+}
+
+// out_circ returns the equivalent of https://easings.net/#easeOutCirc .
+@[inline]
+pub fn out_circ(x f64) f64 {
+	return sqrt(1.0 - pow(x - 1.0, 2.0))
+}
+
+// in_out_circ returns the equivalent of https://easings.net/#easeInOutCirc .
+@[inline]
+pub fn in_out_circ(x f64) f64 {
+	return if x < 0.5 {
+		(1.0 - sqrt(1.0 - pow(2.0 * x, 2.0))) / 2.0
+	} else {
+		(sqrt(1.0 - pow(-2.0 * x + 2.0, 2.0)) + 1.0) / 2.0
+	}
+}
+
+// in_back returns the equivalent of https://easings.net/#easeInBack .
+@[inline]
+pub fn in_back(x f64) f64 {
+	return c3 * x * x * x - c1 * x * x
+}
+
+// out_back returns the equivalent of https://easings.net/#easeOutBack .
+@[inline]
+pub fn out_back(x f64) f64 {
+	return 1.0 + c3 * pow(x - 1.0, 3.0) + c1 * pow(x - 1.0, 2.0)
+}
+
+// in_out_back returns the equivalent of https://easings.net/#easeInOutBack .
+@[inline]
+pub fn in_out_back(x f64) f64 {
+	return if x < 0.5 {
+		(pow(2.0 * x, x) * ((c2 + 1) * 2.0 * x - c2)) / 2.0
+	} else {
+		(pow(2.0 * x - 2.0, 2.0) * ((c2 + 1.0) * (x * 2.0 - 2.0) + c2) + 2.0) / 2.0
+	}
+}
+
+// in_elastic returns the equivalent of https://easings.net/#easeInElastic .
+@[inline]
+pub fn in_elastic(x f64) f64 {
+	return if math.close(x, 0.0) {
+		0.0
+	} else if math.close(x, 1.0) {
+		1.0
+	} else {
+		-pow(2.0, 10.0 * x - 10.0) * sin((x * 10.0 - 10.75) * c4)
+	}
+}
+
+// out_elastic returns the equivalent of https://easings.net/#easeOutElastic .
+@[inline]
+pub fn out_elastic(x f64) f64 {
+	return if math.close(x, 0.0) {
+		0.0
+	} else if math.close(x, 1.0) {
+		1.0
+	} else {
+		pow(2.0, -10.0 * x) * sin((x * 10.0 - 0.75) * c4) + 1.0
+	}
+}
+
+// in_out_elastic returns the equivalent of https://easings.net/#easeInOutElastic .
+@[inline]
+pub fn in_out_elastic(x f64) f64 {
+	return if math.close(x, 0.0) {
+		0.0
+	} else if math.close(x, 1.0) {
+		1.0
+	} else if x < 0.5 {
+		-(pow(2.0, 20.0 * x - 10.0) * sin((20.0 * x - 11.125) * c5)) / 2.0
+	} else {
+		(pow(2.0, -20.0 * x + 10.0) * sin((20.0 * x - 11.125) * c5)) / 2.0 + 1.0
+	}
+}
+
+// in_bounce returns the equivalent of https://easings.net/#easeInBounce .
+@[inline]
+pub fn in_bounce(x f64) f64 {
+	return 1.0 - out_bounce(1.0 - x)
+}
+
+// out_bounce returns the equivalent of https://easings.net/#easeOutBounce .
+pub fn out_bounce(x f64) f64 {
+	if math.close(x, 1.0) {
+		return 1.0
+	}
+	xd1 := x * d1
+	return n1 * (if xd1 < 1.0 {
+		x * x
+	} else if xd1 < 2.0 {
+		pow((x - 1.5 / d1), 2.0) + 0.75
+	} else if xd1 < 2.5 {
+		pow((x - 2.25 / d1), 2.0) + 0.9375
+	} else {
+		pow((x - 2.625 / d1), 2.0) + 0.984375
+	})
+}
+
+// in_out_bounce returns the equivalent of https://easings.net/#easeInOutBounce .
