include <../std.scad>

// Simple Calculations

module test_quant() {
    assert_equal(quant(-4,3), -3);
    assert_equal(quant(-3,3), -3);
    assert_equal(quant(-2,3), -3);
    assert_equal(quant(-1,3), 0);
    assert_equal(quant(0,3), 0);
    assert_equal(quant(1,3), 0);
    assert_equal(quant(2,3), 3);
    assert_equal(quant(3,3), 3);
    assert_equal(quant(4,3), 3);
    assert_equal(quant(7,3), 6);
    assert_equal(quant(12,2.5), 12.5);
    assert_equal(quant(11,2.5), 10.0);
    assert_equal(quant([12,13,13.1,14,14.1,15,16],4), [12,12,12,16,16,16,16]);
    assert_equal(quant([9,10,10.4,10.5,11,12],3), [9,9,9,12,12,12]);
    assert_equal(quant([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[12,12,12]]);
}
test_quant();


module test_quantdn() {
    assert_equal(quantdn(-4,3), -6);
    assert_equal(quantdn(-3,3), -3);
    assert_equal(quantdn(-2,3), -3);
    assert_equal(quantdn(-1,3), -3);
    assert_equal(quantdn(0,3), 0);
    assert_equal(quantdn(1,3), 0);
    assert_equal(quantdn(2,3), 0);
    assert_equal(quantdn(3,3), 3);
    assert_equal(quantdn(4,3), 3);
    assert_equal(quantdn(7,3), 6);
    assert_equal(quantdn(12,2.5), 10.0);
    assert_equal(quantdn(11,2.5), 10.0);
    assert_equal(quantdn([12,13,13.1,14,14.1,15,16],4), [12,12,12,12,12,12,16]);
    assert_equal(quantdn([9,10,10.4,10.5,11,12],3), [9,9,9,9,9,12]);
    assert_equal(quantdn([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[9,9,12]]);
}
test_quantdn();


module test_quantup() {
    assert_equal(quantup(-4,3), -3);
    assert_equal(quantup(-3,3), -3);
    assert_equal(quantup(-2,3), 0);
    assert_equal(quantup(-1,3), 0);
    assert_equal(quantup(0,3), 0);
    assert_equal(quantup(1,3), 3);
    assert_equal(quantup(2,3), 3);
    assert_equal(quantup(3,3), 3);
    assert_equal(quantup(4,3), 6);
    assert_equal(quantup(7,3), 9);
    assert_equal(quantup(12,2.5), 12.5);
    assert_equal(quantup(11,2.5), 12.5);
    assert_equal(quantup([12,13,13.1,14,14.1,15,16],4), [12,16,16,16,16,16,16]);
    assert_equal(quantup([9,10,10.4,10.5,11,12],3), [9,12,12,12,12,12]);
    assert_equal(quantup([[9,10,10.4],[10.5,11,12]],3), [[9,12,12],[12,12,12]]);
}
test_quantup();


module test_constrain() {
    assert_equal(constrain(-2,-1,1), -1);
    assert_equal(constrain(-1.75,-1,1), -1);
    assert_equal(constrain(-1,-1,1), -1);
    assert_equal(constrain(-0.75,-1,1), -0.75);
    assert_equal(constrain(0,-1,1), 0);
    assert_equal(constrain(0.75,-1,1), 0.75);
    assert_equal(constrain(1,-1,1), 1);
    assert_equal(constrain(1.75,-1,1), 1);
    assert_equal(constrain(2,-1,1), 1);
}
test_constrain();



module test_all_integer() {
    assert(!all_integer(undef));
    assert(!all_integer(true));
    assert(!all_integer(false));
    assert(!all_integer(4.3));
    assert(!all_integer("foo"));
    assert(!all_integer([]));
    assert(!all_integer([3,4.1,5,7]));
    assert(!all_integer([[1,2,3],[4,5,6],[7,8]]));
    assert(all_integer(-4));
    assert(all_integer(0));
    assert(all_integer(5));
    assert(all_integer([-3]));
    assert(all_integer([0]));
    assert(all_integer([3]));
    assert(all_integer([2,-4,0,5,7,9876543210]));
}
test_all_integer();




