Module: CCMath

Defined in:
lib/ccmath.rb,
ext/ccmath/ccmath.c

Defined Under Namespace

Classes: DomainError

Constant Summary collapse

PI = 
DBL2NUM(atan(1.0)*4.0)
E = 
DBL2NUM(exp(1.0))

Class Method Summary collapse

Class Method Details

.acos(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 393

static VALUE
ccmath_acos(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d = NUM2DBL_F(z);
        if (d < -1.0 || 1.0 < d) domain_error("acos");
        return DBL2NUM(acos(d));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(acos(z_real), 0.0);

        return rb_funcall(DBL2NUM(M_PI / 2.0), '-', 1, ccmath_asin(obj, z));
    }
}

.acosh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 368

static VALUE
ccmath_acosh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d = NUM2DBL_F(z);
        if (d < 1.0) domain_error("acosh");
        return DBL2NUM(acosh(d));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(acosh(z_real), 0.0);

        VALUE s1 = DBLS2COMP(z_real - 1.0, z_imag);
        VALUE s2 = DBLS2COMP(z_real + 1.0, z_imag);

        s1 = ccmath_sqrt(obj, s1);
        s2 = ccmath_sqrt(obj, s2);
        EXTRACT_DBLS(s1);
        EXTRACT_DBLS(s2);

        return DBLS2COMP(asinh(s1_real * s2_real + s1_imag * s2_imag), 2.0 * atan2(s1_imag, s2_real));
    }
}

.asin(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 349

static VALUE
ccmath_asin(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d = NUM2DBL_F(z);
        if (d < -1.0 || 1.0 < d) domain_error("asin");
        return DBL2NUM(asin(d));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(asin(z_real), 0.0);

        VALUE s = ccmath_asinh(obj, DBLS2COMP(-z_imag, z_real));
        EXTRACT_DBLS(s);
        return DBLS2COMP(s_imag, -s_real);
    }
}

.asinh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 326

static VALUE
ccmath_asinh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(asinh(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(asinh(z_real), 0.0);

        VALUE s1 = DBLS2COMP(1.0 + z_imag, -z_real);
        VALUE s2 = DBLS2COMP(1.0 - z_imag, z_real);

        s1 = ccmath_sqrt(obj, s1);
        s2 = ccmath_sqrt(obj, s2);
        EXTRACT_DBLS(s1);
        EXTRACT_DBLS(s2);

        return DBLS2COMP(asinh(s1_real * s2_imag - s2_real * s1_imag), atan2(z_imag, s1_real * s2_real - s1_imag * s2_imag));
    }
}

.atan(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 433

static VALUE
ccmath_atan(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(atan(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(atan(z_real), 0.0);

        VALUE s = ccmath_atanh(obj, DBLS2COMP(-z_imag, z_real));
        EXTRACT_DBLS(s);
        return DBLS2COMP(s_imag, -s_real);
    }
}

.atanh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 410

static VALUE
ccmath_atanh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d = NUM2DBL_F(z);

        if (d <  -1.0 || +1.0 <  d) domain_error("atanh");
        if (d == -1.0) return DBL2NUM(-INFINITY);
        if (d == +1.0) return DBL2NUM(+INFINITY);
        return DBL2NUM(atanh(d));
    }
    else {
        EXTRACT_DBLS(z);;

        if (z_imag == 0.0) return DBLS2COMP(atanh(z_real), 0.0);

        double sq_imag = z_imag * z_imag;

        return DBLS2COMP(m_log1p(4.0 * z_real / ((1.0 - z_real) * (1.0 - z_real) + sq_imag)) / 4.0,
                        -m_atan2(-2.0 * z_imag, (1.0 - z_real) * (1.0 + z_real) - sq_imag) / 2.0);
    }
}

.cos(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 247

static VALUE
ccmath_cos(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(cos(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;
        if (z_real == 0.0) return DBLS2COMP(cosh(z_imag), 0.0);
        if (z_imag == 0.0) return DBLS2COMP(cos(z_real), 0.0);
        return DBLS2COMP(cos(z_real) * cosh(z_imag), -sin(z_real) * sinh(z_imag));
    }
}

.cosh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 287

static VALUE
ccmath_cosh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(cosh(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;
        if (z_real == 0.0) return DBLS2COMP(cos(z_imag), 0.0);
        if (z_imag == 0.0) return DBLS2COMP(cosh(z_real), 0.0);
        return DBLS2COMP(cosh(z_real) * cos(z_imag), sinh(z_real) * sin(z_imag));
    }
}

.exp(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 128

static VALUE
ccmath_exp(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(exp(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);
        if (z_imag == 0.0) return DBLS2COMP(exp(z_real), 0.0);

        double ere = exp(z_real);
        return DBLS2COMP(ere * cos(z_imag), ere * sin(z_imag));
    }
}

