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author | Indrajith K L | 2022-12-03 17:00:20 +0530 |
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committer | Indrajith K L | 2022-12-03 17:00:20 +0530 |
commit | f5c4671bfbad96bf346bd7e9a21fc4317b4959df (patch) | |
tree | 2764fc62da58f2ba8da7ed341643fc359873142f /v_windows/v/old/vlib/math/complex | |
download | cli-tools-windows-f5c4671bfbad96bf346bd7e9a21fc4317b4959df.tar.gz cli-tools-windows-f5c4671bfbad96bf346bd7e9a21fc4317b4959df.tar.bz2 cli-tools-windows-f5c4671bfbad96bf346bd7e9a21fc4317b4959df.zip |
Diffstat (limited to 'v_windows/v/old/vlib/math/complex')
-rw-r--r-- | v_windows/v/old/vlib/math/complex/complex.v | 374 | ||||
-rw-r--r-- | v_windows/v/old/vlib/math/complex/complex_test.v | 797 |
2 files changed, 1171 insertions, 0 deletions
diff --git a/v_windows/v/old/vlib/math/complex/complex.v b/v_windows/v/old/vlib/math/complex/complex.v new file mode 100644 index 0000000..9fd7cc8 --- /dev/null +++ b/v_windows/v/old/vlib/math/complex/complex.v @@ -0,0 +1,374 @@ +// Copyright (c) 2019-2021 Alexander Medvednikov. All rights reserved. +// Use of this source code is governed by an MIT license +// that can be found in the LICENSE file. + +module complex + +import math + +pub struct Complex { +pub: + re f64 + im f64 +} + +pub fn complex(re f64, im f64) Complex { + return Complex{re, im} +} + +// To String method +pub fn (c Complex) str() string { + mut out := '${c.re:.6f}' + out += if c.im >= 0 { '+${c.im:.6f}' } else { '${c.im:.6f}' } + out += 'i' + return out +} + +// Complex Modulus value +// mod() and abs() return the same +pub fn (c Complex) abs() f64 { + return C.hypot(c.re, c.im) +} + +pub fn (c Complex) mod() f64 { + return c.abs() +} + +// Complex Angle +pub fn (c Complex) angle() f64 { + return math.atan2(c.im, c.re) +} + +// Complex Addition c1 + c2 +pub fn (c1 Complex) + (c2 Complex) Complex { + return Complex{c1.re + c2.re, c1.im + c2.im} +} + +// Complex Substraction c1 - c2 +pub fn (c1 Complex) - (c2 Complex) Complex { + return Complex{c1.re - c2.re, c1.im - c2.im} +} + +// Complex Multiplication c1 * c2 +pub fn (c1 Complex) * (c2 Complex) Complex { + return Complex{(c1.re * c2.re) + ((c1.im * c2.im) * -1), (c1.re * c2.im) + (c1.im * c2.re)} +} + +// Complex Division c1 / c2 +pub fn (c1 Complex) / (c2 Complex) Complex { + denom := (c2.re * c2.re) + (c2.im * c2.im) + return Complex{((c1.re * c2.re) + ((c1.im * -c2.im) * -1)) / denom, ((c1.re * -c2.im) + + (c1.im * c2.re)) / denom} +} + +// Complex Addition c1.add(c2) +pub fn (c1 Complex) add(c2 Complex) Complex { + return c1 + c2 +} + +// Complex Subtraction c1.subtract(c2) +pub fn (c1 Complex) subtract(c2 Complex) Complex { + return c1 - c2 +} + +// Complex Multiplication c1.multiply(c2) +pub fn (c1 Complex) multiply(c2 Complex) Complex { + return Complex{(c1.re * c2.re) + ((c1.im * c2.im) * -1), (c1.re * c2.im) + (c1.im * c2.re)} +} + +// Complex Division c1.divide(c2) +pub fn (c1 Complex) divide(c2 Complex) Complex { + denom := (c2.re * c2.re) + (c2.im * c2.im) + return Complex{((c1.re * c2.re) + ((c1.im * -c2.im) * -1)) / denom, ((c1.re * -c2.im) + + (c1.im * c2.re)) / denom} +} + +// Complex Conjugate +pub fn (c Complex) conjugate() Complex { + return Complex{c.re, -c.im} +} + +// Complex Additive Inverse +// Based on +// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx +pub fn (c Complex) addinv() Complex { + return Complex{-c.re, -c.im} +} + +// Complex Multiplicative Inverse +// Based on +// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx +pub fn (c Complex) mulinv() Complex { + return Complex{c.re / (c.re * c.re + c.im * c.im), -c.im / (c.re * c.re + c.im * c.im)} +} + +// Complex Power +// Based on +// https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-and-dividing-complex-numbers-in-polar-form/a/complex-number-polar-form-review +pub fn (c Complex) pow(n f64) Complex { + r := math.pow(c.abs(), n) + angle := c.angle() + return Complex{r * math.cos(n * angle), r * math.sin(n * angle)} +} + +// Complex nth root +pub fn (c Complex) root(n f64) Complex { + return c.pow(1.0 / n) +} + +// Complex Exponential +// Using Euler's Identity +// Based on +// https://www.math.wisc.edu/~angenent/Free-Lecture-Notes/freecomplexnumbers.pdf +pub fn (c Complex) exp() Complex { + a := math.exp(c.re) + return Complex{a * math.cos(c.im), a * math.sin(c.im)} +} + +// Complex Natural Logarithm +// Based on +// http://www.chemistrylearning.com/logarithm-of-complex-number/ +pub fn (c Complex) ln() Complex { + return Complex{math.log(c.abs()), c.angle()} +} + +// Complex Log Base Complex +// Based on +// http://www.milefoot.com/math/complex/summaryops.htm +pub fn (c Complex) log(base Complex) Complex { + return