v/vlib/math/math.v

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// Copyright (c) 2019-2022 Alexander Medvednikov. All rights reserved.
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// Use of this source code is governed by an MIT license
// that can be found in the LICENSE file.
module math
// aprox_sin returns an approximation of sin(a) made using lolremez
pub fn aprox_sin(a f64) f64 {
a0 := 1.91059300966915117e-31
a1 := 1.00086760103908896
a2 := -1.21276126894734565e-2
a3 := -1.38078780785773762e-1
a4 := -2.67353392911981221e-2
a5 := 2.08026600266304389e-2
a6 := -3.03996055049204407e-3
a7 := 1.38235642404333740e-4
return a0 + a * (a1 + a * (a2 + a * (a3 + a * (a4 + a * (a5 + a * (a6 + a * a7))))))
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}
// aprox_cos returns an approximation of sin(a) made using lolremez
pub fn aprox_cos(a f64) f64 {
a0 := 9.9995999154986614e-1
a1 := 1.2548995793001028e-3
a2 := -5.0648546280678015e-1
a3 := 1.2942246466519995e-2
a4 := 2.8668384702547972e-2
a5 := 7.3726485210586547e-3
a6 := -3.8510875386947414e-3
a7 := 4.7196604604366623e-4
a8 := -1.8776444013090451e-5
return a0 + a * (a1 + a * (a2 + a * (a3 + a * (a4 + a * (a5 + a * (a6 + a * (a7 + a * a8)))))))
}
// copysign returns a value with the magnitude of x and the sign of y
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[inline]
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pub fn copysign(x f64, y f64) f64 {
return f64_from_bits((f64_bits(x) & ~sign_mask) | (f64_bits(y) & sign_mask))
}
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// degrees converts from radians to degrees.
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[inline]
pub fn degrees(radians f64) f64 {
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return radians * (180.0 / pi)
}
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// angle_diff calculates the difference between angles in radians
[inline]
pub fn angle_diff(radian_a f64, radian_b f64) f64 {
mut delta := fmod(radian_b - radian_a, tau)
delta = fmod(delta + 1.5 * tau, tau)
delta -= .5 * tau
return delta
}
[params]
pub struct DigitParams {
base int = 10
reverse bool
}
// digits returns an array of the digits of `num` in the given optional `base`.
// The `num` argument accepts any integer type (i8|i16|int|isize|i64), and will be cast to i64
// The `base:` argument is optional, it will default to base: 10.
// This function returns an array of the digits in reverse order i.e.:
// Example: assert math.digits(12345, base: 10) == [5,4,3,2,1]
// You can also use it, with an explicit `reverse: true` parameter,
// (it will do a reverse of the result array internally => slower):
// Example: assert math.digits(12345, reverse: true) == [1,2,3,4,5]
pub fn digits(num i64, params DigitParams) []int {
// set base to 10 initially and change only if base is explicitly set.
mut b := params.base
if b < 2 {
panic('digits: Cannot find digits of n with base $b')
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}
mut n := num
mut sign := 1
if n < 0 {
sign = -1
n = -n
}
mut res := []int{}
if n == 0 {
// short-circuit and return 0
res << 0
return res
}
for n != 0 {
next_n := n / b
res << int(n - next_n * b)
n = next_n
}
if sign == -1 {
res[res.len - 1] *= sign
}
if params.reverse {
res = res.reverse()
}
return res
}
// count_digits return the number of digits in the number passed.
// Number argument accepts any integer type (i8|i16|int|isize|i64) and will be cast to i64
pub fn count_digits(number i64) int {
mut n := number
if n == 0 {
return 1
}
mut c := 0
for n != 0 {
n = n / 10
c++
}
return c
}
// minmax returns the minimum and maximum value of the two provided.
pub fn minmax(a f64, b f64) (f64, f64) {
if a < b {
return a, b
}
return b, a
}
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// clamp returns x constrained between a and b
[inline]
pub fn clamp(x f64, a f64, b f64) f64 {
if x < a {
return a
}
if x > b {
return b
}
return x
}
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// sign returns the corresponding sign -1.0, 1.0 of the provided number.
// if n is not a number, its sign is nan too.
[inline]
pub fn sign(n f64) f64 {
if is_nan(n) {
return nan()
}
return copysign(1.0, n)
}
// signi returns the corresponding sign -1.0, 1.0 of the provided number.
[inline]
pub fn signi(n f64) int {
return int(copysign(1.0, n))
}
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// radians converts from degrees to radians.
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[inline]
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pub fn radians(degrees f64) f64 {
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return degrees * (pi / 180.0)
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}
// signbit returns a value with the boolean representation of the sign for x
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[inline]
pub fn signbit(x f64) bool {
return f64_bits(x) & sign_mask != 0
}
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// tolerance checks if a and b difference are less than or equal to the tolerance value
pub fn tolerance(a f64, b f64, tol f64) bool {
mut ee := tol
// Multiplying by ee here can underflow denormal values to zero.
// Check a==b so that at least if a and b are small and identical
// we say they match.
if a == b {
return true
}
mut d := a - b
if d < 0 {
d = -d
}
// note: b is correct (expected) value, a is actual value.
// make error tolerance a fraction of b, not a.
if b != 0 {
ee = ee * b
if ee < 0 {
ee = -ee
}
}
return d < ee
}
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// close checks if a and b are within 1e-14 of each other
pub fn close(a f64, b f64) bool {
return tolerance(a, b, 1e-14)
}
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// veryclose checks if a and b are within 4e-16 of each other
pub fn veryclose(a f64, b f64) bool {
return tolerance(a, b, 4e-16)
}
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// alike checks if a and b are equal
pub fn alike(a f64, b f64) bool {
if is_nan(a) && is_nan(b) {
return true
} else if a == b {
return signbit(a) == signbit(b)
}
return false
}
fn is_odd_int(x f64) bool {
xi, xf := modf(x)
return xf == 0 && (i64(xi) & 1) == 1
}
fn is_neg_int(x f64) bool {
if x < 0 {
_, xf := modf(x)
return xf == 0
}
return false
}