[SCM] Lisaac compiler branch, master, updated. 248017b0e58ba0ca73716356794fbcc6571c5ad4
Benoit Sonntag
sonntag at icps.u-strasbg.fr
Tue Jul 28 17:25:31 UTC 2009
The following commit has been merged in the master branch:
commit 248017b0e58ba0ca73716356794fbcc6571c5ad4
Author: Benoit Sonntag <sonntag at icps.u-strasbg.fr>
Date: Tue Jul 28 19:25:27 2009 +0200
rm integer_big
diff --git a/lib2/number/#integer_big.li# b/lib2/number/#integer_big.li#
deleted file mode 100755
index 574ebb5..0000000
--- a/lib2/number/#integer_big.li#
+++ /dev/null
@@ -1,3263 +0,0 @@
-Section Header
-
- + name := INTEGER_BIG;
-
- - comment :=
- " A class used to represent multiprecision integers that makes efficient use \
- \ of allocated space by allowing a number to occupy only part of an array so \
- \ that the arrays do not have to be reallocated as often. When performing an \
- \ operation with many iterations the array used to hold a number is only \
- \ reallocated when necessary and does not have to be the same size as the \
- \ number it represents. A mutable number allows calculations to occur on the \
- \ same number without having to create a new number for every step of the \
- \ calculation as it occurs with NUMBERs.";
-
-Section Inherit
-
- - parent_hashable:HASHABLE := HASHABLE;
-
- - parent_comparable:COMPARABLE := COMPARABLE;
-
-Section Insert
-
- - parent_object:OBJECT := OBJECT;
-
-Section Public
-
-creation {ANY}
- from_integer, from_integer_64, from_string, copy
-
- //
- // Creation / initialization from INTEGER_32 or INTEGER_64:
- //
-
- - from_integer value:INTEGER :SELF <-
- // Create or initialize `Current' using `value' as an initializer.
- (
- (capacity = 0).if {
- storage := storage.calloc 4;
- capacity := 4;
- };
- offset := 0;
- (value > 0).if {
- negative := FALSE;
- put value to 0;
- integer_length := 1;
- }.elseif {value < 0} then {
- negative := TRUE;
- put(#-value, 0)
- integer_length := 1;
- } else {
- ? {value = 0};
- set_with_zero;
- };
- )
- [
- ? {to_integer_32 = value};
- ];
-
- is_integer_32: BOOLEAN is
- -- Does `Current' fit on an INTEGER_32?
- do
- if integer_length = 0 then
- Result := True
- elseif integer_length = 1 then
- if item(offset) > 0 then
- Result := True
- elseif negative then
- Result := item(offset) = 0x80000000
- end
- end
- ensure
- Result implies is_integer_64
- Result implies integer_length <= 1
- end
-
- is_integer: BOOLEAN is
- obsolete "Now use `is_integer_32' instead (march 2006)."
- do
- Result := is_integer_32
- end
-
- to_integer_32: INTEGER is
- -- Convert `Current' as a 32 bit INTEGER.
- require
- is_integer_32
- do
- if integer_length > 0 then
- Result := item(offset)
- if negative then
- Result := #-Result
- end
- end
- end
-
- to_integer: INTEGER is
- obsolete "Now use `to_integer_32' instead (march 2006)."
- do
- Result := to_integer_32
- end
-
- from_integer_64 (value: INTEGER_64) is
- -- Create or set `Current' using `value' as an initializer.
- local
- v32: INTEGER
- do
- if capacity < 2 then
- storage := storage.calloc(4)
- capacity := 4
- end
- if value > 0 then
- negative := False
- put(value.low_32, 0)
- offset := 0
- v32 := value.high_32
- if v32 = 0 then
- integer_length := 1
- else
- put(v32, 1)
- integer_length := 2
- end
- elseif value < 0 then
- negative := True
- put((#-value).low_32, 0)
- offset := 0
- v32 := (#-value).high_32
- if v32 = 0 then
- integer_length := 1
- else
- put(v32, 1)
- integer_length := 2
- end
- else
- check
- value = 0
- end
- set_with_zero
- end
- ensure
- to_integer_64 = value
- end
-
- is_integer_64: BOOLEAN is
- -- Does `Current' fit on an INTEGER_64?
- do
- if integer_length <= 1 then
- Result := True
- elseif integer_length = 2 then
- if negative then
- if item(offset + 1) > 0 then
- Result := True
- elseif item(offset) = 0 then
- Result := item(offset + 1) = 0x80000000
- end
- else
- Result := item(offset + 1) > 0
- end
- end
- ensure
- not Result implies not is_integer_32
- Result implies integer_length <= 2
- end
-
- to_integer_64: INTEGER_64 is
- -- Convert `Current' as a INTEGER_64.
- require
- is_integer_64
- local
- v: INTEGER_64
- do
- inspect
- integer_length
- when 0 then
- when 1 then
- Result := unsigned_32_to_integer_64(item(offset))
- if negative then
- Result := -Result
- end
- when 2 then
- Result := unsigned_32_to_integer_64(item(offset))
- v := item(offset + 1)
- v := v.bit_shift_left(32)
- Result := Result.bit_xor(v)
- if negative then
- Result := #-Result
- end
- end
- end
-
-feature {ANY} -- Creation / initialization from STRING:
- from_string (str: STRING) is
- -- Create or initialize `Current' using `value' as an
- -- initializer. (value = [-][0-9]^+)
- local
- i: INTEGER; cc: CHARACTER; neg: BOOLEAN; ten: like Current
- do
- --|*** This feature should be improved one day... (Vincent Croizier, 25/12/2004)
- create ten.from_integer(10)
- from
- i := 1
- variant
- str.count - i
- until
- not str.item(i).is_separator
- loop
- i := i + 1
- end
- cc := str.item(i)
- i := i + 1
- if cc = '+' then
- cc := str.item(i)
- i := i + 1
- elseif cc = '-' then
- neg := True
- cc := str.item(i)
- i := i + 1
- end
- check
- cc.is_digit
- end
- from_integer(cc.value)
- from
- variant
- str.count - i
- until
- i > str.count
- loop
- cc := str.item(i)
- if cc.is_digit then
- multiply(ten)
- add_integer(cc.value)
- else
- check
- cc.is_separator
- end
- i := str.count -- terminate the loop
- end
- i := i + 1
- end
- if neg then
- negate
- end
- end
-
-feature {ANY} -- Conversion tool
- force_to_real_64: REAL_64 is
- -- only a tool
- -- unsigned conversion *** require ou changer export ? *** (Dom Oct 4th 2004) ***
- local
- i: INTEGER
- do
- from
- i := offset + integer_length - 1
- until
- i < offset or else Result > Maximum_real_64
- loop
- Result := Result * Real_base + unsigned_32_to_integer_64(storage.item(i)).force_to_real_64
- i := i - 1
- end
- if Result = Maximum_real_64 and then storage.item(offset) /= 0 then
- Result := Maximum_real_64 * 2
- end
- if negative then
- Result := -Result
- end
- end
-
-feature {NUMBER}
- from_native_array (na: NATIVE_ARRAY[INTEGER); cap: INTEGER; neg: BOOLEAN) is
- require
- na.item(cap - 1) /= 0
- do
- negative := neg
- offset := 0
- integer_length := cap
- if cap > capacity then
- capacity := capacity_from_lower_bound(capacity, cap)
- storage := storage.calloc(capacity)
- end
- storage.slice_copy(0, na, 0, cap - 1)
- end
-
- to_integer_general_number: INTEGER_GENERAL_NUMBER is
- local
- na: like storage
- do
- if is_integer_64 then
- create {INTEGER_64_NUMBER} Result.make(to_integer_64)
- else
- na := storage.calloc(integer_length)
- na.slice_copy(0, storage, offset, offset + integer_length - 1)
- create {BIG_INTEGER_NUMBER} Result.from_native_array(na, integer_length, negative)
- end
- end
-
-feature {ANY} -- Addition:
- add (other: like Current) is
- -- Add `other' into `Current'.
- --
- -- See also `add_integer', `add_integer_64', `add_natural'.
- require
- other /= Void
- do
- -- Choose the appropriate absolute operator depending on `Current' and `other' sign.
- if other.integer_length = 0 then
- -- Nothing to do, `Current' remains unchanged.
- elseif integer_length = 0 then
- -- `Current' is zero so simply copy the value of other
- Current.copy(other)
- elseif negative = other.negative then
- -- same sign
- add_magnitude(other)
- else
- -- different sign
- subtract_magnitude(other)
- end
- end
-
- add_to (other, res: like Current) is
- -- Add `other' and `Current', and put the result in `res'.
- require
- other /= Void
- res /= Void
- res /= Current
- res /= other
- do
- --|*** Must be optimized later (Vincent Croizier, 15/07/04) ***
- res.copy(Current)
- res.add(other)
- end
-
- add_integer (other: INTEGER) is
- -- Add `other' into `Current'.
- local
- inc: BOOLEAN; v, i, n: INTEGER
- do
- if other = 0 then
- -- Nothing to do, `Current' remains unchanged
- elseif integer_length = 0 then
- -- `Current' is null so simply copy the value of other
- from_integer(other)
- elseif negative = (other < 0) then
- -- Same sign
- if other < 0 then
- v := #-other
- else
- v := other
- end
- -- Add `v' into `storage'
- from
- inc := mbi_add(item(offset), v, storage_at(storage, offset))
- i := offset + 1
- n := offset + integer_length
- until
- not inc or else i >= n
- loop
- inc := mbi_inc(storage_at(storage, i))
- i := i + 1
- end
- if inc then
- check
- i = n
- end
- -- Extend the number length by 1
- if n < capacity then
- integer_length := integer_length + 1
- put(1, n)
- else
- -- It's good only if the reallocation initialize
- -- `storage' with 0.
- v := item(offset)
- capacity := capacity * 2
- storage := storage.calloc(capacity)
- offset := 0
- put(v, 0)
- put(1, integer_length)
- integer_length := integer_length + 1
- end
- end
- -- Different sign
- elseif integer_length = 1 then
- if other < 0 then
- v := #-other
- else
- v := other
- end
- if mbi_subtract(item(offset), v, storage_at(storage, offset)) then
- negative := not negative
- put(-item(offset), offset)
- end
- if item(offset) = 0 then
- integer_length := 0
- negative := False
- end
- else
- if other < 0 then
- v := #-other
- else
- v := other
- end
- if mbi_subtract(item(offset), v, storage_at(storage, offset)) then
- from
- i := offset + 1
- inc := mbi_dec(storage_at(storage, i))
- n := offset + integer_length - 1
- until
- not inc
- loop
- check
- i < n
- end
- i := i + 1
- inc := mbi_dec(storage_at(storage, i))
- end
- if item(n) = 0 then
- integer_length := integer_length - 1
- end
- end
- end
- end
-
- add_integer_64 (other: INTEGER_64) is
- -- Add `other' into `Current'.
- do
- register1.from_integer_64(other)
- add(register1)
- end
-
- add_natural (other: like Current) is
- -- Same behavior as `add', but this one works only when `Current'
- -- and `other' are both positive numbers and are both greater than
- -- zero. The only one advantage of using `add_natural' instead of the
- -- general `add' is the gain of efficiency.
- require
- not is_zero and not is_negative
- not other.is_zero and not other.is_negative
- do
- add_magnitude(other)
- end
-
-feature {ANY} -- Subtract:
- subtract (other: like Current) is
- -- Subtract `other' from `Current'.
- require
- other /= Void
- do
- if other = Current then
- set_with_zero
- elseif other.integer_length = 0 then
- -- nothing to do, `Current' remains unchanged
- elseif integer_length = 0 then
- -- current is null so simply copy the value of other, the sign is also fixed
- copy(other)
- negative := not other.negative
- elseif negative = other.negative then
- -- same sign
- subtract_magnitude(other)
- else
- -- different sign
- add_magnitude(other)
- end
- end
-
- subtract_to (other, res: like Current) is
- -- Subtract `other' from `Current' and put it in `res'.
- require
- other /= Void
- res /= Void
- res /= Current
- res /= other
- do
- --|*** Must be optimized later (Vincent Croizier, 15/07/04) ***
- res.copy(Current)
- res.subtract(other)
- end
-
- subtract_integer (other: INTEGER) is
- do
- if other = Minimum_integer then
- add_integer(1)
- add_integer(Maximum_integer)
- else
- add_integer(-other)
- end
- end
-
-feature {ANY} -- To divide:
- divide (other: like Current) is
- -- Put the the quotient of the Euclidian division of
- -- `Current' by `other' in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- other /= Current
- do
- -- `divide_with_remainder_to' already use `register1'.
- divide_with_remainder_to(other, register2)
- end
-
- mod (other: like Current) is
- -- Put the the remainder of the Euclidian division of
- -- `Current' by `other' in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- other /= Current
- local
- quotient: like Current
- do
- --|*** Must be optimized (Vincent Croizier, 12/07/04) ***
- create quotient.from_integer(0)
- remainder_with_quotient_to(other, quotient)
- ensure
- not negative and abs_compare(other) = -1
- end
-
- divide_with_remainder_to (other, remainder: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'.
- -- Quotient is put in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- remainder /= Void
- remainder /= other
- remainder /= Current
- do
- Current.remainder_with_quotient_to(other, remainder)
- Current.swap_with(remainder)
- ensure
- not remainder.negative and remainder.abs_compare(other) = -1
- end
-
- remainder_with_quotient_to (other, quotient: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'.
- -- Remainder is put in `Current'.
- -- (The contents of `other' is not changed.)
- --
- -- Note: Uses Algorithm D in Knuth section 4.3.1.
- require
- not other.is_zero
- quotient /= Void
- quotient /= other
- quotient /= Current
- local
- cmp, shift, dlen, qlen, j, k, v1, v2, u1, u2, rem: INTEGER; qhat, rhat, v2qhat_1, v2qhat_2, d_offset: INTEGER
- q_storage, d_storage: like storage; q_capacity: like capacity; current_negative, borrow: BOOLEAN
- do
- if integer_length = 0 then
- -- Dividend is zero:
- quotient.set_with_zero
- set_with_zero
- else
- current_negative := negative
- cmp := Current.abs_compare(other)
- if cmp < 0 then
- -- Dividend less than divisor:
- quotient.set_with_zero
- -- Sign correction
- set_negative(False)
- divide_sign_correction_bis(other, quotient, current_negative)
- elseif cmp = 0 then
- -- Dividend equal to divisor:
- if negative = other.negative then
- quotient.from_integer(1)
- else
- quotient.from_integer(-1)
- end
- set_with_zero
- elseif other.integer_length = 1 then
- -- Special case one word divisor:
- quotient.swap_with(Current)
- --|*** replace by "from_unsigned_integer" ? (Vincent Croizier)
- set_with_zero
- rem := quotient.divide_one_word(other.item(other.offset))
- if rem /= 0 then
- put(rem, 0)
- set_integer_length(1)
- else
- check
- is_zero
- end
- end
- -- Sign correction
- divide_sign_correction_bis(other, quotient, current_negative)
- else
- -- Copy divisor storage to protect divisor:
- register1.copy(other)
- -- D1 normalize the divisor:
- shift := register1.normalize
- if shift /= 0 then
- shift_left(shift)
- end
- -- D2 Initialize j:
- from
- d_storage := register1.storage
- d_offset := register1.offset
- dlen := register1.integer_length
- j := offset + integer_length - 1
- u2 := storage.item(j)
- k := register1.offset + dlen - 1
- v1 := register1.item(k)
- v2 := register1.item(k - 1)
- if unsigned_greater_or_equal(u2, v1) then
- k := integer_length - dlen
- qlen := k + 1
- else
- qlen := integer_length - dlen
- k := qlen - 1
- j := j - 1
- u1 := u2
- u2 := storage.item(j)
- end
- -- Resize quotient if necessary
- q_capacity := quotient.capacity
- if q_capacity < qlen then
- -- reallocation
- q_capacity := capacity_from_lower_bound(q_capacity, qlen)
- q_storage := storage.calloc(q_capacity)
- else
- q_storage := quotient.storage
- end
- -- To avoid invariant violation on `quotient'
- quotient.set_with_zero
- until
- k < 0
- loop
- j := j - 1 -- D3 Calculate qhat - estimate qhat
- if u1 = v1 then
- qhat := ~0
- else
- qhat := mbi_divide(u1, u2, v1, $rhat) -- Correct qhat
- if qhat = 0 then
- else
- v2qhat_1 := mbi_multiply(v2, qhat, $v2qhat_2)
- if unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- if mbi_subtract(v2qhat_2, v2, $v2qhat_2) then
- v2qhat_1 := v2qhat_1 - 1
- end
- if mbi_add(rhat, v1, $rhat) then
- elseif unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, storage.item(j)) then
- qhat := qhat - 1
- end
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, storage.item(j)) then
- qhat := qhat - 1
- end
- end
- end
- -- D4 Multiply and subtract:
- if qhat = 0 then
- q_storage.put(0, k)
- else
- borrow := multiply_and_subtract(u1, qhat, d_storage, d_offset, storage, j - dlen + 2, dlen)
- -- D5 Test remainder: Result is negative ?
- if borrow then
- -- D6 Add back
- borrow := add_back(u1, d_storage, d_offset, storage, j - dlen + 2, dlen)
- check
- borrow
- end
- q_storage.put(qhat - 1, k)
- else
- q_storage.put(qhat, k)
- end
- end
- -- D7 loop on j
- k := k - 1
- u1 := storage.item(j + 1)
- u2 := storage.item(j)
- end
- -- Remove leading zero of quotient
- k := qlen - 1
- if q_storage.item(k) = 0 then
- qlen := k
- end
- quotient.set_all(q_storage, q_capacity, qlen, 0, False)
- -- Remove leading zero of remainder
- from
- j := dlen - 1
- until
- j < 0 or else storage.item(j) /= 0
- loop
- j := j - 1
- end
- j := j + 1
- check
- j >= 0
- end
- if j = 0 then
- set_with_zero
- else
- offset := 0
- integer_length := j
- negative := False
- end
- -- D8 Unnormalize:
- if shift > 0 then
- shift_right(shift)
- end
- -- Sign correction
- divide_sign_correction_bis(other, quotient, current_negative)
- end
- end
- ensure
- not negative and abs_compare(other) = -1
- end
-
- divide_to (other, quotient, remainder: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'. (The contents of `Current' and `other' are
- -- not changed.)
- --
- -- Note: Uses Algorithm D in Knuth section 4.3.1.