module test_posmod() {
    assert_equal(posmod(-5,3), 1);
    assert_equal(posmod(-4,3), 2);
    assert_equal(posmod(-3,3), 0);
    assert_equal(posmod(-2,3), 1);
    assert_equal(posmod(-1,3), 2);
    assert_equal(posmod(0,3), 0);
    assert_equal(posmod(1,3), 1);
    assert_equal(posmod(2,3), 2);
    assert_equal(posmod(3,3), 0);
}
test_posmod();


module test_modang() {
    assert_equal(modang(-700), 20);
    assert_equal(modang(-270), 90);
    assert_equal(modang(-120), -120);
    assert_equal(modang(120), 120);
    assert_equal(modang(270), -90);
    assert_equal(modang(700), -20);
}
test_modang();


module test_sqr() {
    assert_equal(sqr(-3), 9);
    assert_equal(sqr(0), 0);
    assert_equal(sqr(1), 1);
    assert_equal(sqr(2), 4);
    assert_equal(sqr(2.5), 6.25);
    assert_equal(sqr(3), 9);
    assert_equal(sqr(16), 256);
    assert_equal(sqr([2,3,4]), 29);
    assert_equal(sqr([[2,3,4],[3,5,7],[3,5,1]]), [[25,41,33],[42,69,54],[24,39,48]]);
}
test_sqr();


module test_log2() {
    assert_equal(log2(0.125), -3);
    assert_equal(log2(16), 4);
    assert_equal(log2(256), 8);
}
test_log2();


module test_rand_int() {
    nums = rand_int(-100,100,1000,seed=2134);
    assert_equal(len(nums), 1000);
    for (num = nums) {
        assert(num>=-100);
        assert(num<=100);
        assert_equal(num, floor(num));
    }
}
test_rand_int();


module test_gaussian_rands() {
    nums1 = gaussian_rands(1000,0,10,seed=2132);
    nums2 = gaussian_rands(1000,0,10,seed=2130);
    nums3 = gaussian_rands(1000,0,10,seed=2132);
    assert_equal(len(nums1), 1000);
    assert_equal(len(nums2), 1000);
    assert_equal(len(nums3), 1000);
    assert_equal(nums1, nums3);
    assert(nums1!=nums2);

    R = [[4,2],[2,17]];
    data = gaussian_rands(100000,[0,0],R,seed=49);
    assert(approx(mean(data), [0,0], eps=1e-2));
    assert(approx(transpose(data)*data/len(data), R, eps=2e-2));
    
    R2 = [[4,2,-1],[2,17,4],[-1,4,11]];
    data3 = gaussian_rands(100000,[1,2,3],R2,seed=97);
    assert(approx(mean(data3),[1,2,3], eps=1e-2));
    cdata = move(-mean(data3),data3);    
    assert(approx(transpose(cdata)*cdata/len(cdata),R2,eps=.1));
}
test_gaussian_rands();



module test_lerp() {
    assert_equal(lerp(-20,20,0), -20);
    assert_equal(lerp(-20,20,0.25), -10);
    assert_equal(lerp(-20,20,0.5), 0);
    assert_equal(lerp(-20,20,0.75), 10);
    assert_equal(lerp(-20,20,1), 20);
    assert_equal(lerp(-20,20,[0,0.25,0.5,0.75,1]), [-20,-10,0,10,20]);
    assert_equal(lerp(-20,20,[0:0.25:1]), [-20,-10,0,10,20]);
    assert_equal(lerp([10,10],[30,-10],0.5), [20,0]);
}
test_lerp();


module test_u_add() {
    assert_equal(u_add(1,2),3);
    assert_equal(u_add(1,-2),-1);
    assert_equal(u_add(-1,2),1);
    assert_equal(u_add(-1,-2),-3);
    assert_equal(u_add(243,-27),216);
    assert_equal(u_add([2,3,4],[8,7,9]),[10,10,13]);
    assert_equal(u_add(undef,27),undef);
    assert_equal(u_add(undef,-27),undef);
    assert_equal(u_add(243,undef),undef);
    assert_equal(u_add(-43,undef),undef);
    assert_equal(u_add(undef,[8,7,9]),undef);
    assert_equal(u_add([2,3,4],undef),undef);
}
test_u_add();


