fast uint waveforms

#include<cstdint>
//compiled with gcc flag -O3
//approx -UIMAX/2*sin((2*x*pi)/UIMAX)+UIMAX/2       https://www.desmos.com/calculator/lyyy678gdw
//sine both input [0.0,2pi] and output [-1.0,1.0] are mapped to [0,4294967295]
//Convert VALUE[0,4294967295] to range[-1.0,1.0] using (-1.0)*((float)VALUE/(UIMAX/2)-1)
//2.8% error, 3-6x faster than sin() with num=rand()%(1+i++), up to ~20x faster with num=i++
//Fast sine approximation.
uint32_t u32kaelSin(uint32_t num) {
    bool secondHalf = (num>>31); //second half of uint
    num<<=1; //2x input for 2 parabola period
    uint64_t buf = (static_cast<uint64_t>(num)<<1)-UINT32_MAX; //<cast>64b-32b and flip vertically
    num = (buf * buf) >> 33; //compute parabola
    num = secondHalf ? ~num : num; //flip horizontally if past mid point
    return num;
}
uint16_t u16kaelSin(uint16_t num) {
    bool secondHalf = (num>>15);
    num<<=1;
    uint32_t buf = (static_cast<uint32_t>(num)<<1)-UINT16_MAX;
    num = (buf * buf) >> 17;
    num = secondHalf ? ~num : num;
    return num;
}
uint8_t u8kaelSin(uint8_t num) {
    bool secondHalf = (num>>7);
    num<<=1;
    uint16_t buf = (static_cast<uint16_t>(num)<<1)-UINT8_MAX;
    num = (buf * buf) >> 9;
    num = secondHalf ? ~num : num;
    return num;
}

//Triangle wave
template <typename T>
T ukaelTriangle(T num) {
    bool flip = num>>(sizeof(num)<<3-2)==0 | num>>(sizeof(num)<<3-2)==3;    //first and last quarters
    num<<=1;
    num+=~T(0)>>1;
    return flip ? ~num : num;
}

//Saw wave
template <typename T>
T ukaelSaw(T num){
    return num<<=1;
}

//Square wave
template <typename T>
T ukaelSquare(T num){
    return ( num>>(sizeof(num)<<3-1) ) ? 0 : ~T(0);
}

//Pulse square wave
template <typename T>
T ukaelPulse(T num, T dutyCycle) {
    return (num > dutyCycle) ? 0 : ~T(0);
}

//noise function
template <typename T>
T ukaelNoise(T num) {
    uint sz=sizeof(num)<<1;
    num^=num>>(num&sz)+4;
    num*=4763;
    num^=num<<(num&sz)+4;
    return num;
}

//helps making 8bit noise less repetitive when input is linear. Small as 32 wroks
const uint8_t u8randomTable[]{
33, 138,142,237,100,84, 241,4,  139,149,159,233,64, 201,75, 235,
116,248,10, 116,247,112,214,245,221,58, 158,124,196,227,255,39,
51, 238,5,  253,76, 6,  65, 104,106,81, 230,171,55, 245,21, 244,
99, 162,98, 34, 78, 28, 195,184,229,205,14, 154,57, 224,249,45,
226,233,77, 124,10, 50, 81, 103,26, 30, 18, 18, 185,98, 214,48,
244,118,214,17, 67, 215,209,34, 134,100,177,206,190,70, 133,219,
194,66, 123,57, 26, 129,5,  64, 36, 59, 237,122,207,87, 22, 164,
133,200,191,47, 15, 54, 194,223,129,166,52, 8,  49, 193,235,254,
62, 122,55, 93, 190,241,171,91, 25, 101,233,151,224,113,69, 71,
235,253,55, 247,143,240,205,52, 229,223,229,229,211,244,252,2,
159,141,91, 4,  46, 233,78, 127,236,237,167,248,37, 253,140,89,
155,138,185,162,65, 115,117,196,57, 195,107,39, 205,189,216,73,
57, 243,10, 107,193,226,182,204,200,165,234,253,208,185,137,151,
238,49, 18, 189,98, 185,169,67, 94, 77, 73, 165,127,121,65, 202,
148,165,101,186,131,207,252,86, 204,225,108,82, 129,133,184,179,
236,17, 223,163,11, 1,  60, 251,118,243,105,190,74, 52, 200,235
};

//8-bit noise function. actually slower than ukaelNoise()
uint8_t u8kaelNoise(uint16_t num) {
    num^=num<<7;
    num*=17;
    num^=num>>7;
    num^=u8randomTable[(num>>8)]; //num>>8 for 256 table
    return num;
}

/* too slow for random generation, seeding maybe
uint64_t rdtsc(){
    unsigned int lo,hi;
    __asm__ __volatile__ ("rdtsc" : "=a" (lo), "=d" (hi));
    return ((uint64_t)hi << 32) | lo;
}
*/

/*
Time warmup()           0.67921 seconds
For loop overhead       0.10994 seconds
Time ukaelNoi()         2.45002 seconds
Time u32kaelSin()       1.62207 seconds
Time ukaelTri()         0.61627 seconds
Time ukaelSqu()         1.02044 seconds
Time ukaelSaw()         0.41214 seconds
Time ukaelPul()         0.61336 seconds
Time math.h sin()       13.2384 seconds
*/