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cmath: Added Cot,Sec,Cosec support for complex

pull/1102/head
Archan Patkar 2019-07-12 16:26:21 +05:30 committed by Alexander Medvednikov
parent 7f4c3cda4d
commit 846d4e2210
2 changed files with 378 additions and 3 deletions
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153
vlib/cmath/complex.v
View File

@ -187,6 +187,27 @@ 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
@ -234,6 +255,27 @@ pub fn (c Complex) atan() Complex {
)
}
// 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
@ -261,6 +303,27 @@ 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
@ -300,8 +363,8 @@ pub fn (c Complex) acosh() Complex {
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) atanh() Complex {
one := complex(1,0)
if(c.re < 1) {
one := complex(1,0)
return complex(1.0/2,0).multiply(
one
.add(c)
@ -313,7 +376,6 @@ pub fn (c Complex) atanh() Complex {
)
}
else {
one := complex(1,0)
return complex(1.0/2,0).multiply(
one
.add(c)
@ -327,7 +389,92 @@ pub fn (c Complex) atanh() Complex {
}
}
// 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()
}
if(c.re > 0) {
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)
}
}

228
vlib/cmath/complex_test.v
View File

@ -311,6 +311,63 @@ fn test_complex_tan() {
assert result.str().eq(c2.str())
}
fn test_complex_cot() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(0.000188,-1.000644)
result = c1.cot()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.032798,0.984329)
result = c1.cot()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_sec() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.036253,-0.005164)
result = c1.sec()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(0.151176,0.226974)
result = c1.sec()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_csc() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.005174,0.036276)
result = c1.csc()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.228375,0.141363)
result = c1.csc()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_asin() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
@ -368,6 +425,63 @@ fn test_complex_atan() {
assert result.str().eq(c2.str())
}
fn test_complex_acot() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.122489,-0.158997)
result = c1.acot()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.231824,0.402359)
result = c1.acot()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_asec() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(1.689547,0.160446)
result = c1.asec()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(1.757114,-0.396568)
result = c1.asec()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_acsc() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.118751,-0.160446)
result = c1.acsc()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.186318,0.396568)
result = c1.acsc()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_sinh() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
@ -424,7 +538,64 @@ fn test_complex_tanh() {
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_coth() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.999267,-0.004901)
result = c1.coth()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.821330,-0.171384)
result = c1.coth()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_sech() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.065294,-0.075225)
result = c1.sech()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.413149,-0.687527)
result = c1.sech()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_csch() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(0.064877,0.075490)
result = c1.csch()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(0.221501,0.635494)
result = c1.csch()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_asinh() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
@ -480,4 +651,61 @@ fn test_complex_atanh() {
result = c1.atanh()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_acoth() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.117501,-0.160875)
result = c1.acoth()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.173287,0.392699)
result = c1.acoth()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
// fn test_complex_asech() {
// // Tests were also verified on Wolfram Alpha
// mut c1 := cmath.complex(5,7)
// mut c2 := cmath.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().eq(c2.str())
// c1 = cmath.complex(-3,4)
// c2 = cmath.complex(0.160446,-1.689547)
// result = c1.asech()
// // Some issue with precision comparison in f64 using == operator hence serializing to string
// assert result.str().eq(c2.str())
// c1 = cmath.complex(-1,-2)
// c2 = cmath.complex(0.396568,1.757114)
// result = c1.asech()
// // Some issue with precision comparison in f64 using == operator hence serializing to string
// assert result.str().eq(c2.str())
// }
fn test_complex_acsch() {
// Tests were also verified on Wolfram Alpha
mut c1 := cmath.complex(5,7)
mut c2 := cmath.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().eq(c2.str())
c1 = cmath.complex(-3,4)
c2 = cmath.complex(-0.121246,-0.159507)
result = c1.acsch()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = cmath.complex(-1,-2)
c2 = cmath.complex(-0.215612,0.401586)
result = c1.acsch()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}