module test_u_sub() {
    assert_equal(u_sub(1,2),-1);
    assert_equal(u_sub(1,-2),3);
    assert_equal(u_sub(-1,2),-3);
    assert_equal(u_sub(-1,-2),1);
    assert_equal(u_sub(243,-27),270);
    assert_equal(u_sub([2,3,4],[8,7,9]),[-6,-4,-5]);
    assert_equal(u_sub(undef,27),undef);
    assert_equal(u_sub(undef,-27),undef);
    assert_equal(u_sub(243,undef),undef);
    assert_equal(u_sub(-43,undef),undef);
    assert_equal(u_sub(undef,[8,7,9]),undef);
    assert_equal(u_sub([2,3,4],undef),undef);
}
test_u_sub();


module test_u_mul() {
    assert_equal(u_mul(3,2),6);
    assert_equal(u_mul(3,-2),-6);
    assert_equal(u_mul(-3,2),-6);
    assert_equal(u_mul(-3,-2),6);
    assert_equal(u_mul(243,-27),-6561);
    assert_equal(u_mul([2,3,4],[8,7,9]),[16,21,36]);
    assert_equal(u_mul(undef,27),undef);
    assert_equal(u_mul(undef,-27),undef);
    assert_equal(u_mul(243,undef),undef);
    assert_equal(u_mul(-43,undef),undef);
    assert_equal(u_mul(undef,[8,7,9]),undef);
    assert_equal(u_mul([2,3,4],undef),undef);
}
test_u_mul();


module test_u_div() {
    assert_equal(u_div(1,2),1/2);
    assert_equal(u_div(1,-2),-1/2);
    assert_equal(u_div(-1,2),-1/2);
    assert_equal(u_div(-1,-2),1/2);
    assert_equal(u_div(243,-27),-9);
    assert_equal(u_div([8,7,9],[2,3,4]),[4,7/3,9/4]);
    assert_equal(u_div(undef,27),undef);
    assert_equal(u_div(undef,-27),undef);
    assert_equal(u_div(243,undef),undef);
    assert_equal(u_div(-43,undef),undef);
    assert_equal(u_div(undef,[8,7,9]),undef);
    assert_equal(u_div([2,3,4],undef),undef);
}
test_u_div();


module test_hypot() {
    assert_approx(hypot(20,30), norm([20,30]));
}
test_hypot();


module test_sinh() {
    assert_approx(sinh(-2), -3.6268604078);
    assert_approx(sinh(-1), -1.1752011936);
    assert_approx(sinh(0), 0);
    assert_approx(sinh(1), 1.1752011936);
    assert_approx(sinh(2), 3.6268604078);
}
test_sinh();


module test_cosh() {
    assert_approx(cosh(-2), 3.7621956911);
    assert_approx(cosh(-1), 1.5430806348);
    assert_approx(cosh(0), 1);
    assert_approx(cosh(1), 1.5430806348);
    assert_approx(cosh(2), 3.7621956911);
}
test_cosh();


module test_tanh() {
    assert_approx(tanh(-2), -0.9640275801);
    assert_approx(tanh(-1), -0.761594156);
    assert_approx(tanh(0), 0);
    assert_approx(tanh(1), 0.761594156);
    assert_approx(tanh(2), 0.9640275801);
}
test_tanh();


module test_asinh() {
    assert_approx(asinh(sinh(-2)), -2);
    assert_approx(asinh(sinh(-1)), -1);
    assert_approx(asinh(sinh(0)), 0);
    assert_approx(asinh(sinh(1)), 1);
    assert_approx(asinh(sinh(2)), 2);
}
test_asinh();


module test_acosh() {
    assert_approx(acosh(cosh(-2)), 2);
    assert_approx(acosh(cosh(-1)), 1);
    assert_approx(acosh(cosh(0)), 0);
    assert_approx(acosh(cosh(1)), 1);
    assert_approx(acosh(cosh(2)), 2);
}
test_acosh();


module test_atanh() {
    assert_approx(atanh(tanh(-2)), -2);
    assert_approx(atanh(tanh(-1)), -1);
    assert_approx(atanh(tanh(0)), 0);
    assert_approx(atanh(tanh(1)), 1);
    assert_approx(atanh(tanh(2)), 2);
}
test_atanh();


