diff options
Diffstat (limited to 'numeric.c')
| -rw-r--r-- | numeric.c | 641 |
1 files changed, 407 insertions, 234 deletions
@@ -576,7 +576,7 @@ num_imaginary(VALUE num) * call-seq: * -self -> numeric * - * Unary Minus---Returns the receiver, negated. + * Returns +self+, negated. */ static VALUE @@ -595,8 +595,8 @@ num_uminus(VALUE num) * fdiv(other) -> float * * Returns the quotient <tt>self/other</tt> as a float, - * using method +/+ in the derived class of +self+. - * (\Numeric itself does not define method +/+.) + * using method +/+ as defined in the subclass of \Numeric. + * (\Numeric itself does not define +/+.) * * Of the Core and Standard Library classes, * only BigDecimal uses this implementation. @@ -614,8 +614,8 @@ num_fdiv(VALUE x, VALUE y) * div(other) -> integer * * Returns the quotient <tt>self/other</tt> as an integer (via +floor+), - * using method +/+ in the derived class of +self+. - * (\Numeric itself does not define method +/+.) + * using method +/+ as defined in the subclass of \Numeric. + * (\Numeric itself does not define +/+.) * * Of the Core and Standard Library classes, * Only Float and Rational use this implementation. @@ -633,7 +633,7 @@ num_div(VALUE x, VALUE y) * call-seq: * self % other -> real_numeric * - * Returns +self+ modulo +other+ as a real number. + * Returns +self+ modulo +other+ as a real numeric (\Integer, \Float, or \Rational). * * Of the Core and Standard Library classes, * only Rational uses this implementation. @@ -829,7 +829,7 @@ rb_int_zero_p(VALUE num) * Of the Core and Standard Library classes, * Integer, Float, Rational, and Complex use this implementation. * - * Related: #zero? + * Related: #zero? * */ @@ -847,7 +847,8 @@ num_nonzero_p(VALUE num) * to_int -> integer * * Returns +self+ as an integer; - * converts using method +to_i+ in the derived class. + * converts using method +to_i+ in the subclass of \Numeric. + * (\Numeric itself does not define +to_i+.) * * Of the Core and Standard Library classes, * only Rational and Complex use this implementation. @@ -857,7 +858,7 @@ num_nonzero_p(VALUE num) * Rational(1, 2).to_int # => 0 * Rational(2, 1).to_int # => 2 * Complex(2, 0).to_int # => 2 - * Complex(2, 1) # Raises RangeError (non-zero imaginary part) + * Complex(2, 1).to_int # Raises RangeError (non-zero imaginary part) * */ @@ -905,88 +906,6 @@ num_negative_p(VALUE num) return RBOOL(rb_num_negative_int_p(num)); } - -/******************************************************************** - * - * Document-class: Float - * - * A \Float object represents a sometimes-inexact real number using the native - * architecture's double-precision floating point representation. - * - * Floating point has a different arithmetic and is an inexact number. - * So you should know its esoteric system. See following: - * - * - https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html - * - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#-why-are-rubys-floats-imprecise - * - https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems - * - * You can create a \Float object explicitly with: - * - * - A {floating-point literal}[rdoc-ref:syntax/literals.rdoc@Float+Literals]. - * - * You can convert certain objects to Floats with: - * - * - \Method #Float. - * - * == What's Here - * - * First, what's elsewhere. \Class \Float: - * - * - Inherits from - * {class Numeric}[rdoc-ref:Numeric@What-27s+Here] - * and {class Object}[rdoc-ref:Object@What-27s+Here]. - * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here]. - * - * Here, class \Float provides methods for: - * - * - {Querying}[rdoc-ref:Float@Querying] - * - {Comparing}[rdoc-ref:Float@Comparing] - * - {Converting}[rdoc-ref:Float@Converting] - * - * === Querying - * - * - #finite?: Returns whether +self+ is finite. - * - #hash: Returns the integer hash code for +self+. - * - #infinite?: Returns whether +self+ is infinite. - * - #nan?: Returns whether +self+ is a NaN (not-a-number). - * - * === Comparing - * - * - #<: Returns whether +self+ is less than the given value. - * - #<=: Returns whether +self+ is less than