.log(*args) ⇒ Object

log(d * 2 ** numbits)



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# File 'ext/ccmath/ccmath.c', line 170

static VALUE
ccmath_log(int argc, const VALUE* argv, VALUE obj)
{
    VALUE z, base;
    rb_scan_args(argc, argv, "11", &z, &base);

    if (codomain_check(z)) {
        double d = internal_log(z);
        if (argc == 2) {
            d /= internal_log(base);
        }
        return DBL2NUM(d);
    }
    else {
        EXTRACT_DBLS(z);;
        float r = hypot(z_real, z_imag);
        if (argc == 2) {
            if (!rb_respond_to(base, id_real_p)) rb_raise(rb_eTypeError, "Numeric Number required");
            EXTRACT_DBLS(base);
            if (base_imag != 0.0) domain_error("log");
            if (base_real > 0.0) {
                double ln_base = log(base_real);
                return DBLS2COMP(log(r) / ln_base, m_atan2(z_imag, z_real) / ln_base);
            }
            else {
                VALUE ln_base = DBLS2COMP(log(fabs(base_real)), M_PI);
                return rb_funcall(DBLS2COMP(log(r), m_atan2(z_imag, z_real)), '/', 1, ln_base);
            }
        }
        else {
            return DBLS2COMP(log(r), m_atan2(z_imag, z_real));
        }
    }
}

.log10(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 226

static VALUE
ccmath_log10(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d;
        size_t numbits;

        assing_numbits(z, &d, &numbits);

        if (d < 0.0) domain_error("log10");
        if (d == 0.0) return DBL2NUM(-INFINITY);

        return DBL2NUM(log10(d) + numbits * log10(2));
    }
    else {
        EXTRACT_DBLS(z);;
        float r = hypot(z_real, z_imag);
        return DBLS2COMP(log(r) / M_LN10, m_atan2(z_imag, z_real) / M_LN10);
    }
}

.log2(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 205

static VALUE
ccmath_log2(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d;
        size_t numbits;

        assing_numbits(z, &d, &numbits);

        if (d < 0.0) domain_error("log2");
        if (d == 0.0) return DBL2NUM(-INFINITY);

        return DBL2NUM(log2(d) + numbits);
    }
    else {
        EXTRACT_DBLS(z);;
        float r = hypot(z_real, z_imag);
        return DBLS2COMP(log(r) / M_LN2, m_atan2(z_imag, z_real) / M_LN2);
    }
}

.set=(str) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 450

static VALUE
ccmath_define_set(VALUE obj, VALUE str)
{
    rb_ivar_set(obj, id_codomain, str);
    return obj;
}

.sin(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 261

static VALUE
ccmath_sin(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(sin(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;
        if (z_real == 0.0) return DBLS2COMP(0.0, sinh(z_imag));
        if (z_imag == 0.0) return DBLS2COMP(sin(z_real), 0.0);
        return DBLS2COMP(sin(z_real) * cosh(z_imag), cos(z_real) * sinh(z_imag));
    }

}

.sinh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 301

static VALUE
ccmath_sinh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(sinh(NUM2DBL_F(z)));
    }
    else {
        EXTRACT_DBLS(z);;
        if (z_real == 0.0) return DBLS2COMP(0.0, sin(z_imag));
        if (z_imag == 0.0) return DBLS2COMP(sinh(z_real), 0.0);
        return DBLS2COMP(sinh(z_real) * cos(z_imag), cosh(z_real) * sin(z_imag));
    }
}

.sqrt(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 102

static VALUE
ccmath_sqrt(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        double d = NUM2DBL_F(z);
        if (d < 0.0) domain_error("sqrt");
        if (d == 0.0) return DBL2NUM(0.0);
        return DBL2NUM(sqrt(d));
    }
    else {
        EXTRACT_DBLS(z);
        if (z_imag == 0.0) {
            if (z_real < 0.0) {
                return DBLS2COMP(0.0, sqrt(fabs(z_real)));
            }
            else {
                return DBLS2COMP(sqrt(z_real), 0.0);
            }
        }
        else {
            double s = sqrt((hypot(z_real, z_imag) + z_real) / 2.0);
            return DBLS2COMP(s, z_imag / (2 * s));
        }
    }
}

.tan(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 276

static VALUE
ccmath_tan(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(tan(NUM2DBL_F(z)));
    }
    else {
        return rb_funcall(ccmath_sin(obj, z), '/', 1, ccmath_cos(obj, z));
    }
}

.tanh(z) ⇒ Object 



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# File 'ext/ccmath/ccmath.c', line 315

static VALUE
ccmath_tanh(VALUE obj, VALUE z)
{
    if (codomain_check(z)) {
        return DBL2NUM(tanh(NUM2DBL_F(z)));
    }
    else {
        return rb_funcall(ccmath_sinh(obj, z), '/', 1, ccmath_cosh(obj, z));
    }
}