/* fixed.h */
/* Simple fixed-point transcendental functions. */
/* Copyright 1997 by Ka-Ping Yee.  All rights reserved. */

/* Fixed numbers have an 8-bit integer part and an 8-bit fractional part. */
typedef Short Fixed;

/* Convert between fixed and integer. */
#define fint(x) (((x)+127) >> 8)
#define intf(x) ((Fixed) (x) << 8)

/* Multiply two fixed-point numbers. */
Fixed fmul(Fixed a, Fixed b)
    { Long result = (Long) a * b; return (result+127) >> 8; }

/* Find the cosine of a fixed-point angle given in radians. */
Fixed fcos(Fixed angle)
    {
    Fixed result;
    int neg = 0;

    /* Normalize to the interval [-pi/2, 3*pi/2].  For example, the */
    /* fixed-point number 402 corresponds to 402/256 =~ 1.57 =~ pi/2. */
    while (angle < -402) angle += 1608;
    while (angle > 1206) angle -= 1608;

    /* Shift the angle into the first quadrant. */
    if (angle > 402) { angle -= 804; neg = 1; }
    if (angle < 0) angle = -angle;

    /* Special case removes a hiccup. */
    if (angle == 263) result = 133;

    /* Quick answer for the almost linear region. */
    else if (angle >= 332 && angle <= 472)
        result = 402 - angle;

    /* Remember Taylor series?  They actually do come in handy some days... */
    else
        {
        result = fmul(angle, angle);
        result = 256 - fmul(result, 256/2 - fmul(result, 256/24));

        /* Another fix to remove a hiccup. */
        if (angle >= 255 && angle <= 328) result++;
        }

    return neg ? -result : result;
    }

/* Find the sine of a fixed-point angle given in radians. */
Fixed fsin(Fixed angle)
    { return fcos(angle - 402); }