or equal to the given value. - * - #<=>: Returns a number indicating whether +self+ is less than, equal - * to, or greater than the given value. - * - #== (aliased as #=== and #eql?): Returns whether +self+ is equal to - * the given value. - * - #>: Returns whether +self+ is greater than the given value. - * - #>=: Returns whether +self+ is greater than or equal to the given value. - * - * === Converting - * - * - #% (aliased as #modulo): Returns +self+ modulo the given value. - * - #*: Returns the product of +self+ and the given value. - * - #**: Returns the value of +self+ raised to the power of the given value. - * - #+: Returns the sum of +self+ and the given value. - * - #-: Returns the difference of +self+ and the given value. - * - #/: Returns the quotient of +self+ and the given value. - * - #ceil: Returns the smallest number greater than or equal to +self+. - * - #coerce: Returns a 2-element array containing the given value converted to a \Float - * and +self+ - * - #divmod: Returns a 2-element array containing the quotient and remainder - * results of dividing +self+ by the given value. - * - #fdiv: Returns the \Float result of dividing +self+ by the given value. - * - #floor: Returns the greatest number smaller than or equal to +self+. - * - #next_float: Returns the next-larger representable \Float. - * - #prev_float: Returns the next-smaller representable \Float. - * - #quo: Returns the quotient from dividing +self+ by the given value. - * - #round: Returns +self+ rounded to the nearest value, to a given precision. - * - #to_i (aliased as #to_int): Returns +self+ truncated to an Integer. - * - #to_s (aliased as #inspect): Returns a string containing the place-value - * representation of +self+ in the given radix. - * - #truncate: Returns +self+ truncated to a given precision. - * - */ - VALUE rb_float_new_in_heap(double d) { @@ -1131,15 +1050,21 @@ rb_float_uminus(VALUE flt) /* * call-seq: - * self + other -> numeric + * self + other -> float or complex * - * Returns a new \Float which is the sum of +self+ and +other+: + * Returns the sum of +self+ and +other+; + * the result may be inexact (see Float): * - * f = 3.14 - * f + 1 # => 4.140000000000001 - * f + 1.0 # => 4.140000000000001 - * f + Rational(1, 1) # => 4.140000000000001 - * f + Complex(1, 0) # => (4.140000000000001+0i) + * 3.14 + 0 # => 3.14 + * 3.14 + 1 # => 4.140000000000001 + * -3.14 + 0 # => -3.14 + * -3.14 + 1 # => -2.14 + + * 3.14 + -3.14 # => 0.0 + * -3.14 + -3.14 # => -6.28 + * + * 3.14 + Complex(1, 0) # => (4.140000000000001+0i) + * 3.14 + Rational(1, 1) # => 4.140000000000001 * */ @@ -1164,7 +1089,7 @@ rb_float_plus(VALUE x, VALUE y) * call-seq: * self - other -> numeric * - * Returns a new \Float which is the difference of +self+ and +other+: + * Returns the difference of +self+ and +other+: * * f = 3.14 * f - 1 # => 2.14 @@ -1195,13 +1120,14 @@ rb_float_minus(VALUE x, VALUE y) * call-seq: * self * other -> numeric * - * Returns a new \Float which is the product of +self+ and +other+: + * Returns the numeric product of +self+ and +other+: * * f = 3.14 * f * 2 # => 6.28 * f * 2.0 # => 6.28 * f * Rational(1, 2) # => 1.57 * f * Complex(2, 0) # => (6.28+0.0i) + * */ VALUE @@ -1249,7 +1175,7 @@ rb_flo_div_flo(VALUE x, VALUE y) * call-seq: * self / other -> numeric * - * Returns a new \Float which is the result of dividing +self+ by +other+: + * Returns the quotient of +self+ and +other+: * * f = 3.14 * f / 2 # => 1.57 @@ -1358,7 +1284,7 @@ ruby_float_mod(double x, double y) * call-seq: * self % other -> float * - * Returns +self+ modulo +other+ as a float. + * Returns +self+ modulo +other+ as a \Float. * * For float +f+ and real number +r+, these expressions are equivalent: * @@ -1464,9 +1390,9 @@ flo_divmod(VALUE x, VALUE y) /* * call-seq: - * self ** other -> numeric + * self ** exponent -> numeric * - * Raises +self+ to the power of +other+: + * Returns +self+ raised to the power +exponent+: * * f = 3.14 * f ** 2 # => 9.8596 @@ -1521,7 +1447,7 @@ rb_float_pow(VALUE x, VALUE y) * 1.eql?(Rational(1, 1)) # => false * 1.eql?