003

Author: Michael Abbott

README.md

@@ -3,19 +3,19 @@
 Provides Bhaskara I's sine approximation formula
 
 ```julia
-sinπ(θ) = 16(π-θ)θ / (5π^2 - 4(π-θ)θ)      # < 0.1% error, θ ∈ [0,π]
+bsin(θ) = 16(π-θ)θ / (5π^2 - 4(π-θ)θ)      # error < 0.002, θ ∈ [0,π]
 ```
 
-There is also `sin2π(θ)` for `θ ∈ [-π,π]`, and `Bhaskara.sin(θ)` for `θ ∈ 𝐑`,
+There is also `b2sin(θ)` for `θ ∈ [-π,π]`, and `Bhaskara.sin(θ)` for `θ ∈ 𝐑`,
 by inserting appropriate `mod(,2π)` and `sign()*abs()` bits. 
-Similarly `cosπ(θ)` is for `θ ∈ [-π/2,π/2]`, and `Bhaskara.cos(θ)` for all `θ ∈ 𝐑`.
+Similarly `bcos(θ)` is for `θ ∈ [-π/2,π/2]`, and `Bhaskara.cos(θ)` for all `θ ∈ 𝐑`.
 
 <img src="sin.png?raw=true" width="600" height="400" alt="versions of sin" align="center" padding="5">
 
 <!--
 using Bhaskara, Plots
-plot(-2π:0.01:2π, sinπ.(-2π:0.01:2π), lab="sin\\pi")
-plot!(-2π:0.01:2π, sin2π.(-2π:0.01:2π), lab="sin2\\pi")
+plot(-2π:0.01:2π, bsin.(-2π:0.01:2π), lab="bsin")
+plot!(-2π:0.01:2π, b2sin.(-2π:0.01:2π), lab="b2sin")
 plot!(-2π:0.01:2π, Bhaskara.sin.(-2π:0.01:2π), lab="sin")
 plot!(xticks=([-2π,-π,0,π,2π],["-2\\pi","-\\pi","0","\\pi","2\\pi"]), ylim=[-2,2])
 savefig("sin.png")

REQUIRE

@@ -0,0 +1 @@
+julia 1.0

sin.png

@@ -1,25 +1,25 @@
 module Bhaskara
 
-export sinπ, sin2π, cosπ, sind180
+export bsin, b2sin, bcos
 
 
-sinπ(θ) = 16(π-θ)θ / (5π^2 - 4(π-θ)θ)
+bsin(θ) = 16(π-θ)θ / (5π^2 - 4(π-θ)θ)
 
-sin2π(θ) = sign(θ) * sinπ(abs(θ))
+b2sin(θ) = sign(θ) * bsin(abs(θ))
 
-sin(θ::T) where T<:Number = sin2π(mod(θ+π, T(2)*π) - π)
+sin(θ::T) where T<:Number = b2sin(mod(θ+π, T(2)*π) - π)
 
 
 sind180(x) = 4(180-x)x / (40500 - (180-x)x)
 
-sind360(x) = sign(x) * sin180(abs(x))
+sind360(x) = sign(x) * sind180(abs(x))
 
 sind(x::Number) = sind360(mod(x+180,360)-180)
 
 
-cosπ(θ) = (π^2 - 4θ^2) / (π^2+θ^2)
+bcos(θ) = (π^2 - 4θ^2) / (π^2+θ^2)
 
-cos(θ::T) where T<:Number = sin2π(mod(θ+π/T(2), T(2)*π) - π)
+cos(θ::T) where T<:Number = b2sin(mod(θ-π/T(2), T(2)*π) - π)
 
 
 tan(θ::Number) = sin(θ) / cos(θ)

src/Bhaskara.jl

@@ -0,0 +1,17 @@
+using Test
+using Bhaskara
+
+test(f, g, r=0:0.001:π, e=0.002) = maximum(@. abs(f(r)-g(r)) ) < e
+
+@test test(bsin, Base.sin)
+@test test(b2sin, Base.sin, -π:0.001:π)
+@test test(Bhaskara.sin, Base.sin, -3π:0.001:3π)
+
+@test test(Bhaskara.sind180, Base.sind, 0:0.1:180)
+@test test(Bhaskara.sind360, Base.sind, -180:0.1:180)
+@test test(Bhaskara.sind, Base.sind, -1000:0.1:1000)
+
+@test test(bcos, Base.cos, -0.5π:0.001:0.5π)
+@test test(Bhaskara.cos, Base.cos, -3π:0.001:3π)
+
+@test bsin(big(0.1)) isa BigFloat