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big: add div by 3.

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This commit is contained in:
Jeroen van Rijn
2021-07-24 19:01:55 +02:00
parent 31c94bd7f8
commit 2884fa5506
2 changed files with 119 additions and 6 deletions
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104
core/math/big/basic.odin
View File

@@ -953,4 +953,108 @@ _int_sqr :: proc(dest, src: ^Int) -> (err: Error) {
swap(dest, t);
destroy(t);
return err;
}
/*
Fivide by three (based on routine from MPI and the GMP manual).
*/
_int_div_3 :: proc(quotient, numerator: ^Int) -> (remainder: int, err: Error) {
/*
b = 2**MP_DIGIT_BIT / 3
*/
b := _WORD(1) << _WORD(_DIGIT_BITS) / _WORD(3);
q := &Int{};
if err = grow(q, numerator.used); err != .None { return -1, err; }
q.used = numerator.used;
q.sign = numerator.sign;
w, t: _WORD;
for ix := numerator.used; ix >= 0; ix -= 1 {
w = (w << _WORD(_DIGIT_BITS)) | _WORD(numerator.digit[ix]);
if w >= 3 {
/*
Multiply w by [1/3].
*/
t = (w * b) >> _WORD(_DIGIT_BITS);
/*
Now subtract 3 * [w/3] from w, to get the remainder.
*/
w -= t+t+t;
/*
Fixup the remainder as required since the optimization is not exact.
*/
for w >= 3 {
t += 1;
w -= 3;
}
} else {
t = 0;
}
q.digit[ix] = DIGIT(t);
}
remainder = int(w);
/*
[optional] store the quotient.
*/
if quotient != nil {
err = clamp(q);
swap(q, quotient);
}
destroy(q);
return remainder, .None;
}
/*
Slower bit-bang division... also smaller.
*/
_int_div_small :: proc(quotient, remainder, numerator, denominator: ^Int) -> (err: Error) {
// mp_int ta, tb, tq, q;
// int n;
// bool neg;
// mp_err err;
// /* init our temps */
// if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
// return err;
// }
// mp_set(&tq, 1uL);
// n = mp_count_bits(a) - mp_count_bits(b);
// if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR;
// if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR;
// if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR;
// if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR;
// while (n-- >= 0) {
// if (mp_cmp(&tb, &ta) != MP_GT) {
// if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR;
// if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR;
// }
// if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR;
// if ((err = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY) goto LBL_ERR;
// }
// /* now q == quotient and ta == remainder */
// neg = (a->sign != b->sign);
// if (c != NULL) {
// mp_exch(c, &q);
// c->sign = ((neg && !mp_iszero(c)) ? MP_NEG : MP_ZPOS);
// }
// if (d != NULL) {
// mp_exch(d, &ta);
// d->sign = (mp_iszero(d) ? MP_ZPOS : a->sign);
// }
// LBL_ERR:
// mp_clear_multi(&ta, &tb, &tq, &q, NULL);
// return err;
return .None;
}

21
core/math/big/example.odin
View File

@@ -26,6 +26,7 @@ print_configation :: proc() {
SQR_KARATSUBA_CUTOFF %v
MUL_TOOM_CUTOFF %v
SQR_TOOM_CUTOFF %v
`, _DIGIT_BITS,
_MIN_DIGIT_COUNT,
_MAX_DIGIT_COUNT,
@@ -37,8 +38,6 @@ _SQR_KARATSUBA_CUTOFF,
_MUL_TOOM_CUTOFF,
_SQR_TOOM_CUTOFF,
);
fmt.println();
}
print :: proc(name: string, a: ^Int, base := i8(16)) {
@@ -54,11 +53,21 @@ print :: proc(name: string, a: ^Int, base := i8(16)) {
demo :: proc() {
err: Error;
a, b, c := &Int{}, &Int{}, &Int{};
defer destroy(a, b, c);
i: int;
destination, source, quotient, remainder, numerator, denominator := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(destination, source, quotient, remainder, numerator, denominator);
err = set(a, 5125);
print("a", a);
err = set(numerator, 15625);
err = set(denominator, 3);
print("numerator ", numerator, 10);
print("denominator", denominator, 10);
i, err = _int_div_3(quotient, numerator);
print("quotient ", quotient, 10);
fmt.println("remainder ", i);
fmt.println("error", err);
}
main :: proc() {