- require
- not other.is_zero
- quotient /= Void
- remainder /= Void
- quotient /= other
- quotient /= Current
- remainder /= other
- remainder /= Current
- local
- cmp, shift, nlen, dlen, qlen, j, k, v1, v2, u1, u2, rem: INTEGER
- qhat, rhat, v2qhat_1, v2qhat_2, d_offset: INTEGER; q_storage, r_storage, d_storage: like storage
- q_capacity, r_capacity: like capacity; borrow: BOOLEAN
- do
- if integer_length = 0 then
- -- Dividend is zero:
- quotient.set_with_zero
- remainder.set_with_zero
- else
- cmp := Current.abs_compare(other)
- if cmp < 0 then
- -- Dividend less than divisor:
- quotient.set_with_zero
- remainder.copy(Current)
- -- Sign correction
- remainder.set_negative(False)
- divide_sign_correction(other, quotient, remainder)
- elseif cmp = 0 then
- -- Dividend equal to divisor:
- if negative = other.negative then
- quotient.from_integer(1)
- else
- quotient.from_integer(-1)
- end
- remainder.set_with_zero
- elseif other.integer_length = 1 then
- -- Special case one word divisor:
- quotient.copy(Current)
- --|*** replace by "from_unsigned_integer" ? (Vincent Croizier)
- remainder.set_with_zero
- rem := quotient.divide_one_word(other.item(other.offset))
- if rem /= 0 then
- remainder.put(rem, 0)
- remainder.set_ilo(1, 0)
- else
- check
- remainder.is_zero
- end
- end
- -- Sign correction
- divide_sign_correction(other, quotient, remainder)
- else
- -- Copy divisor storage to protect divisor:
- register1.copy(other)
- --|***
- remainder.copy(Current)
- -- D1 normalize the divisor:
- shift := register1.normalize
- if shift /= 0 then
- remainder.shift_left(shift)
- end
- -- D2 Initialize j:
- from
- r_storage := remainder.storage
- r_capacity := remainder.capacity
- check
- remainder.offset = 0
- end
- nlen := remainder.integer_length -- To avoid invariant class violation
- remainder.set_with_zero
- d_storage := register1.storage
- d_offset := register1.offset
- dlen := register1.integer_length
- j := nlen - 1
- u2 := r_storage.item(j)
- k := register1.offset + dlen - 1
- v1 := register1.item(k)
- v2 := register1.item(k - 1)
- if unsigned_greater_or_equal(u2, v1) then
- k := nlen - dlen
- qlen := k + 1
- else
- qlen := nlen - dlen
- k := qlen - 1
- j := j - 1
- u1 := u2
- u2 := r_storage.item(j)
- end
- -- Resize quotient if necessary
- q_capacity := quotient.capacity
- if q_capacity < qlen then
- -- reallocation
- q_capacity := capacity_from_lower_bound(q_capacity, qlen)
- q_storage := storage.calloc(q_capacity)
- else
- q_storage := quotient.storage
- end
- -- To avoid invariant violation on `quotient'
- quotient.set_with_zero
- until
- k < 0
- loop
- j := j - 1 -- D3 Calculate qhat - estimate qhat
- if u1 = v1 then
- qhat := ~0
- else
- qhat := mbi_divide(u1, u2, v1, $rhat) -- Correct qhat
- if qhat = 0 then
- else
- v2qhat_1 := mbi_multiply(v2, qhat, $v2qhat_2)
- if unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- if mbi_subtract(v2qhat_2, v2, $v2qhat_2) then
- v2qhat_1 := v2qhat_1 - 1
- end
- if mbi_add(rhat, v1, $rhat) then
- elseif unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, r_storage.item(j)) then
- qhat := qhat - 1
- end
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, r_storage.item(j)) then
- qhat := qhat - 1
- end
- end
- end
- -- D4 Multiply and subtract:
- if qhat = 0 then
- q_storage.put(0, k)
- else
- borrow := multiply_and_subtract(u1, qhat, d_storage, d_offset, r_storage, j - dlen + 2, dlen)
- -- D5 Test remainder: Result is negative ?
- if borrow then
- -- D6 Add back
- borrow := add_back(u1, d_storage, d_offset, r_storage, j - dlen + 2, dlen)
- check
- borrow
- end
- q_storage.put(qhat - 1, k)
- else
- q_storage.put(qhat, k)
- end
- end
- -- D7 loop on j
- k := k - 1
- u1 := r_storage.item(j + 1)
- u2 := r_storage.item(j)
- end
- -- Remove leading zero of quotient
- k := qlen - 1
- if q_storage.item(k) = 0 then
- qlen := k
- end
- quotient.set_all(q_storage, q_capacity, qlen, 0, False)
- -- Remove leading zero of remainder
- from
- j := dlen - 1
- until
- j < 0 or else r_storage.item(j) /= 0
- loop
- j := j - 1
- end
- j := j + 1
- check
- j >= 0
- end
- if j = 0 then
- check
- remainder.is_zero
- end
- else
- remainder.set_all(r_storage, r_capacity, j, 0, False)
- end
- -- D8 Unnormalize:
- if shift > 0 then
- remainder.shift_right(shift)
- end
- -- Sign correction
- divide_sign_correction(other, quotient, remainder)
- end
- end
- ensure
- is_a_good_divide(other, quotient, remainder)
- not remainder.negative and remainder.abs_compare(other) = -1
- end
-
- shift_left (n: INTEGER) is
- -- Shift bits of magnitude by `n' position left. (Note that no bit can
- -- be lost because the `storage' area is automatically extended when
- -- it is necessary.)
- require
- n > 0
- local
- new_storage: like storage; left, right: INTEGER_8
- new_capacity, new_integer_length, new_head, word_shift, i, j, k, val1, val2, val3: INTEGER
- do
- if integer_length > 0 then
- word_shift := n |>>> 5
- left := (n & 0x0000001F).to_integer_8 -- Optimistic prediction
- new_integer_length := integer_length + word_shift
- if left = 0 then
- -- Just word shift
- if offset >= word_shift then
- -- no need to deplace the number in the storage
- from
- i := offset
- offset := offset - word_shift
- integer_length := new_integer_length
- until
- i = offset
- loop
- i := i - 1
- put(0, i)
- end
- elseif capacity >= new_integer_length then
- -- deplacing the number
- from
- i := offset + integer_length - 1
- j := word_shift + integer_length - 1
- until
- i < offset
- loop
- put(item(i), j)
- i := i - 1
- j := j - 1
- end
- from
- check
- j = word_shift - 1
- end
- until
- j < 0
- loop
- put(0, j)
- j := j - 1
- end
- offset := 0
- integer_length := new_integer_length
- else
- -- reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- i := offset + integer_length
- j := word_shift + integer_length
- until
- i = offset
- loop
- i := i - 1
- j := j - 1
- new_storage.put(item(i), j)
- end
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- end
- else
- right := 32 - left -- Compute real `integer_length'
- i := offset + integer_length - 1
- val1 := item(i)
- new_head := val1 |>>> right
- if new_head = 0 then
- -- new_integer_length is good
- if capacity < new_integer_length then
- -- reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- j := new_integer_length - 1
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- new_storage.put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- new_storage.put(val1 |<< left, j)
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- elseif offset > word_shift then
- from
- check
- j = 0
- end
- until
- j = word_shift
- loop
- put(0, j)
- j := j + 1
- end
- from
- k := offset
- check
- i = offset + integer_length - 1
- j = word_shift
- end
- until
- k = i
- loop
- val3 := item(k)
- put(val3 |<< left | (val2 |>>> right), j)
- val2 := val3
- k := k + 1
- j := j + 1
- end
- put(val1 |<< left | (val2 |>>> right), j)
- offset := 0
- integer_length := new_integer_length
- else
- from
- j := new_integer_length - 1
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- put(val1 |<< left, j)
- from
- until
- j = 0
- loop
- j := j - 1
- put(0, j)
- end
- offset := 0
- integer_length := new_integer_length
- end
- else
- new_integer_length := new_integer_length + 1
- if capacity < new_integer_length then
- -- Reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- j := new_integer_length - 2
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- new_storage.put(new_head, j + 1)
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- new_storage.put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- new_storage.put(val1 |<< left, j)
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- elseif offset > word_shift then
- from
- check
- j = 0
- end
- until
- j = word_shift
- loop
- put(0, j)
- j := j + 1
- end
- from
- k := offset
- check
- i = offset + integer_length - 1
- end
- until
- k = i
- loop
- val3 := item(k)
- put(val3 |<< left | (val2 |>>> right), j)
- val2 := val3
- k := k + 1
- j := j + 1
- end
- put(val1 |<< left | (val2 |>>> right), j)
- put(new_head, j + 1)
- offset := 0
- integer_length := new_integer_length
- else
- from
- j := new_integer_length - 2
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- put(val1 |<< left, j)
- put(new_head, new_integer_length - 1)
- from
- until
- j = 0
- loop
- j := j - 1
- put(0, j)
- end
- offset := 0
- integer_length := new_integer_length
- end
- end
- end
- end
- end
-
- shift_right (n: INTEGER) is
- -- Right shift `Current' n bits. (`Current' is left in normal form.)
- require
- n > 0
- local
- n_ints, n_bits: INTEGER
- do
- if integer_length > 0 then
- n_ints := n |>>> 5
- n_bits := n & 0x0000001F
- integer_length := integer_length - n_ints
- offset := offset + n_ints
- if n_bits = 0 then
- else
- primitive_shift_right(n_bits.to_integer_8)
- end
- end
- end
-
-feature {ANY} -- GCD
- gcd (other: like Current) is
- -- Compute GCD of `Current' and `other'.
- -- GCD is put in `Current' (`other' is not modified).
- require
- other /= Void
- do
- if other = Current then
- Current.abs
- elseif other.is_zero then
- Current.abs
- elseif Current.is_zero then
- Current.copy(other)
- Current.abs
- else
- from
- register2.copy(other)
- Current.mod(register2)
- if Current.is_zero then
- Current.swap_with(register2)
- Current.abs
- else
- register2.mod(Current)
- end
- until
- register2.is_zero
- loop
- Current.mod(register2)
- if Current.is_zero then
- Current.swap_with(register2)
- else
- register2.mod(Current)
- end
- end
- end
- ensure
- is_positive or is_zero and other.is_zero
- end
-
-feature {ANY} -- To multiply:
- multiply (other: like Current) is
- -- Multiply `Current' by `other'.
- require
- other /= Void
- do
- if other = Current then
- multiply_to(other, register1)
- swap_with(register1)
- elseif is_zero or other.is_zero then
- set_with_zero
- elseif Current.is_one then
- copy(other)
- elseif other.is_one then
- elseif Current.is_one_negative then
- copy(other)
- set_negative(not negative)
- elseif other.is_one_negative then
- set_negative(not negative)
- else
- --|*** Must be replace by an algorithm switch. (Vincent Croizier, 09/07/04)
- multiply_like_human(other)
- end
- end
-
- multiply_to (other, res: like Current) is
- -- Multiply the contents of `Current' and `other' and place the
- -- result in `res'. (`Current' and `other' are not modified.)
- require
- other /= Void
- res /= Void
- res /= Current
- do
- if is_zero or other.is_zero then
- res.set_with_zero
- elseif Current.is_one then
- res.copy(other)
- elseif other.is_one then
- res.copy(Current)
- elseif Current.is_one_negative then
- res.copy(other)
- res.set_negative(not res.negative)
- elseif other.is_one_negative then
- res.copy(Current)
- res.set_negative(not negative)
- else
- --|*** Must be replace by an algorithm switch. (Vincent Croizier, 01/05/04)
- multiply_to_like_human(other, res)
- end
- end
-
- multiply_integer (other: INTEGER; res: like Current) is
- -- Multiply the contents of `Current' and `other' and place the
- -- result in `res'. (`Current' is not modified.)
- require
- res /= Current
- res /= Void
- local
- overflow, res_integer_length, res_capacity, i, k, up_i, v: INTEGER; res_storage: like storage
- do
- if other = 0 or else is_zero then
- res.set_with_zero
- elseif other = Minimum_integer then
- res.set_negative(not negative)
- shift_left(31)
- else
- if other > 0 then
- res.set_negative(negative)
- v := other
- else
- res.set_negative(not negative)
- v := -other
- end
- -- Pessimistique estimation
- res_integer_length := integer_length + 1 -- Reallocation ?
- if res.capacity < res_integer_length then
- if capacity < res_integer_length then
- res_capacity := capacity * 2
- else
- res_capacity := capacity_from_upper_bound(capacity, res_integer_length)
- end
- set_capacity(res_capacity)
- res_storage := storage.calloc(res_capacity)
- res.set_storage(res_storage)
- else
- res_storage := res.storage
- end
- res.set_offset(0)
- -- Multiply
- from
- k := 0
- i := offset
- up_i := offset + integer_length - 1
- overflow := mbi_multiply(item(i), v, storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(item(i), v, overflow, storage_at(res_storage, k))
- end
- if overflow = 0 then
- res.set_integer_length(res_integer_length - 1)
- else
- check
- k + 1 = integer_length
- end
- res.put(overflow, integer_length)
- end
- end
- end
-
-feature {MUTABLE_BIG_INTEGER} -- to multiply
- multiply_like_human (other: like Current) is
- -- Simple multiply.
- -- Complexity = O(`integer_length'*`other.integer_length').
- require
- not is_zero
- not other.is_zero
- local
- old_offset, new_integer_length: INTEGER
- do
- -- Pessimistique estimation
- new_integer_length := integer_length + other.integer_length -- Reallocation ?
- if capacity < new_integer_length then
- register1.swap_with(Current)
- register1.multiply_to_like_human(other, Current)
- -- Multiply in place
- elseif offset + new_integer_length <= capacity then
- multiply_like_human_aux_reverse(other)
- elseif offset >= other.integer_length then
- multiply_like_human_aux(other)
- else
- old_offset := offset
- offset := capacity - integer_length
- storage.slice_copy(offset, storage, old_offset, old_offset + integer_length - 1)
- multiply_like_human_aux(other)
- end
- end
-
- multiply_like_human_aux (other: like Current) is
- -- Only used by `multiply_to_like_human'.
- require
- not is_zero
- not other.is_zero
- offset >= other.integer_length
- local
- other_offset, other_integer_length, overflow, i, j, k, up_i, up_j, down_k, v: INTEGER
- other_storage: like storage
- do
- other_offset := other.offset
- other_integer_length := other.integer_length
- other_storage := other.storage -- First pass
- from
- k := 0
- i := other_offset
- up_i := other_offset + other_integer_length - 1
- j := offset
- up_j := offset + integer_length - 1
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(other_storage.item(i), v, overflow, storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j
- end
- storage.put(overflow, k)
- from
- down_k := 1
- until
- j = up_j
- loop
- j := j + 1
- from
- k := down_k
- i := other_offset
- v := storage.item(j)
- overflow := mbi_multiply_with_add(other_storage.item(i), v, storage.item(k), storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(other_storage.item(i), v, overflow, storage.item(k), storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j
- end
- storage.put(overflow, k)
- down_k := down_k + 1
- end
- -- Adjust `res.integer_length'
- if overflow = 0 then
- integer_length := integer_length + other_integer_length - 1
- else
- integer_length := integer_length + other_integer_length
- end
- negative := negative /= other.negative
- offset := 0
- end
-
- multiply_like_human_aux_reverse (other: like Current) is
- -- Only used by `multiply_to_like_human'.
- require
- not is_zero
- not other.is_zero
- offset + integer_length <= capacity - other.integer_length
- local
- other_offset, other_integer_length, overflow, i, j, k, up_i, down_j, down_k, v: INTEGER
- other_storage: like storage; inc: BOOLEAN
- do
- other_offset := other.offset
- other_integer_length := other.integer_length
- other_storage := other.storage -- First pass
- from
- i := other_offset
- up_i := other_offset + other_integer_length - 1
- down_j := offset
- j := offset + integer_length - 1
- k := j
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(other_storage.item(i), v, overflow, storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j + other_integer_length
- end
- storage.put(overflow, k)
- from
- down_k := j - 1
- until
- j = down_j
- loop
- j := j - 1
- from
- k := down_k
- i := other_offset
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(other_storage.item(i), v, overflow, storage.item(k), storage_at(storage, k))
- end
- k := k + 1
- inc := mbi_add(storage.item(k), overflow, storage_at(storage, k))
- check
- k < offset + integer_length + other_integer_length
- end
- from
- until
- not inc
- loop
- k := k + 1
- check
- k < offset + integer_length + other_integer_length
- end
- inc := mbi_inc(storage_at(storage, k))
- end
- down_k := down_k - 1
- end
- -- Adjust `res.integer_length'
- if storage.item(offset + integer_length + other_integer_length - 1) = 0 then
- integer_length := integer_length + other_integer_length - 1
- else
- integer_length := integer_length + other_integer_length
- end
- negative := negative /= other.negative
- end
-
- multiply_to_like_human (other, res: like Current) is
- -- Simple multiply.
- -- Complexity = O(`integer_length'*`other.integer_length').
- require
- res /= Current
- not is_zero
- not other.is_zero
- local
- overflow, res_integer_length, res_capacity, i, j, k, up_i, up_j, down_k, v: INTEGER
- res_storage: like storage; res_negative: BOOLEAN
- do
- res_negative := negative /= other.negative -- Pessimistique estimation
- res_integer_length := integer_length + other.integer_length -- Reallocation ?
- res_capacity := res.capacity
- if res_capacity < res_integer_length then
- res_capacity := capacity_from_lower_bound(res_capacity, res_integer_length)
- res_storage := storage.calloc(res_capacity)
- else
- res_storage := res.storage
- end
- -- To avoid class invariant violation
- res.set_with_zero
- -- Multiply
- -- First pass
- from
- k := 0
- i := offset
- up_i := offset + integer_length - 1
- j := other.offset
- up_j := j + other.integer_length - 1
- v := other.item(j)
- overflow := mbi_multiply(item(i), v, storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(item(i), v, overflow, storage_at(res_storage, k))
- end
- k := k + 1
- res_storage.put(overflow, k)
- from
- down_k := 1
- until
- j = up_j
- loop
- j := j + 1
- from
- k := down_k
- i := offset
- v := other.item(j)
- overflow := mbi_multiply_with_add(item(i), v, res_storage.item(k), storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(item(i), v, overflow, res_storage.item(k), storage_at(res_storage, k))
- end
- k := k + 1
- res_storage.put(overflow, k)
- down_k := down_k + 1
- end
- -- Adjust `res.integer_length'
- if overflow = 0 then
- res.set_all(res_storage, res_capacity, res_integer_length - 1, 0, res_negative)
- else
- res.set_all(res_storage, res_capacity, res_integer_length, 0, res_negative)
- end
- end
-
-feature {ANY} -- Comparison:
- is_zero: BOOLEAN is
- -- Is it 0?