+pub fn in_out_bounce(x f64) f64 {
+	if math.close(x, 1.0) {
+		return 1.0
+	}
+	return if x < 0.5 {
+		(1.0 - out_bounce(1.0 - 2.0 * x)) / 2.0
+	} else {
+		(1.0 + out_bounce(2.0 * x - 1.0)) / 2.0
+	}
+}

vlib/math/easing/easing_test.v

@@ -0,0 +1,11 @@
+import math.easing
+
+// Note: most of the checks are done not here, but by comparing the produced table,
+// in the .vv/.out pair, checked by:
+// `v run vlib/v/slow_tests/inout/math_easing_tables.vv > vlib/v/slow_tests/inout/math_easing_tables.out`
+
+fn test_linear() {
+	for x := -10.0; x <= 10.0; x += 0.1 {
+		assert easing.linear(x) == x
+	}
+}

vlib/v/slow_tests/inout/math_easing_tables.out

@@ -0,0 +1,78 @@
+                                  in_ functions, compared to the linear one
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+|  x   |  linear |   sine  |   quad  |   cubic |   quart |   quint |   expo  |    circ |   back  | elastic |  bounce |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+| -0.5 |  -0.500 |   0.293 |   0.250 |  -0.125 |   0.063 |  -0.031 |   0.000 |   0.134 |  -0.763 |   0.000 |  -8.694 |
+| -0.4 |  -0.400 |   0.191 |   0.160 |  -0.064 |   0.026 |  -0.010 |   0.000 |   0.083 |  -0.445 |  -0.000 |  -7.945 |
+| -0.3 |  -0.300 |   0.109 |   0.090 |  -0.027 |   0.008 |  -0.002 |   0.000 |   0.046 |  -0.226 |  -0.000 |  -7.347 |
+| -0.2 |  -0.200 |   0.049 |   0.040 |  -0.008 |   0.002 |  -0.000 |   0.000 |   0.020 |  -0.090 |   0.000 |  -6.900 |
+| -0.1 |  -0.100 |   0.012 |   0.010 |  -0.001 |   0.000 |  -0.000 |   0.000 |   0.005 |  -0.020 |  -0.000 |  -6.604 |
+| -0.0 |  -0.000 |   0.000 |   0.000 |  -0.000 |   0.000 |  -0.000 |   0.000 |   0.000 |  -0.000 |   0.000 |   0.000 |
+|  0.1 |   0.100 |   0.012 |   0.010 |   0.001 |   0.000 |   0.000 |   0.002 |   0.005 |  -0.014 |   0.002 |  -6.140 |
+|  0.2 |   0.200 |   0.049 |   0.040 |   0.008 |   0.002 |   0.000 |   0.004 |   0.020 |  -0.046 |  -0.002 |  -6.092 |
+|  0.3 |   0.300 |   0.109 |   0.090 |   0.027 |   0.008 |   0.002 |   0.008 |   0.046 |  -0.080 |  -0.004 |  -4.853 |
+|  0.4 |   0.400 |   0.191 |   0.160 |   0.064 |   0.026 |   0.010 |   0.016 |   0.083 |  -0.099 |   0.016 |  -4.694 |
+|  0.5 |   0.500 |   0.293 |   0.250 |   0.125 |   0.063 |   0.031 |   0.031 |   0.134 |  -0.088 |  -0.016 |  -4.688 |
+|  0.6 |   0.600 |   0.412 |   0.360 |   0.216 |   0.130 |   0.078 |   0.063 |   0.200 |  -0.029 |  -0.031 |  -4.832 |
+|  0.7 |   0.700 |   0.546 |   0.490 |   0.343 |   0.240 |   0.168 |   0.125 |   0.286 |   0.093 |   0.125 |   0.319 |
+|  0.8 |   0.800 |   0.691 |   0.640 |   0.512 |   0.410 |   0.328 |   0.250 |   0.400 |   0.294 |  -0.125 |   0.697 |
+|  0.9 |   0.900 |   0.844 |   0.810 |   0.729 |   0.656 |   0.590 |   0.500 |   0.564 |   0.591 |  -0.250 |   0.924 |
+|  1.0 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |
+|  1.1 |   1.100 |   1.156 |   1.210 |   1.331 |   1.464 |   1.611 |   2.000 |     nan |   1.537 |  -1.000 |   0.924 |
+|  1.2 |   1.200 |   1.309 |   1.440 |   1.728 |   2.074 |   2.488 |   4.000 |     nan |   2.218 |  -2.000 |   0.698 |