module test_sum() {
    assert_equal(sum([]), 0);
    assert_equal(sum([],dflt=undef), undef);
    assert_equal(sum([1,2,3]), 6);
    assert_equal(sum([-2,-1,0,1,2]), 0);
    assert_equal(sum([[1,2,3], [3,4,5], [5,6,7]]), [9,12,15]);
}
test_sum();


module test_cumsum() {
    assert_equal(cumsum([]), []);
    assert_equal(cumsum([1,1,1]), [1,2,3]);
    assert_equal(cumsum([2,2,2]), [2,4,6]);
    assert_equal(cumsum([1,2,3]), [1,3,6]);
    assert_equal(cumsum([-2,-1,0,1,2]), [-2,-3,-3,-2,0]);
    assert_equal(cumsum([[1,2,3], [3,4,5], [5,6,7]]), [[1,2,3],[4,6,8],[9,12,15]]);
}
test_cumsum();


module test_sum_of_sines() {
    assert_equal(sum_of_sines(0, [[3,4,0],[2,2,0]]), 0);
    assert_equal(sum_of_sines(45, [[3,4,0],[2,2,0]]), 2);
    assert_equal(sum_of_sines(90, [[3,4,0],[2,2,0]]), 0);
    assert_equal(sum_of_sines(135, [[3,4,0],[2,2,0]]), -2);
    assert_equal(sum_of_sines(180, [[3,4,0],[2,2,0]]), 0);
}
test_sum_of_sines();


module test_deltas() {
    assert_equal(deltas([2,5,9,17]), [3,4,8]);
    assert_equal(deltas([2,5,9,17],wrap=true), [3,4,8,-15]);
    assert_equal(deltas([[1,2,3], [3,6,8], [4,8,11]]), [[2,4,5], [1,2,3]]);
    assert_equal(deltas([[1,2,3], [3,6,8], [4,8,11]],wrap=true), [[2,4,5], [1,2,3], [-3,-6,-8]]);
}
test_deltas();


module test_product() {
    assert_equal(product([]),[]);
    assert_equal(product([2,3,4]), 24);
    assert_equal(product([[1,2,3], [3,4,5], [5,6,7]]), [15, 48, 105]);
    m1 = [[2,3,4],[4,5,6],[6,7,8]];
    m2 = [[4,1,2],[3,7,2],[8,7,4]];
    m3 = [[3,7,8],[9,2,4],[5,8,3]];
    assert_equal(product([m1,m2,m3]), m1*m2*m3);
}
test_product();


module test_mean() {
    assert_equal(mean([2,3,4]), 3);
    assert_equal(mean([[1,2,3], [3,4,5], [5,6,7]]), [3,4,5]);
}
test_mean();


module test_median() {
    assert_equal(median([2,3,7]), 3);
    assert_equal(median([2,4,5,8]), 4.5);
}
test_median();



module test_convolve() {
    assert_equal(convolve([],[1,2,1]), []);
    assert_equal(convolve([1,1],[]), []);
    assert_equal(convolve([1,1],[1,2,1]), [1,3,3,1]);
    assert_equal(convolve([1,2,3],[1,2,1]), [1,4,8,8,3]);
    assert_equal(convolve([1,2,3],[[1],[2],[1]]),  [[1], [4], [8], [8], [3]]);
    assert_equal(convolve([[1],[2],[3]],[[1],[2],[1]]), [1,4,8,8,3]);
    assert_equal(convolve([[1,0],[2,1],[3,2]],[[1,0],[2,1],[1,2]]), [1,4,9,12,7]);
    assert_equal(convolve([1,2,3],[[1,0],[2,1],[1,2]]), [[1,0],[4,1],[8,4],[8,7],[3,6]]);
}
test_convolve();