- do
- Result := integer_length = 0
- ensure
- Result implies not is_negative
- end
-
- is_one: BOOLEAN is
- -- Is it 1?
- do
- if integer_length = 1 then
- if not negative then
- Result := item(offset) = 1
- end
- end
- ensure
- Result implies not is_negative
- end
-
- is_one_negative: BOOLEAN is
- -- Is it -1 ?
- do
- if integer_length = 1 then
- if negative then
- Result := item(offset) = 1
- end
- end
- ensure
- Result implies is_negative
- end
-
- is_negative: BOOLEAN is
- -- Is `Current' negative integer?
- do
- Result := negative
- ensure
- Result implies not is_positive
- end
-
- is_positive: BOOLEAN is
- -- Is `Current' positive integer?
- do
- Result := not negative and then integer_length /= 0
- ensure
- Result implies not is_negative
- end
-
- is_even: BOOLEAN is
- -- Is `Current' even?
- do
- if integer_length = 0 then
- Result := True
- else
- Result := item(offset).is_even
- end
- ensure
- Result = not Current.is_odd
- end
-
- is_odd: BOOLEAN is
- -- Is `Current' odd?
- do
- if integer_length > 0 then
- Result := item(offset).is_odd
- end
- ensure
- Result = not Current.is_even
- end
-
- is_equal (other: like Current): BOOLEAN is
- local
- a, b, c: INTEGER
- do
- if Current = other then
- Result := True
- elseif integer_length /= other.integer_length then
- elseif negative /= other.negative then
- else
- check
- other.integer_length = integer_length
- end
- from
- c := offset + integer_length
- a := offset
- b := other.offset
- Result := True
- until
- a = c
- loop
- if item(a) /= other.item(b) then
- Result := False
- a := c
- else
- a := a + 1
- b := b + 1
- end
- end
- end
- end
-
- infix "<" (other: like Current): BOOLEAN is
- local
- a, b: INTEGER; va, vb: INTEGER
- do
- if Current = other then
- elseif negative /= other.negative then
- Result := negative
- elseif integer_length /= other.integer_length then
- Result := integer_length < other.integer_length xor negative
- else
- check
- other.negative = negative
- end
- check
- other.integer_length = integer_length
- end
- from
- a := offset + integer_length - 1
- b := other.offset + integer_length - 1
- until
- a < offset
- loop
- va := item(a)
- vb := other.item(b)
- if unsigned_less_than(va, vb) then
- Result := not negative
- a := -1
- elseif unsigned_less_than(vb, va) then
- Result := negative
- a := -1
- else
- a := a - 1
- b := b - 1
- end
- end
- end
- end
-
- abs_compare (other: like Current): INTEGER is
- -- Compare the magnitude of `Current' and `other'. Returns -1, 0 or 1
- -- as this MutableBigInteger is numerically less than, equal to, or
- -- greater than other.
- local
- a, b: INTEGER; va, vb: INTEGER
- do
- if Current = other then
- --Result := 0
- elseif integer_length < other.integer_length then
- Result := -1
- elseif integer_length > other.integer_length then
- Result := 1
- else
- check
- other.integer_length = integer_length
- end
- from
- a := offset + integer_length
- b := other.offset + integer_length
- check
- Result = 0
- end
- until
- a <= offset
- loop
- a := a - 1
- b := b - 1
- va := item(a)
- vb := other.item(b)
- if unsigned_less_than(va, vb) then
- Result := -1
- a := -1
- elseif unsigned_less_than(vb, va) then
- Result := 1
- a := -1
- end
- end
- end
- end
-
-feature {ANY} -- Printing:
- to_string: STRING is
- -- The decimal view of `Current' into a new allocated STRING.
- -- For example, if `Current' is -1 the `Result' is "-1".
- --
- -- See also `append_in', `to_string_format', `to_unicode_string', `to_integer'.
- do
- string_buffer.clear_count
- append_in(string_buffer)
- Result := string_buffer.twin
- end
-
- to_unicode_string: UNICODE_STRING is
- -- The decimal view of `Current' into a new allocated UNICODE_STRING.
- -- For example, if `Current' represents -1 the `Result' is U"-1".
- --
- -- See also `append_in_unicode', `to_unicode_string_format', `to_string'.
- do
- unicode_string_buffer.clear_count
- append_in_unicode(unicode_string_buffer)
- Result := unicode_string_buffer.twin
- end
-
- append_in (buffer: STRING) is
- -- Append in the `buffer' the equivalent of `to_string'. No new
- -- STRING creation during the process.
- require
- is_printable
- local
- k: INTEGER
- do
- if is_zero then
- buffer.extend('0')
- else
- -- Put the sign in `buffer'
- if negative then
- buffer.extend('-')
- end
- -- Put it in `buffer'
- from
- k := append_in_char_buffer
- until
- k = 0
- loop
- k := k - 1
- buffer.extend(char_buffer.item(k))
- end
- end
- end
-
- append_in_unicode (buffer: UNICODE_STRING) is
- -- Append in the `buffer' the equivalent of `to_string'. No new
- -- STRING creation during the process.
- require
- is_printable
- local
- k: INTEGER
- do
- if is_zero then
- buffer.extend('0'.code)
- else
- -- Put the sign in `buffer'
- if negative then
- buffer.extend('-'.code)
- end
- -- Put it in `buffer'
- from
- k := append_in_char_buffer
- until
- k = 0
- loop
- k := k - 1
- buffer.extend(char_buffer.item(k).code)
- end
- end
- end
-
- to_string_format (s: INTEGER): STRING is
- -- Same as `to_string' but the result is on `s' character and the
- -- number is right aligned.
- -- Note: see `append_in_format' to save memory.
- require
- to_string.count <= s
- do
- create Result.make(s)
- append_in_format(Result, s)
- ensure
- Result.count = s
- end
-
- to_unicode_string_format (s: INTEGER): UNICODE_STRING is
- -- Same as `to_unicode_string' but the result is on `s' character and
- -- the number is right aligned.
- -- Note: see `append_in_unicode_format' to save memory.
- require
- to_string.count <= s
- do
- create Result.make(s)
- append_in_unicode_format(Result, s)
- ensure
- Result.count = s
- end
-
- append_in_format (str: STRING; s: INTEGER) is
- -- Append the equivalent of `to_string_format' at the end of
- -- `str'. Thus you can save memory because no other
- -- STRING is allocated for the job.
- require
- to_string.count <= s
- local
- i, k: INTEGER
- do
- if is_zero then
- -- Put spaces
- from
- i := s - 1
- variant
- i
- until
- i = 0
- loop
- str.extend(' ')
- i := i - 1
- end
- -- Put number
- str.extend('0')
- else
- k := append_in_char_buffer
- -- Put spaces
- from
- if negative then
- i := s - k - 1
- else
- i := s - k
- end
- variant
- i
- until
- i = 0
- loop
- str.extend(' ')
- i := i - 1
- end
- -- Put number
- from
- -- Put the sign in `buffer'
- if negative then
- str.extend('-')
- end
- variant
- k
- until
- k = 0
- loop
- k := k - 1
- str.extend(char_buffer.item(k))
- end
- end
- ensure
- str.count >= old str.count + s
- end
-
- append_in_unicode_format (str: UNICODE_STRING; s: INTEGER) is
- -- Append the equivalent of `to_unicode_string_format' at the end of
- -- `str'. Thus you can save memory because no other
- -- UNICODE_STRING is allocated for the job.
- require
- to_string.count <= s
- local
- i, k: INTEGER
- do
- if is_zero then
- -- Put spaces
- from
- i := s - 1
- variant
- i
- until
- i = 0
- loop
- str.extend(' '.code)
- i := i - 1
- end
- -- Put number
- str.extend('0'.code)
- else
- k := append_in_char_buffer
- -- Put spaces
- from
- if negative then
- i := s - k - 1
- else
- i := s - k
- end
- variant
- i
- until
- i = 0
- loop
- str.extend(' '.code)
- i := i - 1
- end
- -- Put number
- from
- -- Put the sign in `buffer'
- if negative then
- str.extend('-'.code)
- end
- variant
- k
- until
- k = 0
- loop
- k := k - 1
- str.extend(char_buffer.item(k).code)
- end
- end
- ensure
- str.count >= old str.count + s
- end
-
- is_printable: BOOLEAN is
- -- True if decimal view of `Current' is short enougth
- -- to be put in a STRING.
- do
- --|*** MUST BE REWRITE (Vincent Croizier, 14/07/04) ***
- Result := integer_length <= 2 ^ 27
- end
-
- out_in_tagged_out_memory, fill_tagged_out_memory is
- do
- append_in(tagged_out_memory)
- end
-
-feature {ANY} -- Miscellaneous:
- negate is
- -- Negate the sign of `Current'.
- do
- if integer_length /= 0 then
- negative := not negative
- end
- end
-
- abs is
- -- Absolute value of `Current'.
- do
- negative := False
- end
-
- sign: INTEGER_8 is
- -- Sign of `Current' (0 -1 or 1).
- do
- if negative then
- Result := -1
- elseif integer_length > 0 then
- Result := 1
- else
- check
- is_zero
- end
- end
- end
-
- set_with_zero is
- do
- integer_length := 0
- negative := False
- ensure
- is_zero
- end
-
- hash_code: INTEGER is
- local
- i, c, v: INTEGER
- do
- from
- i := offset
- c := 2
- until
- c = 0 or else i = offset + integer_length
- loop
- v := item(i)
- if v /= 0 then
- Result := Result #+ v
- c := c - 1
- end
- i := i + 1
- end
- Result := integer_length #* Result
- if negative then
- Result := Result #+ 1
- end
- if Result < 0 then
- Result := ~Result
- end
- end
-
- copy (other: like Current) is
- do
- negative := other.negative
- offset := 0
- integer_length := other.integer_length
- if capacity < other.integer_length then
- capacity := capacity_from_upper_bound(other.capacity, integer_length)
- storage := storage.calloc(capacity)
- elseif capacity = 0 then
- capacity := 4
- storage := storage.calloc(capacity)
- end
- if integer_length /= 0 then
- storage.slice_copy(offset, other.storage, other.offset, other.offset + integer_length - 1)
- end
- end
-
- swap_with (other: like Current) is
- -- Swap the value of `Current' with the value of `other'.
- local
- s: like storage; c: like capacity; il: like integer_length; o: like offset; n: like negative
- do
- s := other.storage
- c := other.capacity
- il := other.integer_length
- o := other.offset
- n := other.negative -- Put Current in other
- other.set_all(storage, capacity, integer_length, offset, negative)
- --
- storage := s
- capacity := c
- integer_length := il
- offset := o
- negative := n
- end
-
-feature {MUTABLE_BIG_INTEGER}
- storage: NATIVE_ARRAY[INTEGER)
- -- Holds the magnitude of `Current' in natural order (the most
- -- significant INTEGER_32 word has the highest address). To avoid many
- -- reallocation of this `storage' area, only some words are
- -- significant. The magnitude is stored in the following significant
- -- range [`offset' .. `offset + integer_length - 1'].
-
- capacity: INTEGER
- -- Of the allocated `storage' area.
-
- integer_length: INTEGER
- -- The number of significant INTEGER_32 words in the `storage' area.
-
- offset: INTEGER
- -- The `offset' of the less significant word into the `storage' area.
-
- negative: BOOLEAN
- -- True when `Current' is negative.
-
- item (index: INTEGER): INTEGER_32 is
- require
- -- index.in_range(0, capacity - 1)
- index.in_range(offset, offset + integer_length - 1)
- do
- Result := storage.item(index)
- end
-
- put (value: INTEGER; index: INTEGER) is
- require
- index.in_range(0, capacity - 1)
- do
- storage.put(value, index)
- end
-
- set_negative (n: like negative) is
- require
- n implies not is_zero
- do
- negative := n
- ensure
- negative = n or is_zero
- end
-
- set_integer_length (il: like integer_length) is
- require
- il.in_range(0, capacity - offset)
- do
- integer_length := il
- ensure
- integer_length = il
- end
-
- set_offset (o: like offset) is
- require
- o.in_range(0, capacity - integer_length)
- do
- offset := o
- ensure
- offset = o
- end
-
- set_ilo (il: like integer_length; o: like offset) is
- require
- il.in_range(0, capacity)
- o.in_range(0, capacity - il)
- do
- integer_length := il
- offset := o
- ensure
- integer_length = il
- offset = o
- end
-
- set_storage (new_storage: like storage) is
- do
- storage := new_storage
- end
-
- set_capacity (new_capacity: like capacity) is
- do
- capacity := new_capacity
- end
-
- set_all (new_storage: like storage; new_capacity, new_integer_length, new_offset: INTEGER; new_negative: BOOLEAN) is
- require
- new_capacity > 0
- new_storage.is_not_null
- new_integer_length.in_range(0, new_capacity)
- new_integer_length /= 0 implies new_offset.in_range(0, new_capacity - new_integer_length) and new_storage.item(new_offset + new_integer_length - 1) /= 0
- new_integer_length = 0 implies not new_negative
- new_capacity.is_a_power_of_2
- do
- storage := new_storage
- capacity := new_capacity
- integer_length := new_integer_length
- offset := new_offset
- negative := new_negative
- ensure
- storage = new_storage
- capacity = new_capacity
- integer_length = new_integer_length
- offset = new_offset
- negative = new_negative
- end
-
- primitive_shift_left (n: INTEGER_8) is
- -- Left shift `Current' with no need to extend the `storage'.
- --|*** Can be a little faster (Vincent Croizier, 26/04/04) ***
- require
- integer_length > 0
- n.in_range(1, 31)
- no_bit_lost: item(offset + integer_length - 1) |<< n |>>> n = item(offset + integer_length - 1)
- local
- n2: INTEGER_8; i, up, b, c: INTEGER
- do
- n2 := 32 - n
- from
- i := offset
- up := i + integer_length - 1
- until
- i > up
- loop
- b := item(i)
- put(b |<< n | c, i)
- c := b |>>> n2
- i := i + 1
- end
- check
- c = 0
- end
- end
-
- primitive_shift_right (n: INTEGER_8) is
- -- Right shift `Current' of `n' bits.
- require
- integer_length > 0
- n.in_range(1, 31)
- local
- n2: INTEGER_8; i, j, up, b, c: INTEGER
- do
- n2 := 32 - n
- from
- up := integer_length - 1
- j := 0
- i := offset
- c := item(i)
- until
- j >= up
- loop
- b := c
- i := i + 1
- c := item(i)
- put(b |>>> n | (c |<< n2), j)
- j := j + 1
- end
- check
- j = up
- i = offset + j
- end
- put(c |>>> n, up)
- offset := 0
- if item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- end
- ensure
- offset = 0
- end
-
- divide_one_word (divisor: INTEGER): INTEGER is
- -- This method is used by `divide'. The one word divisor is
- -- specified by `divisor' is saw as unsigned.
- -- `Current' is the dividend (saw positive) at invocation but is replaced by
- -- the quotient. The remainder is returned as unsigned INTEGER.
- -- Note: `Current' is modified by this method.
- require
- divisor /= 0
- local
- i, remainder_word1, remainder_word0: INTEGER
- do
- if integer_length = 1 then
- Result := item(offset)
- if unsigned_less_than(Result, divisor) then
- integer_length := 0
- negative := False
- else
- put(mbi_divide(0, Result, divisor, $remainder_word1), offset)
- Result := remainder_word1
- end
- else
- from
- i := offset + integer_length - 1
- until
- i < offset
- loop
- remainder_word0 := item(i)
- put(mbi_divide(remainder_word1, remainder_word0, divisor, $remainder_word1), i)
- i := i - 1
- end
- if item(offset + integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- item(offset + integer_length - 1) /= 0
- end
- end
- Result := remainder_word1
- end
- end
-
- divide_sign_correction (other, quotient, remainder: like Current) is
- -- Correct the value of `quotient' and `remainder' after an
- -- "unsigned" division.
- -- Only used by `divide'.
- require
- not remainder.is_negative
- do
- if remainder.is_zero then
- quotient.set_negative(negative /= other.negative)
- elseif negative then
- quotient.set_negative(False)
- if other.negative then
- quotient.add_integer(1)
- remainder.set_negative(True)
- -- other is negative
- remainder.subtract(other)
- check
- not remainder.is_negative
- end
- else
- quotient.add_integer(1)
- quotient.set_negative(True)
- remainder.set_negative(True)
- remainder.add(other)
- check
- not remainder.is_negative
- end
- end
- elseif other.negative then
- quotient.set_negative(True)
- else
- quotient.set_negative(False)
- end
- ensure
- not remainder.is_negative
- end
-
- divide_sign_correction_bis (other, quotient: like Current; current_negative: BOOLEAN) is
- -- Correct the value of `quotient' and `remainder' after an
- -- "unsigned" division.
- -- Only used by `divide'.
- require
- not is_negative
- do
- if is_zero then
- quotient.set_negative(current_negative /= other.negative)
- elseif current_negative then
- quotient.set_negative(False)
- if other.negative then
- quotient.add_integer(1)
- set_negative(True)
- -- other is negative
- subtract(other)
- check
- not is_negative
- end
- else
- quotient.add_integer(1)
- quotient.set_negative(True)
- set_negative(True)
- add(other)
- check
- not is_negative
- end
- end
- elseif other.negative then
- quotient.set_negative(True)
- else
- quotient.set_negative(False)
- end
- ensure
- not is_negative
- end
-
- multiply_and_subtract (u1, qhat: INTEGER; d_storage: like storage; d_offset: INTEGER; r_storage: like storage
- r_offset, length: INTEGER): BOOLEAN is
- -- Only used by `divide'.
