In Files
- bigdecimal/bigdecimal.c
- bigdecimal/lib/bigdecimal/math.rb
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BigMath
mathematical functions
Provides mathematical functions.
Example:
require "bigdecimal" require "bigdecimal/math" include BigMath a = BigDecimal((PI(100)/2).to_s) puts sin(a,100) # -> 0.10000000000000000000......E1
Public Class Methods
exp(x, prec)
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Computes the value of e (the base of natural logarithms) raised to the power of x, to the specified number of digits of precision.
If x is infinity, returns Infinity.
If x 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, x1, y, z;
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 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);
negative = VpGetSign(vx) < 0;
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(INT2NUM(0), prec, 1));
}
else {
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 (vx == NULL) {
cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
}
x = RB_GC_GUARD(vx->obj);
n = prec + rmpd_double_figures();
negative = VpGetSign(vx) < 0;
if (negative) {
VpSetSign(vx, 1);
}
RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
RB_GC_GUARD(x1) = one;
RB_GC_GUARD(y) = one;
RB_GC_GUARD(d) = y;
RB_GC_GUARD(z) = one;
i = 0;
while (!VpIsZero((Real*)DATA_PTR(d))) {
VALUE argv[2];
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();
}
x1 = BigDecimal_mult2(x1, x, SSIZET2NUM(n));
++i;
z = BigDecimal_mult(z, SSIZET2NUM(i));
argv[0] = z;
argv[1] = SSIZET2NUM(m);
d = BigDecimal_div2(2, argv, x1);
y = BigDecimal_add(y, d);
}
if (negative) {
VALUE argv[2];
argv[0] = y;
argv[1] = vprec;
return BigDecimal_div2(2, argv, one);
}
else {
vprec = SSIZET2NUM(prec - VpExponent10(DATA_PTR(y)));
return BigDecimal_round(1, &vprec, y);
}
}
log(x, prec)
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Computes the natural logarithm of x to the specified number of digits of precision.
If x is zero or negative, raises Math::DomainError.
If x is positive infinity, returns Infinity.
If x 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 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%"PRIdVALUE, -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;
}
Public Instance Methods
E(prec)
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Computes e (the base of natural logarithms) to the specified number of digits of precision.
# File bigdecimal/lib/bigdecimal/math.rb, line 188
def E(prec)
raise ArgumentError, "Zero or negative precision for E" if prec <= 0
n = prec + BigDecimal.double_fig
one = BigDecimal("1")
y = one
d = y
z = one
i = 0
while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
m = BigDecimal.double_fig if m < BigDecimal.double_fig
i += 1
z *= i
d = one.div(z,m)
y += d
end
y
end
PI(prec)
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Computes the value of pi to the specified number of digits of precision.
# File bigdecimal/lib/bigdecimal/math.rb, line 148
def PI(prec)
raise ArgumentError, "Zero or negative argument 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
w = 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
w = 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
atan(x, prec)
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Computes the arctangent of x to the specified number of digits of precision.
If x is NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 119
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
cos(x, prec)
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Computes the cosine of x to the specified number of digits of precision.
If x is infinite or NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 83
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
sin(x, prec)
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Computes the sine of x to the specified number of digits of precision.
If x is infinite or NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 47
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
sqrt(x,prec)
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Computes the square root of x to the specified number of digits of precision.
BigDecimal.new('2').sqrt(16).to_s
-> "0.14142135623730950488016887242096975E1"
# File bigdecimal/lib/bigdecimal/math.rb, line 40
def sqrt(x,prec)
x.sqrt(prec)
end