// Logic



module test_any() {
    assert_equal(any([0,false,undef]), false);
    assert_equal(any([1,false,undef]), true);
    assert_equal(any([1,5,true]), true);
    assert_equal(any([[0,0], [0,0]]), true);
    assert_equal(any([[0,0], [1,0]]), true);
    assert_equal(any([[false,false],[[false,[false],[[[true]]]],false],[false,false]]), true);
    assert_equal(any([[false,false],[[false,[false],[[[false]]]],false],[false,false]]), true);
    assert_equal(any([]), false);
    assert_equal(any([1,3,5,7,9], function (a) a%2==0),false);
    assert_equal(any([1,3,6,7,9], function (a) a%2==0),true);
    assert_equal(any([1,3,5,7,9], function (a) a%2!=0),true);
}
test_any();


module test_all() {
    assert_equal(all([0,false,undef]), false);
    assert_equal(all([1,false,undef]), false);
    assert_equal(all([1,5,true]), true);
    assert_equal(all([[0,0], [0,0]]), true);
    assert_equal(all([[0,0], [1,0]]), true);
    assert_equal(all([[1,1], [1,1]]), true);
    assert_equal(all([[true,true],[[true,[true],[[[true]]]],true],[true,true]]), true);
    assert_equal(all([[true,true],[[true,[true],[[[false]]]],true],[true,true]]), true);
    assert_equal(all([]), true);
    assert_equal(all([1,3,5,7,9], function (a) a%2==0),false);
    assert_equal(all([1,3,6,8,9], function (a) a%2==0),false);
    assert_equal(all([1,3,5,7,9], function (a) a%2!=0),true);
}
test_all();


module test_factorial() {
    assert_equal(factorial(0), 1);
    assert_equal(factorial(1), 1);
    assert_equal(factorial(2), 2);
    assert_equal(factorial(3), 6);
    assert_equal(factorial(4), 24);
    assert_equal(factorial(5), 120);
    assert_equal(factorial(6), 720);
    assert_equal(factorial(7), 5040);
    assert_equal(factorial(8), 40320);
    assert_equal(factorial(25,21), 303600);
    assert_equal(factorial(25,25), 1);
}
test_factorial();


module test_binomial() {
    assert_equal(binomial(1), [1,1]);
    assert_equal(binomial(2), [1,2,1]);
    assert_equal(binomial(3), [1,3,3,1]);
    assert_equal(binomial(5), [1,5,10,10,5,1]);
}
test_binomial();


module test_binomial_coefficient() {
    assert_equal(binomial_coefficient(2,1), 2);
    assert_equal(binomial_coefficient(3,2), 3);
    assert_equal(binomial_coefficient(4,2), 6);
    assert_equal(binomial_coefficient(10,7), 120);
    assert_equal(binomial_coefficient(10,7), binomial(10)[7]);
    assert_equal(binomial_coefficient(15,4), binomial(15)[4]);
}
test_binomial_coefficient();


module test_gcd() {
    assert_equal(gcd(15,25), 5);
    assert_equal(gcd(15,27), 3);
    assert_equal(gcd(270,405), 135);
    assert_equal(gcd(39, 101),1);
    assert_equal(gcd(15,-25), 5);
    assert_equal(gcd(-15,25), 5);
    assert_equal(gcd(5,0), 5);
    assert_equal(gcd(0,5), 5);
}
test_gcd();


module test_lcm() {
    assert_equal(lcm(15,25), 75);
    assert_equal(lcm(15,27), 135);
    assert_equal(lcm(270,405), 810);
    assert_equal(lcm([3,5,15,25,35]),525);
}
test_lcm();

module test_rational_approx()
{
   pq1 = rational_approx(PI,10);       // Returns: [22,7]
   pq2 = rational_approx(PI,10000);    // Returns: [355, 113]
   pq3 = rational_approx(221/323,500); // Returns: [13,19]
   pq4 = rational_approx(0,50);        // Returns: [0,1]
   assert_equal(pq1,[22,7]);
   assert_equal(pq2,[355,113]);
   assert_equal(pq3,[13,19]);
   assert_equal(pq4,[0,1]);
   assert_equal(rational_approx(-PI,10),[-22,7]);
   assert_equal(rational_approx(7,10), [7,1]);
}
test_rational_approx();





module test_complex(){
    assert_equal( complex(ident(4)), c_ident(4));
    assert_equal( complex(3), [3,0]);
    assert_equal( complex([1,2]), [[1,0],[2,0]]);
    assert_equal( complex([[1,2],[3,4]]), [[ [1,0],[2,0] ], [ [3,0],[4,0]]]);
}
test_complex();