- require
- qhat /= 0
- local
- i, j, jmax, m1, m2: INTEGER; dec: BOOLEAN
- do
- if qhat = 1 then
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- if dec then
- dec := mbi_subtract_with_dec(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- else
- dec := mbi_subtract(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if dec then
- if u1 = 0 then
- Result := True
- else
- Result := mbi_dec(storage_at(r_storage, j))
- check
- not Result
- end
- end
- end
- else
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- m1 := mbi_multiply_with_add(qhat, d_storage.item(i), m1, $m2)
- if dec then
- dec := mbi_subtract_with_dec(r_storage.item(j), m2, storage_at(r_storage, j))
- else
- dec := mbi_subtract(r_storage.item(j), m2, storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if dec then
- if u1 = 0 then
- Result := True
- else
- Result := mbi_subtract_with_dec(r_storage.item(j), m1, storage_at(r_storage, j))
- end
- elseif m1 = 0 then
- -- nothing to do
- elseif u1 = 0 then
- Result := True
- else
- Result := mbi_subtract(r_storage.item(j), m1, storage_at(r_storage, j))
- end
- end
- end
-
- add_back (old_u1: INTEGER; d_storage: like storage; d_offset: INTEGER; r_storage: like storage
- r_offset, length: INTEGER): BOOLEAN is
- -- Only used by `divide'.
- -- `old_u1' is the value of `u1' before `multiply_and_subtract'.
- local
- i, j, jmax: INTEGER; inc: BOOLEAN
- do
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- if inc then
- inc := mbi_add_with_inc(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- else
- inc := mbi_add(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if inc then
- if old_u1 = 0 then
- Result := True
- else
- Result := mbi_inc(storage_at(r_storage, j))
- end
- end
- end
-
- is_a_good_divide (other, quotient, remainder: like Current): BOOLEAN is
- require
- other /= Void
- quotient /= Void
- remainder /= Void
- local
- v: like Current
- do
- v := other.twin
- v.multiply(quotient)
- v.add(remainder)
- Result := Current.is_equal(v)
- end
-
- normalize: INTEGER_8 is
- -- Shift left until the most significant bit is on.
- -- Result give the number of left shift.
- require
- not is_zero
- local
- head: INTEGER
- do
- head := item(offset + integer_length - 1)
- from
- until
- head < 0
- loop
- head := head.bit_shift_left(1)
- Result := Result + 1
- end
- if Result > 0 then
- shift_left(Result)
- end
- ensure
- item(offset + integer_length - 1) < 0
- end
-
-feature {MUTABLE_BIG_INTEGER} -- Implementation:
- register1: MUTABLE_BIG_INTEGER is
- once
- create Result.from_integer(0)
- end
-
- register2: MUTABLE_BIG_INTEGER is
- once
- create Result.from_integer(0)
- end
-
- Real_base: REAL_64 is
- once
- Result := (0x0000000100000000).force_to_real_64
- end
-
- add_magnitude (other: like Current) is
- -- Add the magnitude of `Current' and `other' regardless of signs.
- require
- not is_zero
- not other.is_zero
- local
- a, b: like Current; inc: BOOLEAN; i, j, k, n: INTEGER; new_storage, a_storage, b_storage: like storage
- new_capacity, a_capacity, a_offset, a_integer_length, b_offset, b_integer_length: INTEGER
- do
- --|*** First tests can be certainely optimized.
- --|*** (Vincent Croizier, 26/03/2004)
- if integer_length > other.integer_length and then capacity - offset > integer_length then
- ---- Add in place (`offset' doesn't change)
- -- Add common parts of both numbers:
- from
- i := offset
- j := other.offset
- n := j + other.integer_length
- until
- j = n
- loop
- if inc then
- -- overflow in the last addition step
- inc := mbi_add_with_inc(item(i), other.item(j), storage_at(storage, i))
- else
- -- no overflow in the last addition step
- inc := mbi_add(item(i), other.item(j), storage_at(storage, i))
- end
- i := i + 1
- j := j + 1
- end
- -- Add remainder of the longer number with increment (if necessary):
- from
- n := offset + integer_length
- until
- not inc or else i = n
- loop
- inc := mbi_inc(storage_at(storage, i))
- i := i + 1
- end
- if inc then
- storage.put(1, n)
- check
- n < capacity
- end
- integer_length := integer_length + 1
- end
- else
- ---- Add, after this `offset' will be 0
- -- Set `a' to the longest number and `b' to the smallest.
- if integer_length >= other.integer_length then
- a := Current
- b := other
- else
- a := other
- b := Current
- end
- a_capacity := a.capacity
- a_storage := a.storage
- b_storage := b.storage
- a_integer_length := a.integer_length
- b_integer_length := b.integer_length
- a_offset := a.offset
- b_offset := b.offset -- Verify capacity
- if capacity < a_integer_length then
- new_capacity := capacity_from_lower_bound(capacity, a_integer_length)
- new_storage := new_storage.calloc(new_capacity)
- elseif capacity = a_integer_length then
- --|*** It's possible to make a more restrictive test
- --|*** that can exclude more case of reallocation. (Vincent Croizier, 24/03/2004)
- new_capacity := capacity_from_lower_bound(capacity, a_integer_length + 1)
- new_storage := new_storage.calloc(new_capacity)
- elseif a = other then
- -- protect `other'
- new_storage := a_storage.calloc(a_capacity)
- new_capacity := a_capacity
- else
- new_storage := a_storage
- new_capacity := a_capacity
- end
- -- Add common parts of both numbers:
- n := b_integer_length
- check
- n.in_range(0, new_capacity)
- end
- from
- i := a_offset
- j := b_offset -- k := 0
- until
- k = n
- loop
- if inc then
- -- overflow in the last addition step
- inc := mbi_add_with_inc(a_storage.item(i), b_storage.item(j), storage_at(new_storage, k))
- else
- -- no overflow in the last addition step
- inc := mbi_add(a_storage.item(i), b_storage.item(j), storage_at(new_storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- -- Add remainder of the longer number with increment (if necessary):
- from
- n := a_integer_length
- until
- not inc or else k = a_integer_length
- loop
- new_storage.put(a_storage.item(i), k)
- inc := mbi_inc(storage_at(new_storage, k))
- i := i + 1
- k := k + 1
- end
- if inc then
- new_storage.put(1, k)
- check
- n < new_capacity
- end
- n := n + 1
- else
- -- copy the reste of `a'
- from
- until
- k = n
- loop
- new_storage.put(a_storage.item(i), k)
- i := i + 1
- k := k + 1
- end
- end
- capacity := new_capacity
- storage := new_storage
- integer_length := n
- offset := 0
- end
- end
-
-feature {MUTABLE_BIG_INTEGER} -- Implementation:
- subtract_magnitude (other: like Current) is
- -- Subtract `other' from `Current' (The result is placed in `Current')
- -- and change `negative' (the sign) if necessary.
- require
- not is_zero
- not other.is_zero
- local
- i, j, v1, v2: INTEGER; test: BOOLEAN; new: like Current
- do
- -- Compare the number
- if integer_length = other.integer_length then
- -- Compare the most significant part of the numbers
- from
- i := offset + integer_length - 1
- j := other.offset + integer_length - 1
- v1 := item(i)
- v2 := other.item(j)
- test := v1 /= v2
- until
- test or else i = offset
- loop
- integer_length := integer_length - 1
- i := i - 1
- j := j - 1
- v1 := item(i)
- v2 := other.item(j)
- test := v1 /= v2
- end
- if test then
- if unsigned_greater_than(v1, v2) then
- -- Current > other
- subtract_magnitude_raw_truncated(other)
- if storage.item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- integer_length /= 0 implies item(integer_length - 1) /= 0
- end
- end
- else
- -- Current < other
- check
- unsigned_less_than(v1, v2)
- end
- negative := not negative
- subtract_magnitude_raw_reverse_truncated(other)
- if storage.item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- integer_length /= 0 implies item(integer_length - 1) /= 0
- end
- end
- end
- else
- -- Current = other
- set_with_zero
- end
- elseif integer_length > other.integer_length then
- subtract_magnitude_raw(other)
- elseif capacity >= other.integer_length then
- negative := not negative
- subtract_magnitude_raw_reverse(other)
- else
- -- Reallocation
- --|*** Can be faster (Vincent Croizier, 10/06/04) ***
- create new.copy(other)
- new.subtract_magnitude(Current)
- negative := not negative
- integer_length := new.integer_length
- storage := new.storage
- offset := new.offset
- end
- end
-
- subtract_magnitude_raw (other: like Current) is
- -- Subtract (raw) the storage of `other' from `Current'.
- -- Used by `subtract_magnitude'.
- require
- not is_zero
- not other.is_zero
- abs_compare(other) = 1
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := other.integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(item(i), other.item(j), storage_at(storage, k))
- else
- dec := mbi_subtract(item(i), other.item(j), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- from
- until
- not dec
- loop
- --|*** Could be done in one step with a mbi_dec_bis
- --| routine (Vincent Croizier, 10/06/04) ***
- put(item(i), k)
- dec := mbi_dec(storage_at(storage, k))
- i := i + 1
- k := k + 1
- end
- if k = integer_length then
- from
- k := k - 1
- until
- item(k) /= 0
- loop
- k := k - 1
- end
- integer_length := k + 1
- end
- offset := 0
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_reverse (other: like Current) is
- -- Subtract (raw) the storage of `Current' from `other' and
- -- put it in `Current'.
- -- Used by `subtract_magnitude'.
- require
- not is_zero
- not other.is_zero
- abs_compare(other) = -1
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- -- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(other.item(j), item(i), storage_at(storage, k))
- else
- dec := mbi_subtract(other.item(j), item(i), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- from
- until
- not dec
- loop
- --|*** Could be done in one step with a mbi_dec_bis
- --| routine (Vincent Croizier, 10/06/04) ***
- put(other.item(j), k)
- dec := mbi_dec(storage_at(storage, k))
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- up := other.integer_length
- if k < up then
- from
- until
- k = up
- loop
- put(other.item(j), k)
- j := j + 1
- k := k + 1
- end
- integer_length := up
- else
- check
- k = up
- end
- from
- k := k - 1
- until
- storage.item(k) /= 0
- loop
- k := k - 1
- end
- integer_length := k + 1
- offset := 0
- end
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_truncated (other: like Current) is
- -- Subtract (raw) the storage of `other' from `Current'
- -- where `other' is truncated to the size of `Current'.
- -- Used by `subtract_magnitude'.
- require
- not other.is_zero
- other.integer_length >= integer_length
- unsigned_greater_than(item(offset + integer_length - 1), other.item(offset + integer_length - 1))
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(item(i), other.item(j), storage_at(storage, k))
- else
- dec := mbi_subtract(item(i), other.item(j), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- offset := 0
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_reverse_truncated (other: like Current) is
- -- Subtract (raw) the storage of `Current' from `other' and
- -- put it in `Current',
- -- where `other' is truncated to the size of `Current'.
- -- Used by `subtract_magnitude'.
- require
- not other.is_zero
- other.integer_length >= integer_length
- unsigned_less_than(item(offset + integer_length - 1), other.item(offset + integer_length - 1))
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(other.item(j), item(i), storage_at(storage, k))
- else
- dec := mbi_subtract(other.item(j), item(i), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- offset := 0
- ensure
- offset = 0
- end
-
-feature {} -- For printing
- char_buffer: FAST_ARRAY[CHARACTER] is
- once
- create Result.make(4096)
- end
-
- append_in_char_buffer: INTEGER is
- -- Tool for `append_in' and `append_in_unicode'.
- -- Put absolute value of Current in `char_buffer' and return
- -- the number of characteres really used.
- require
- is_printable
- not is_zero
- local
- base, max_char, i, r: INTEGER
- do
- -- Allocate space in `char_buffer'
- max_char := integer_length * 9 + (2 * integer_length + 2) #// 3
- if char_buffer.capacity < max_char then
- char_buffer.resize(max_char)
- end
- -- Begin of extracting digits
- register1.copy(Current)
- base := 1000000000
- from
- r := register1.divide_one_word(base)
- until
- register1.is_zero
- loop
- check
- r >= 0
- end
- from
- i := 9
- until
- r = 0
- loop
- char_buffer.put((r #\\ 10).decimal_digit, Result)
- r := r #// 10
- Result := Result + 1
- i := i - 1
- end
- from
- until
- i = 0
- loop
- char_buffer.put('0', Result)
- Result := Result + 1
- i := i - 1
- end
- -- extract next digit group
- r := register1.divide_one_word(base)
- end
- from
- check
- r > 0
- end
- until
- r = 0
- loop
- char_buffer.put((r #\\ 10).decimal_digit, Result)
- r := r #// 10
- Result := Result + 1
- end
- end
-
-feature {} -- Tools for capacity:
- capacity_from_lower_bound (actual_capacity, needed_capacity: INTEGER): INTEGER is
- -- Give the smallest power of 2 greater than
- -- `needed_capacity' and `actual_capacity'.
- -- Based on `actual_capacity' (the actual capacity).
- require
- actual_capacity.is_a_power_of_2
- actual_capacity >= 4
- do
- from
- Result := actual_capacity
- until
- Result >= needed_capacity
- loop
- Result := Result.bit_shift_left(1)
- end
- ensure
- Result.is_a_power_of_2
- Result >= 4
- Result >= actual_capacity
- Result >= needed_capacity
- Result = actual_capacity or Result #// 2 < needed_capacity
- end
-
- capacity_from_upper_bound (actual_capacity, needed_capacity: INTEGER): INTEGER is
- -- Give the smallest power of 2 greater than `needed_capacity'.
- -- Based on `actual_capacity' (the actual capacity).
- require
- actual_capacity >= 4
- actual_capacity >= needed_capacity
- actual_capacity.is_a_power_of_2
- local
- v: INTEGER
- do
- from
- Result := actual_capacity
- v := Result.bit_shift_right(1)
- until
- v < needed_capacity or else v = 2
- loop
- Result := v
- v := Result.bit_shift_right(1)
- end
- ensure
- Result.is_a_power_of_2
- Result <= actual_capacity
- Result >= needed_capacity
- Result = 4 or Result.bit_shift_right(1) < needed_capacity
- end
-
-feature {}
- unsigned_less_than (a, b: INTEGER): BOOLEAN is
- -- Unsigned "<".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_less_than"
- }"
- end
-
- unsigned_greater_than (a, b: INTEGER): BOOLEAN is
- -- Unsigned ">".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_greater_than"
- }"
- end
-
- unsigned_greater_or_equal (a, b: INTEGER): BOOLEAN is
- -- Unsigned ">=".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_greater_or_equal"
- }"
- end
-
- unsigned_32_to_integer_64 (integer_32: INTEGER): INTEGER_64 is
- -- Return the unsigned value of the `integer_32'.
- --
- --|*** Ajouter ou pas cette fonction dans INTEGER_32 ? plug_in ou built_in ?(Dom. 27/02/2004) ***
- --
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_32_to_integer_64"
- }"
- end
-
- storage_at (s: like storage; n: INTEGER): POINTER is
- -- Give the address of the corresponding word of `s'.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_storage_at"
- }"
- end
-
- mbi_inc (integer_32_adr: POINTER): BOOLEAN is
- -- Increment the value at `integer_32_adr'. The `Result' is True only in case of overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_inc"
- }"
- end
-
- mbi_add (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a + b
- -- Overflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_add"
- }"
- end
-
- mbi_add_with_inc (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a + b + 1
- -- Overflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_add_with_inc"
- }"
- end
-
- mbi_dec (integer_32_adr: POINTER): BOOLEAN is
- -- Put a - 1 in the item n in the NATIVE_ARRAY t.
- -- t.item(n) := a - 1
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_dec"
- }"
- end
-
- mbi_subtract (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a - b
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_subtract"
- }"
- end
-
- mbi_subtract_with_dec (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a - b - 1
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_subtract_with_dec"
- }"
- end
-
- mbi_multiply (a, b: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply"
- }"
- end
-
- mbi_multiply_with_add (a, b, c: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b + c in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply_with_add"
- }"
- end
-
- mbi_multiply_with_2_add (a, b, c, d: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b + c + d in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply_with_2_add"
- }"
- end
-
- mbi_divide (u1, u0, d: INTEGER; r_int32adr: POINTER): INTEGER_32 is
- -- Divide `u1u0' by `d', put the remainder in `r' and return the quotient.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_divide"
- }"
- end
-
- string_buffer: STRING is
- once
- create Result.make(128)
- end
-
- unicode_string_buffer: UNICODE_STRING is
- once
- create Result.make(128)
- end
-
-invariant
- capacity > 0
- storage.is_not_null
- integer_length.in_range(0, capacity)
- integer_length /= 0 implies offset.in_range(0, capacity - integer_length) and item(offset + integer_length - 1) /= 0
- integer_length = 0 implies not negative
- capacity.is_a_power_of_2
-
-end -- class MUTABLE_BIG_INTEGER
---
--- ------------------------------------------------------------------------------------------------------------
--- Copyright notice below. Please read.
---
--- This file is part of the SmartEiffel standard library.
--- Copyright(C) 1994-2002: INRIA - LORIA (INRIA Lorraine) - ESIAL U.H.P. - University of Nancy 1 - FRANCE
--- Copyright(C) 2003-2006: INRIA - LORIA (INRIA Lorraine) - I.U.T. Charlemagne - University of Nancy 2 - FRANCE
---
--- Authors: Dominique COLNET, Philippe RIBET, Cyril ADRIAN, Vincent CROIZIER, Frederic MERIZEN
---
--- Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
--- documentation files (the "Software"), to deal in the Software without restriction, including without
--- limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
--- the Software, and to permit persons to whom the Software is furnished to do so, subject to the following
--- conditions:
---
--- The above copyright notice and this permission notice shall be included in all copies or substantial
--- portions of the Software.
---
--- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
--- LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
--- EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
--- AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
--- OR OTHER DEALINGS IN THE SOFTWARE.
---
--- http://SmartEiffel.loria.fr - SmartEiffel at loria.fr
--- ------------------------------------------------------------------------------------------------------------
diff --git a/lib2/number/integer_big.li b/lib2/number/integer_big.li
deleted file mode 100644
index 4e8707f..0000000
--- a/lib2/number/integer_big.li
+++ /dev/null
@@ -1,3263 +0,0 @@
-Section Header
-
- + name := INTEGER_BIG;
-
- - comment :=
- " A class used to represent multiprecision integers that makes efficient use \
- \ of allocated space by allowing a number to occupy only part of an array so \
- \ that the arrays do not have to be reallocated as often. When performing an \
- \ operation with many iterations the array used to hold a number is only \
- \ reallocated when necessary and does not have to be the same size as the \
- \ number it represents. A mutable number allows calculations to occur on the \
- \ same number without having to create a new number for every step of the \
- \ calculation as it occurs with NUMBERs.";
-
-Section Inherit
-
- - parent_hashable:HASHABLE := HASHABLE;
-
- - parent_comparable:COMPARABLE := COMPARABLE;
-
-Section Insert
-
- - parent_object:OBJECT := OBJECT;
-
-Section Public
-
-creation {ANY}
- from_integer, from_integer_64, from_string, copy
-
- //
- // Creation / initialization from INTEGER_32 or INTEGER_64:
- //
-
- - from_integer value:INTEGER :SELF <-
- // Create or initialize `Current' using `value' as an initializer.