(Complex(1, 0)) # => false * - * \Method +eql?+ is different from <tt>==</tt> in that +eql?+ requires matching types, + * Method +eql?+ is different from <tt>==</tt> in that +eql?+ requires matching types, * while <tt>==</tt> does not. * */ @@ -1542,10 +1468,17 @@ num_eql(VALUE x, VALUE y) * call-seq: * self <=> other -> zero or nil * - * Returns zero if +self+ is the same as +other+, +nil+ otherwise. + * Compares +self+ and +other+. * - * No subclass in the Ruby Core or Standard Library uses this implementation. + * Returns: + * + * - Zero, if +self+ is the same as +other+. + * - +nil+, otherwise. * + * \Class \Numeric includes module Comparable, + * each of whose methods uses Numeric#<=> for comparison. + * + * No subclass in the Ruby Core or Standard Library uses this implementation. */ static VALUE @@ -1568,7 +1501,7 @@ num_equal(VALUE x, VALUE y) * call-seq: * self == other -> true or false * - * Returns +true+ if +other+ has the same value as +self+, +false+ otherwise: + * Returns whether +other+ is numerically equal to +self+: * * 2.0 == 2 # => true * 2.0 == 2.0 # => true @@ -1591,17 +1524,11 @@ rb_float_equal(VALUE x, VALUE y) } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(b)) return Qfalse; -#endif } else { return num_equal(x, y); } a = RFLOAT_VALUE(x); -#if MSC_VERSION_BEFORE(1300) - if (isnan(a)) return Qfalse; -#endif return RBOOL(a == b); } @@ -1641,30 +1568,32 @@ rb_dbl_cmp(double a, double b) /* * call-seq: - * self <=> other -> -1, 0, +1, or nil + * self <=> other -> -1, 0, 1, or nil + * + * Compares +self+ and +other+. * - * Returns a value that depends on the numeric relation - * between +self+ and +other+: + * Returns: * - * - -1, if +self+ is less than +other+. - * - 0, if +self+ is equal to +other+. - * - 1, if +self+ is greater than +other+. + * - +-1+, if +self+ is less than +other+. + * - +0+, if +self+ is equal to +other+. + * - +1+, if +self+ is greater than +other+. * - +nil+, if the two values are incommensurate. * * Examples: * + * 2.0 <=> 2.1 # => -1 * 2.0 <=> 2 # => 0 * 2.0 <=> 2.0 # => 0 * 2.0 <=> Rational(2, 1) # => 0 * 2.0 <=> Complex(2, 0) # => 0 * 2.0 <=> 1.9 # => 1 - * 2.0 <=> 2.1 # => -1 * 2.0 <=> 'foo' # => nil * - * This is the basis for the tests in the Comparable module. - * * <tt>Float::NAN <=> Float::NAN</tt> returns an implementation-dependent value. * + * \Class \Float includes module Comparable, + * each of whose methods uses Float#<=> for comparison. + * */ static VALUE @@ -1709,7 +1638,8 @@ rb_float_cmp(VALUE x, VALUE y) * call-seq: * self > other -> true or false * - * Returns +true+ if +self+ is numerically greater than +other+: + * Returns whether the value of +self+ is greater than the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 2.0 > 1 # => true * 2.0 > 1.0 # => true @@ -1734,16 +1664,10 @@ rb_float_gt(VALUE x, VALUE y) } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(b)) return Qfalse; -#endif } else { return rb_num_coerce_relop(x, y, '>'); } -#if MSC_VERSION_BEFORE(1300) - if (isnan(a)) return Qfalse; -#endif return RBOOL(a > b); } @@ -1751,7 +1675,8 @@ rb_float_gt(VALUE x, VALUE y) * call-seq: * self >= other -> true or false * - * Returns +true+ if +self+ is numerically greater than or equal to +other+: + * Returns whether the value of +self+ is greater than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 2.0 >= 1 # => true * 2.0 >= 1.0 # => true @@ -1777,16 +1702,10 @@ flo_ge(VALUE x, VALUE y) } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(b)) return Qfalse; -#endif } else { return rb_num_coerce_relop(x, y, idGE); } -#if MSC_VERSION_BEFORE(1300) - if (isnan(a)) return Qfalse; -#endif return RBOOL(a >= b); } @@ -1794,7 +1713,8 @@ flo_ge(VALUE x, VALUE y) * call-seq: * self < other -> true or false * - * Returns +true+ if +self+ is numerically less than +other+: + * Returns whether the value of +self+ is less than the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 2.0 < 3 # => true * 2.0 < 3.0 # => true @@ -1802,7 +1722,6 @@ flo_ge(VALUE x, VALUE y) * 2.0 < 2.0 # => false * * <tt>Float::NAN < Float::NAN</tt> returns an