Method: BigMath.log

Defined in:

bigdecimal.c

.log(x, vprec) ⇒ Object

BigMath.log(decimal, numeric) -> BigDecimal

Computes the natural logarithm of decimal to the specified number of digits of precision, numeric.

If decimal is zero or negative, raises Math::DomainError.

If decimal is positive infinity, returns Infinity.

If decimal is NaN, returns NaN.

# File 'bigdecimal.c', line 3029

static VALUE
BigMath_s_log(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    SIGNED_VALUE expo;
    Real* vx = NULL;
    VALUE 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 almost 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 = BIGDECIMAL_NEGATIVE_P(vx);
	  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:
        i = FIX2INT(rb_big_cmp(x, INT2FIX(0)));
	zero = i == 0;
	negative = i < 0;
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[DECIMAL_SIZE_OF_BITS(SIZEOF_VALUE * CHAR_BIT) + 4];
	snprintf(buf, sizeof(buf), "1E%"PRIdVALUE, -expo);
	x = BigDecimal_mult2(x, ToValue(VpCreateRbObject(1, buf)), vn);
    }
    else {
	expo = 0;
    }
    w = BigDecimal_sub(x, one);
    x = BigDecimal_div2(w, BigDecimal_add(x, one), vn);
    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;
	d = BigDecimal_div2(x, SSIZET2NUM(i), SSIZET2NUM(m));
	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;
}