+|  1.3 |   1.300 |   1.454 |   1.690 |   2.197 |   2.856 |   3.713 |   8.000 |     nan |   3.060 |   8.000 |   0.319 |
+|  1.4 |   1.400 |   1.588 |   1.960 |   2.744 |   3.842 |   5.378 |  16.000 |     nan |   4.078 |  -8.000 |  -0.210 |
+|  1.5 |   1.500 |   1.707 |   2.250 |   3.375 |   5.063 |   7.594 |  32.000 |     nan |   5.289 | -16.000 |  -0.891 |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+                                  out_ functions, compared to the linear one
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+|  x   |  linear |   sine  |   quad  |   cubic |   quart |   quint |   expo  |    circ |   back  | elastic |  bounce |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+| -0.5 |  -0.500 |  -0.707 |  -1.250 |  -2.375 |  -4.063 |  -6.594 | -31.000 |     nan |  -4.289 |  17.000 |   1.891 |
+| -0.4 |  -0.400 |  -0.588 |  -0.960 |  -1.744 |  -2.842 |  -4.378 | -15.000 |     nan |  -3.078 |   9.000 |   1.210 |
+| -0.3 |  -0.300 |  -0.454 |  -0.690 |  -1.197 |  -1.856 |  -2.713 |  -7.000 |     nan |  -2.060 |  -7.000 |   0.681 |
+| -0.2 |  -0.200 |  -0.309 |  -0.440 |  -0.728 |  -1.074 |  -1.488 |  -3.000 |     nan |  -1.218 |   3.000 |   0.303 |
+| -0.1 |  -0.100 |  -0.156 |  -0.210 |  -0.331 |  -0.464 |  -0.611 |  -1.000 |     nan |  -0.537 |   2.000 |   0.076 |
+| -0.0 |  -0.000 |  -0.000 |   0.000 |   0.000 |   0.000 |   0.000 |  -0.000 |   0.000 |   0.000 |   0.000 |   0.000 |
+|  0.1 |   0.100 |   0.156 |   0.190 |   0.271 |   0.344 |   0.410 |   0.500 |   0.436 |   0.409 |   1.250 |   0.076 |
+|  0.2 |   0.200 |   0.309 |   0.360 |   0.488 |   0.590 |   0.672 |   0.750 |   0.600 |   0.706 |   1.125 |   0.302 |
+|  0.3 |   0.300 |   0.454 |   0.510 |   0.657 |   0.760 |   0.832 |   0.875 |   0.714 |   0.907 |   0.875 |   0.681 |
+|  0.4 |   0.400 |   0.588 |   0.640 |   0.784 |   0.870 |   0.922 |   0.938 |   0.800 |   1.029 |   1.031 |   5.832 |
+|  0.5 |   0.500 |   0.707 |   0.750 |   0.875 |   0.938 |   0.969 |   0.969 |   0.866 |   1.088 |   1.016 |   5.688 |
+|  0.6 |   0.600 |   0.809 |   0.840 |   0.936 |   0.974 |   0.990 |   0.984 |   0.917 |   1.099 |   0.984 |   5.694 |
+|  0.7 |   0.700 |   0.891 |   0.910 |   0.973 |   0.992 |   0.998 |   0.992 |   0.954 |   1.080 |   1.004 |   5.853 |
+|  0.8 |   0.800 |   0.951 |   0.960 |   0.992 |   0.998 |   1.000 |   0.996 |   0.980 |   1.046 |   1.002 |   7.092 |
+|  0.9 |   0.900 |   0.988 |   0.990 |   0.999 |   1.000 |   1.000 |   0.998 |   0.995 |   1.014 |   0.998 |   7.140 |
+|  1.0 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |
+|  1.1 |   1.100 |   0.988 |   0.990 |   1.001 |   1.000 |   1.000 |   1.000 |   0.995 |   1.020 |   1.000 |   7.604 |
+|  1.2 |   1.200 |   0.951 |   0.960 |   1.008 |   0.998 |   1.000 |   1.000 |   0.980 |   1.090 |   1.000 |   7.900 |
+|  1.3 |   1.300 |   0.891 |   0.910 |   1.027 |   0.992 |   1.002 |   1.000 |   0.954 |   1.226 |   1.000 |   8.347 |
+|  1.4 |   1.400 |   0.809 |   0.840 |   1.064 |   0.974 |   1.010 |   1.000 |   0.917 |   1.445 |   1.000 |   8.945 |
