Nuklear 图形库中的数学与几何函数实现解析

#ifndef NK_INV_SQRT
#define NK_INV_SQRT nk_inv_sqrt
NK_LIB float
nk_inv_sqrt(float n)
{
    float x2;
    const float threehalfs = 1.5f;
    union {nk_uint i; float f;} conv = {0};
    conv.f = n;
    x2 = n * 0.5f;
    conv.i = 0x5f375A84 - (conv.i >> 1);
    conv.f = conv.f * (threehalfs - (x2 * conv.f * conv.f));
    return conv.f;
}
#endif

#ifndef NK_SIN
#define NK_SIN nk_sin
NK_LIB float
nk_sin(float x)
{
    NK_STORAGE const float a0 = +1.91059300966915117e-31f;
    NK_STORAGE const float a1 = +1.00086760103908896f;
    NK_STORAGE const float a2 = -1.21276126894734565e-2f;
    NK_STORAGE const float a3 = -1.38078780785773762e-1f;
    NK_STORAGE const float a4 = -2.67353392911981221e-2f;
    NK_STORAGE const float a5 = +2.08026600266304389e-2f;
    NK_STORAGE const float a6 = -3.03996055049204407e-3f;
    NK_STORAGE const float a7 = +1.38235642404333740e-4f;
    return a0 + x*(a1 + x*(a2 + x*(a3 + x*(a4 + x*(a5 + x*(a6 + x*a7))))));
}
#endif

#ifndef NK_COS
#define NK_COS nk_cos
NK_LIB float
nk_cos(float x)
{
    /* New implementation. Also generated using lolremez. */
    /* Old version significantly deviated from expected results. */
    NK_STORAGE const float a0 = 9.9995999154986614e-1f;
    NK_STORAGE const float a1 = 1.2548995793001028e-3f;
    NK_STORAGE const float a2 = -5.0648546280678015e-1f;
    NK_STORAGE const float a3 = 1.2942246466519995e-2f;
    NK_STORAGE const float a4 = 2.8668384702547972e-2f;
    NK_STORAGE const float a5 = 7.3726485210586547e-3f;
    NK_STORAGE const float a6 = -3.8510875386947414e-3f;
    NK_STORAGE const float a7 = 4.7196604604366623e-4f;
    NK_STORAGE const float a8 = -1.8776444013090451e-5f;
    return a0 + x*(a1 + x*(a2 + x*(a3 + x*(a4 + x*(a5 + x*(a6 + x*(a7 + x*a8)))))));
}
#endif

NK_LIB nk_uint
nk_round_up_pow2(nk_uint v)
{
    v--;
    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;
    v |= v >> 8;
    v |= v >> 16;
    v++;
    return v;
}

NK_LIB double
nk_pow(double x, int n)
{
    /*  check the sign of n */
    double r = 1;
    int plus = n >= 0;
    n = (plus) ? n : -n;
    while (n > 0) {
        if ((n & 1) == 1)
            r *= x;
        n /= 2;
        x *= x;
    }
    return plus ? r : 1.0 / r;
}

NK_LIB int
nk_ifloord(double x)
{
    x = (double)((int)x - ((x < 0.0) ? 1 : 0));
    return (int)x;
}

NK_LIB int
nk_ifloorf(float x)
{
    x = (float)((int)x - ((x < 0.0f) ? 1 : 0));
    return (int)x;
}

NK_LIB int
nk_iceilf(float x)
{
    if (x >= 0) {
        int i = (int)x;
        return (x > i) ? i+1: i;
    } else {
        int t = (int)x;
        float r = x - (float)t;
        return (r > 0.0f) ? t+1: t;
    }
}

NK_LIB int
nk_log10(double n)
{
    int neg;
    int ret;
    int exp = 0;

    neg = (n < 0) ? 1 : 0;
    ret = (neg) ? (int)-n : (int)n;
    while ((ret / 10) > 0) {
        ret /= 10;
        exp++;
    }
    if (neg) exp = -exp;
    return exp;
}

NK_API struct nk_vec2
nk_vec2(float x, float y)
{
    struct nk_vec2 ret;
    ret.x = x; ret.y = y;
    return ret;
}

NK_API struct nk_vec2
nk_vec2i(int x, int y)
{
    struct nk_vec2 ret;
    ret.x = (float)x;
    ret.y = (float)y;
    return ret;
}

NK_API struct nk_vec2
nk_vec2v(const float *v)
{
    return nk_vec2(v[0], v[1]);
}

NK_API struct nk_vec2
nk_vec2iv(const int *v)
{
    return nk_vec2i(v[0], v[1]);
}

NK_LIB void
nk_unify(struct nk_rect *clip, const struct nk_rect *a, float x0, float y0,
    float x1, float y1)
{
    NK_ASSERT(a);
    NK_ASSERT(clip);
    clip->x = NK_MAX(a->x, x0);
    clip->y = NK_MAX(a->y, y0);
    clip->w = NK_MIN(a->x + a->w, x1) - clip->x;
    clip->h = NK_MIN(a->y + a->h, y1) - clip->y;
    clip->w = NK_MAX(0, clip->w);
    clip->h = NK_MAX(0, clip->h);
}

NK_API void
nk_triangle_from_direction(struct nk_vec2 *result, struct nk_rect r,
    float pad_x, float pad_y, enum nk_heading direction)
{
    float w_half, h_half;
    NK_ASSERT(result);

    r.w = NK_MAX(2 * pad_x, r.w);
    r.h = NK_MAX(2 * pad_y, r.h);
    r.w = r.w - 2 * pad_x;
    r.h = r.h - 2 * pad_y;

    r.x = r.x + pad_x;
    r.y = r.y + pad_y;

    w_half = r.w / 2.0f;
    h_half = r.h / 2.0f;

    if (direction == NK_UP) {
        result[0] = nk_vec2(r.x + w_half, r.y);
        result[1] = nk_vec2(r.x + r.w, r.y + r.h);
        result[2] = nk_vec2(r.x, r.y + r.h);
    } else if (direction == NK_RIGHT) {
        result[0] = nk_vec2(r.x, r.y);
        result[1] = nk_vec2(r.x + r.w, r.y + h_half);
        result[2] = nk_vec2(r.x, r.y + r.h);
    } else if (direction == NK_DOWN) {
        result[0] = nk_vec2(r.x, r.y);
        result[1] = nk_vec2(r.x + r.w, r.y);
        result[2] = nk_vec2(r.x + w_half, r.y + r.h);
    } else {
        result[0] = nk_vec2(r.x, r.y + h_half);
        result[1] = nk_vec2(r.x + r.w, r.y);
        result[2] = nk_vec2(r.x + r.w, r.y + r.h);
    }
}