Provides mathematical functions.
Example:
require "bigdecimal/math" include BigMath a = BigDecimal((PI(100)/2).to_s) puts sin(a,100) # => 0.99999999999999999999......e0
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, DBLE_FIG, 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) {
VALUE x_zero = INT2NUM(1);
VALUE x_copy = f_BigDecimal(1, &x_zero, klass);
x = BigDecimal_initialize_copy(x_copy, x);
vx = DATA_PTR(x);
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 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_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, DBLE_FIG, 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;
} 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 ext/bigdecimal/lib/bigdecimal/math.rb, line 228 def E(prec) raise ArgumentError, "Zero or negative precision for E" if prec <= 0 BigMath.exp(1, prec) end
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 183
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 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 146
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 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 102
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 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 58
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 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 43 def sqrt(x, prec) x.sqrt(prec) 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"
Ruby Core © 1993–2020 Yukihiro Matsumoto
Licensed under the Ruby License.
Ruby Standard Library © contributors
Licensed under their own licenses.