module BigMath
Provides mathematical functions.
Example:
require "bigdecimal/math" include BigMath a = BigDecimal((PI(100)/2).to_s) puts sin(a,100) # => 0.99999999999999999999......e0
Public Class Methods
Computes the value of e (the base of natural logarithms) raised to the
power of decimal, to the specified number of digits of
precision.
If decimal is infinity, returns Infinity.
If decimal is NaN, returns NaN.
static VALUE
BigMath_s_exp(VALUE klass, VALUE x, VALUE vprec)
{
ssize_t prec, n, i;
Real* vx = NULL;
VALUE one, d, y;
int negative = 0;
int infinite = 0;
int nan = 0;
double flo;
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);
negative = BIGDECIMAL_NEGATIVE_P(vx);
infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
nan = VpIsNaN(vx);
break;
case T_FIXNUM:
/* fall through */
case T_BIGNUM:
vx = GetVpValue(x, 0);
break;
case T_FLOAT:
flo = RFLOAT_VALUE(x);
negative = flo < 0;
infinite = isinf(flo);
nan = isnan(flo);
if (!infinite && !nan) {
vx = GetVpValueWithPrec(x, DBL_DIG+1, 0);
}
break;
case T_RATIONAL:
vx = GetVpValueWithPrec(x, prec, 0);
break;
default:
break;
}
if (infinite) {
if (negative) {
return ToValue(GetVpValueWithPrec(INT2FIX(0), prec, 1));
}
else {
Real* vy;
vy = VpCreateRbObject(prec, "#0");
VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
RB_GC_GUARD(vy->obj);
return ToValue(vy);
}
}
else if (nan) {
Real* vy;
vy = VpCreateRbObject(prec, "#0");
VpSetNaN(vy);
RB_GC_GUARD(vy->obj);
return ToValue(vy);
}
else if (vx == NULL) {
cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
}
x = vx->obj;
n = prec + rmpd_double_figures();
negative = BIGDECIMAL_NEGATIVE_P(vx);
if (negative) {
VpSetSign(vx, 1);
}
one = ToValue(VpCreateRbObject(1, "1"));
y = one;
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);
rb_thread_check_ints();
if (m <= 0) {
break;
}
else if ((size_t)m < rmpd_double_figures()) {
m = rmpd_double_figures();
}
d = BigDecimal_mult(d, x); /* d <- d * x */
d = BigDecimal_div2(d, SSIZET2NUM(i), SSIZET2NUM(m)); /* d <- d / i */
y = BigDecimal_add(y, d); /* y <- y + d */
++i; /* i <- i + 1 */
}
if (negative) {
return BigDecimal_div2(one, y, vprec);
}
else {
vprec = SSIZET2NUM(prec - VpExponent10(DATA_PTR(y)));
return BigDecimal_round(1, &vprec, y);
}
RB_GC_GUARD(one);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
RB_GC_GUARD(d);
}
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.
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;
}
Public Instance Methods
Computes e (the base of natural logarithms) to the specified number of
digits of precision, numeric.
BigMath.E(10).to_s #=> "0.271828182845904523536028752390026306410273e1"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 227 def E(prec) raise ArgumentError, "Zero or negative precision for E" if prec <= 0 BigMath.exp(1, prec) end
Computes the value of pi to the specified number of digits of precision,
numeric.
BigMath.PI(10).to_s #=> "0.3141592653589793238462643388813853786957412e1"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 182 def PI(prec) raise ArgumentError, "Zero or negative precision for PI" if prec <= 0 n = prec + BigDecimal.double_fig zero = BigDecimal("0") one = BigDecimal("1") two = BigDecimal("2") m25 = BigDecimal("-0.04") m57121 = BigDecimal("-57121") pi = zero d = one k = one t = BigDecimal("-80") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = t*m25 d = t.div(k,m) k = k+two pi = pi + d end d = one k = one t = BigDecimal("956") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = t.div(m57121,n) d = t.div(k,m) pi = pi + d k = k+two end pi end
Computes the arctangent of decimal to the specified number of
digits of precision, numeric.
If decimal is NaN, returns NaN.
BigMath.atan(BigDecimal('-1'), 16).to_s #=> "-0.785398163397448309615660845819878471907514682065e0"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 145 def atan(x, prec) raise ArgumentError, "Zero or negative precision for atan" if prec <= 0 return BigDecimal("NaN") if x.nan? pi = PI(prec) x = -x if neg = x < 0 return pi.div(neg ? -2 : 2, prec) if x.infinite? return pi / (neg ? -4 : 4) if x.round(prec) == 1 x = BigDecimal("1").div(x, prec) if inv = x > 1 x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5 n = prec + BigDecimal.double_fig y = x d = y t = x r = BigDecimal("3") x2 = x.mult(x,n) while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = -t.mult(x2,n) d = t.div(r,m) y += d r += 2 end y *= 2 if dbl y = pi / 2 - y if inv y = -y if neg y end
Computes the cosine of decimal to the specified number of
digits of precision, numeric.
If decimal is Infinity or NaN, returns NaN.
BigMath.cos(BigMath.PI(4), 16).to_s #=> "-0.999999999999999999999999999999856613163740061349e0"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 101 def cos(x, prec) raise ArgumentError, "Zero or negative precision for cos" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x = -x if x < 0 if x > (twopi = two * BigMath.PI(prec)) if x > 30 x %= twopi else x -= twopi while x > twopi end end x1 = one x2 = x.mult(x,n) sign = 1 y = one d = y i = BigDecimal("0") z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z *= (i-one) * i d = sign * x1.div(z,m) y += d end y end
Computes the sine of decimal to the specified number of digits
of precision, numeric.
If decimal is Infinity or NaN, returns NaN.
BigMath.sin(BigMath.PI(5)/4, 5).to_s #=> "0.70710678118654752440082036563292800375e0"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 57 def sin(x, prec) raise ArgumentError, "Zero or negative precision for sin" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x = -x if neg = x < 0 if x > (twopi = two * BigMath.PI(prec)) if x > 30 x %= twopi else x -= twopi while x > twopi end end x1 = x x2 = x.mult(x,n) sign = 1 y = x d = y i = one z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z *= (i-one) * i d = sign * x1.div(z,m) y += d end neg ? -y : y end
Computes the square root of decimal to the specified number of
digits of precision, numeric.
BigMath.sqrt(BigDecimal('2'), 16).to_s #=> "0.1414213562373095048801688724e1"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 42 def sqrt(x, prec) x.sqrt(prec) end