base.ln().divide(c.ln()) +} + +// Complex Argument +// Based on +// http://mathworld.wolfram.com/ComplexArgument.html +pub fn (c Complex) arg() f64 { + return math.atan2(c.im, c.re) +} + +// Complex raised to Complex Power +// Based on +// http://mathworld.wolfram.com/ComplexExponentiation.html +pub fn (c Complex) cpow(p Complex) Complex { + a := c.arg() + b := math.pow(c.re, 2) + math.pow(c.im, 2) + d := p.re * a + (1.0 / 2) * p.im * math.log(b) + t1 := math.pow(b, p.re / 2) * math.exp(-p.im * a) + return Complex{t1 * math.cos(d), t1 * math.sin(d)} +} + +// Complex Sin +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) sin() Complex { + return Complex{math.sin(c.re) * math.cosh(c.im), math.cos(c.re) * math.sinh(c.im)} +} + +// Complex Cosine +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) cos() Complex { + return Complex{math.cos(c.re) * math.cosh(c.im), -(math.sin(c.re) * math.sinh(c.im))} +} + +// Complex Tangent +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) tan() Complex { + return c.sin().divide(c.cos()) +} + +// Complex Cotangent +// Based on +// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm +pub fn (c Complex) cot() Complex { + return c.cos().divide(c.sin()) +} + +// Complex Secant +// Based on +// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm +pub fn (c Complex) sec() Complex { + return complex(1, 0).divide(c.cos()) +} + +// Complex Cosecant +// Based on +// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm +pub fn (c Complex) csc() Complex { + return complex(1, 0).divide(c.sin()) +} + +// Complex Arc Sin / Sin Inverse +// Based on +// http://www.milefoot.com/math/complex/summaryops.htm +pub fn (c Complex) asin() Complex { + return complex(0, -1).multiply(complex(0, 1).multiply(c).add(complex(1, 0).subtract(c.pow(2)).root(2)).ln()) +} + +// Complex Arc Consine / Consine Inverse +// Based on +// http://www.milefoot.com/math/complex/summaryops.htm +pub fn (c Complex) acos() Complex { + return complex(0, -1).multiply(c.add(complex(0, 1).multiply(complex(1, 0).subtract(c.pow(2)).root(2))).ln()) +} + +// Complex Arc Tangent / Tangent Inverse +// Based on +// http://www.milefoot.com/math/complex/summaryops.htm +pub fn (c Complex) atan() Complex { + i := complex(0, 1) + return complex(0, 1.0 / 2).multiply(i.add(c).divide(i.subtract(c)).ln()) +} + +// Complex Arc Cotangent / Cotangent Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse_Functions.htm +pub fn (c Complex) acot() Complex { + return complex(1, 0).divide(c).atan() +} + +// Complex Arc Secant / Secant Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse_Functions.htm +pub fn (c Complex) asec() Complex { + return complex(1, 0).divide(c).acos() +} + +// Complex Arc Cosecant / Cosecant Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse_Functions.htm +pub fn (c Complex) acsc() Complex { + return complex(1, 0).divide(c).asin() +} + +// Complex Hyperbolic Sin +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) sinh() Complex { + return Complex{math.cos(c.im) * math.sinh(c.re), math.sin(c.im) * math.cosh(c.re)} +} + +// Complex Hyperbolic Cosine +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) cosh() Complex { + return Complex{math.cos(c.im) * math.cosh(c.re), math.sin(c.im) * math.sinh(c.re)} +} + +// Complex Hyperbolic Tangent +// Based on +// http://www.milefoot.com/math/complex/functionsofi.htm +pub fn (c Complex) tanh() Complex { + return c.sinh().divide(c.cosh()) +} + +// Complex Hyperbolic Cotangent +// Based on +// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm +pub fn (c Complex) coth() Complex { + return c.cosh().divide(c.sinh()) +} + +// Complex Hyperbolic Secant +// Based on +// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm +pub fn (c Complex) sech() Complex { + return complex(1, 0).divide(c.cosh()) +} + +// Complex Hyperbolic Cosecant +// Based on +// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm +pub fn (c Complex) csch() Complex { + return complex(1, 0).divide(c.sinh()) +} + +// Complex Hyperbolic Arc Sin / Sin Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +pub fn (c Complex) asinh() Complex { + return c.add(c.pow(2).add(complex(1, 0)).root(2)).ln() +} + +// Complex Hyperbolic Arc Consine / Consine Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +pub fn (c Complex) acosh() Complex { + if c.re > 1 { + return c.add(c.pow(2).subtract(complex(1, 0)).root(2)).ln() + } else { + one := complex(1, 0) + return c.add(c.add(one).root(2).multiply(c.subtract(one).root(2))).ln() + } +} + +// Complex Hyperbolic Arc Tangent / Tangent Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +pub fn (c Complex) atanh() Complex { + one := complex(1, 0) + if c.re < 1 { + return complex(1.0 / 2, 