- (
- (capacity = 0).if {
- storage := storage.calloc 4;
- capacity := 4;
- };
- offset := 0;
- (value > 0).if {
- negative := FALSE;
- put value to 0;
- integer_length := 1;
- }.elseif {value < 0} then {
- negative := TRUE;
- put(#-value, 0)
- integer_length := 1;
- } else {
- ? {value = 0};
- set_with_zero;
- };
- )
- [
- ? {to_integer_32 = value};
- ];
-
- is_integer_32: BOOLEAN is
- -- Does `Current' fit on an INTEGER_32?
- do
- if integer_length = 0 then
- Result := True
- elseif integer_length = 1 then
- if item(offset) > 0 then
- Result := True
- elseif negative then
- Result := item(offset) = 0x80000000
- end
- end
- ensure
- Result implies is_integer_64
- Result implies integer_length <= 1
- end
-
- is_integer: BOOLEAN is
- obsolete "Now use `is_integer_32' instead (march 2006)."
- do
- Result := is_integer_32
- end
-
- to_integer_32: INTEGER is
- -- Convert `Current' as a 32 bit INTEGER.
- require
- is_integer_32
- do
- if integer_length > 0 then
- Result := item(offset)
- if negative then
- Result := #-Result
- end
- end
- end
-
- to_integer: INTEGER is
- obsolete "Now use `to_integer_32' instead (march 2006)."
- do
- Result := to_integer_32
- end
-
- from_integer_64 (value: INTEGER_64) is
- -- Create or set `Current' using `value' as an initializer.
- local
- v32: INTEGER
- do
- if capacity < 2 then
- storage := storage.calloc(4)
- capacity := 4
- end
- if value > 0 then
- negative := False
- put(value.low_32, 0)
- offset := 0
- v32 := value.high_32
- if v32 = 0 then
- integer_length := 1
- else
- put(v32, 1)
- integer_length := 2
- end
- elseif value < 0 then
- negative := True
- put((#-value).low_32, 0)
- offset := 0
- v32 := (#-value).high_32
- if v32 = 0 then
- integer_length := 1
- else
- put(v32, 1)
- integer_length := 2
- end
- else
- check
- value = 0
- end
- set_with_zero
- end
- ensure
- to_integer_64 = value
- end
-
- is_integer_64: BOOLEAN is
- -- Does `Current' fit on an INTEGER_64?
- do
- if integer_length <= 1 then
- Result := True
- elseif integer_length = 2 then
- if negative then
- if item(offset + 1) > 0 then
- Result := True
- elseif item(offset) = 0 then
- Result := item(offset + 1) = 0x80000000
- end
- else
- Result := item(offset + 1) > 0
- end
- end
- ensure
- not Result implies not is_integer_32
- Result implies integer_length <= 2
- end
-
- to_integer_64: INTEGER_64 is
- -- Convert `Current' as a INTEGER_64.
- require
- is_integer_64
- local
- v: INTEGER_64
- do
- inspect
- integer_length
- when 0 then
- when 1 then
- Result := unsigned_32_to_integer_64(item(offset))
- if negative then
- Result := -Result
- end
- when 2 then
- Result := unsigned_32_to_integer_64(item(offset))
- v := item(offset + 1)
- v := v.bit_shift_left(32)
- Result := Result.bit_xor(v)
- if negative then
- Result := #-Result
- end
- end
- end
-
-feature {ANY} -- Creation / initialization from STRING:
- from_string (str: STRING) is
- -- Create or initialize `Current' using `value' as an
- -- initializer. (value = [-][0-9]^+)
- local
- i: INTEGER; cc: CHARACTER; neg: BOOLEAN; ten: like Current
- do
- --|*** This feature should be improved one day... (Vincent Croizier, 25/12/2004)
- create ten.from_integer(10)
- from
- i := 1
- variant
- str.count - i
- until
- not str.item(i).is_separator
- loop
- i := i + 1
- end
- cc := str.item(i)
- i := i + 1
- if cc = '+' then
- cc := str.item(i)
- i := i + 1
- elseif cc = '-' then
- neg := True
- cc := str.item(i)
- i := i + 1
- end
- check
- cc.is_digit
- end
- from_integer(cc.value)
- from
- variant
- str.count - i
- until
- i > str.count
- loop
- cc := str.item(i)
- if cc.is_digit then
- multiply(ten)
- add_integer(cc.value)
- else
- check
- cc.is_separator
- end
- i := str.count -- terminate the loop
- end
- i := i + 1
- end
- if neg then
- negate
- end
- end
-
-feature {ANY} -- Conversion tool
- force_to_real_64: REAL_64 is
- -- only a tool
- -- unsigned conversion *** require ou changer export ? *** (Dom Oct 4th 2004) ***
- local
- i: INTEGER
- do
- from
- i := offset + integer_length - 1
- until
- i < offset or else Result > Maximum_real_64
- loop
- Result := Result * Real_base + unsigned_32_to_integer_64(storage.item(i)).force_to_real_64
- i := i - 1
- end
- if Result = Maximum_real_64 and then storage.item(offset) /= 0 then
- Result := Maximum_real_64 * 2
- end
- if negative then
- Result := -Result
- end
- end
-
-feature {NUMBER}
- from_native_array (na: NATIVE_ARRAY[INTEGER]; cap: INTEGER; neg: BOOLEAN) is
- require
- na.item(cap - 1) /= 0
- do
- negative := neg
- offset := 0
- integer_length := cap
- if cap > capacity then
- capacity := capacity_from_lower_bound(capacity, cap)
- storage := storage.calloc(capacity)
- end
- storage.slice_copy(0, na, 0, cap - 1)
- end
-
- to_integer_general_number: INTEGER_GENERAL_NUMBER is
- local
- na: like storage
- do
- if is_integer_64 then
- create {INTEGER_64_NUMBER} Result.make(to_integer_64)
- else
- na := storage.calloc(integer_length)
- na.slice_copy(0, storage, offset, offset + integer_length - 1)
- create {BIG_INTEGER_NUMBER} Result.from_native_array(na, integer_length, negative)
- end
- end
-
-feature {ANY} -- Addition:
- add (other: like Current) is
- -- Add `other' into `Current'.
- --
- -- See also `add_integer', `add_integer_64', `add_natural'.
- require
- other /= Void
- do
- -- Choose the appropriate absolute operator depending on `Current' and `other' sign.
- if other.integer_length = 0 then
- -- Nothing to do, `Current' remains unchanged.
- elseif integer_length = 0 then
- -- `Current' is zero so simply copy the value of other
- Current.copy(other)
- elseif negative = other.negative then
- -- same sign
- add_magnitude(other)
- else
- -- different sign
- subtract_magnitude(other)
- end
- end
-
- add_to (other, res: like Current) is
- -- Add `other' and `Current', and put the result in `res'.
- require
- other /= Void
- res /= Void
- res /= Current
- res /= other
- do
- --|*** Must be optimized later (Vincent Croizier, 15/07/04) ***
- res.copy(Current)
- res.add(other)
- end
-
- add_integer (other: INTEGER) is
- -- Add `other' into `Current'.
- local
- inc: BOOLEAN; v, i, n: INTEGER
- do
- if other = 0 then
- -- Nothing to do, `Current' remains unchanged
- elseif integer_length = 0 then
- -- `Current' is null so simply copy the value of other
- from_integer(other)
- elseif negative = (other < 0) then
- -- Same sign
- if other < 0 then
- v := #-other
- else
- v := other
- end
- -- Add `v' into `storage'
- from
- inc := mbi_add(item(offset), v, storage_at(storage, offset))
- i := offset + 1
- n := offset + integer_length
- until
- not inc or else i >= n
- loop
- inc := mbi_inc(storage_at(storage, i))
- i := i + 1
- end
- if inc then
- check
- i = n
- end
- -- Extend the number length by 1
- if n < capacity then
- integer_length := integer_length + 1
- put(1, n)
- else
- -- It's good only if the reallocation initialize
- -- `storage' with 0.
- v := item(offset)
- capacity := capacity * 2
- storage := storage.calloc(capacity)
- offset := 0
- put(v, 0)
- put(1, integer_length)
- integer_length := integer_length + 1
- end
- end
- -- Different sign
- elseif integer_length = 1 then
- if other < 0 then
- v := #-other
- else
- v := other
- end
- if mbi_subtract(item(offset), v, storage_at(storage, offset)) then
- negative := not negative
- put(-item(offset), offset)
- end
- if item(offset) = 0 then
- integer_length := 0
- negative := False
- end
- else
- if other < 0 then
- v := #-other
- else
- v := other
- end
- if mbi_subtract(item(offset), v, storage_at(storage, offset)) then
- from
- i := offset + 1
- inc := mbi_dec(storage_at(storage, i))
- n := offset + integer_length - 1
- until
- not inc
- loop
- check
- i < n
- end
- i := i + 1
- inc := mbi_dec(storage_at(storage, i))
- end
- if item(n) = 0 then
- integer_length := integer_length - 1
- end
- end
- end
- end
-
- add_integer_64 (other: INTEGER_64) is
- -- Add `other' into `Current'.
- do
- register1.from_integer_64(other)
- add(register1)
- end
-
- add_natural (other: like Current) is
- -- Same behavior as `add', but this one works only when `Current'
- -- and `other' are both positive numbers and are both greater than
- -- zero. The only one advantage of using `add_natural' instead of the
- -- general `add' is the gain of efficiency.
- require
- not is_zero and not is_negative
- not other.is_zero and not other.is_negative
- do
- add_magnitude(other)
- end
-
-feature {ANY} -- Subtract:
- subtract (other: like Current) is
- -- Subtract `other' from `Current'.
- require
- other /= Void
- do
- if other = Current then
- set_with_zero
- elseif other.integer_length = 0 then
- -- nothing to do, `Current' remains unchanged
- elseif integer_length = 0 then
- -- current is null so simply copy the value of other, the sign is also fixed
- copy(other)
- negative := not other.negative
- elseif negative = other.negative then
- -- same sign
- subtract_magnitude(other)
- else
- -- different sign
- add_magnitude(other)
- end
- end
-
- subtract_to (other, res: like Current) is
- -- Subtract `other' from `Current' and put it in `res'.
- require
- other /= Void
- res /= Void
- res /= Current
- res /= other
- do
- --|*** Must be optimized later (Vincent Croizier, 15/07/04) ***
- res.copy(Current)
- res.subtract(other)
- end
-
- subtract_integer (other: INTEGER) is
- do
- if other = Minimum_integer then
- add_integer(1)
- add_integer(Maximum_integer)
- else
- add_integer(-other)
- end
- end
-
-feature {ANY} -- To divide:
- divide (other: like Current) is
- -- Put the the quotient of the Euclidian division of
- -- `Current' by `other' in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- other /= Current
- do
- -- `divide_with_remainder_to' already use `register1'.
- divide_with_remainder_to(other, register2)
- end
-
- mod (other: like Current) is
- -- Put the the remainder of the Euclidian division of
- -- `Current' by `other' in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- other /= Current
- local
- quotient: like Current
- do
- --|*** Must be optimized (Vincent Croizier, 12/07/04) ***
- create quotient.from_integer(0)
- remainder_with_quotient_to(other, quotient)
- ensure
- not negative and abs_compare(other) = -1
- end
-
- divide_with_remainder_to (other, remainder: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'.
- -- Quotient is put in `Current'.
- -- (The contents of `other' is not changed.)
- require
- not other.is_zero
- remainder /= Void
- remainder /= other
- remainder /= Current
- do
- Current.remainder_with_quotient_to(other, remainder)
- Current.swap_with(remainder)
- ensure
- not remainder.negative and remainder.abs_compare(other) = -1
- end
-
- remainder_with_quotient_to (other, quotient: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'.
- -- Remainder is put in `Current'.
- -- (The contents of `other' is not changed.)
- --
- -- Note: Uses Algorithm D in Knuth section 4.3.1.
- require
- not other.is_zero
- quotient /= Void
- quotient /= other
- quotient /= Current
- local
- cmp, shift, dlen, qlen, j, k, v1, v2, u1, u2, rem: INTEGER; qhat, rhat, v2qhat_1, v2qhat_2, d_offset: INTEGER
- q_storage, d_storage: like storage; q_capacity: like capacity; current_negative, borrow: BOOLEAN
- do
- if integer_length = 0 then
- -- Dividend is zero:
- quotient.set_with_zero
- set_with_zero
- else
- current_negative := negative
- cmp := Current.abs_compare(other)
- if cmp < 0 then
- -- Dividend less than divisor:
- quotient.set_with_zero
- -- Sign correction
- set_negative(False)
- divide_sign_correction_bis(other, quotient, current_negative)
- elseif cmp = 0 then
- -- Dividend equal to divisor:
- if negative = other.negative then
- quotient.from_integer(1)
- else
- quotient.from_integer(-1)
- end
- set_with_zero
- elseif other.integer_length = 1 then
- -- Special case one word divisor:
- quotient.swap_with(Current)
- --|*** replace by "from_unsigned_integer" ? (Vincent Croizier)
- set_with_zero
- rem := quotient.divide_one_word(other.item(other.offset))
- if rem /= 0 then
- put(rem, 0)
- set_integer_length(1)
- else
- check
- is_zero
- end
- end
- -- Sign correction
- divide_sign_correction_bis(other, quotient, current_negative)
- else
- -- Copy divisor storage to protect divisor:
- register1.copy(other)
- -- D1 normalize the divisor:
- shift := register1.normalize
- if shift /= 0 then
- shift_left(shift)
- end
- -- D2 Initialize j:
- from
- d_storage := register1.storage
- d_offset := register1.offset
- dlen := register1.integer_length
- j := offset + integer_length - 1
- u2 := storage.item(j)
- k := register1.offset + dlen - 1
- v1 := register1.item(k)
- v2 := register1.item(k - 1)
- if unsigned_greater_or_equal(u2, v1) then
- k := integer_length - dlen
- qlen := k + 1
- else
- qlen := integer_length - dlen
- k := qlen - 1
- j := j - 1
- u1 := u2
- u2 := storage.item(j)
- end
- -- Resize quotient if necessary
- q_capacity := quotient.capacity
- if q_capacity < qlen then
- -- reallocation
- q_capacity := capacity_from_lower_bound(q_capacity, qlen)
- q_storage := storage.calloc(q_capacity)
- else
- q_storage := quotient.storage
- end
- -- To avoid invariant violation on `quotient'
- quotient.set_with_zero
- until
- k < 0
- loop
- j := j - 1 -- D3 Calculate qhat - estimate qhat
- if u1 = v1 then
- qhat := ~0
- else
- qhat := mbi_divide(u1, u2, v1, $rhat) -- Correct qhat
- if qhat = 0 then
- else
- v2qhat_1 := mbi_multiply(v2, qhat, $v2qhat_2)
- if unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- if mbi_subtract(v2qhat_2, v2, $v2qhat_2) then
- v2qhat_1 := v2qhat_1 - 1
- end
- if mbi_add(rhat, v1, $rhat) then
- elseif unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, storage.item(j)) then
- qhat := qhat - 1
- end
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, storage.item(j)) then
- qhat := qhat - 1
- end
- end
- end
- -- D4 Multiply and subtract:
- if qhat = 0 then
- q_storage.put(0, k)
- else
- borrow := multiply_and_subtract(u1, qhat, d_storage, d_offset, storage, j - dlen + 2, dlen)
- -- D5 Test remainder: Result is negative ?
- if borrow then
- -- D6 Add back
- borrow := add_back(u1, d_storage, d_offset, storage, j - dlen + 2, dlen)
- check
- borrow
- end
- q_storage.put(qhat - 1, k)
- else
- q_storage.put(qhat, k)
- end
- end
- -- D7 loop on j
- k := k - 1
- u1 := storage.item(j + 1)
- u2 := storage.item(j)
- end
- -- Remove leading zero of quotient
- k := qlen - 1
- if q_storage.item(k) = 0 then
- qlen := k
- end
- quotient.set_all(q_storage, q_capacity, qlen, 0, False)
- -- Remove leading zero of remainder
- from
- j := dlen - 1
- until
- j < 0 or else storage.item(j) /= 0
- loop
- j := j - 1
- end
- j := j + 1
- check
- j >= 0
- end
- if j = 0 then
- set_with_zero
- else
- offset := 0
- integer_length := j
- negative := False
- end
- -- D8 Unnormalize:
- if shift > 0 then
- shift_right(shift)
- end
- -- Sign correction
- divide_sign_correction_bis(other, quotient, current_negative)
- end
- end
- ensure
- not negative and abs_compare(other) = -1
- end
-
- divide_to (other, quotient, remainder: like Current) is
- -- Euclidian division.
- -- Calculates the `quotient' and `remainder' of `Current'
- -- divided by `other'. (The contents of `Current' and `other' are
- -- not changed.)
- --
- -- Note: Uses Algorithm D in Knuth section 4.3.1.
