def mpf_ci_si(x, prec, rnd=round_fast, which=2):
    wp = prec + 20
    sign, man, exp, bc = x
    ci, si = None, None
    if not man:
        if x == fzero:
            return (fninf, fzero)
        if x == fnan:
            return (x, x)
        ci = fzero
        if which != 0:
            if x == finf:
                si = mpf_shift(mpf_pi(prec, rnd), -1)
            if x == fninf:
                si = mpf_neg(mpf_shift(mpf_pi(prec, negative_rnd[rnd]), -1))
        return (ci, si)
    # For small x: Ci(x) ~ euler + log(x), Si(x) ~ x
    mag = exp+bc
    if mag < -wp:
        if which != 0:
            si = mpf_perturb(x, 1-sign, prec, rnd)
        if which != 1:
            y = mpf_euler(wp)
            xabs = mpf_abs(x)
            ci = mpf_add(y, mpf_log(xabs, wp), prec, rnd)
        return ci, si
    # For huge x: Ci(x) ~ sin(x)/x, Si(x) ~ pi/2
    elif mag > wp:
        if which != 0:
            if sign:
                si = mpf_neg(mpf_pi(prec, negative_rnd[rnd]))
            else:
                si = mpf_pi(prec, rnd)
            si = mpf_shift(si, -1)
        if which != 1:
            ci = mpf_div(mpf_sin(x, wp), x, prec, rnd)
        return ci, si
    else:
        wp += abs(mag)
    # Use an asymptotic series? The smallest value of n!/x^n
    # occurs for n ~ x, where the magnitude is ~ exp(-x).
    asymptotic = mag-1 > math.log(wp, 2)
    # Case 1: convergent series near 0
    if not asymptotic:
        if which != 0:
            si = mpf_pos(mpf_ci_si_taylor(x, wp, 1), prec, rnd)
        if which != 1:
            ci = mpf_ci_si_taylor(x, wp, 0)
            ci = mpf_add(ci, mpf_euler(wp), wp)
            ci = mpf_add(ci, mpf_log(mpf_abs(x), wp), prec, rnd)
        return ci, si
    x = mpf_abs(x)
    # Case 2: asymptotic series for x >> 1
    xf = to_fixed(x, wp)
    xr = (MPZ_ONE<<(2*wp)) // xf   # 1/x
    s1 = (MPZ_ONE << wp)
    s2 = xr
    t = xr
    k = 2
    while t:
        t = -t
        t = (t*xr*k)>>wp
        k += 1
        s1 += t
        t = (t*xr*k)>>wp
        k += 1
        s2 += t
    s1 = from_man_exp(s1, -wp)
    s2 = from_man_exp(s2, -wp)
    s1 = mpf_div(s1, x, wp)
    s2 = mpf_div(s2, x, wp)
    cos, sin = mpf_cos_sin(x, wp)
    # Ci(x) = sin(x)*s1-cos(x)*s2
    # Si(x) = pi/2-cos(x)*s1-sin(x)*s2
    if which != 0:
        si = mpf_add(mpf_mul(cos, s1), mpf_mul(sin, s2), wp)
        si = mpf_sub(mpf_shift(mpf_pi(wp), -1), si, wp)
        if sign:
            si = mpf_neg(si)
        si = mpf_pos(si, prec, rnd)
    if which != 1:
        ci = mpf_sub(mpf_mul(sin, s1), mpf_mul(cos, s2), prec, rnd)
    return ci, si
Calculation of Ci(x), Si(x) for real x.
dataset/ETHPy150Open fredrik-johansson/mpmath/mpmath/libmp/libhyper.py/mpf_ci_si