Module: BigMath
- Defined in:
- lib/bigdecimal/math.rb,
ext/bigdecimal/bigdecimal.c
Overview
– Contents:
sqrt(x, prec)
sin (x, prec)
cos (x, prec)
atan(x, prec) Note: |x|<1, x=0.9999 may not converge.
PI (prec)
E (prec) == exp(1.0,prec)
where:
x ... BigDecimal number to be computed.
|x| must be small enough to get convergence.
prec ... Number of digits to be obtained.
++
Provides mathematical functions.
Example:
require "bigdecimal/math"
include BigMath
a = BigDecimal((PI(100)/2).to_s)
puts sin(a,100) # => 0.99999999999999999999......e0
Class Method Summary collapse
-
.atan(x, prec) ⇒ Object
call-seq: atan(decimal, numeric) -> BigDecimal.
-
.cos(x, prec) ⇒ Object
call-seq: cos(decimal, numeric) -> BigDecimal.
-
.E(prec) ⇒ Object
call-seq: E(numeric) -> BigDecimal.
-
.exp(x, vprec) ⇒ Object
BigMath.exp(decimal, numeric) -> BigDecimal.
-
.log(x, vprec) ⇒ Object
BigMath.log(decimal, numeric) -> BigDecimal.
-
.PI(prec) ⇒ Object
call-seq: PI(numeric) -> BigDecimal.
-
.sin(x, prec) ⇒ Object
call-seq: sin(decimal, numeric) -> BigDecimal.
-
.sqrt(x, prec) ⇒ Object
call-seq: sqrt(decimal, numeric) -> BigDecimal.
Class Method Details
.atan(x, prec) ⇒ Object
call-seq:
atan(decimal, numeric) -> BigDecimal
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"
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# File '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 |
.cos(x, prec) ⇒ Object
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# File '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 |
.E(prec) ⇒ Object
call-seq:
E(numeric) -> BigDecimal
Computes e (the base of natural logarithms) to the specified number of digits of precision, numeric
.
BigMath.E(10).to_s
#=> "0.271828182845904523536028752390026306410273e1"
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# File '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 |
.exp(x, vprec) ⇒ Object
BigMath.exp(decimal, numeric) -> BigDecimal
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.
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# File 'ext/bigdecimal/bigdecimal.c', line 3719
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, 0, 0);
}
break;
case T_RATIONAL:
vx = GetVpValueWithPrec(x, prec, 0);
break;
default:
break;
}
if (infinite) {
if (negative) {
return VpCheckGetValue(GetVpValueWithPrec(INT2FIX(0), prec, 1));
}
else {
Real* vy;
vy = VpCreateRbObject(prec, "#0", true);
VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
RB_GC_GUARD(vy->obj);
return VpCheckGetValue(vy);
}
}
else if (nan) {
Real* vy;
vy = VpCreateRbObject(prec, "#0", true);
VpSetNaN(vy);
RB_GC_GUARD(vy->obj);
return VpCheckGetValue(vy);
}
else if (vx == NULL) {
cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
}
x = vx->obj;
n = prec + BIGDECIMAL_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 = VpCheckGetValue(VpCreateRbObject(1, "1", true));
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 < BIGDECIMAL_DOUBLE_FIGURES) {
m = BIGDECIMAL_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);
}
|
.log(x, vprec) ⇒ Object
BigMath.log(decimal, numeric) -> BigDecimal
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.
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# File 'ext/bigdecimal/bigdecimal.c', line 3854
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, 0, 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", true);
RB_GC_GUARD(vy->obj);
VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
return VpCheckGetValue(vy);
}
else if (nan) {
Real* vy;
vy = VpCreateRbObject(prec, "#0", true);
RB_GC_GUARD(vy->obj);
VpSetNaN(vy);
return VpCheckGetValue(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 = VpCheckGetValue(vx);
RB_GC_GUARD(one) = VpCheckGetValue(VpCreateRbObject(1, "1", true));
RB_GC_GUARD(two) = VpCheckGetValue(VpCreateRbObject(1, "2", true));
n = prec + BIGDECIMAL_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, VpCheckGetValue(VpCreateRbObject(1, buf, true)), 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 < BIGDECIMAL_DOUBLE_FIGURES) {
m = BIGDECIMAL_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 = VpCheckGetValue(GetVpValue(SSIZET2NUM(expo), 1));
dy = BigDecimal_mult(log10, vexpo);
y = BigDecimal_add(y, dy);
}
return y;
}
|
.PI(prec) ⇒ Object
call-seq:
PI(numeric) -> BigDecimal
Computes the value of pi to the specified number of digits of precision, numeric
.
BigMath.PI(10).to_s
#=> "0.3141592653589793238462643388813853786957412e1"
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# File '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 |
.sin(x, prec) ⇒ Object
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# File '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 |
.sqrt(x, prec) ⇒ Object
call-seq:
sqrt(decimal, numeric) -> BigDecimal
Computes the square root of decimal
to the specified number of digits of precision, numeric
.
BigMath.sqrt(BigDecimal('2'), 16).to_s
#=> "0.1414213562373095048801688724e1"
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# File 'lib/bigdecimal/math.rb', line 43 def sqrt(x, prec) x.sqrt(prec) end |