- require
- not other.is_zero
- quotient /= Void
- remainder /= Void
- quotient /= other
- quotient /= Current
- remainder /= other
- remainder /= Current
- local
- cmp, shift, nlen, dlen, qlen, j, k, v1, v2, u1, u2, rem: INTEGER
- qhat, rhat, v2qhat_1, v2qhat_2, d_offset: INTEGER; q_storage, r_storage, d_storage: like storage
- q_capacity, r_capacity: like capacity; borrow: BOOLEAN
- do
- if integer_length = 0 then
- -- Dividend is zero:
- quotient.set_with_zero
- remainder.set_with_zero
- else
- cmp := Current.abs_compare(other)
- if cmp < 0 then
- -- Dividend less than divisor:
- quotient.set_with_zero
- remainder.copy(Current)
- -- Sign correction
- remainder.set_negative(False)
- divide_sign_correction(other, quotient, remainder)
- elseif cmp = 0 then
- -- Dividend equal to divisor:
- if negative = other.negative then
- quotient.from_integer(1)
- else
- quotient.from_integer(-1)
- end
- remainder.set_with_zero
- elseif other.integer_length = 1 then
- -- Special case one word divisor:
- quotient.copy(Current)
- --|*** replace by "from_unsigned_integer" ? (Vincent Croizier)
- remainder.set_with_zero
- rem := quotient.divide_one_word(other.item(other.offset))
- if rem /= 0 then
- remainder.put(rem, 0)
- remainder.set_ilo(1, 0)
- else
- check
- remainder.is_zero
- end
- end
- -- Sign correction
- divide_sign_correction(other, quotient, remainder)
- else
- -- Copy divisor storage to protect divisor:
- register1.copy(other)
- --|***
- remainder.copy(Current)
- -- D1 normalize the divisor:
- shift := register1.normalize
- if shift /= 0 then
- remainder.shift_left(shift)
- end
- -- D2 Initialize j:
- from
- r_storage := remainder.storage
- r_capacity := remainder.capacity
- check
- remainder.offset = 0
- end
- nlen := remainder.integer_length -- To avoid invariant class violation
- remainder.set_with_zero
- d_storage := register1.storage
- d_offset := register1.offset
- dlen := register1.integer_length
- j := nlen - 1
- u2 := r_storage.item(j)
- k := register1.offset + dlen - 1
- v1 := register1.item(k)
- v2 := register1.item(k - 1)
- if unsigned_greater_or_equal(u2, v1) then
- k := nlen - dlen
- qlen := k + 1
- else
- qlen := nlen - dlen
- k := qlen - 1
- j := j - 1
- u1 := u2
- u2 := r_storage.item(j)
- end
- -- Resize quotient if necessary
- q_capacity := quotient.capacity
- if q_capacity < qlen then
- -- reallocation
- q_capacity := capacity_from_lower_bound(q_capacity, qlen)
- q_storage := storage.calloc(q_capacity)
- else
- q_storage := quotient.storage
- end
- -- To avoid invariant violation on `quotient'
- quotient.set_with_zero
- until
- k < 0
- loop
- j := j - 1 -- D3 Calculate qhat - estimate qhat
- if u1 = v1 then
- qhat := ~0
- else
- qhat := mbi_divide(u1, u2, v1, $rhat) -- Correct qhat
- if qhat = 0 then
- else
- v2qhat_1 := mbi_multiply(v2, qhat, $v2qhat_2)
- if unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- if mbi_subtract(v2qhat_2, v2, $v2qhat_2) then
- v2qhat_1 := v2qhat_1 - 1
- end
- if mbi_add(rhat, v1, $rhat) then
- elseif unsigned_greater_than(v2qhat_1, rhat) then
- qhat := qhat - 1
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, r_storage.item(j)) then
- qhat := qhat - 1
- end
- elseif j < 0 then
- if v2qhat_1 = rhat and then v2qhat_2 /= 0 then
- qhat := qhat - 1
- end
- elseif v2qhat_1 = rhat and then unsigned_greater_than(v2qhat_2, r_storage.item(j)) then
- qhat := qhat - 1
- end
- end
- end
- -- D4 Multiply and subtract:
- if qhat = 0 then
- q_storage.put(0, k)
- else
- borrow := multiply_and_subtract(u1, qhat, d_storage, d_offset, r_storage, j - dlen + 2, dlen)
- -- D5 Test remainder: Result is negative ?
- if borrow then
- -- D6 Add back
- borrow := add_back(u1, d_storage, d_offset, r_storage, j - dlen + 2, dlen)
- check
- borrow
- end
- q_storage.put(qhat - 1, k)
- else
- q_storage.put(qhat, k)
- end
- end
- -- D7 loop on j
- k := k - 1
- u1 := r_storage.item(j + 1)
- u2 := r_storage.item(j)
- end
- -- Remove leading zero of quotient
- k := qlen - 1
- if q_storage.item(k) = 0 then
- qlen := k
- end
- quotient.set_all(q_storage, q_capacity, qlen, 0, False)
- -- Remove leading zero of remainder
- from
- j := dlen - 1
- until
- j < 0 or else r_storage.item(j) /= 0
- loop
- j := j - 1
- end
- j := j + 1
- check
- j >= 0
- end
- if j = 0 then
- check
- remainder.is_zero
- end
- else
- remainder.set_all(r_storage, r_capacity, j, 0, False)
- end
- -- D8 Unnormalize:
- if shift > 0 then
- remainder.shift_right(shift)
- end
- -- Sign correction
- divide_sign_correction(other, quotient, remainder)
- end
- end
- ensure
- is_a_good_divide(other, quotient, remainder)
- not remainder.negative and remainder.abs_compare(other) = -1
- end
-
- shift_left (n: INTEGER) is
- -- Shift bits of magnitude by `n' position left. (Note that no bit can
- -- be lost because the `storage' area is automatically extended when
- -- it is necessary.)
- require
- n > 0
- local
- new_storage: like storage; left, right: INTEGER_8
- new_capacity, new_integer_length, new_head, word_shift, i, j, k, val1, val2, val3: INTEGER
- do
- if integer_length > 0 then
- word_shift := n |>>> 5
- left := (n & 0x0000001F).to_integer_8 -- Optimistic prediction
- new_integer_length := integer_length + word_shift
- if left = 0 then
- -- Just word shift
- if offset >= word_shift then
- -- no need to deplace the number in the storage
- from
- i := offset
- offset := offset - word_shift
- integer_length := new_integer_length
- until
- i = offset
- loop
- i := i - 1
- put(0, i)
- end
- elseif capacity >= new_integer_length then
- -- deplacing the number
- from
- i := offset + integer_length - 1
- j := word_shift + integer_length - 1
- until
- i < offset
- loop
- put(item(i), j)
- i := i - 1
- j := j - 1
- end
- from
- check
- j = word_shift - 1
- end
- until
- j < 0
- loop
- put(0, j)
- j := j - 1
- end
- offset := 0
- integer_length := new_integer_length
- else
- -- reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- i := offset + integer_length
- j := word_shift + integer_length
- until
- i = offset
- loop
- i := i - 1
- j := j - 1
- new_storage.put(item(i), j)
- end
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- end
- else
- right := 32 - left -- Compute real `integer_length'
- i := offset + integer_length - 1
- val1 := item(i)
- new_head := val1 |>>> right
- if new_head = 0 then
- -- new_integer_length is good
- if capacity < new_integer_length then
- -- reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- j := new_integer_length - 1
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- new_storage.put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- new_storage.put(val1 |<< left, j)
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- elseif offset > word_shift then
- from
- check
- j = 0
- end
- until
- j = word_shift
- loop
- put(0, j)
- j := j + 1
- end
- from
- k := offset
- check
- i = offset + integer_length - 1
- j = word_shift
- end
- until
- k = i
- loop
- val3 := item(k)
- put(val3 |<< left | (val2 |>>> right), j)
- val2 := val3
- k := k + 1
- j := j + 1
- end
- put(val1 |<< left | (val2 |>>> right), j)
- offset := 0
- integer_length := new_integer_length
- else
- from
- j := new_integer_length - 1
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- put(val1 |<< left, j)
- from
- until
- j = 0
- loop
- j := j - 1
- put(0, j)
- end
- offset := 0
- integer_length := new_integer_length
- end
- else
- new_integer_length := new_integer_length + 1
- if capacity < new_integer_length then
- -- Reallocation
- new_capacity := capacity_from_lower_bound(capacity, new_integer_length)
- new_storage := storage.calloc(new_capacity)
- from
- j := new_integer_length - 2
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- new_storage.put(new_head, j + 1)
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- new_storage.put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- new_storage.put(val1 |<< left, j)
- storage := new_storage
- capacity := new_capacity
- offset := 0
- integer_length := new_integer_length
- elseif offset > word_shift then
- from
- check
- j = 0
- end
- until
- j = word_shift
- loop
- put(0, j)
- j := j + 1
- end
- from
- k := offset
- check
- i = offset + integer_length - 1
- end
- until
- k = i
- loop
- val3 := item(k)
- put(val3 |<< left | (val2 |>>> right), j)
- val2 := val3
- k := k + 1
- j := j + 1
- end
- put(val1 |<< left | (val2 |>>> right), j)
- put(new_head, j + 1)
- offset := 0
- integer_length := new_integer_length
- else
- from
- j := new_integer_length - 2
- check
- i = offset + integer_length - 1
- j = word_shift + integer_length - 1
- val1 = item(i)
- end
- until
- i = offset
- loop
- i := i - 1
- val2 := item(i)
- put(val1 |<< left | (val2 |>>> right), j)
- val1 := val2
- j := j - 1
- end
- put(val1 |<< left, j)
- put(new_head, new_integer_length - 1)
- from
- until
- j = 0
- loop
- j := j - 1
- put(0, j)
- end
- offset := 0
- integer_length := new_integer_length
- end
- end
- end
- end
- end
-
- shift_right (n: INTEGER) is
- -- Right shift `Current' n bits. (`Current' is left in normal form.)
- require
- n > 0
- local
- n_ints, n_bits: INTEGER
- do
- if integer_length > 0 then
- n_ints := n |>>> 5
- n_bits := n & 0x0000001F
- integer_length := integer_length - n_ints
- offset := offset + n_ints
- if n_bits = 0 then
- else
- primitive_shift_right(n_bits.to_integer_8)
- end
- end
- end
-
-feature {ANY} -- GCD
- gcd (other: like Current) is
- -- Compute GCD of `Current' and `other'.
- -- GCD is put in `Current' (`other' is not modified).
- require
- other /= Void
- do
- if other = Current then
- Current.abs
- elseif other.is_zero then
- Current.abs
- elseif Current.is_zero then
- Current.copy(other)
- Current.abs
- else
- from
- register2.copy(other)
- Current.mod(register2)
- if Current.is_zero then
- Current.swap_with(register2)
- Current.abs
- else
- register2.mod(Current)
- end
- until
- register2.is_zero
- loop
- Current.mod(register2)
- if Current.is_zero then
- Current.swap_with(register2)
- else
- register2.mod(Current)
- end
- end
- end
- ensure
- is_positive or is_zero and other.is_zero
- end
-
-feature {ANY} -- To multiply:
- multiply (other: like Current) is
- -- Multiply `Current' by `other'.
- require
- other /= Void
- do
- if other = Current then
- multiply_to(other, register1)
- swap_with(register1)
- elseif is_zero or other.is_zero then
- set_with_zero
- elseif Current.is_one then
- copy(other)
- elseif other.is_one then
- elseif Current.is_one_negative then
- copy(other)
- set_negative(not negative)
- elseif other.is_one_negative then
- set_negative(not negative)
- else
- --|*** Must be replace by an algorithm switch. (Vincent Croizier, 09/07/04)
- multiply_like_human(other)
- end
- end
-
- multiply_to (other, res: like Current) is
- -- Multiply the contents of `Current' and `other' and place the
- -- result in `res'. (`Current' and `other' are not modified.)
- require
- other /= Void
- res /= Void
- res /= Current
- do
- if is_zero or other.is_zero then
- res.set_with_zero
- elseif Current.is_one then
- res.copy(other)
- elseif other.is_one then
- res.copy(Current)
- elseif Current.is_one_negative then
- res.copy(other)
- res.set_negative(not res.negative)
- elseif other.is_one_negative then
- res.copy(Current)
- res.set_negative(not negative)
- else
- --|*** Must be replace by an algorithm switch. (Vincent Croizier, 01/05/04)
- multiply_to_like_human(other, res)
- end
- end
-
- multiply_integer (other: INTEGER; res: like Current) is
- -- Multiply the contents of `Current' and `other' and place the
- -- result in `res'. (`Current' is not modified.)
- require
- res /= Current
- res /= Void
- local
- overflow, res_integer_length, res_capacity, i, k, up_i, v: INTEGER; res_storage: like storage
- do
- if other = 0 or else is_zero then
- res.set_with_zero
- elseif other = Minimum_integer then
- res.set_negative(not negative)
- shift_left(31)
- else
- if other > 0 then
- res.set_negative(negative)
- v := other
- else
- res.set_negative(not negative)
- v := -other
- end
- -- Pessimistique estimation
- res_integer_length := integer_length + 1 -- Reallocation ?
- if res.capacity < res_integer_length then
- if capacity < res_integer_length then
- res_capacity := capacity * 2
- else
- res_capacity := capacity_from_upper_bound(capacity, res_integer_length)
- end
- set_capacity(res_capacity)
- res_storage := storage.calloc(res_capacity)
- res.set_storage(res_storage)
- else
- res_storage := res.storage
- end
- res.set_offset(0)
- -- Multiply
- from
- k := 0
- i := offset
- up_i := offset + integer_length - 1
- overflow := mbi_multiply(item(i), v, storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(item(i), v, overflow, storage_at(res_storage, k))
- end
- if overflow = 0 then
- res.set_integer_length(res_integer_length - 1)
- else
- check
- k + 1 = integer_length
- end
- res.put(overflow, integer_length)
- end
- end
- end
-
-feature {MUTABLE_BIG_INTEGER} -- to multiply
- multiply_like_human (other: like Current) is
- -- Simple multiply.
- -- Complexity = O(`integer_length'*`other.integer_length').
- require
- not is_zero
- not other.is_zero
- local
- old_offset, new_integer_length: INTEGER
- do
- -- Pessimistique estimation
- new_integer_length := integer_length + other.integer_length -- Reallocation ?
- if capacity < new_integer_length then
- register1.swap_with(Current)
- register1.multiply_to_like_human(other, Current)
- -- Multiply in place
- elseif offset + new_integer_length <= capacity then
- multiply_like_human_aux_reverse(other)
- elseif offset >= other.integer_length then
- multiply_like_human_aux(other)
- else
- old_offset := offset
- offset := capacity - integer_length
- storage.slice_copy(offset, storage, old_offset, old_offset + integer_length - 1)
- multiply_like_human_aux(other)
- end
- end
-
- multiply_like_human_aux (other: like Current) is
- -- Only used by `multiply_to_like_human'.
- require
- not is_zero
- not other.is_zero
- offset >= other.integer_length
- local
- other_offset, other_integer_length, overflow, i, j, k, up_i, up_j, down_k, v: INTEGER
- other_storage: like storage
- do
- other_offset := other.offset
- other_integer_length := other.integer_length
- other_storage := other.storage -- First pass
- from
- k := 0
- i := other_offset
- up_i := other_offset + other_integer_length - 1
- j := offset
- up_j := offset + integer_length - 1
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(other_storage.item(i), v, overflow, storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j
- end
- storage.put(overflow, k)
- from
- down_k := 1
- until
- j = up_j
- loop
- j := j + 1
- from
- k := down_k
- i := other_offset
- v := storage.item(j)
- overflow := mbi_multiply_with_add(other_storage.item(i), v, storage.item(k), storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(other_storage.item(i), v, overflow, storage.item(k), storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j
- end
- storage.put(overflow, k)
- down_k := down_k + 1
- end
- -- Adjust `res.integer_length'
- if overflow = 0 then
- integer_length := integer_length + other_integer_length - 1
- else
- integer_length := integer_length + other_integer_length
- end
- negative := negative /= other.negative
- offset := 0
- end
-
- multiply_like_human_aux_reverse (other: like Current) is
- -- Only used by `multiply_to_like_human'.
- require
- not is_zero
- not other.is_zero
- offset + integer_length <= capacity - other.integer_length
- local
- other_offset, other_integer_length, overflow, i, j, k, up_i, down_j, down_k, v: INTEGER
- other_storage: like storage; inc: BOOLEAN
- do
- other_offset := other.offset
- other_integer_length := other.integer_length
- other_storage := other.storage -- First pass
- from
- i := other_offset
- up_i := other_offset + other_integer_length - 1
- down_j := offset
- j := offset + integer_length - 1
- k := j
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(other_storage.item(i), v, overflow, storage_at(storage, k))
- end
- k := k + 1
- check
- k <= j + other_integer_length
- end
- storage.put(overflow, k)
- from
- down_k := j - 1
- until
- j = down_j
- loop
- j := j - 1
- from
- k := down_k
- i := other_offset
- v := storage.item(j)
- overflow := mbi_multiply(other_storage.item(i), v, storage_at(storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(other_storage.item(i), v, overflow, storage.item(k), storage_at(storage, k))
- end
- k := k + 1
- inc := mbi_add(storage.item(k), overflow, storage_at(storage, k))
- check
- k < offset + integer_length + other_integer_length
- end
- from
- until
- not inc
- loop
- k := k + 1
- check
- k < offset + integer_length + other_integer_length
- end
- inc := mbi_inc(storage_at(storage, k))
- end
- down_k := down_k - 1
- end
- -- Adjust `res.integer_length'
- if storage.item(offset + integer_length + other_integer_length - 1) = 0 then
- integer_length := integer_length + other_integer_length - 1
- else
- integer_length := integer_length + other_integer_length
- end
- negative := negative /= other.negative
- end
-
- multiply_to_like_human (other, res: like Current) is
- -- Simple multiply.
- -- Complexity = O(`integer_length'*`other.integer_length').
- require
- res /= Current
- not is_zero
- not other.is_zero
- local
- overflow, res_integer_length, res_capacity, i, j, k, up_i, up_j, down_k, v: INTEGER
- res_storage: like storage; res_negative: BOOLEAN
- do
- res_negative := negative /= other.negative -- Pessimistique estimation
- res_integer_length := integer_length + other.integer_length -- Reallocation ?
- res_capacity := res.capacity
- if res_capacity < res_integer_length then
- res_capacity := capacity_from_lower_bound(res_capacity, res_integer_length)
- res_storage := storage.calloc(res_capacity)
- else
- res_storage := res.storage
- end
- -- To avoid class invariant violation
- res.set_with_zero
- -- Multiply
- -- First pass
- from
- k := 0
- i := offset
- up_i := offset + integer_length - 1
- j := other.offset
- up_j := j + other.integer_length - 1
- v := other.item(j)
- overflow := mbi_multiply(item(i), v, storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_add(item(i), v, overflow, storage_at(res_storage, k))
- end
- k := k + 1
- res_storage.put(overflow, k)
- from
- down_k := 1
- until
- j = up_j
- loop
- j := j + 1
- from
- k := down_k
- i := offset
- v := other.item(j)
- overflow := mbi_multiply_with_add(item(i), v, res_storage.item(k), storage_at(res_storage, k))
- until
- i = up_i
- loop
- i := i + 1
- k := k + 1
- overflow := mbi_multiply_with_2_add(item(i), v, overflow, res_storage.item(k), storage_at(res_storage, k))
- end
- k := k + 1
- res_storage.put(overflow, k)
- down_k := down_k + 1
- end
- -- Adjust `res.integer_length'
- if overflow = 0 then
- res.set_all(res_storage, res_capacity, res_integer_length - 1, 0, res_negative)
- else
- res.set_all(res_storage, res_capacity, res_integer_length, 0, res_negative)
- end
- end
-
-feature {ANY} -- Comparison:
- is_zero: BOOLEAN is
- -- Is it 0?
