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// Language is OpenGL ES, but gist.github.com doesn't know that language
//
// Approximation is based on multiply/accumulate, because thats the only
// thing Videocore can do quickly!

precision highp float;

float sinf(float x)
{
  x*=0.159155;

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# Improved support for Eleduino 1024x600 LCD panel
hdmi_group=2
hdmi_mode=87
#Safer option at 50.4MHz pixel clock
#hdmi_timings=1024 0 48 32 240 600 0 3 32 13 0 0 0 60 0 50400000 6
#Safer option at data sheet max clock of 65.2
#hdmi_timings=1024 0 48 32 240 600 0 3 32 13 0 0 0 60 0 65200000 6
hdmi_timings=1024 0 48 32 216 600 0 2 14 0 0 0 0 60 0 65200000 6
max_usb_current=1

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;; Calculate exp2(x) = 2**x natively in WebAssembly.
;; Compiles to 49 bytes of WebAssembly code
(module
    (func $exp2 (param $x f32) (result f32)
        (local $xf f32)
        ;; Parse result as a float bitfield
        (f32.reinterpret_i32
            (i32.add
                ;; Compute mantissa of result
                ;; Compute polynomial to cover f(x) = 2**23 * ( 2^(x) - 1 ) where 0 <= x < 1

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(module
;; Calculate sin(tau x) natively in WebAssembly.
;; Compiles to 57 bytes of WebAssembly code
;; Uses angle units of 0 to 1 for a circle (useful for synths). Pre-divide by 2*pi to use radians.
;; Using Bhaskara I's approximation
;; https://en.wikipedia.org/wiki/Bhaskara_I%27s_sine_approximation_formula
;; Accurate to about 0.2%
  (export "sintau" (func $sintau))
  (func $sintau (param $x f32) (result f32)
    (local $s f32)

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;; From https://github.com/vsariola/sointu
;; Compiles to 19 bytes of WebAssembly code
;;
;; Returns pseudorandom numbers in the range 0 to 1
(module
  (global $randseed (mut i32) (i32.const 1))
  (export "rand" (func $rand))
  (func $rand (result f32)
    (set_global $randseed (i32.mul (get_global $randseed) (i32.const 16007)))
    (f32.div (f32.convert_s/i32 (get_global $randseed)) (f32.const -2147483648))

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;; Calculate log2(x) = ln(x)/ln(2) natively in WebAssembly.
;; Compiles to 75 bytes of WebAssembly code
(module
    (export "log2" (func $log2))
    (func $log2 (param $x f32) (result f32)
        (local $x2 f32)
        (f32.add
            ;; Extract exponent of $x
            (f32.convert_s/i32
                (i32.sub

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;; Native implementations of sin, log and exp functions.
;; sintau: 41 bytes code, 34 bytes shared code, 24 bytes data
;; exp2: 25 bytes code, 34 bytes shared code, 20 bytes data
;; log2: 37 bytes code, 34 bytes shared code, 24 bytes data
;; Total 137 bytes code, 68 bytes data

;; Wasm-opt -Oz tries to optimise out $half by converting to f32.consts, but that actually takes up more space, not less.

;; Polynomial coefficients calculated by accompanying python script.
;; call $evalpoly parameters will need to be manually changed for different length polynomials.

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# -*- coding: utf-8 -*-
#%%

from sympy import symbols, cos, pi, factor_list
from sympy.core.numbers import One
from sympy.utilities.lambdify import lambdify
from math import sin, pi
import numpy as np

def chebyshev(func, interval, degree=7, precision=20):

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