0).multiply(one.add(c).divide(one.subtract(c)).ln()) + } else { + return complex(1.0 / 2, 0).multiply(one.add(c).ln().subtract(one.subtract(c).ln())) + } +} + +// Complex Hyperbolic Arc Cotangent / Cotangent Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +pub fn (c Complex) acoth() Complex { + one := complex(1, 0) + if c.re < 0 || c.re > 1 { + return complex(1.0 / 2, 0).multiply(c.add(one).divide(c.subtract(one)).ln()) + } else { + div := one.divide(c) + return complex(1.0 / 2, 0).multiply(one.add(div).ln().subtract(one.subtract(div).ln())) + } +} + +// Complex Hyperbolic Arc Secant / Secant Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +// For certain scenarios, Result mismatch in crossverification with Wolfram Alpha - analysis pending +// pub fn (c Complex) asech() Complex { +// one := complex(1,0) +// if(c.re < -1.0) { +// return one.subtract( +// one.subtract( +// c.pow(2) +// ) +// .root(2) +// ) +// .divide(c) +// .ln() +// } +// else { +// return one.add( +// one.subtract( +// c.pow(2) +// ) +// .root(2) +// ) +// .divide(c) +// .ln() +// } +// } + +// Complex Hyperbolic Arc Cosecant / Cosecant Inverse +// Based on +// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm +pub fn (c Complex) acsch() Complex { + one := complex(1, 0) + if c.re < 0 { + return one.subtract(one.add(c.pow(2)).root(2)).divide(c).ln() + } else { + return one.add(one.add(c.pow(2)).root(2)).divide(c).ln() + } +} + +// Complex Equals +pub fn (c1 Complex) equals(c2 Complex) bool { + return (c1.re == c2.re) && (c1.im == c2.im) +} diff --git a/v_windows/v/old/vlib/math/complex/complex_test.v b/v_windows/v/old/vlib/math/complex/complex_test.v new file mode 100644 index 0000000..ccd448e --- /dev/null +++ b/v_windows/v/old/vlib/math/complex/complex_test.v @@ -0,0 +1,797 @@ +import math +import math.complex as cmplx + +fn tst_res(str1 string, str2 string) bool { + if (math.abs(str1.f64() - str2.f64())) < 1e-5 { + return true + } + return false +} + +fn test_complex_addition() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c1 := cmplx.complex(0, -10) + mut c2 := cmplx.complex(-40, 8) + mut result := c1 + c2 + assert result.equals(cmplx.complex(-40, -2)) + c1 = cmplx.complex(-71, 2) + c2 = cmplx.complex(88, -12) + result = c1 + c2 + assert result.equals(cmplx.complex(17, -10)) + c1 = cmplx.complex(0, -30) + c2 = cmplx.complex(52, -30) + result = c1 + c2 + assert result.equals(cmplx.complex(52, -60)) + c1 = cmplx.complex(12, -9) + c2 = cmplx.complex(32, -6) + result = c1 + c2 + assert result.equals(cmplx.complex(44, -15)) +} + +fn test_complex_subtraction() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c1 := cmplx.complex(-8, 0) + mut c2 := cmplx.complex(6, 30) + mut result := c1 - c2 + assert result.equals(cmplx.complex(-14, -30)) + c1 = cmplx.complex(-19, 7) + c2 = cmplx.complex(29, 32) + result = c1 - c2 + assert result.equals(cmplx.complex(-48, -25)) + c1 = cmplx.complex(12, 0) + c2 = cmplx.complex(23, 13) + result = c1 - c2 + assert result.equals(cmplx.complex(-11, -13)) + c1 = cmplx.complex(-14, 3) + c2 = cmplx.complex(0, 14) + result = c1 - c2 + assert result.equals(cmplx.complex(-14, -11)) +} + +fn test_complex_multiplication() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c1 := cmplx.complex(1, 2) + mut c2 := cmplx.complex(1, -4) + mut result := c1 * c2 + assert result.equals(cmplx.complex(9, -2)) + c1 = cmplx.complex(-4, -4) + c2 = cmplx.complex(-5, -3) + result = c1 * c2 + assert result.equals(cmplx.complex(8, 32)) + c1 = cmplx.complex(4, 4) + c2 = cmplx.complex(-2, -5) + result = c1 * c2 + assert result.equals(cmplx.complex(12, -28)) + c1 = cmplx.complex(2, -2) + c2 = cmplx.complex(4, -4) + result = c1 * c2 + assert result.equals(cmplx.complex(0, -16)) +} + +fn test_complex_division() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c1 := cmplx.complex(-9, -6) + mut c2 := cmplx.complex(-3, -2) + mut result := c1 / c2 + assert result.equals(cmplx.complex(3, 0)) + c1 = cmplx.complex(-23, 11) + c2 = cmplx.complex(5, 1) + result = c1 / c2 + assert result.equals(cmplx.complex(-4, 3)) + c1 = cmplx.complex(8, -2) + c2 = cmplx.complex(-4, 1) + result = c1 / c2 + assert result.equals(cmplx.complex(-2, 0)) + c1 = cmplx.complex(11, 24) + c2 = cmplx.complex(-4, -1) + result = c1 / c2 + assert result.equals(cmplx.complex(-4, -5)) +} + +fn test_complex_conjugate() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c1 := cmplx.complex(0, 8) + mut result := c1.conjugate() + assert result.equals(cmplx.complex(0, -8)) + c1 = cmplx.complex(7, 3) + result = c1.conjugate() + assert result.equals(cmplx.complex(7, -3)) + c1 = cmplx.complex(2, 2) + result = c1.conjugate() + assert result.equals(cmplx.complex(2, -2)) + c1 = cmplx.complex(7, 0) + result = c1.conjugate() + assert