first commit

Author: faretek1

README.md

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+ # cmath.gs
+ This is a math library for complex numbers which is built for [goboscript](https://github.com/aspizu/goboscript).
+ It is designed to be used with [backpack](https://github.com/aspizu/backpack)
+ 
+ ## Installation
+ To use this, make sure to install [backpack](https://github.com/aspizu/backpack)
+ 
+ You can use the standard library by adding these lines to goboscript.toml:
+ ```toml
+ [dependencies]
+ std = "https://github.com/FAReTek1/cmath@<the version you want to use>"
+ ```
+ 
+ Then, add this %include to your gs file:
+ you can also use this to just %include everything
+ ```rs
+ %include backpack/cmath/cmath
+ ```

cmath.gs

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+# dependencies
+
+%include backpack/std/std
+
+################################################################
+
+%include backpack/cmath/cmath/complex
+
+%include backpack/cmath/cmath/operations

cmath/complex.gs

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+# Operations to do with the Complex struct (non-mathematical) and the struct itself
+struct Complex {
+ real,
+ imag
+}
+
+func complex(real, imag) Complex {
+ # This reduces the amount of 'boilerplate' code for making complex structs.
+
+ return Complex{
+ real: $real,
+ imag: $imag
+ };
+}
+
+func c_tostr(Complex z) {
+ if $z.imag > 0 {
+ return $z.real & " + " & $z.imag & "i";
+ } else {
+ return $z.real & " - " & -$z.imag & "i";
+ }
+}

cmath/operations.gs

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+# Mathematical operations with the Complex struct
+
+################################################################
+# Basic operations
+# Perhaps these should be macros? I don't know...
+func c_add(Complex a, Complex b) Complex {
+ return Complex{
+ real: $a.real + $b.real,
+ imag: $a.imag + $b.imag
+ };
+}
+
+func c_sub(Complex a, Complex b) Complex {
+ return Complex{
+ real: $a.real - $b.real,
+ imag: $a.imag - $b.imag
+ };
+}
+
+func c_mul(Complex a, Complex b) Complex {
+ return Complex{
+ real: $a.real * $b.real - $a.imag * $b.imag,
+ imag: $a.real * $b.imag + $a.imag * $b.real
+ };
+}
+
+func c_div(Complex a, Complex b) Complex {
+ local denom = $b.real * $b.real + $b.imag * $b.imag;
+
+ return Complex{
+ real: ($a.real * $b.real + $a.imag * $b.imag) / denom,
+ imag: ($a.imag * $b.real - $a.real * $b.imag) / denom
+ };
+}
+
+# No power operator here because it uses exp and ln
+
+################################################################
+# Advanced functions
+
+func c_abs(Complex z) {
+ return sqrt($z.real * $z.real + $z.imag * $z.imag);
+}
+
+func c_arg(Complex z) {
+ return ATAN2($z.imag, $z.real);
+}
+
+func c_sgn(complex z) Complex {
+ # Complex number on the unit circle that is in the direction of the complex number z
+ return c_div(
+ $z, Complex{
+ real: c_abs($z),
+ imag: 0
+ }
+ );
+}
+
+func c_exp(Complex z) Complex {
+ # Same as antiln
+ return Complex {
+ real: antiln($z.real) * cos($z.imag * 57.2957795131),
+ imag: antiln($z.real) * sin($z.imag * 57.2957795131)
+ };
+} 
+
+func c_ln(Complex z) Complex {
+ return Complex {
+ real: ln(c_abs($z)),
+ imag: ATAN2($z.imag, $z.real)
+ };
+}
+
+func c_pow(Complex a, Complex b) Complex {
+ return c_exp(
+ c_mul($b, c_ln($a))
+ );
+}
+
+func c_conj(Complex z) Complex {
+ return Complex {
+ real: $z.real,
+ imag: -$z.imag
+ };
+}
+
+func c_sqrt(Complex z) Complex {
+ return c_pow($z, Complex{real: 0.5, imag: 0});
+}
+
+################################################################
+# Trigonometric functions
+
+func c_sin(Complex z) Complex {
+ return c_div(c_sub(
+ c_exp(Complex{real: -$z.imag, imag: $z.real}), 
+ c_exp(Complex{real: $z.imag, imag: -$z.real})
+ ), Complex{real: 0, imag:2});
+}
+
+func c_cos(Complex z) Complex {
+ return c_div(c_add(
+ c_exp(Complex{real: -$z.imag, imag: $z.real}), 
+ c_exp(Complex{real: $z.imag, imag: -$z.real})
+ ), Complex{real: 2, imag:0});
+}
+
+func c_tan(Complex z) Complex {
+ # Yeah I didn't have this pre-coded so this is a lazy implementation
+ return c_div(
+ c_sin($z), c_cos($z)
+ );
+}
+
+################################################################
+# Inverse trigonometric functions
+
+func c_asin(Complex z) Complex {
+ return c_mul(
+ c_ln(
+ c_add(
+ Complex{real:-$z.imag, imag:$z.real},
+ c_sqrt(
+ c_sub(
+ Complex{real:1, imag:0}, 
+ c_mul($z, $z)
+ )
+ )
+ )
+ ),
+ Complex{real:0, imag:-1}
+ );
+}
+
+func c_acos(Complex z) Complex {
+ local Complex a = c_sqrt(
+ c_sub(
+ Complex{real:1, imag:0}, 
+ c_mul($z, $z)
+ )
+ );
+
+ return 
+ c_mul(
+ c_ln(
+ c_add(
+ $z,
+ Complex{
+ real:-a.imag, imag:a.real
+ }
+ )
+ ),
+ Complex{real:0, imag:-1}
+ );
+}
+
+func c_atan(Complex z) Complex {
+ return 
+ c_mul(c_ln(
+ c_div(
+ Complex{real: $z.real, imag: $z.imag + 1},
+ Complex{real: -$z.real, imag: 1-$z.imag}
+ )
+ ), Complex{real: 0, imag:0.5});
+}
+
+################################################################
+# Hyperbolic trigonometric functions
+func c_sinh(Complex z) Complex {
+ return Complex{
+ real: SINH($z.real) * cos($z.imag * 57.2957795131),
+ imag: COSH($z.real) * sin($z.imag * 57.2957795131)
+ };
+}
+
+func c_cosh(Complex z) Complex {
+ return Complex{
+ real: COSH($z.real) * cos($z.imag * 57.2957795131),
+ imag: -SINH($z.real) * sin($z.imag * 57.2957795131)
+ };
+}
+
+################################################################
+# Inverse hyperbolic trigonometric functions
+
+func c_asinh(Complex z) Complex {
+ # This might need to be improved
+ return 
+ c_ln(
+ c_add(
+ $z,
+ c_sqrt(
+ c_add(
+ c_mul($z, $z), 
+ Complex{real:1, imag:0}
+ )
+ )
+ )
+ );
+}
+
+func c_acosh(Complex z) Complex {
+ local Complex a = c_mul($z, $z);
+
+ return 
+ c_ln(
+ c_div(
+ $z,
+ c_sqrt(Complex{real:-a.real, imag:a.imag})
+ )
+ );
+}

goboscript.toml

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+[dependencies]
+std = "https://github.com/FAReTek1/std@v0.0.9"

test/blank.svg

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+no_miscellaneous_limits = false
+no_sprite_fencing = false
+frame_interpolation = false
+high_quality_pen = false

test/goboscript.toml

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+costumes "blank.svg";
+
+onflag {
+ say "Hello, World!";
+}

test/main.gs

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+costumes "blank.svg";