log

static VALUE
BigMath_s_log(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    SIGNED_VALUE expo;
    Real* vx = NULL;
    VALUE argv[2], vn, one, two, w, x2, y, d;
    int zero = 0;
    int negative = 0;
    int infinite = 0;
    int nan = 0;
    double flo;
    long fix;

    if (!is_integer(vprec)) {
        rb_raise(rb_eArgError, "precision must be an Integer");
    }

    prec = NUM2SSIZET(vprec);
    if (prec <= 0) {
        rb_raise(rb_eArgError, "Zero or negative precision for exp");
    }

    /* TODO: the following switch statement is almostly the same as one in the
     *       BigDecimalCmp function. */
    switch (TYPE(x)) {
      case T_DATA:
          if (!is_kind_of_BigDecimal(x)) break;
          vx = DATA_PTR(x);
          zero = VpIsZero(vx);
          negative = VpGetSign(vx) < 0;
          infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
          nan = VpIsNaN(vx);
          break;

      case T_FIXNUM:
        fix = FIX2LONG(x);
        zero = fix == 0;
        negative = fix < 0;
        goto get_vp_value;

      case T_BIGNUM:
        zero = RBIGNUM_ZERO_P(x);
        negative = RBIGNUM_NEGATIVE_P(x);
get_vp_value:
        if (zero || negative) break;
        vx = GetVpValue(x, 0);
        break;

      case T_FLOAT:
        flo = RFLOAT_VALUE(x);
        zero = flo == 0;
        negative = flo < 0;
        infinite = isinf(flo);
        nan = isnan(flo);
        if (!zero && !negative && !infinite && !nan) {
            vx = GetVpValueWithPrec(x, DBL_DIG+1, 1);
        }
        break;

      case T_RATIONAL:
        zero = RRATIONAL_ZERO_P(x);
        negative = RRATIONAL_NEGATIVE_P(x);
        if (zero || negative) break;
        vx = GetVpValueWithPrec(x, prec, 1);
        break;

      case T_COMPLEX:
        rb_raise(rb_eMathDomainError,
                 "Complex argument for BigMath.log");

      default:
        break;
    }
    if (infinite && !negative) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
        return ToValue(vy);
    }
    else if (nan) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetNaN(vy);
        return ToValue(vy);
    }
    else if (zero || negative) {
        rb_raise(rb_eMathDomainError,
                 "Zero or negative argument for log");
    }
    else if (vx == NULL) {
        cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
    }
    x = ToValue(vx);

    RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
    RB_GC_GUARD(two) = ToValue(VpCreateRbObject(1, "2"));

    n = prec + rmpd_double_figures();
    RB_GC_GUARD(vn) = SSIZET2NUM(n);
    expo = VpExponent10(vx);
    if (expo < 0 || expo >= 3) {
        char buf[16];
        snprintf(buf, 16, "1E%ld", -expo);
        x = BigDecimal_mult2(x, ToValue(VpCreateRbObject(1, buf)), vn);
    }
    else {
        expo = 0;
    }
    w = BigDecimal_sub(x, one);
    argv[0] = BigDecimal_add(x, one);
    argv[1] = vn;
    x = BigDecimal_div2(2, argv, w);
    RB_GC_GUARD(x2) = BigDecimal_mult2(x, x, vn);
    RB_GC_GUARD(y)  = x;
    RB_GC_GUARD(d)  = y;
    i = 1;
    while (!VpIsZero((Real*)DATA_PTR(d))) {
        SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
        SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
        ssize_t m = n - vabs(ey - ed);
        if (m <= 0) {
            break;
        }
        else if ((size_t)m < rmpd_double_figures()) {
            m = rmpd_double_figures();
        }

        x = BigDecimal_mult2(x2, x, vn);
        i += 2;
        argv[0] = SSIZET2NUM(i);
        argv[1] = SSIZET2NUM(m);
        d = BigDecimal_div2(2, argv, x);
        y = BigDecimal_add(y, d);
    }

    y = BigDecimal_mult(y, two);
    if (expo != 0) {
        VALUE log10, vexpo, dy;
        log10 = BigMath_s_log(klass, INT2FIX(10), vprec);
        vexpo = ToValue(GetVpValue(SSIZET2NUM(expo), 1));
        dy = BigDecimal_mult(log10, vexpo);
        y = BigDecimal_add(y, dy);
    }

    return y;
}