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big: Add _private_int_sqr_toom.

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Jeroen van Rijn
2021-08-11 20:59:54 +02:00
parent 2b274fefbb
commit 5f34ff9f9f
4 changed files with 131 additions and 25 deletions
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core/math/big/private.odin
+121 -13
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@@ -387,37 +387,145 @@ _private_int_sqr_karatsuba :: proc(dest, src: ^Int, allocator := context.allocat
x0.used = B;
x1.used = src.used - B;
internal_copy_digits(x0, src, x0.used);
#force_inline internal_copy_digits(x0, src, x0.used);
#force_inline mem.copy_non_overlapping(&x1.digit[0], &src.digit[B], size_of(DIGIT) * x1.used);
internal_clamp(x0);
#force_inline internal_clamp(x0);
/*
Now calc the products x0*x0 and x1*x1.
*/
if err = internal_sqr(x0x0, x0); err != nil { return err; }
if err = internal_sqr(x1x1, x1); err != nil { return err; }
if err = internal_sqr(x0x0, x0); err != nil { return err; }
if err = internal_sqr(x1x1, x1); err != nil { return err; }
/*
Now calc (x1+x0)^2
*/
if err = internal_add(t1, x0, x1); err != nil { return err; }
if err = internal_sqr(t1, t1); err != nil { return err; }
if err = internal_add(t1, x0, x1); err != nil { return err; }
if err = internal_sqr(t1, t1); err != nil { return err; }
/*
Add x0y0
*/
if err = internal_add(t2, x0x0, x1x1); err != nil { return err; }
if err = internal_sub(t1, t1, t2); err != nil { return err; }
if err = internal_add(t2, x0x0, x1x1); err != nil { return err; }
if err = internal_sub(t1, t1, t2); err != nil { return err; }
/*
Shift by B.
*/
if err = internal_shl_digit(t1, B); err != nil { return err; }
if err = internal_shl_digit(x1x1, B * 2); err != nil { return err; }
if err = internal_add(t1, t1, x0x0); err != nil { return err; }
if err = internal_add(dest, t1, x1x1); err != nil { return err; }
if err = internal_shl_digit(t1, B); err != nil { return err; }
if err = internal_shl_digit(x1x1, B * 2); err != nil { return err; }
if err = internal_add(t1, t1, x0x0); err != nil { return err; }
if err = internal_add(dest, t1, x1x1); err != nil { return err; }
return internal_clamp(dest);
return #force_inline internal_clamp(dest);
}
/*
Squaring using Toom-Cook 3-way algorithm.
Setup and interpolation from algorithm SQR_3 in Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
*/
_private_int_sqr_toom :: proc(dest, src: ^Int, allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
S0, a0, a1, a2 := &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(S0, a0, a1, a2);
/*
Init temps.
*/
if err = internal_zero(S0); err != nil { return err; }
/*
B
*/
B := src.used / 3;
/*
a = a2 * x^2 + a1 * x + a0;
*/
if err = internal_grow(a0, B); err != nil { return err; }
if err = internal_grow(a1, B); err != nil { return err; }
if err = internal_grow(a2, src.used - (2 * B)); err != nil { return err; }
a0.used = B;
a1.used = B;
a2.used = src.used - 2 * B;
#force_inline mem.copy_non_overlapping(&a0.digit[0], &src.digit[ 0], size_of(DIGIT) * a0.used);
#force_inline mem.copy_non_overlapping(&a1.digit[0], &src.digit[ B], size_of(DIGIT) * a1.used);
#force_inline mem.copy_non_overlapping(&a2.digit[0], &src.digit[2 * B], size_of(DIGIT) * a2.used);
internal_clamp(a0);
internal_clamp(a1);
internal_clamp(a2);
/** S0 = a0^2; */
if err = internal_sqr(S0, a0); err != nil { return err; }
/** \\S1 = (a2 + a1 + a0)^2 */
/** \\S2 = (a2 - a1 + a0)^2 */
/** \\S1 = a0 + a2; */
/** a0 = a0 + a2; */
if err = internal_add(a0, a0, a2); err != nil { return err; }
/** \\S2 = S1 - a1; */
/** b = a0 - a1; */
if err = internal_sub(dest, a0, a1); err != nil { return err; }
/** \\S1 = S1 + a1; */
/** a0 = a0 + a1; */
if err = internal_add(a0, a0, a1); err != nil { return err; }
/** \\S1 = S1^2; */
/** a0 = a0^2; */
if err = internal_sqr(a0, a0); err != nil { return err; }
/** \\S2 = S2^2; */
/** b = b^2; */
if err = internal_sqr(dest, dest); err != nil { return err; }
/** \\ S3 = 2 * a1 * a2 */
/** \\S3 = a1 * a2; */
/** a1 = a1 * a2; */
if err = internal_mul(a1, a1, a2); err != nil { return err; }
/** \\S3 = S3 << 1; */
/** a1 = a1 << 1; */
if err = internal_shl(a1, a1, 1); err != nil { return err; }
/** \\S4 = a2^2; */
/** a2 = a2^2; */
if err = internal_sqr(a2, a2); err != nil { return err; }
/** \\ tmp = (S1 + S2)/2 */
/** \\tmp = S1 + S2; */
/** b = a0 + b; */
if err = internal_add(dest, a0, dest); err != nil { return err; }
/** \\tmp = tmp >> 1; */
/** b = b >> 1; */
if err = internal_shr(dest, dest, 1); err != nil { return err; }
/** \\ S1 = S1 - tmp - S3 */
/** \\S1 = S1 - tmp; */
/** a0 = a0 - b; */
if err = internal_sub(a0, a0, dest); err != nil { return err; }
/** \\S1 = S1 - S3; */
/** a0 = a0 - a1; */
if err = internal_sub(a0, a0, a1); err != nil { return err; }
/** \\S2 = tmp - S4 -S0 */
/** \\S2 = tmp - S4; */
/** b = b - a2; */
if err = internal_sub(dest, dest, a2); err != nil { return err; }
/** \\S2 = S2 - S0; */
/** b = b - S0; */
if err = internal_sub(dest, dest, S0); err != nil { return err; }
/** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */
/** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */
if err = internal_shl_digit( a2, 4 * B); err != nil { return err; }
if err = internal_shl_digit( a1, 3 * B); err != nil { return err; }
if err = internal_shl_digit(dest, 2 * B); err != nil { return err; }
if err = internal_shl_digit( a0, 1 * B); err != nil { return err; }
if err = internal_add(a2, a2, a1); err != nil { return err; }
if err = internal_add(dest, dest, a2); err != nil { return err; }
if err = internal_add(dest, dest, a0); err != nil { return err; }
if err = internal_add(dest, dest, S0); err != nil { return err; }
/** a^2 - P */
return #force_inline internal_clamp(dest);
}
/*