+|  1.5 |   1.500 |   0.707 |   0.750 |   1.125 |   0.937 |   1.031 |   1.000 |   0.866 |   1.763 |   1.000 |   9.694 |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+                                  in_out_ functions, compared to the linear one
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+|  x   |  linear |   sine  |   quad  |   cubic |   quart |   quint |   expo  |    circ |   back  | elastic |  bounce |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
+| -0.5 |  -0.500 |   0.500 |   0.500 |  -0.500 |   0.500 |  -0.500 |   0.000 |   0.500 |     nan |  -0.000 |  -7.355 |
+| -0.4 |  -0.400 |   0.345 |   0.320 |  -0.256 |   0.205 |  -0.164 |   0.000 |   0.200 |     nan |   0.000 |  -5.925 |
+| -0.3 |  -0.300 |   0.206 |   0.180 |  -0.108 |   0.065 |  -0.039 |   0.000 |   0.100 |     nan |  -0.000 |  -4.797 |
+| -0.2 |  -0.200 |   0.095 |   0.080 |  -0.032 |   0.013 |  -0.005 |   0.000 |   0.042 |     nan |   0.000 |  -3.972 |
+| -0.1 |  -0.100 |   0.024 |   0.020 |  -0.004 |   0.001 |  -0.000 |   0.000 |   0.010 |     nan |  -0.000 |  -3.450 |
+| -0.0 |  -0.000 |  -0.000 |   0.000 |  -0.000 |   0.000 |  -0.000 |   0.000 |   0.000 |     nan |   0.000 |   0.000 |
+|  0.1 |   0.100 |   0.024 |   0.020 |   0.004 |   0.001 |   0.000 |   0.002 |   0.010 |  -0.799 |   0.000 |  -3.046 |
+|  0.2 |   0.200 |   0.095 |   0.080 |   0.032 |   0.013 |   0.005 |   0.008 |   0.042 |  -0.482 |  -0.004 |  -2.347 |
+|  0.3 |   0.300 |   0.206 |   0.180 |   0.108 |   0.065 |   0.039 |   0.031 |   0.100 |  -0.188 |   0.024 |  -2.416 |
+|  0.4 |   0.400 |   0.345 |   0.320 |   0.256 |   0.205 |   0.164 |   0.125 |   0.200 |   0.129 |  -0.117 |   0.349 |
+|  0.5 |   0.500 |   0.500 |   0.500 |   0.500 |   0.500 |   0.500 |   1.500 |   0.500 |   0.500 |   0.500 |   0.500 |
+|  0.6 |   0.600 |   0.655 |   0.680 |   0.744 |   0.795 |   0.836 |   1.875 |   0.800 |   0.910 |   1.117 |   0.651 |
+|  0.7 |   0.700 |   0.794 |   0.820 |   0.892 |   0.935 |   0.961 |   1.969 |   0.900 |   1.079 |   0.976 |   3.416 |
+|  0.8 |   0.800 |   0.905 |   0.920 |   0.968 |   0.987 |   0.995 |   1.992 |   0.958 |   1.093 |   1.004 |   3.347 |
+|  0.9 |   0.900 |   0.976 |   0.980 |   0.996 |   0.999 |   1.000 |   1.998 |   0.990 |   1.038 |   1.000 |   4.046 |
+|  1.0 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |   1.000 |
+|  1.1 |   1.100 |   0.976 |   0.980 |   1.004 |   0.999 |   1.000 |   2.000 |   0.990 |   1.066 |   1.000 |   4.450 |
+|  1.2 |   1.200 |   0.905 |   0.920 |   1.032 |   0.987 |   1.005 |   2.000 |   0.958 |   1.323 |   1.000 |   4.972 |
+|  1.3 |   1.300 |   0.794 |   0.820 |   1.108 |   0.935 |   1.039 |   2.000 |   0.900 |   1.855 |   1.000 |   5.797 |
+|  1.4 |   1.400 |   0.655 |   0.680 |   1.256 |   0.795 |   1.164 |   2.000 |   0.800 |   2.751 |   1.000 |   6.925 |
+|  1.5 |   1.500 |   0.500 |   0.500 |   1.500 |   0.500 |   1.500 |   2.000 |     nan |   4.095 |   1.000 |   8.355 |
++------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+