implementation-dependent value. - * */ static VALUE @@ -1819,16 +1738,10 @@ flo_lt(VALUE x, VALUE y) } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(b)) return Qfalse; -#endif } else { return rb_num_coerce_relop(x, y, '<'); } -#if MSC_VERSION_BEFORE(1300) - if (isnan(a)) return Qfalse; -#endif return RBOOL(a < b); } @@ -1836,7 +1749,8 @@ flo_lt(VALUE x, VALUE y) * call-seq: * self <= other -> true or false * - * Returns +true+ if +self+ is numerically less than or equal to +other+: + * Returns whether the value of +self+ is less than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 2.0 <= 3 # => true * 2.0 <= 3.0 # => true @@ -1862,16 +1776,10 @@ flo_le(VALUE x, VALUE y) } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(b)) return Qfalse; -#endif } else { return rb_num_coerce_relop(x, y, idLE); } -#if MSC_VERSION_BEFORE(1300) - if (isnan(a)) return Qfalse; -#endif return RBOOL(a <= b); } @@ -1899,10 +1807,7 @@ rb_float_eql(VALUE x, VALUE y) if (RB_FLOAT_TYPE_P(y)) { double a = RFLOAT_VALUE(x); double b = RFLOAT_VALUE(y); -#if MSC_VERSION_BEFORE(1300) - if (isnan(a) || isnan(b)) return Qfalse; -#endif - return RBOOL(a == b); + return RBOOL(a == b); } return Qfalse; } @@ -2708,7 +2613,7 @@ flo_truncate(int argc, VALUE *argv, VALUE num) * floor(ndigits = 0) -> float or integer * * Returns the largest float or integer that is less than or equal to +self+, - * as specified by the given `ndigits`, + * as specified by the given +ndigits+, * which must be an * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects]. * @@ -2728,7 +2633,7 @@ num_floor(int argc, VALUE *argv, VALUE num) * ceil(ndigits = 0) -> float or integer * * Returns the smallest float or integer that is greater than or equal to +self+, - * as specified by the given `ndigits`, + * as specified by the given +ndigits+, * which must be an * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects]. * @@ -3527,6 +3432,232 @@ rb_num2ull(VALUE val) #endif /* HAVE_LONG_LONG */ +// Conversion functions for unified 128-bit integer structures, +// These work with or without native 128-bit integer support. + +#ifndef HAVE_UINT128_T +// Helper function to build 128-bit value from bignum digits (fallback path). +static inline void +rb_uint128_from_bignum_digits_fallback(rb_uint128_t *result, BDIGIT *digits, size_t length) +{ + // Build the 128-bit value from bignum digits: + for (long i = length - 1; i >= 0; i--) { + // Shift both low and high parts: + uint64_t carry = result->parts.low >> (64 - (SIZEOF_BDIGIT * CHAR_BIT)); + result->parts.low = (result->parts.low << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + result->parts.high = (result->parts.high << (SIZEOF_BDIGIT * CHAR_BIT)) | carry; + } +} + +// Helper function to convert absolute value of negative bignum to two's complement. +// Ruby stores negative bignums as absolute values, so we need to convert to two's complement. +static inline void +rb_uint128_twos_complement_negate(rb_uint128_t *value) +{ + if (value->parts.low == 0) { + value->parts.high = ~value->parts.high + 1; + } + else { + value->parts.low = ~value->parts.low + 1; + value->parts.high = ~value->parts.high + (value->parts.low == 0 ? 1 : 0); + } +} +#endif + +rb_uint128_t +rb_numeric_to_uint128(VALUE x) +{ + rb_uint128_t result = {0}; + if (RB_FIXNUM_P(x)) { + long value = RB_FIX2LONG(x); + if (value < 0) { + rb_raise(rb_eRangeError, "negative integer cannot be converted to unsigned 128-bit integer"); + } +#ifdef HAVE_UINT128_T + result.value = (uint128_t)value; +#else + result.parts.low = (uint64_t)value; + result.parts.high = 0; +#endif + return result; + } + else if (RB_BIGNUM_TYPE_P(x)) { + if (BIGNUM_NEGATIVE_P(x)) { + rb_raise(rb_eRangeError, "negative integer cannot be converted to unsigned 128-bit integer"); + } + size_t length = BIGNUM_LEN(x); +#ifdef HAVE_UINT128_T + if (length > roomof(SIZEOF_INT128_T, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'unsigned 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + result.value = 0; + for (long i = length - 1; i >= 0; i--) { + result.value = (result.value << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + } +#else + // Check if bignum fits in 128 bits (16 bytes) + if (length > roomof(16, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'unsigned 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + rb_uint128_from_bignum_digits_fallback(&result, digits, length); +#endif + return result; + } + else { + rb_raise(rb_eTypeError, "not an integer"); + } +} + +rb_int128_t +rb_numeric_to_int128(VALUE x) +{ + rb_int128_t result = {0}; + if (RB_FIXNUM_P(x)) { + long value = RB_FIX2LONG(x); +#ifdef HAVE_UINT128_T + result.value = (int128_t)value; +#else + if (value < 0) { + // Two's complement representation: for negative values, sign extend + // Convert to unsigned: for -1, we want all bits set + result.parts.low = (uint64_t)value; // This will be the two's complement representation + result.parts.high = UINT64_MAX; // Sign extend: all bits set for negative + } + else { + result.parts.low = (uint64_t)value; + result.parts.high = 0; + } +#endif + return result; + } + else if (RB_BIGNUM_TYPE_P(x)) { + size_t length = BIGNUM_LEN(x); +#ifdef HAVE_UINT128_T + if (length > roomof(SIZEOF_INT128_T, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + uint128_t unsigned_result = 0; + for (long i = length - 1; i >= 0; i--) { + unsigned_result = (unsigned_result << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + } + if (BIGNUM_NEGATIVE_P(x)) { + // Convert from two's complement + // Maximum negative value is 2^127 + if (unsigned_result > ((uint128_t)1 << 127)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.value = -(int128_t)(unsigned_result - 1) - 1; + } + else { + // Maximum positive value is 2^127 - 1 + if (unsigned_result > (((uint128_t)1 << 127) - 1)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.value = (int128_t)unsigned_result; + } +#else + if (length > roomof(16, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + rb_uint128_t unsigned_result = {0}; + rb_uint128_from_bignum_digits_fallback(&unsigned_result, digits, length); + if (BIGNUM_NEGATIVE_P(x)) { + // Check if value fits in signed 128-bit (max negative is 2^127) + uint64_t max_neg_high = (uint64_t)1 << 63; + if (unsigned_result.parts.high > max_neg_high || (unsigned_result.parts.high == max_neg_high && unsigned_result.parts.low > 0)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + // Convert from absolute value to two's complement (Ruby stores negative as absolute value) + rb_uint128_twos_complement_negate(&unsigned_result); + result.parts.low = unsigned_result.parts.low; + result.parts.high = (int64_t)unsigned_result.parts.high; // Sign extend + } + else { + // Check if value fits in signed 128-bit (max positive is 2^127 - 1) + // Max positive: high = 0x7FFFFFFFFFFFFFFF, low = 0xFFFFFFFFFFFFFFFF + uint64_t max_pos_high = ((uint64_t)1 << 63) - 1; + if (unsigned_result.parts.high > max_pos_high) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.parts.low = unsigned_result.parts.low; + result.parts.high = unsigned_result.parts.high; + } +#endif + return result; + } + else { + rb_raise(rb_eTypeError, "not an integer"); + } +} + +VALUE +rb_uint128_to_numeric(rb_uint128_t n) +{ +#ifdef HAVE_UINT128_T + if (n.value <= (uint128_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.value); + } + return rb_uint128t2big(n.value); +#else + // If high part is zero and low part fits in fixnum + if (n.parts.high == 0 && n.parts.low <= (uint64_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.parts.low); + } + // Convert to bignum by building it from the two 64-bit parts + VALUE bignum = rb_ull2big(n.parts.low); + if (n.parts.high > 0) { + VALUE high_bignum = rb_ull2big(n.parts.high); + // Multiply high part by 2^64 and add to low part + VALUE shifted_value = rb_int_lshift(high_bignum, INT2FIX(64)); + bignum = rb_int_plus(bignum, shifted_value); + } + return bignum; +#endif +} + +VALUE +rb_int128_to_numeric(rb_int128_t n) +{ +#ifdef HAVE_UINT128_T + if (FIXABLE(n.value)) { + return LONG2FIX((long)n.value); + } + return rb_int128t2big(n.value); +#else + int64_t high = (int64_t)n.parts.high; + // If it's a small positive value that fits in fixnum + if (high == 0 && n.parts.low <= (uint64_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.parts.low); + } + // Check if it's negative (high bit of high part is set) + if (high < 0) { + // Negative value - convert from two's complement to absolute value + rb_uint128_t unsigned_value = {0}; + if (n.parts.low == 0) { + unsigned_value.parts.low = 0; + unsigned_value.parts.high = ~n.parts.high + 1; + } + else { + unsigned_value.parts.low = ~n.parts.low + 1; + unsigned_value.parts.high = ~n.parts.high + (unsigned_value.parts.low == 0 ? 