- do
- Result := integer_length = 0
- ensure
- Result implies not is_negative
- end
-
- is_one: BOOLEAN is
- -- Is it 1?
- do
- if integer_length = 1 then
- if not negative then
- Result := item(offset) = 1
- end
- end
- ensure
- Result implies not is_negative
- end
-
- is_one_negative: BOOLEAN is
- -- Is it -1 ?
- do
- if integer_length = 1 then
- if negative then
- Result := item(offset) = 1
- end
- end
- ensure
- Result implies is_negative
- end
-
- is_negative: BOOLEAN is
- -- Is `Current' negative integer?
- do
- Result := negative
- ensure
- Result implies not is_positive
- end
-
- is_positive: BOOLEAN is
- -- Is `Current' positive integer?
- do
- Result := not negative and then integer_length /= 0
- ensure
- Result implies not is_negative
- end
-
- is_even: BOOLEAN is
- -- Is `Current' even?
- do
- if integer_length = 0 then
- Result := True
- else
- Result := item(offset).is_even
- end
- ensure
- Result = not Current.is_odd
- end
-
- is_odd: BOOLEAN is
- -- Is `Current' odd?
- do
- if integer_length > 0 then
- Result := item(offset).is_odd
- end
- ensure
- Result = not Current.is_even
- end
-
- is_equal (other: like Current): BOOLEAN is
- local
- a, b, c: INTEGER
- do
- if Current = other then
- Result := True
- elseif integer_length /= other.integer_length then
- elseif negative /= other.negative then
- else
- check
- other.integer_length = integer_length
- end
- from
- c := offset + integer_length
- a := offset
- b := other.offset
- Result := True
- until
- a = c
- loop
- if item(a) /= other.item(b) then
- Result := False
- a := c
- else
- a := a + 1
- b := b + 1
- end
- end
- end
- end
-
- infix "<" (other: like Current): BOOLEAN is
- local
- a, b: INTEGER; va, vb: INTEGER
- do
- if Current = other then
- elseif negative /= other.negative then
- Result := negative
- elseif integer_length /= other.integer_length then
- Result := integer_length < other.integer_length xor negative
- else
- check
- other.negative = negative
- end
- check
- other.integer_length = integer_length
- end
- from
- a := offset + integer_length - 1
- b := other.offset + integer_length - 1
- until
- a < offset
- loop
- va := item(a)
- vb := other.item(b)
- if unsigned_less_than(va, vb) then
- Result := not negative
- a := -1
- elseif unsigned_less_than(vb, va) then
- Result := negative
- a := -1
- else
- a := a - 1
- b := b - 1
- end
- end
- end
- end
-
- abs_compare (other: like Current): INTEGER is
- -- Compare the magnitude of `Current' and `other'. Returns -1, 0 or 1
- -- as this MutableBigInteger is numerically less than, equal to, or
- -- greater than other.
- local
- a, b: INTEGER; va, vb: INTEGER
- do
- if Current = other then
- --Result := 0
- elseif integer_length < other.integer_length then
- Result := -1
- elseif integer_length > other.integer_length then
- Result := 1
- else
- check
- other.integer_length = integer_length
- end
- from
- a := offset + integer_length
- b := other.offset + integer_length
- check
- Result = 0
- end
- until
- a <= offset
- loop
- a := a - 1
- b := b - 1
- va := item(a)
- vb := other.item(b)
- if unsigned_less_than(va, vb) then
- Result := -1
- a := -1
- elseif unsigned_less_than(vb, va) then
- Result := 1
- a := -1
- end
- end
- end
- end
-
-feature {ANY} -- Printing:
- to_string: STRING is
- -- The decimal view of `Current' into a new allocated STRING.
- -- For example, if `Current' is -1 the `Result' is "-1".
- --
- -- See also `append_in', `to_string_format', `to_unicode_string', `to_integer'.
- do
- string_buffer.clear_count
- append_in(string_buffer)
- Result := string_buffer.twin
- end
-
- to_unicode_string: UNICODE_STRING is
- -- The decimal view of `Current' into a new allocated UNICODE_STRING.
- -- For example, if `Current' represents -1 the `Result' is U"-1".
- --
- -- See also `append_in_unicode', `to_unicode_string_format', `to_string'.
- do
- unicode_string_buffer.clear_count
- append_in_unicode(unicode_string_buffer)
- Result := unicode_string_buffer.twin
- end
-
- append_in (buffer: STRING) is
- -- Append in the `buffer' the equivalent of `to_string'. No new
- -- STRING creation during the process.
- require
- is_printable
- local
- k: INTEGER
- do
- if is_zero then
- buffer.extend('0')
- else
- -- Put the sign in `buffer'
- if negative then
- buffer.extend('-')
- end
- -- Put it in `buffer'
- from
- k := append_in_char_buffer
- until
- k = 0
- loop
- k := k - 1
- buffer.extend(char_buffer.item(k))
- end
- end
- end
-
- append_in_unicode (buffer: UNICODE_STRING) is
- -- Append in the `buffer' the equivalent of `to_string'. No new
- -- STRING creation during the process.
- require
- is_printable
- local
- k: INTEGER
- do
- if is_zero then
- buffer.extend('0'.code)
- else
- -- Put the sign in `buffer'
- if negative then
- buffer.extend('-'.code)
- end
- -- Put it in `buffer'
- from
- k := append_in_char_buffer
- until
- k = 0
- loop
- k := k - 1
- buffer.extend(char_buffer.item(k).code)
- end
- end
- end
-
- to_string_format (s: INTEGER): STRING is
- -- Same as `to_string' but the result is on `s' character and the
- -- number is right aligned.
- -- Note: see `append_in_format' to save memory.
- require
- to_string.count <= s
- do
- create Result.make(s)
- append_in_format(Result, s)
- ensure
- Result.count = s
- end
-
- to_unicode_string_format (s: INTEGER): UNICODE_STRING is
- -- Same as `to_unicode_string' but the result is on `s' character and
- -- the number is right aligned.
- -- Note: see `append_in_unicode_format' to save memory.
- require
- to_string.count <= s
- do
- create Result.make(s)
- append_in_unicode_format(Result, s)
- ensure
- Result.count = s
- end
-
- append_in_format (str: STRING; s: INTEGER) is
- -- Append the equivalent of `to_string_format' at the end of
- -- `str'. Thus you can save memory because no other
- -- STRING is allocated for the job.
- require
- to_string.count <= s
- local
- i, k: INTEGER
- do
- if is_zero then
- -- Put spaces
- from
- i := s - 1
- variant
- i
- until
- i = 0
- loop
- str.extend(' ')
- i := i - 1
- end
- -- Put number
- str.extend('0')
- else
- k := append_in_char_buffer
- -- Put spaces
- from
- if negative then
- i := s - k - 1
- else
- i := s - k
- end
- variant
- i
- until
- i = 0
- loop
- str.extend(' ')
- i := i - 1
- end
- -- Put number
- from
- -- Put the sign in `buffer'
- if negative then
- str.extend('-')
- end
- variant
- k
- until
- k = 0
- loop
- k := k - 1
- str.extend(char_buffer.item(k))
- end
- end
- ensure
- str.count >= old str.count + s
- end
-
- append_in_unicode_format (str: UNICODE_STRING; s: INTEGER) is
- -- Append the equivalent of `to_unicode_string_format' at the end of
- -- `str'. Thus you can save memory because no other
- -- UNICODE_STRING is allocated for the job.
- require
- to_string.count <= s
- local
- i, k: INTEGER
- do
- if is_zero then
- -- Put spaces
- from
- i := s - 1
- variant
- i
- until
- i = 0
- loop
- str.extend(' '.code)
- i := i - 1
- end
- -- Put number
- str.extend('0'.code)
- else
- k := append_in_char_buffer
- -- Put spaces
- from
- if negative then
- i := s - k - 1
- else
- i := s - k
- end
- variant
- i
- until
- i = 0
- loop
- str.extend(' '.code)
- i := i - 1
- end
- -- Put number
- from
- -- Put the sign in `buffer'
- if negative then
- str.extend('-'.code)
- end
- variant
- k
- until
- k = 0
- loop
- k := k - 1
- str.extend(char_buffer.item(k).code)
- end
- end
- ensure
- str.count >= old str.count + s
- end
-
- is_printable: BOOLEAN is
- -- True if decimal view of `Current' is short enougth
- -- to be put in a STRING.
- do
- --|*** MUST BE REWRITE (Vincent Croizier, 14/07/04) ***
- Result := integer_length <= 2 ^ 27
- end
-
- out_in_tagged_out_memory, fill_tagged_out_memory is
- do
- append_in(tagged_out_memory)
- end
-
-feature {ANY} -- Miscellaneous:
- negate is
- -- Negate the sign of `Current'.
- do
- if integer_length /= 0 then
- negative := not negative
- end
- end
-
- abs is
- -- Absolute value of `Current'.
- do
- negative := False
- end
-
- sign: INTEGER_8 is
- -- Sign of `Current' (0 -1 or 1).
- do
- if negative then
- Result := -1
- elseif integer_length > 0 then
- Result := 1
- else
- check
- is_zero
- end
- end
- end
-
- set_with_zero is
- do
- integer_length := 0
- negative := False
- ensure
- is_zero
- end
-
- hash_code: INTEGER is
- local
- i, c, v: INTEGER
- do
- from
- i := offset
- c := 2
- until
- c = 0 or else i = offset + integer_length
- loop
- v := item(i)
- if v /= 0 then
- Result := Result #+ v
- c := c - 1
- end
- i := i + 1
- end
- Result := integer_length #* Result
- if negative then
- Result := Result #+ 1
- end
- if Result < 0 then
- Result := ~Result
- end
- end
-
- copy (other: like Current) is
- do
- negative := other.negative
- offset := 0
- integer_length := other.integer_length
- if capacity < other.integer_length then
- capacity := capacity_from_upper_bound(other.capacity, integer_length)
- storage := storage.calloc(capacity)
- elseif capacity = 0 then
- capacity := 4
- storage := storage.calloc(capacity)
- end
- if integer_length /= 0 then
- storage.slice_copy(offset, other.storage, other.offset, other.offset + integer_length - 1)
- end
- end
-
- swap_with (other: like Current) is
- -- Swap the value of `Current' with the value of `other'.
- local
- s: like storage; c: like capacity; il: like integer_length; o: like offset; n: like negative
- do
- s := other.storage
- c := other.capacity
- il := other.integer_length
- o := other.offset
- n := other.negative -- Put Current in other
- other.set_all(storage, capacity, integer_length, offset, negative)
- --
- storage := s
- capacity := c
- integer_length := il
- offset := o
- negative := n
- end
-
-feature {MUTABLE_BIG_INTEGER}
- storage: NATIVE_ARRAY[INTEGER]
- -- Holds the magnitude of `Current' in natural order (the most
- -- significant INTEGER_32 word has the highest address). To avoid many
- -- reallocation of this `storage' area, only some words are
- -- significant. The magnitude is stored in the following significant
- -- range [`offset' .. `offset + integer_length - 1'].
-
- capacity: INTEGER
- -- Of the allocated `storage' area.
-
- integer_length: INTEGER
- -- The number of significant INTEGER_32 words in the `storage' area.
-
- offset: INTEGER
- -- The `offset' of the less significant word into the `storage' area.
-
- negative: BOOLEAN
- -- True when `Current' is negative.
-
- item (index: INTEGER): INTEGER_32 is
- require
- -- index.in_range(0, capacity - 1)
- index.in_range(offset, offset + integer_length - 1)
- do
- Result := storage.item(index)
- end
-
- put (value: INTEGER; index: INTEGER) is
- require
- index.in_range(0, capacity - 1)
- do
- storage.put(value, index)
- end
-
- set_negative (n: like negative) is
- require
- n implies not is_zero
- do
- negative := n
- ensure
- negative = n or is_zero
- end
-
- set_integer_length (il: like integer_length) is
- require
- il.in_range(0, capacity - offset)
- do
- integer_length := il
- ensure
- integer_length = il
- end
-
- set_offset (o: like offset) is
- require
- o.in_range(0, capacity - integer_length)
- do
- offset := o
- ensure
- offset = o
- end
-
- set_ilo (il: like integer_length; o: like offset) is
- require
- il.in_range(0, capacity)
- o.in_range(0, capacity - il)
- do
- integer_length := il
- offset := o
- ensure
- integer_length = il
- offset = o
- end
-
- set_storage (new_storage: like storage) is
- do
- storage := new_storage
- end
-
- set_capacity (new_capacity: like capacity) is
- do
- capacity := new_capacity
- end
-
- set_all (new_storage: like storage; new_capacity, new_integer_length, new_offset: INTEGER; new_negative: BOOLEAN) is
- require
- new_capacity > 0
- new_storage.is_not_null
- new_integer_length.in_range(0, new_capacity)
- new_integer_length /= 0 implies new_offset.in_range(0, new_capacity - new_integer_length) and new_storage.item(new_offset + new_integer_length - 1) /= 0
- new_integer_length = 0 implies not new_negative
- new_capacity.is_a_power_of_2
- do
- storage := new_storage
- capacity := new_capacity
- integer_length := new_integer_length
- offset := new_offset
- negative := new_negative
- ensure
- storage = new_storage
- capacity = new_capacity
- integer_length = new_integer_length
- offset = new_offset
- negative = new_negative
- end
-
- primitive_shift_left (n: INTEGER_8) is
- -- Left shift `Current' with no need to extend the `storage'.
- --|*** Can be a little faster (Vincent Croizier, 26/04/04) ***
- require
- integer_length > 0
- n.in_range(1, 31)
- no_bit_lost: item(offset + integer_length - 1) |<< n |>>> n = item(offset + integer_length - 1)
- local
- n2: INTEGER_8; i, up, b, c: INTEGER
- do
- n2 := 32 - n
- from
- i := offset
- up := i + integer_length - 1
- until
- i > up
- loop
- b := item(i)
- put(b |<< n | c, i)
- c := b |>>> n2
- i := i + 1
- end
- check
- c = 0
- end
- end
-
- primitive_shift_right (n: INTEGER_8) is
- -- Right shift `Current' of `n' bits.
- require
- integer_length > 0
- n.in_range(1, 31)
- local
- n2: INTEGER_8; i, j, up, b, c: INTEGER
- do
- n2 := 32 - n
- from
- up := integer_length - 1
- j := 0
- i := offset
- c := item(i)
- until
- j >= up
- loop
- b := c
- i := i + 1
- c := item(i)
- put(b |>>> n | (c |<< n2), j)
- j := j + 1
- end
- check
- j = up
- i = offset + j
- end
- put(c |>>> n, up)
- offset := 0
- if item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- end
- ensure
- offset = 0
- end
-
- divide_one_word (divisor: INTEGER): INTEGER is
- -- This method is used by `divide'. The one word divisor is
- -- specified by `divisor' is saw as unsigned.
- -- `Current' is the dividend (saw positive) at invocation but is replaced by
- -- the quotient. The remainder is returned as unsigned INTEGER.
- -- Note: `Current' is modified by this method.
- require
- divisor /= 0
- local
- i, remainder_word1, remainder_word0: INTEGER
- do
- if integer_length = 1 then
- Result := item(offset)
- if unsigned_less_than(Result, divisor) then
- integer_length := 0
- negative := False
- else
- put(mbi_divide(0, Result, divisor, $remainder_word1), offset)
- Result := remainder_word1
- end
- else
- from
- i := offset + integer_length - 1
- until
- i < offset
- loop
- remainder_word0 := item(i)
- put(mbi_divide(remainder_word1, remainder_word0, divisor, $remainder_word1), i)
- i := i - 1
- end
- if item(offset + integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- item(offset + integer_length - 1) /= 0
- end
- end
- Result := remainder_word1
- end
- end
-
- divide_sign_correction (other, quotient, remainder: like Current) is
- -- Correct the value of `quotient' and `remainder' after an
- -- "unsigned" division.
- -- Only used by `divide'.
- require
- not remainder.is_negative
- do
- if remainder.is_zero then
- quotient.set_negative(negative /= other.negative)
- elseif negative then
- quotient.set_negative(False)
- if other.negative then
- quotient.add_integer(1)
- remainder.set_negative(True)
- -- other is negative
- remainder.subtract(other)
- check
- not remainder.is_negative
- end
- else
- quotient.add_integer(1)
- quotient.set_negative(True)
- remainder.set_negative(True)
- remainder.add(other)
- check
- not remainder.is_negative
- end
- end
- elseif other.negative then
- quotient.set_negative(True)
- else
- quotient.set_negative(False)
- end
- ensure
- not remainder.is_negative
- end
-
- divide_sign_correction_bis (other, quotient: like Current; current_negative: BOOLEAN) is
- -- Correct the value of `quotient' and `remainder' after an
- -- "unsigned" division.
- -- Only used by `divide'.
- require
- not is_negative
- do
- if is_zero then
- quotient.set_negative(current_negative /= other.negative)
- elseif current_negative then
- quotient.set_negative(False)
- if other.negative then
- quotient.add_integer(1)
- set_negative(True)
- -- other is negative
- subtract(other)
- check
- not is_negative
- end
- else
- quotient.add_integer(1)
- quotient.set_negative(True)
- set_negative(True)
- add(other)
- check
- not is_negative
- end
- end
- elseif other.negative then
- quotient.set_negative(True)
- else
- quotient.set_negative(False)
- end
- ensure
- not is_negative
- end
-
- multiply_and_subtract (u1, qhat: INTEGER; d_storage: like storage; d_offset: INTEGER; r_storage: like storage
- r_offset, length: INTEGER): BOOLEAN is
- -- Only used by `divide'.
- require
- qhat /= 0
- local
- i, j, jmax, m1, m2: INTEGER; dec: BOOLEAN
- do
- if qhat = 1 then
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- if dec then
- dec := mbi_subtract_with_dec(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- else
- dec := mbi_subtract(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if dec then
- if u1 = 0 then
- Result := True
- else
- Result := mbi_dec(storage_at(r_storage, j))
- check
- not Result
- end
- end
- end
- else
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- m1 := mbi_multiply_with_add(qhat, d_storage.item(i), m1, $m2)
- if dec then
- dec := mbi_subtract_with_dec(r_storage.item(j), m2, storage_at(r_storage, j))
- else
- dec := mbi_subtract(r_storage.item(j), m2, storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if dec then
- if u1 = 0 then
- Result := True
- else
- Result := mbi_subtract_with_dec(r_storage.item(j), m1, storage_at(r_storage, j))
- end
- elseif m1 = 0 then
- -- nothing to do
- elseif u1 = 0 then
- Result := True
- else
- Result := mbi_subtract(r_storage.item(j), m1, storage_at(r_storage, j))
- end
- end
- end
-
- add_back (old_u1: INTEGER; d_storage: like storage; d_offset: INTEGER; r_storage: like storage
- r_offset, length: INTEGER): BOOLEAN is
- -- Only used by `divide'.