module test_c_mul() {
    assert_equal(c_mul([4,5],[9,-4]), [56,29]);
    assert_equal(c_mul([-7,2],[24,3]), [-174, 27]);
    assert_equal(c_mul([3,4], [[3,-7], [4,9], [4,8]]), [[37,-9],[-24,43], [-20,40]]);
    assert_equal(c_mul([[3,-7], [4,9], [4,8]], [[1,1],[3,4],[-3,4]]), [-58,31]);
    M = [
           [ [3,4], [9,-1], [4,3] ],
           [ [2,9], [4,9], [3,-1] ]
        ];
    assert_equal(c_mul(M, [ [3,4], [4,4],[5,5]]), [[38,91], [-30, 97]]);
    assert_equal(c_mul([[4,4],[9,1]], M), [[5,111],[67,117], [32,22]]);
    assert_equal(c_mul(M,transpose(M)), [  [[80,30], [30, 117]], [[30,117], [-134, 102]]]);
    assert_equal(c_mul(transpose(M),M), [  [[-84,60],[-42,87],[15,50]], [[-42,87],[15,54],[60,46]], [[15,50],[60,46],[15,18]]]);
}
test_c_mul();


module test_c_div() {
    assert_equal(c_div([56,29],[9,-4]), [4,5]);
    assert_equal(c_div([-174,27],[-7,2]), [24,3]);
}    
test_c_div();

module test_c_conj(){
    assert_equal(c_conj([3,4]), [3,-4]);
    assert_equal(c_conj(           [ [2,9], [4,9], [3,-1] ]),            [ [2,-9], [4,-9], [3,1] ]);
    M = [
           [ [3,4], [9,-1], [4,3] ],
           [ [2,9], [4,9], [3,-1] ]
        ];
    Mc = [
           [ [3,-4], [9,1], [4,-3] ],
           [ [2,-9], [4,-9], [3,1] ]
        ];
    assert_equal(c_conj(M), Mc);
}
test_c_conj();

module test_c_real(){
    M = [
           [ [3,4], [9,-1], [4,3] ],
           [ [2,9], [4,9], [3,-1] ]
        ];
    assert_equal(c_real(M), [[3,9,4],[2,4,3]]);
    assert_equal(c_real(           [ [3,4], [9,-1], [4,3] ]), [3,9,4]);
    assert_equal(c_real([3,4]),3);
}
test_c_real();


module test_c_imag(){
    M = [
           [ [3,4], [9,-1], [4,3] ],
           [ [2,9], [4,9], [3,-1] ]
        ];
    assert_equal(c_imag(M), [[4,-1,3],[9,9,-1]]);
    assert_equal(c_imag(           [ [3,4], [9,-1], [4,3] ]), [4,-1,3]);
    assert_equal(c_imag([3,4]),4);
}
test_c_imag();


module test_c_ident(){
  assert_equal(c_ident(3), [[[1, 0], [0, 0], [0, 0]], [[0, 0], [1, 0], [0, 0]], [[0, 0], [0, 0], [1, 0]]]);
}
test_c_ident();

module test_c_norm(){
  assert_equal(c_norm([3,4]), 5);
  assert_approx(c_norm([[3,4],[5,6]]), 9.273618495495704);
}
test_c_norm();



module test_cumprod(){
  assert_equal(cumprod([1,2,3,4]), [1,2,6,24]);
  assert_equal(cumprod([4]), [4]);
  assert_equal(cumprod([]),[]);
  assert_equal(cumprod([[2,3],[4,5],[6,7]]), [[2,3],[8,15],[48,105]]);
  assert_equal(cumprod([[5,6,7]]),[[5,6,7]]);
  assert_equal(cumprod([up(5),down(5)]), [up(5),IDENT]);
  assert_equal(cumprod([
                        [[1,2],[3,4]],
                        [[-4,5],[6,4]],
                        [[9,-3],[4,3]]
                       ]),
                       [
                        [[1,2],[3,4]],
                        [[11,12],[18,28]],
                        [[45,24],[98,132]]
                       ]);
  assert_equal(cumprod([
                        [[1,2],[3,4]],
                        [[-4,5],[6,4]],
                        [[9,-3],[4,3]]
                       ],right=true),
                       [
                        [[1,2],[3,4]],
                        [[8, 13],[12,31]],
                        [[124, 15],[232,57]]
                       ]);
  assert_equal(cumprod([[[1,2],[3,4]]]), [[[1,2],[3,4]]]);
}
test_cumprod();
                         


