BigMath
module BigMath
提供数学函数。
例：
require "bigdecimal/math"
include BigMath
a = BigDecimal((PI(100)/2).to_s)
puts sin(a,100) # => 0.99999999999999999999......e0
公共类方法
exp（十进制，数字）→BigDecimal显示源
计算e（自然对数的底数）的值decimal增加到指定的精度位数。
如果decimal是无穷大，则返回Infinity。
如果decimal是NaN，则返回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
}
日志（十进制，数字）→BigDecimal显示源
计算decimal精度的指定位数的自然对数numeric。
如果decimal是零或负数，则引发Math :: DomainError。
如果decimal是正无穷，则返回Infinity。
如果decimal是NaN，则返回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;
}
公共实例方法
E（数字）→BigDecimal显示源
计算e（自然对数的底数）为指定的精度位数，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
PI（数字）→BigDecimal显示源
计算pi的值到指定的精度位数，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
atan（十进制，数字）→BigDecimal显示源
计算decimal精度的指定位数的反正切值numeric。
如果decimal是NaN，则返回NaN。
BigMath.atan(BigDecimal.new('-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
cos（十进制，数字）→BigDecimal显示源
计算decimal精度的指定位数的余弦值，numeric。
如果decimal是Infinity或NaN，则返回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
sin（十进制，数字）→BigDecimal显示源
计算decimal精度的指定位数的正弦值，numeric。
如果decimal是Infinity或NaN，则返回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
sqrt（十进制，数字）→BigDecimal显示源
计算decimal精度的指定位数的平方根，numeric。
BigMath.sqrt(BigDecimal.new('2'), 16).to_s
#=> "0.1414213562373095048801688724e1"
# File ext/bigdecimal/lib/bigdecimal/math.rb, line 42
def sqrt(x, prec)
x.sqrt(prec)
end