- -- `old_u1' is the value of `u1' before `multiply_and_subtract'.
- local
- i, j, jmax: INTEGER; inc: BOOLEAN
- do
- from
- i := d_offset
- j := r_offset
- jmax := r_offset + length
- until
- j = jmax
- loop
- if inc then
- inc := mbi_add_with_inc(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- else
- inc := mbi_add(r_storage.item(j), d_storage.item(i), storage_at(r_storage, j))
- end
- i := i + 1
- j := j + 1
- end
- if inc then
- if old_u1 = 0 then
- Result := True
- else
- Result := mbi_inc(storage_at(r_storage, j))
- end
- end
- end
-
- is_a_good_divide (other, quotient, remainder: like Current): BOOLEAN is
- require
- other /= Void
- quotient /= Void
- remainder /= Void
- local
- v: like Current
- do
- v := other.twin
- v.multiply(quotient)
- v.add(remainder)
- Result := Current.is_equal(v)
- end
-
- normalize: INTEGER_8 is
- -- Shift left until the most significant bit is on.
- -- Result give the number of left shift.
- require
- not is_zero
- local
- head: INTEGER
- do
- head := item(offset + integer_length - 1)
- from
- until
- head < 0
- loop
- head := head.bit_shift_left(1)
- Result := Result + 1
- end
- if Result > 0 then
- shift_left(Result)
- end
- ensure
- item(offset + integer_length - 1) < 0
- end
-
-feature {MUTABLE_BIG_INTEGER} -- Implementation:
- register1: MUTABLE_BIG_INTEGER is
- once
- create Result.from_integer(0)
- end
-
- register2: MUTABLE_BIG_INTEGER is
- once
- create Result.from_integer(0)
- end
-
- Real_base: REAL_64 is
- once
- Result := (0x0000000100000000).force_to_real_64
- end
-
- add_magnitude (other: like Current) is
- -- Add the magnitude of `Current' and `other' regardless of signs.
- require
- not is_zero
- not other.is_zero
- local
- a, b: like Current; inc: BOOLEAN; i, j, k, n: INTEGER; new_storage, a_storage, b_storage: like storage
- new_capacity, a_capacity, a_offset, a_integer_length, b_offset, b_integer_length: INTEGER
- do
- --|*** First tests can be certainely optimized.
- --|*** (Vincent Croizier, 26/03/2004)
- if integer_length > other.integer_length and then capacity - offset > integer_length then
- ---- Add in place (`offset' doesn't change)
- -- Add common parts of both numbers:
- from
- i := offset
- j := other.offset
- n := j + other.integer_length
- until
- j = n
- loop
- if inc then
- -- overflow in the last addition step
- inc := mbi_add_with_inc(item(i), other.item(j), storage_at(storage, i))
- else
- -- no overflow in the last addition step
- inc := mbi_add(item(i), other.item(j), storage_at(storage, i))
- end
- i := i + 1
- j := j + 1
- end
- -- Add remainder of the longer number with increment (if necessary):
- from
- n := offset + integer_length
- until
- not inc or else i = n
- loop
- inc := mbi_inc(storage_at(storage, i))
- i := i + 1
- end
- if inc then
- storage.put(1, n)
- check
- n < capacity
- end
- integer_length := integer_length + 1
- end
- else
- ---- Add, after this `offset' will be 0
- -- Set `a' to the longest number and `b' to the smallest.
- if integer_length >= other.integer_length then
- a := Current
- b := other
- else
- a := other
- b := Current
- end
- a_capacity := a.capacity
- a_storage := a.storage
- b_storage := b.storage
- a_integer_length := a.integer_length
- b_integer_length := b.integer_length
- a_offset := a.offset
- b_offset := b.offset -- Verify capacity
- if capacity < a_integer_length then
- new_capacity := capacity_from_lower_bound(capacity, a_integer_length)
- new_storage := new_storage.calloc(new_capacity)
- elseif capacity = a_integer_length then
- --|*** It's possible to make a more restrictive test
- --|*** that can exclude more case of reallocation. (Vincent Croizier, 24/03/2004)
- new_capacity := capacity_from_lower_bound(capacity, a_integer_length + 1)
- new_storage := new_storage.calloc(new_capacity)
- elseif a = other then
- -- protect `other'
- new_storage := a_storage.calloc(a_capacity)
- new_capacity := a_capacity
- else
- new_storage := a_storage
- new_capacity := a_capacity
- end
- -- Add common parts of both numbers:
- n := b_integer_length
- check
- n.in_range(0, new_capacity)
- end
- from
- i := a_offset
- j := b_offset -- k := 0
- until
- k = n
- loop
- if inc then
- -- overflow in the last addition step
- inc := mbi_add_with_inc(a_storage.item(i), b_storage.item(j), storage_at(new_storage, k))
- else
- -- no overflow in the last addition step
- inc := mbi_add(a_storage.item(i), b_storage.item(j), storage_at(new_storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- -- Add remainder of the longer number with increment (if necessary):
- from
- n := a_integer_length
- until
- not inc or else k = a_integer_length
- loop
- new_storage.put(a_storage.item(i), k)
- inc := mbi_inc(storage_at(new_storage, k))
- i := i + 1
- k := k + 1
- end
- if inc then
- new_storage.put(1, k)
- check
- n < new_capacity
- end
- n := n + 1
- else
- -- copy the reste of `a'
- from
- until
- k = n
- loop
- new_storage.put(a_storage.item(i), k)
- i := i + 1
- k := k + 1
- end
- end
- capacity := new_capacity
- storage := new_storage
- integer_length := n
- offset := 0
- end
- end
-
-feature {MUTABLE_BIG_INTEGER} -- Implementation:
- subtract_magnitude (other: like Current) is
- -- Subtract `other' from `Current' (The result is placed in `Current')
- -- and change `negative' (the sign) if necessary.
- require
- not is_zero
- not other.is_zero
- local
- i, j, v1, v2: INTEGER; test: BOOLEAN; new: like Current
- do
- -- Compare the number
- if integer_length = other.integer_length then
- -- Compare the most significant part of the numbers
- from
- i := offset + integer_length - 1
- j := other.offset + integer_length - 1
- v1 := item(i)
- v2 := other.item(j)
- test := v1 /= v2
- until
- test or else i = offset
- loop
- integer_length := integer_length - 1
- i := i - 1
- j := j - 1
- v1 := item(i)
- v2 := other.item(j)
- test := v1 /= v2
- end
- if test then
- if unsigned_greater_than(v1, v2) then
- -- Current > other
- subtract_magnitude_raw_truncated(other)
- if storage.item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- integer_length /= 0 implies item(integer_length - 1) /= 0
- end
- end
- else
- -- Current < other
- check
- unsigned_less_than(v1, v2)
- end
- negative := not negative
- subtract_magnitude_raw_reverse_truncated(other)
- if storage.item(integer_length - 1) = 0 then
- integer_length := integer_length - 1
- check
- integer_length /= 0 implies item(integer_length - 1) /= 0
- end
- end
- end
- else
- -- Current = other
- set_with_zero
- end
- elseif integer_length > other.integer_length then
- subtract_magnitude_raw(other)
- elseif capacity >= other.integer_length then
- negative := not negative
- subtract_magnitude_raw_reverse(other)
- else
- -- Reallocation
- --|*** Can be faster (Vincent Croizier, 10/06/04) ***
- create new.copy(other)
- new.subtract_magnitude(Current)
- negative := not negative
- integer_length := new.integer_length
- storage := new.storage
- offset := new.offset
- end
- end
-
- subtract_magnitude_raw (other: like Current) is
- -- Subtract (raw) the storage of `other' from `Current'.
- -- Used by `subtract_magnitude'.
- require
- not is_zero
- not other.is_zero
- abs_compare(other) = 1
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := other.integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(item(i), other.item(j), storage_at(storage, k))
- else
- dec := mbi_subtract(item(i), other.item(j), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- from
- until
- not dec
- loop
- --|*** Could be done in one step with a mbi_dec_bis
- --| routine (Vincent Croizier, 10/06/04) ***
- put(item(i), k)
- dec := mbi_dec(storage_at(storage, k))
- i := i + 1
- k := k + 1
- end
- if k = integer_length then
- from
- k := k - 1
- until
- item(k) /= 0
- loop
- k := k - 1
- end
- integer_length := k + 1
- end
- offset := 0
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_reverse (other: like Current) is
- -- Subtract (raw) the storage of `Current' from `other' and
- -- put it in `Current'.
- -- Used by `subtract_magnitude'.
- require
- not is_zero
- not other.is_zero
- abs_compare(other) = -1
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- -- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(other.item(j), item(i), storage_at(storage, k))
- else
- dec := mbi_subtract(other.item(j), item(i), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- from
- until
- not dec
- loop
- --|*** Could be done in one step with a mbi_dec_bis
- --| routine (Vincent Croizier, 10/06/04) ***
- put(other.item(j), k)
- dec := mbi_dec(storage_at(storage, k))
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- up := other.integer_length
- if k < up then
- from
- until
- k = up
- loop
- put(other.item(j), k)
- j := j + 1
- k := k + 1
- end
- integer_length := up
- else
- check
- k = up
- end
- from
- k := k - 1
- until
- storage.item(k) /= 0
- loop
- k := k - 1
- end
- integer_length := k + 1
- offset := 0
- end
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_truncated (other: like Current) is
- -- Subtract (raw) the storage of `other' from `Current'
- -- where `other' is truncated to the size of `Current'.
- -- Used by `subtract_magnitude'.
- require
- not other.is_zero
- other.integer_length >= integer_length
- unsigned_greater_than(item(offset + integer_length - 1), other.item(offset + integer_length - 1))
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(item(i), other.item(j), storage_at(storage, k))
- else
- dec := mbi_subtract(item(i), other.item(j), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- offset := 0
- ensure
- offset = 0
- end
-
- subtract_magnitude_raw_reverse_truncated (other: like Current) is
- -- Subtract (raw) the storage of `Current' from `other' and
- -- put it in `Current',
- -- where `other' is truncated to the size of `Current'.
- -- Used by `subtract_magnitude'.
- require
- not other.is_zero
- other.integer_length >= integer_length
- unsigned_less_than(item(offset + integer_length - 1), other.item(offset + integer_length - 1))
- local
- i, j, k, up: INTEGER; dec: BOOLEAN
- do
- from
- k := 0
- i := offset
- j := other.offset
- up := integer_length - 1
- until
- k > up
- loop
- if dec then
- dec := mbi_subtract_with_dec(other.item(j), item(i), storage_at(storage, k))
- else
- dec := mbi_subtract(other.item(j), item(i), storage_at(storage, k))
- end
- i := i + 1
- j := j + 1
- k := k + 1
- end
- check
- not dec
- end
- offset := 0
- ensure
- offset = 0
- end
-
-feature {} -- For printing
- char_buffer: FAST_ARRAY[CHARACTER] is
- once
- create Result.make(4096)
- end
-
- append_in_char_buffer: INTEGER is
- -- Tool for `append_in' and `append_in_unicode'.
- -- Put absolute value of Current in `char_buffer' and return
- -- the number of characteres really used.
- require
- is_printable
- not is_zero
- local
- base, max_char, i, r: INTEGER
- do
- -- Allocate space in `char_buffer'
- max_char := integer_length * 9 + (2 * integer_length + 2) #// 3
- if char_buffer.capacity < max_char then
- char_buffer.resize(max_char)
- end
- -- Begin of extracting digits
- register1.copy(Current)
- base := 1000000000
- from
- r := register1.divide_one_word(base)
- until
- register1.is_zero
- loop
- check
- r >= 0
- end
- from
- i := 9
- until
- r = 0
- loop
- char_buffer.put((r #\\ 10).decimal_digit, Result)
- r := r #// 10
- Result := Result + 1
- i := i - 1
- end
- from
- until
- i = 0
- loop
- char_buffer.put('0', Result)
- Result := Result + 1
- i := i - 1
- end
- -- extract next digit group
- r := register1.divide_one_word(base)
- end
- from
- check
- r > 0
- end
- until
- r = 0
- loop
- char_buffer.put((r #\\ 10).decimal_digit, Result)
- r := r #// 10
- Result := Result + 1
- end
- end
-
-feature {} -- Tools for capacity:
- capacity_from_lower_bound (actual_capacity, needed_capacity: INTEGER): INTEGER is
- -- Give the smallest power of 2 greater than
- -- `needed_capacity' and `actual_capacity'.
- -- Based on `actual_capacity' (the actual capacity).
- require
- actual_capacity.is_a_power_of_2
- actual_capacity >= 4
- do
- from
- Result := actual_capacity
- until
- Result >= needed_capacity
- loop
- Result := Result.bit_shift_left(1)
- end
- ensure
- Result.is_a_power_of_2
- Result >= 4
- Result >= actual_capacity
- Result >= needed_capacity
- Result = actual_capacity or Result #// 2 < needed_capacity
- end
-
- capacity_from_upper_bound (actual_capacity, needed_capacity: INTEGER): INTEGER is
- -- Give the smallest power of 2 greater than `needed_capacity'.
- -- Based on `actual_capacity' (the actual capacity).
- require
- actual_capacity >= 4
- actual_capacity >= needed_capacity
- actual_capacity.is_a_power_of_2
- local
- v: INTEGER
- do
- from
- Result := actual_capacity
- v := Result.bit_shift_right(1)
- until
- v < needed_capacity or else v = 2
- loop
- Result := v
- v := Result.bit_shift_right(1)
- end
- ensure
- Result.is_a_power_of_2
- Result <= actual_capacity
- Result >= needed_capacity
- Result = 4 or Result.bit_shift_right(1) < needed_capacity
- end
-
-feature {}
- unsigned_less_than (a, b: INTEGER): BOOLEAN is
- -- Unsigned "<".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_less_than"
- }"
- end
-
- unsigned_greater_than (a, b: INTEGER): BOOLEAN is
- -- Unsigned ">".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_greater_than"
- }"
- end
-
- unsigned_greater_or_equal (a, b: INTEGER): BOOLEAN is
- -- Unsigned ">=".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_greater_or_equal"
- }"
- end
-
- unsigned_32_to_integer_64 (integer_32: INTEGER): INTEGER_64 is
- -- Return the unsigned value of the `integer_32'.
- --
- --|*** Ajouter ou pas cette fonction dans INTEGER_32 ? plug_in ou built_in ?(Dom. 27/02/2004) ***
- --
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_unsigned_32_to_integer_64"
- }"
- end
-
- storage_at (s: like storage; n: INTEGER): POINTER is
- -- Give the address of the corresponding word of `s'.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_storage_at"
- }"
- end
-
- mbi_inc (integer_32_adr: POINTER): BOOLEAN is
- -- Increment the value at `integer_32_adr'. The `Result' is True only in case of overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_inc"
- }"
- end
-
- mbi_add (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a + b
- -- Overflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_add"
- }"
- end
-
- mbi_add_with_inc (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a + b + 1
- -- Overflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_add_with_inc"
- }"
- end
-
- mbi_dec (integer_32_adr: POINTER): BOOLEAN is
- -- Put a - 1 in the item n in the NATIVE_ARRAY t.
- -- t.item(n) := a - 1
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_dec"
- }"
- end
-
- mbi_subtract (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a - b
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_subtract"
- }"
- end
-
- mbi_subtract_with_dec (a, b: INTEGER; integer_32_adr: POINTER): BOOLEAN is
- -- t.item(n) := a - b - 1
- -- Underflow if "Result = True".
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_subtract_with_dec"
- }"
- end
-
- mbi_multiply (a, b: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply"
- }"
- end
-
- mbi_multiply_with_add (a, b, c: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b + c in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply_with_add"
- }"
- end
-
- mbi_multiply_with_2_add (a, b, c, d: INTEGER; integer_32_adr: POINTER): INTEGER_32 is
- -- put a * b + c + d in t at n and return the overflow.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_multiply_with_2_add"
- }"
- end
-
- mbi_divide (u1, u0, d: INTEGER; r_int32adr: POINTER): INTEGER_32 is
- -- Divide `u1u0' by `d', put the remainder in `r' and return the quotient.
- external "plug_in"
- alias "{
- location: "${sys}/runtime"
- module_name: "mutable_big_integer"
- feature_name: "mbi_divide"
- }"
- end
-
- string_buffer: STRING is
- once
- create Result.make(128)
- end
-
- unicode_string_buffer: UNICODE_STRING is
- once
- create Result.make(128)
- end
-
-invariant
- capacity > 0
- storage.is_not_null
- integer_length.in_range(0, capacity)
- integer_length /= 0 implies offset.in_range(0, capacity - integer_length) and item(offset + integer_length - 1) /= 0
- integer_length = 0 implies not negative
- capacity.is_a_power_of_2
-
-end -- class MUTABLE_BIG_INTEGER
---
--- ------------------------------------------------------------------------------------------------------------
--- Copyright notice below. Please read.
---
--- This file is part of the SmartEiffel standard library.
--- Copyright(C) 1994-2002: INRIA - LORIA (INRIA Lorraine) - ESIAL U.H.P. - University of Nancy 1 - FRANCE
--- Copyright(C) 2003-2006: INRIA - LORIA (INRIA Lorraine) - I.U.T. Charlemagne - University of Nancy 2 - FRANCE
---
--- Authors: Dominique COLNET, Philippe RIBET, Cyril ADRIAN, Vincent CROIZIER, Frederic MERIZEN
---
--- Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
--- documentation files (the "Software"), to deal in the Software without restriction, including without
--- limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
--- the Software, and to permit persons to whom the Software is furnished to do so, subject to the following
--- conditions:
---
--- The above copyright notice and this permission notice shall be included in all copies or substantial
--- portions of the Software.
---
--- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
--- LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
--- EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
--- AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
--- OR OTHER DEALINGS IN THE SOFTWARE.
---
--- http://SmartEiffel.loria.fr - SmartEiffel at loria.fr
--- ------------------------------------------------------------------------------------------------------------
--
Lisaac compiler
More information about the Lisaac-commits
mailing list