module test_deriv(){
  pent = [for(x=[0:70:359]) [cos(x), sin(x)]];
  assert_approx(deriv(pent,closed=true), 
        [[-0.321393804843,0.556670399226],
         [-0.883022221559,0.321393804843],
         [-0.604022773555,-0.719846310393],
         [0.469846310393,-0.813797681349],
         [0.925416578398,0.163175911167],
         [0.413175911167,0.492403876506]]);
  assert_approx(deriv(pent,closed=true,h=2), 
     0.5*[[-0.321393804843,0.556670399226],
         [-0.883022221559,0.321393804843],
         [-0.604022773555,-0.719846310393],
         [0.469846310393,-0.813797681349],
         [0.925416578398,0.163175911167],
         [0.413175911167,0.492403876506]]);
  assert_approx(deriv(pent,closed=false),
        [[-0.432937491789,1.55799143673],
         [-0.883022221559,0.321393804843],
         [-0.604022773555,-0.719846310393],
         [0.469846310393,-0.813797681349],
         [0.925416578398,0.163175911167],
         [0.696902572292,1.45914323952]]);
  spent = yscale(8,p=pent);
  lens = path_segment_lengths(spent,closed=true);
  assert_approx(deriv(spent, closed=true, h=lens),
         [[-0.0381285841663,0.998065839726],
          [-0.254979378104,0.0449763331253],
          [-0.216850793938,-0.953089506601],
          [0.123993253223,-0.982919228715],
          [0.191478335034,0.0131898128456],
          [0.0674850818111,0.996109041561]]);
  assert_approx(deriv(spent, closed=false, h=select(lens,0,-2)),
         [[-0.0871925973657,0.996191473044],
          [-0.254979378104,0.0449763331253],
          [-0.216850793938,-0.953089506601],
          [0.123993253223,-0.982919228715],
          [0.191478335034,0.0131898128456],
          [0.124034734589,0.992277876714]]);
}
test_deriv();


module test_deriv2(){
    oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
    assert_approx(deriv2(oct),
           [[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
            [0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
            [0,0.585786437627],[-0.636634192232,0.534938683021]]);
    assert_approx(deriv2(oct,closed=false),
           [[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
            [0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
            [0,0.585786437627],[-0.636634192232,0.534938683021]]);
    assert_approx(deriv2(oct,closed=true),
           [[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
            [0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
            [0,0.585786437627],[-0.414213562373,0.414213562373]]);
    assert_approx(deriv2(oct,closed=false,h=2),
         0.25*[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
            [0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
            [0,0.585786437627],[-0.636634192232,0.534938683021]]);
    assert_approx(deriv2(oct,closed=true,h=2),
         0.25* [[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
            [0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
            [0,0.585786437627],[-0.414213562373,0.414213562373]]);
}
test_deriv2();


module test_deriv3(){
    oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
    assert_approx(deriv3(oct),
           [[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
            [0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
            [-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
    assert_approx(deriv3(oct,closed=false),
           [[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
            [0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
            [-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
    assert_approx(deriv3(oct,closed=false,h=2),
           [[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
            [0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
            [-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]/8);
    assert_approx(deriv3(oct,closed=true),
           [[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
            [0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]);
    assert_approx(deriv3(oct,closed=true,h=2),
           [[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
            [0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]/8);
}
test_deriv3();
  


module test_polynomial(){
  assert_equal(polynomial([0],12),0);
  assert_equal(polynomial([0],[12,4]),[0,0]);
//  assert_equal(polynomial([],12),0);
//  assert_equal(polynomial([],[12,4]),[0,0]);
  assert_equal(polynomial([1,2,3,4],3),58);
  assert_equal(polynomial([1,2,3,4],[3,-1]),[47,-41]);
  assert_equal(polynomial([0,0,2],4),2);
}
test_polynomial();