1 : 0); + } + VALUE bignum = rb_uint128_to_numeric(unsigned_value); + return rb_int_uminus(bignum); + } + else { + // Positive value + union uint128_int128_conversion conversion = { + .int128 = n + }; + return rb_uint128_to_numeric(conversion.uint128); + } +#endif +} + /******************************************************************** * * Document-class: Integer @@ -3539,14 +3670,14 @@ rb_num2ull(VALUE val) * * You can convert certain objects to Integers with: * - * - \Method #Integer. + * - Method #Integer. * * An attempt to add a singleton method to an instance of this class * causes an exception to be raised. * * == What's Here * - * First, what's elsewhere. \Class \Integer: + * First, what's elsewhere. Class \Integer: * * - Inherits from * {class Numeric}[rdoc-ref:Numeric@What-27s+Here] @@ -3592,6 +3723,7 @@ rb_num2ull(VALUE val) * - #>>: Returns the value of +self+ after a rightward bit-shift. * - #[]: Returns a slice of bits from +self+. * - #^: Returns the bitwise EXCLUSIVE OR of +self+ and the given value. + * - #|: Returns the bitwise OR of +self+ and the given value. * - #ceil: Returns the smallest number greater than or equal to +self+. * - #chr: Returns a 1-character string containing the character * represented by the value of +self+. @@ -3611,7 +3743,6 @@ rb_num2ull(VALUE val) * - #to_s (aliased as #inspect): Returns a string containing the place-value * representation of +self+ in the given radix. * - #truncate: Returns +self+ truncated to the given precision. - * - #|: Returns the bitwise OR of +self+ and the given value. * * === Other * @@ -4030,17 +4161,20 @@ rb_fix_plus(VALUE x, VALUE y) /* * call-seq: - * self + numeric -> numeric_result + * self + other -> numeric + * + * Returns the sum of +self+ and +other+: * - * Performs addition: + * 1 + 1 # => 2 + * 1 + -1 # => 0 + * 1 + 0 # => 1 + * 1 + -2 # => -1 + * 1 + Complex(1, 0) # => (2+0i) + * 1 + Rational(1, 1) # => (2/1) * - * 2 + 2 # => 4 - * -2 + 2 # => 0 - * -2 + -2 # => -4 - * 2 + 2.0 # => 4.0 - * 2 + Rational(2, 1) # => (4/1) - * 2 + Complex(2, 0) # => (4+0i) + * For a computation involving Floats, the result may be inexact (see Float#+): * + * 1 + 3.14 # => 4.140000000000001 */ VALUE @@ -4075,9 +4209,9 @@ fix_minus(VALUE x, VALUE y) /* * call-seq: - * self - numeric -> numeric_result + * self - other -> numeric * - * Performs subtraction: + * Returns the difference of +self+ and +other+: * * 4 - 2 # => 2 * -4 - 2 # => -6 @@ -4131,16 +4265,17 @@ fix_mul(VALUE x, VALUE y) /* * call-seq: - * self * numeric -> numeric_result + * self * other -> numeric * - * Performs multiplication: + * Returns the numeric product of +self+ and +other+: * * 4 * 2 # => 8 - * 4 * -2 # => -8 * -4 * 2 # => -8 + * 4 * -2 # => -8 * 4 * 2.0 # => 8.0 * 4 * Rational(1, 3) # => (4/3) * 4 * Complex(2, 0) # => (8+0i) + * */ VALUE @@ -4263,16 +4398,18 @@ fix_div(VALUE x, VALUE y) /* * call-seq: - * self / numeric -> numeric_result + * self / other -> numeric + * + * Returns the quotient of +self+ and +other+. * - * Performs division; for integer +numeric+, truncates the result to an integer: + * For integer +other+, truncates the result to an integer: * * 4 / 3 # => 1 * 4 / -3 # => -2 * -4 / 3 # => -2 * -4 / -3 # => 1 * - * For other +numeric+, returns non-integer result: + * For non-integer +other+, returns a non-integer result: * * 4 / 3.0 # => 1.3333333333333333 * 4 / Rational(3, 1) # => (4/3) @@ -4349,9 +4486,9 @@ fix_mod(VALUE x, VALUE y) /* * call-seq: - * self % other -> real_number + * self % other -> real_numeric * - * Returns +self+ modulo +other+ as a real number. + * Returns +self+ modulo +other+ as a real numeric (\Integer, \Float, or \Rational). * * For integer +n+ and real number +r+, these expressions are equivalent: * @@ -4500,9 +4637,9 @@ rb_int_divmod(VALUE x, VALUE y) /* * call-seq: - * self ** numeric -> numeric_result + * self ** exponent -> numeric * - * Raises +self+ to the power of +numeric+: + * Returns +self+ raised to the power +exponent+: * * 2 ** 3 # => 8 * 2 ** -3 # => (1/8) @@ -4623,17 +4760,47 @@ fix_pow(VALUE x, VALUE y) /* * call-seq: - * self ** numeric -> numeric_result - * - * Raises +self+ to the power of +numeric+: - * - * 2 ** 3 # => 8 - * 2 ** -3 # => (1/8) - * -2 ** 3 # => -8 - * -2 ** -3 # => (-1/8) - * 2 ** 3.3 # => 9.849155306759329 - * 2 ** Rational(3, 1) # => (8/1) - * 2 ** Complex(3, 0) # => (8+0i) + * self ** exponent -> numeric + * + * Returns +self+ raised to the power +exponent+: + * + * # Result for non-negative Integer exponent is Integer. + * 2 ** 0 # => 1 + * 2 ** 1 # => 2 + * 2 ** 2 # => 4 + * 2 ** 3 # => 8 + * -2 ** 3 # => -8 + * # Result for negative Integer exponent is Rational, not Float. + * 2 ** -3 # => (1/8) + * -2 ** -3 # => (-1/8) + * + * # Result for Float exponent is Float. + * 2 ** 0.0 # => 1.0 + * 2 ** 1.0 # => 2.0 + * 2 ** 2.0 # => 4.0 + * 2 ** 3.0 # => 8.0 + * -2 ** 3.0 # => -8.0 + * 2 ** -3.0 # => 0.125 + * -2 ** -3.0 # => -0.125 + * + * # Result for non-negative Complex exponent is Complex with Integer parts. + * 2 ** Complex(0, 0) # => (1+0i) + * 2 ** Complex(1, 0) # => (2+0i) + * 2 ** Complex(2, 0) # => (4+0i) + * 2 ** Complex(3, 0) # => (8+0i) + * -2 ** Complex(3, 0) # => (-8+0i) + * # Result for negative Complex exponent is Complex with Rational parts. + * 2 ** Complex(-3, 0) # => ((1/8)+(0/1)*i) + * -2 ** Complex(-3, 0) # => ((-1/8)+(0/1)*i) + * + * # Result for Rational exponent is Rational. + * 2 ** Rational(0, 1) # => (1/1) + * 2 ** Rational(1, 1) # => (2/1) + * 2 ** Rational(2, 1) # => (4/1) + * 2 ** Rational(3, 1) # => (8/1) + * -2 ** Rational(3, 1) # => (-8/1) + * 2 ** Rational(-3, 1) # => (1/8) + * -2 ** Rational(-3, 1) # => (-1/8) * */ VALUE @@ -4686,7 +4853,7 @@ fix_equal(VALUE x, VALUE y) * call-seq: * self == other -> true or false * - * Returns +true+ if +self+ is numerically equal to +other+; +false+ otherwise. + * Returns whether +self+ is numerically equal to +other+: * * 1 == 2 #=> false * 1 == 1.0 #=> true @@ -4732,28 +4899,29 @@ fix_cmp(VALUE x, VALUE y) /* * call-seq: - * self <=> other -> -1, 0, +1, or nil + * self <=> other -> -1, 0, 1, or nil + * + * Compares +self+ and +other+. * * Returns: * - * - -1, if +self+ is less than +other+. - * - 0, if +self+ is equal to +other+. - * - 1, if +self+ is greater then +other+. + * - +-1+, if +self+ is less than +other+. + * - +0+, if +self+ is equal to +other+. + * - +1+, if +self+ is greater then +other+. * - +nil+, if +self+ and +other+ are incomparable. * * Examples: * * 1 <=> 2 # => -1 * 1 <=> 1 # => 0 - * 1 <=> 0 # => 1 - * 1 <=> 'foo' # => nil - * * 1 <=> 1.0 # => 0 * 1 <=> Rational(1, 1) # => 0 * 1 <=> Complex(1, 0) # => 0 + * 1 <=> 0 # => 1 + * 1 <=> 'foo' # => nil * - * This method is the basis for comparisons in module Comparable. - * + * \Class \Integer includes module Comparable, + * each of whose methods uses Integer#<=> for comparison. */ VALUE @@ -4791,7 +4959,8 @@ fix_gt(VALUE x, VALUE y) * call-seq: * self > other -> true or false * - * Returns +true+ if the value of +self+ is greater than that of +other+: + * Returns whether the value of +self+ is greater than the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 1 > 0 # => true * 1 > 1 # => false @@ -4835,10 +5004,10 @@ fix_ge(VALUE x, VALUE y) /* * call-seq: - * self >= real -> true or false + * self >= other -> true or false * - * Returns +true+ if the value of +self+ is greater than or equal to - * that of +other+: + * Returns whether the value of +self+ is greater than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 1 >= 0 # => true * 1 >= 1 # => true @@ -4883,7 +5052,8 @@ fix_lt(VALUE x, VALUE y) * call-seq: * self < other -> true or false * - * Returns +true+ if the value of +self+ is less than that of +other+: + * Returns whether the value of +self+ is less than the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 1 < 0 # => false * 1 < 1 # => false @@ -4891,8 +5061,6 @@ fix_lt(VALUE x, VALUE y) * 1 < 0.5 # => false * 1 < Rational(1, 2) # => false * - * Raises an exception if the comparison cannot be made. - * */ static VALUE @@ -4927,10 +5095,10 @@ fix_le(VALUE x, VALUE y) /* * call-seq: - * self <= real -> true or false + * self <= other -> true or false * - * Returns +true+ if the value of +self+ is less than or equal to - * that of +other+: + * Returns whether the value of +self+ is less than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: * * 1 <= 0 # => false * 1 <= 1 # => true @@ -5115,8 +5283,8 @@ fix_xor(VALUE x, VALUE y) * */ -static VALUE -int_xor(VALUE x, VALUE y) +VALUE +rb_int_xor(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_xor(x, y); @@ -5289,9 +5457,22 @@ generate_mask(VALUE len) } static VALUE +int_aref2(VALUE num, VALUE beg, VALUE len) +{ + if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_aref2(num, beg, len); + } + else { + num = rb_int_rshift(num, beg); + VALUE mask = generate_mask(len); + return rb_int_and(num, mask); + } +} + +static VALUE int_aref1(VALUE num, VALUE arg) { - VALUE orig_num = num, beg, end; + VALUE beg, end; int excl; if (rb_range_values(arg, &beg, &end, &excl)) { @@ -5311,22 +5492,19 @@ int_aref1(VALUE num, VALUE arg) return INT2FIX(0); } } - num = rb_int_rshift(num, beg); int cmp = compare_indexes(beg, end); if (!NIL_P(end) && cmp < 0) { VALUE len = rb_int_minus(end, beg); if (!excl) len = rb_int_plus(len, INT2FIX(1)); - VALUE mask = generate_mask(len); - num = rb_int_and(num, mask); + return int_aref2(num, beg, len); } else if (cmp == 0) { if (excl) return INT2FIX(0); - num = orig_num; arg = beg; goto one_bit; } - return num; + return rb_int_rshift(num, beg); } one_bit: @@ -5339,15 +5517,6 @@ one_bit: return Qnil; } -static VALUE -int_aref2(VALUE num, VALUE beg, VALUE len) -{ - num = rb_int_rshift(num, beg); - VALUE mask = generate_mask(len); - num = rb_int_and(num, mask); - return num; -} - /* * call-seq: * self[offset] -> 0 or 1 @@ -5552,7 +5721,7 @@ rb_int_digits_bigbase(VALUE num, VALUE base) } bases = rb_ary_new(); - for (VALUE b = base; int_lt(b, num) == Qtrue; b = rb_int_mul(b, b)) { + for (VALUE b = base; int_le(b, num) == Qtrue; b = rb_int_mul(b, b)) { rb_ary_push(bases, b); } digits = rb_ary_new_from_args(1, num); @@ -5978,7 +6147,11 @@ prefix##_isqrt(argtype n) \ while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \ return x; \ } \ - return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ + rettype x = (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ + /* libm sqrt may returns a larger approximation than actual. */ \ + /* Our isqrt always returns a smaller approximation. */ \ + if (x * x > n) x--; \ + return x; \ } #if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG @@ -6190,7 +6363,7 @@ int_s_try_convert(VALUE self, VALUE num) * * == What's Here * - * First, what's elsewhere. \Class \Numeric: + * First, what's elsewhere. Class \Numeric: * * - Inherits from {class Object}[rdoc-ref:Object@What-27s+Here]. * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here]. @@ -6362,7 +6535,7 @@ Init_Numeric(void) rb_define_method(rb_cInteger, "&", rb_int_and, 1); rb_define_method(rb_cInteger, "|", int_or, 1); - rb_define_method(rb_cInteger, "^", int_xor, 1); + rb_define_method(rb_cInteger, "^", rb_int_xor, 1); rb_define_method(rb_cInteger, "[]", int_aref, -1); rb_define_method(rb_cInteger, "<<", rb_int_lshift, 1); @@ -6450,7 +6623,7 @@ Init_Numeric(void) * * If the platform supports denormalized numbers, * there are numbers between zero and Float::MIN. - * 0.0.next_float returns the smallest positive floating point number + * +0.0.next_float+ returns the smallest positive floating point number * including denormalized numbers. */ rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN)); |