result.equals(cmplx.complex(7, 0)) +} + +fn test_complex_equals() { + mut c1 := cmplx.complex(0, 8) + mut c2 := cmplx.complex(0, 8) + assert c1.equals(c2) + c1 = cmplx.complex(-3, 19) + c2 = cmplx.complex(-3, 19) + assert c1.equals(c2) +} + +fn test_complex_abs() { + mut c1 := cmplx.complex(3, 4) + assert c1.abs() == 5 + c1 = cmplx.complex(1, 2) + assert c1.abs() == math.sqrt(5) + assert c1.abs() == c1.conjugate().abs() + c1 = cmplx.complex(7, 0) + assert c1.abs() == 7 +} + +fn test_complex_angle() { + // Test is based on and verified from practice examples of Khan Academy + // https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers + mut c := cmplx.complex(1, 0) + assert c.angle() * 180 / math.pi == 0 + c = cmplx.complex(1, 1) + assert c.angle() * 180 / math.pi == 45 + c = cmplx.complex(0, 1) + assert c.angle() * 180 / math.pi == 90 + c = cmplx.complex(-1, 1) + assert c.angle() * 180 / math.pi == 135 + c = cmplx.complex(-1, -1) + assert c.angle() * 180 / math.pi == -135 + cc := c.conjugate() + assert cc.angle() + c.angle() == 0 +} + +fn test_complex_addinv() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-5, -7) + mut result := c1.addinv() + assert result.equals(c2) + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(3, -4) + result = c1.addinv() + assert result.equals(c2) + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(1, 2) + result = c1.addinv() + assert result.equals(c2) +} + +fn test_complex_mulinv() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.067568, -0.094595) + mut result := c1.mulinv() + // Some issue with precision comparison in f64 using == operator hence serializing to string + println(c2.str()) + println(result.str()) + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.12, -0.16) + result = c1.mulinv() + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.2, 0.4) + result = c1.mulinv() + assert result.equals(c2) +} + +fn test_complex_mod() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut result := c1.mod() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert tst_res(result.str(), '8.602325') + c1 = cmplx.complex(-3, 4) + result = c1.mod() + assert result == 5 + c1 = cmplx.complex(-1, -2) + result = c1.mod() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert tst_res(result.str(), '2.236068') +} + +fn test_complex_pow() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-24.0, 70.0) + mut result := c1.pow(2) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(117, 44) + result = c1.pow(3) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-7, -24) + result = c1.pow(4) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_root() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(2.607904, 1.342074) + mut result := c1.root(2) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(1.264953, 1.150614) + result = c1.root(3) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(1.068059, -0.595482) + result = c1.root(4) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_exp() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(111.889015, 97.505457) + mut result := c1.exp() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.032543, -0.037679) + result = c1.exp() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.153092, -0.334512) + result = c1.exp() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_ln() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(2.152033, 0.950547) + mut result := c1.ln() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(1.609438, 2.214297) + result = c1.ln() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(0.804719, -2.034444) + result = c1.ln() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_arg() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(2.152033, 0.950547) + mut result := c1.arg() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert tst_res(result.str(), '0.950547') + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(1.609438, 2.214297) + result = c1.arg() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert tst_res(result.str(), '2.214297') + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(0.804719, -2.034444) + result = c1.arg() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert tst_res(result.str(), '-2.034444') +} + +fn test_complex_log() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut b1 := cmplx.complex(-6, -2) + mut c2 := cmplx.complex(0.232873, -1.413175) + mut result := c1.log(b1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + b1 = cmplx.complex(3, -1) + c2 = cmplx.complex(0.152198, -0.409312) + result = c1.log(b1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + b1 = cmplx.complex(0, 9) + c2 = cmplx.complex(-0.298243, 1.197981) + result = c1.log(b1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_cpow() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut r1 := cmplx.complex(2, 2) + mut c2 := cmplx.complex(11.022341, -0.861785) + mut result := c1.cpow(r1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + r1 = cmplx.complex(-4, -2) + c2 = cmplx.complex(0.118303, 0.063148) + result = c1.cpow(r1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + r1 = cmplx.complex(8, -9) + c2 = cmplx.complex(-0.000000, 0.000007) + result = c1.cpow(r1) + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_sin() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-525.794515, 155.536550) + mut result := c1.sin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-3.853738, -27.016813) + result = c1.sin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-3.165779, -1.959601) + result = c1.sin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_cos() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(155.536809, 525.793641) + mut result := c1.cos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-27.034946, 3.851153) + result = c1.cos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(2.032723, -3.051898) + result = c1.cos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_tan() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-0.000001, 1.000001) + mut result := c1.tan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(0.000187, 0.999356) + result = c1.tan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.033813, -1.014794) + result = c1.tan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_cot() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-0.000001, -0.999999) + mut result := c1.cot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(0.000188, -1.000644) + result = c1.cot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.032798, 0.984329) + result = c1.cot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_sec() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.000517, -0.001749) + mut result := c1.sec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.036253, -0.005164) + result = c1.sec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(0.151176, 0.226974) + result = c1.sec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_csc() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(-0.001749, -0.000517) + mut result := c1.csc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.005174, 0.036276) + result = c1.csc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.228375, 0.141363) + result = c1.csc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_asin() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.617064, 2.846289) + mut result := c1.asin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.633984, 2.305509) + result = c1.asin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.427079, -1.528571) + result = c1.asin() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_acos() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.953732, -2.846289) + mut result := c1.acos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(2.204780, -2.305509) + result = c1.acos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(1.997875, 1.528571) + result = c1.acos() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_atan() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(1.502727, 0.094441) + mut result := c1.atan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-1.448307, 0.158997) + result = c1.atan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-1.338973, -0.402359) + result = c1.atan() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_acot() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.068069, -0.094441) + mut result := c1.acot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.122489, -0.158997) + result = c1.acot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.231824, 0.402359) + result = c1.acot() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_asec() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(1.503480, 0.094668) + mut result := c1.asec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(1.689547, 0.160446) + result = c1.asec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(1.757114, -0.396568) + result = c1.asec() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_acsc() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.067317, -0.094668) + mut result := c1.acsc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.118751, -0.160446) + result = c1.acsc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.186318, 0.396568) + result = c1.acsc() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_sinh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(55.941968, 48.754942) + mut result := c1.sinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(6.548120, -7.619232) + result = c1.sinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(0.489056, -1.403119) + result = c1.sinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_cosh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(55.947047, 48.750515) + mut result := c1.cosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-6.580663, 7.581553) + result = c1.cosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.642148, 1.068607) + result = c1.cosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_tanh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.999988, 0.000090) + mut result := c1.tanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-1.000710, 0.004908) + result = c1.tanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-1.166736, 0.243458) + result = c1.tanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_coth() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(1.000012, -0.000090) + mut result := c1.coth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.999267, -0.004901) + result = c1.coth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.821330, -0.171384) + result = c1.coth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_sech() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.010160, -0.008853) + mut result := c1.sech() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.065294, -0.075225) + result = c1.sech() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.413149, -0.687527) + result = c1.sech() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_csch() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.010159, -0.008854) + mut result := c1.csch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(0.064877, 0.075490) + result = c1.csch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(0.221501, 0.635494) + result = c1.csch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_asinh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(2.844098, 0.947341) + mut result := c1.asinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-2.299914, 0.917617) + result = c1.asinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-1.469352, -1.063440) + result = c1.asinh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_acosh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(2.846289, 0.953732) + mut result := c1.acosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(2.305509, 2.204780) + result = c1.acosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(1.528571, -1.997875) + result = c1.acosh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_atanh() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.067066, 1.476056) + mut result := c1.atanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.117501, 1.409921) + result = c1.atanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.173287, -1.178097) + result = c1.atanh() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_acoth() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.067066, -0.094740) + mut result := c1.acoth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.117501, -0.160875) + result = c1.acoth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.173287, 0.392699) + result = c1.acoth() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +// fn test_complex_asech() { +// // Tests were also verified on Wolfram Alpha +// mut c1 := cmplx.complex(5,7) +// mut c2 := cmplx.complex(0.094668,-1.503480) +// mut result := c1.asech() +// // Some issue with precision comparison in f64 using == operator hence serializing to string +// assert result.str() == c2.str() +// c1 = cmplx.complex(-3,4) +// c2 = cmplx.complex(0.160446,-1.689547) +// result = c1.asech() +// // Some issue with precision comparison in f64 using == operator hence serializing to string +// assert result.str() c2.str() +// c1 = cmplx.complex(-1,-2) +// c2 = cmplx.complex(0.396568,1.757114) +// result = c1.asech() +// // Some issue with precision comparison in f64 using == operator hence serializing to string +// assert result.str() == c2.str() +// } + +fn test_complex_acsch() { + // Tests were also verified on Wolfram Alpha + mut c1 := cmplx.complex(5, 7) + mut c2 := cmplx.complex(0.067819, -0.094518) + mut result := c1.acsch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-3, 4) + c2 = cmplx.complex(-0.121246, -0.159507) + result = c1.acsch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() + c1 = cmplx.complex(-1, -2) + c2 = cmplx.complex(-0.215612, 0.401586) + result = c1.acsch() + // Some issue with precision comparison in f64 using == operator hence serializing to string + assert result.str() == c2.str() +} + +fn test_complex_re_im() { + c := cmplx.complex(2.1, 9.05) + assert c.re == 2.1 + assert c.im == 9.05 +} |