module test_poly_roots(){
   // Fifth roots of unity
   assert_approx(
        poly_roots([1,0,0,0,0,-1]),
        [[1,0],[0.309016994375,0.951056516295],[-0.809016994375,0.587785252292],
         [-0.809016994375,-0.587785252292],[0.309016994375,-0.951056516295]]);
   assert_approx(poly_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),
               [[1, 1], [5, 5], [1, 2], [-3, 1], [-3, -1], [1, -1], [1, -2], [5, -5]]);
   assert_approx(poly_roots([.124,.231,.942, -.334]),
                 [[0.3242874219074053,0],[-1.093595323856930,2.666477428660098], [-1.093595323856930,-2.666477428660098]]);
}
test_poly_roots();

module test_real_roots(){
   // Wilkinson polynomial is a nasty test:
   assert_approx(
       sort(real_roots(poly_mult([[1,-1],[1,-2],[1,-3],[1,-4],[1,-5],[1,-6],[1,-7],[1,-8],[1,-9],[1,-10]]))),
       count(10,1));
   assert_equal(real_roots([3]), []);
   assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),[]);
   assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,0,0]])),[0,0]);
   assert_approx(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,4]])),[-4]);
   assert(approx(real_roots([1,-10,25]),[5,5],eps=5e-6));
   assert_approx(real_roots([4,-3]), [0.75]);
   assert_approx(real_roots([0,0,0,4,-3]), [0.75]);
}
test_real_roots();



module test_quadratic_roots(){
    assert_approx(quadratic_roots([1,4,4]),[[-2,0],[-2,0]]);
    assert_approx(quadratic_roots([1,4,4],real=true),[-2,-2]);
    assert_approx(quadratic_roots([1,-5,6],real=true), [2,3]);
    assert_approx(quadratic_roots([1,-5,6]), [[2,0],[3,0]]);
}
test_quadratic_roots();



module test_poly_mult(){
  assert_equal(poly_mult([3,2,1],[4,5,6,7]),[12,23,32,38,20,7]);
  assert_equal(poly_mult([[1,2],[3,4],[5,6]]), [15,68,100,48]);
  assert_equal(poly_mult([3,2,1],[0]),[0]);
  assert_equal(poly_mult([[1,2],[0],[5,6]]), [0]);
  assert_equal(poly_mult([[3,4,5],[0,0,0]]), [0]);
  assert_equal(poly_mult([[0],[0,0,0]]),[0]);
}
test_poly_mult();


module test_poly_div(){
  assert_equal(poly_div(poly_mult([4,3,3,2],[2,1,3]), [2,1,3]),[[4,3,3,2],[0]]);
  assert_equal(poly_div([1,2,3,4],[1,2,3,4,5]), [[], [1,2,3,4]]);
  assert_equal(poly_div(poly_add(poly_mult([1,2,3,4],[2,0,2]), [1,1,2]), [1,2,3,4]), [[2,0,2],[1,1,2]]);
  assert_equal(poly_div([1,2,3,4], [1,-3]), [[1,5,18],[58]]);
  assert_equal(poly_div([0], [1,-3]), [[0],[0]]);
}
test_poly_div();


module test_poly_add(){
  assert_equal(poly_add([2,3,4],[3,4,5,6]),[3,6,8,10]);
  assert_equal(poly_add([1,2,3,4],[-1,-2,3,4]), [6,8]);
  assert_equal(poly_add([1,2,3],-[1,2,3]),[0]);
//  assert_equal(poly_add([1,2,3],-[1,2,3]),[]);
}
test_poly_add();


module test_root_find(){
  flist = [
      function(x) x*x*x-2*x-5,
      function(x) 1-1/x/x,
      function(x) pow(x-3,3),
      function(x) pow(x-2,5),
      function(x) (let(xi=0.61489) -3062*(1-xi)*exp(-x)/(xi+(1-xi)*exp(-x)) -1013 + 1628/x),
      function(x) exp(x)-2-.01/x/x + .000002/x/x/x,
  ];
  fint=[
        [0,4],
        [1e-4, 4],
        [0,6],
        [0,4],
        [1e-4,5],
        [-1,4]
  ];
  answers = [2.094551481542328,
             1,
             3,
             2,
             1.037536033287040,
             0.7032048403631350
  ];
  
  roots = [for(i=idx(flist)) root_find(flist[i], fint[i][0], fint[i][1])];
  assert_approx(roots, answers, 1e-10);
}
test_root_find();


// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap