LAMMP 4.2.0
Lamina High-Precision Arithmetic Library
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宏定义 | 函数
sqr_toom4.c 文件参考
#include "../../../include/lammp/impl/mparam.h"
#include "../../../include/lammp/impl/toom_interp.h"
+ sqr_toom4.c 的引用(Include)关系图:

浏览源代码.

宏定义

#define a0   numa
 
#define a1   (numa + n)
 
#define a2   (numa + 2 * n)
 
#define a3   (numa + 3 * n)
 
#define amx   (dst + 4 * n + 2) /* n+1 */
 
#define apx   dst /* n+1 */
 
#define lmmp_sqr_(dst, numa, n)
 Copyright (C) 2026 HJimmyK(Jericho Knox)
 
#define tp   (scratch + 8 * n + 5)
 
#define v0   dst /* 2n */
 
#define v1   (dst + 2 * n) /* 2n+1 */
 
#define v2   scratch /* 2n+1 */
 
#define vh   (scratch + 4 * n + 2) /* 2n+1 */
 
#define vinf   (dst + 6 * n) /* s+t */
 
#define vm1   (scratch + 6 * n + 3) /* 2n+1 */
 
#define vm2   (scratch + 2 * n + 1) /* 2n+1 */
 

函数

void lmmp_sqr_toom4_ (mp_ptr restrict dst, mp_srcptr restrict numa, mp_size_t na)
 

宏定义说明

◆ a0

#define a0   numa

◆ a1

#define a1   (numa + n)

◆ a2

#define a2   (numa + 2 * n)

◆ a3

#define a3   (numa + 3 * n)

◆ amx

#define amx   (dst + 4 * n + 2) /* n+1 */

◆ apx

#define apx   dst /* n+1 */

◆ lmmp_sqr_

#define lmmp_sqr_ (   dst,
  numa,
  n 
)
值:
if ((n) < MUL_TOOM22_THRESHOLD) \
lmmp_sqr_basecase_((dst), (numa), (n)); \
else if ((n) < MUL_TOOM33_THRESHOLD) \
lmmp_sqr_toom2_((dst), (numa), (n)); \
else if ((n < MUL_TOOM44_THRESHOLD)) \
lmmp_sqr_toom3_((dst), (numa), (n)); \
else \
lmmp_sqr_toom4_((dst), (numa), (n))
MUL_TOOM22_THRESHOLD
#define MUL_TOOM22_THRESHOLD
Definition mparam.h:46
MUL_TOOM33_THRESHOLD
#define MUL_TOOM33_THRESHOLD
Definition mparam.h:50
MUL_TOOM44_THRESHOLD
#define MUL_TOOM44_THRESHOLD
Definition mparam.h:52
n
#define n

Copyright (C) 2026 HJimmyK(Jericho Knox)

This file is part of LAMMP.

LAMMP is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed WITHOUT ANY WARRANTY.

See https://www.gnu.org/licenses/.

在文件 sqr_toom4.c 第 21 行定义.

47 {
48 lmmp_param_assert(na > 0);
49 lmmp_param_assert(dst != NULL);
50 lmmp_param_assert(numa != NULL);
51 mp_size_t n, s;
52 mp_limb_t cy;
53
54#define a0 numa
55#define a1 (numa + n)
56#define a2 (numa + 2 * n)
57#define a3 (numa + 3 * n)
58
59 n = (na + 3) >> 2;
60 TEMP_S_DECL;
61 mp_ptr restrict scratch = SALLOC_TYPE(8 * n + 8, mp_limb_t);
62
63 s = na - 3 * n;
64
65 lmmp_debug_assert(0 < s && s <= n);
66
67 /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
68 * following limb, so these must be computed in order, and we need a
69 * one limb gap to tp. */
70#define v0 dst /* 2n */
71#define v1 (dst + 2 * n) /* 2n+1 */
72#define vinf (dst + 6 * n) /* s+t */
73#define v2 scratch /* 2n+1 */
74#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
75#define vh (scratch + 4 * n + 2) /* 2n+1 */
76#define vm1 (scratch + 6 * n + 3) /* 2n+1 */
77#define tp (scratch + 8 * n + 5)
78
79 /* No overlap with v1 */
80#define apx dst /* n+1 */
81#define amx (dst + 4 * n + 2) /* n+1 */
82
83 /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
84 lmmp_toom_eval_dgr3_pm2_(apx, amx, numa, n, s, tp);
85
86 lmmp_sqr_(v2, apx, n + 1); /* v2, 2n+1 limbs */
87 lmmp_sqr_(vm2, amx, n + 1); /* vm2, 2n+1 limbs */
88
89 /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
90 cy = lmmp_addshl1_n_(apx, a1, a0, n);
91 cy = 2 * cy + lmmp_addshl1_n_(apx, a2, apx, n);
92 if (s < n) {
93 mp_limb_t cy2;
94 cy2 = lmmp_addshl1_n_(apx, a3, apx, s);
95 apx[n] = 2 * cy + lmmp_shl_(apx + s, apx + s, n - s, 1);
96 lmmp_inc_1(apx + s, cy2);
97 } else
98 apx[n] = 2 * cy + lmmp_addshl1_n_(apx, a3, apx, n);
99
100 lmmp_debug_assert(apx[n] < 15);
101
102 lmmp_sqr_(vh, apx, n + 1); /* vh, 2n+1 limbs */
103
104 /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
105 lmmp_toom_eval_dgr3_pm1_(apx, amx, numa, n, s, tp);
106
107 lmmp_sqr_(v1, apx, n + 1); /* v1, 2n+1 limbs */
108 lmmp_sqr_(vm1, amx, n + 1); /* vm1, 2n+1 limbs */
109
110 lmmp_sqr_(v0, a0, n);
111 lmmp_sqr_(vinf, a3, s); /* vinf, 2s limbs */
112
113 lmmp_toom_interp7_(dst, n, (enum toom7_flags)0, vm2, vm1, v2, vh, 2 * s, tp);
114 TEMP_S_FREE;
115}
mp_ptr
mp_limb_t * mp_ptr
Definition lmmp.h:80
mp_size_t
uint64_t mp_size_t
Definition lmmp.h:77
lmmp_debug_assert
#define lmmp_debug_assert(x)
Definition lmmp.h:390
mp_limb_t
uint64_t mp_limb_t
Definition lmmp.h:76
lmmp_param_assert
#define lmmp_param_assert(x)
Definition lmmp.h:401
lmmp_addshl1_n_
mp_limb_t lmmp_addshl1_n_(mp_ptr dst, mp_srcptr numa, mp_srcptr numb, mp_size_t n)
加法结合左移1位操作 [dst,n] = [numa,n] + ([numb,n] << 1)
Definition shl.c:66
lmmp_shl_
mp_limb_t lmmp_shl_(mp_ptr dst, mp_srcptr numa, mp_size_t na, mp_size_t shl)
大数左移操作 [dst,na] = [numa,na]<<shl，dst的低shl位填充0
Definition shl.c:19
lmmp_inc_1
#define lmmp_inc_1(p, inc)
大数加指定值宏（预期无进位）
Definition lmmpn.h:950
s
#define s
scratch
#define scratch
lmmp_sqr_
#define lmmp_sqr_(dst, numa, n)
Copyright (C) 2026 HJimmyK(Jericho Knox)
Definition sqr_toom4.c:21
v0
#define v0
a3
#define a3
v2
#define v2
vm1
#define vm1
apx
#define apx
vh
#define vh
a2
#define a2
a0
#define a0
tp
#define tp
a1
#define a1
vinf
#define vinf
amx
#define amx
v1
#define v1
vm2
#define vm2
SALLOC_TYPE
#define SALLOC_TYPE(n, type)
Definition tmp_alloc.h:144
TEMP_S_DECL
#define TEMP_S_DECL
Definition tmp_alloc.h:133
TEMP_S_FREE
#define TEMP_S_FREE
Definition tmp_alloc.h:166
toom7_flags
toom7_flags
Definition toom_interp.h:24
lmmp_toom_interp7_
void lmmp_toom_interp7_(mp_ptr dst, mp_size_t n, enum toom7_flags flags, mp_ptr w1, mp_ptr w3, mp_ptr w4, mp_ptr w5, mp_size_t w6n, mp_ptr tp)
Toom插值计算（7点插值）：用于Toom-44、Toom-53、Toom-62 乘法算法
Definition mul_toom_interp7.c:55
lmmp_toom_eval_dgr3_pm2_
int lmmp_toom_eval_dgr3_pm2_(mp_ptr xp2, mp_ptr xm2, mp_srcptr xp, mp_size_t n, mp_size_t x3n, mp_ptr tp)
Toom-3 专用：3次多项式在 x = +2 和 x = -2 处求值 计算 P(+2) 和 P(-2)，其中 P(x) 是一个3次多项式（4段系数）。
Definition mul_toom_eval.c:39
lmmp_toom_eval_dgr3_pm1_
int lmmp_toom_eval_dgr3_pm1_(mp_ptr xp1, mp_ptr xm1, mp_srcptr xp, mp_size_t n, mp_size_t x3n, mp_ptr tp)
Toom-3 专用：3次多项式在 x = +1 和 x = -1 处求值 计算 P(+1) 和 P(-1)，其中 P(x) 是一个3次多项式（4段系数）。
Definition mul_toom_eval.c:19

◆ tp

#define tp   (scratch + 8 * n + 5)

◆ v0

#define v0   dst /* 2n */

◆ v1

#define v1   (dst + 2 * n) /* 2n+1 */

◆ v2

#define v2   scratch /* 2n+1 */

◆ vh

#define vh   (scratch + 4 * n + 2) /* 2n+1 */

◆ vinf

#define vinf   (dst + 6 * n) /* s+t */

◆ vm1

#define vm1   (scratch + 6 * n + 3) /* 2n+1 */

◆ vm2

#define vm2   (scratch + 2 * n + 1) /* 2n+1 */

函数说明

◆ lmmp_sqr_toom4_()

void lmmp_sqr_toom4_ ( mp_ptr restrict  dst,
mp_srcptr restrict  numa,
mp_size_t  na 
)

在文件 sqr_toom4.c 第 47 行定义.

47 {
48 lmmp_param_assert(na > 0);
49 lmmp_param_assert(dst != NULL);
50 lmmp_param_assert(numa != NULL);
51 mp_size_t n, s;
52 mp_limb_t cy;
53
54#define a0 numa
55#define a1 (numa + n)
56#define a2 (numa + 2 * n)
57#define a3 (numa + 3 * n)
58
59 n = (na + 3) >> 2;
60 TEMP_S_DECL;
61 mp_ptr restrict scratch = SALLOC_TYPE(8 * n + 8, mp_limb_t);
62
63 s = na - 3 * n;
64
65 lmmp_debug_assert(0 < s && s <= n);
66
67 /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
68 * following limb, so these must be computed in order, and we need a
69 * one limb gap to tp. */
70#define v0 dst /* 2n */
71#define v1 (dst + 2 * n) /* 2n+1 */
72#define vinf (dst + 6 * n) /* s+t */
73#define v2 scratch /* 2n+1 */
74#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
75#define vh (scratch + 4 * n + 2) /* 2n+1 */
76#define vm1 (scratch + 6 * n + 3) /* 2n+1 */
77#define tp (scratch + 8 * n + 5)
78
79 /* No overlap with v1 */
80#define apx dst /* n+1 */
81#define amx (dst + 4 * n + 2) /* n+1 */
82
83 /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
84 lmmp_toom_eval_dgr3_pm2_(apx, amx, numa, n, s, tp);
85
86 lmmp_sqr_(v2, apx, n + 1); /* v2, 2n+1 limbs */
87 lmmp_sqr_(vm2, amx, n + 1); /* vm2, 2n+1 limbs */
88
89 /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
90 cy = lmmp_addshl1_n_(apx, a1, a0, n);
91 cy = 2 * cy + lmmp_addshl1_n_(apx, a2, apx, n);
92 if (s < n) {
93 mp_limb_t cy2;
94 cy2 = lmmp_addshl1_n_(apx, a3, apx, s);
95 apx[n] = 2 * cy + lmmp_shl_(apx + s, apx + s, n - s, 1);
96 lmmp_inc_1(apx + s, cy2);
97 } else
98 apx[n] = 2 * cy + lmmp_addshl1_n_(apx, a3, apx, n);
99
100 lmmp_debug_assert(apx[n] < 15);
101
102 lmmp_sqr_(vh, apx, n + 1); /* vh, 2n+1 limbs */
103
104 /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
105 lmmp_toom_eval_dgr3_pm1_(apx, amx, numa, n, s, tp);
106
107 lmmp_sqr_(v1, apx, n + 1); /* v1, 2n+1 limbs */
108 lmmp_sqr_(vm1, amx, n + 1); /* vm1, 2n+1 limbs */
109
110 lmmp_sqr_(v0, a0, n);
111 lmmp_sqr_(vinf, a3, s); /* vinf, 2s limbs */
112
113 lmmp_toom_interp7_(dst, n, (enum toom7_flags)0, vm2, vm1, v2, vh, 2 * s, tp);
114 TEMP_S_FREE;
115}

引用了 a0, a1, a2, a3, amx, apx, lmmp_addshl1_n_(), lmmp_debug_assert, lmmp_inc_1, lmmp_param_assert, lmmp_shl_(), lmmp_sqr_, lmmp_toom_eval_dgr3_pm1_(), lmmp_toom_eval_dgr3_pm2_(), lmmp_toom_interp7_(), n, s, SALLOC_TYPE, scratch, TEMP_S_DECL, TEMP_S_FREE, tp, v0, v1, v2, vh, vinf, vm1 , 以及 vm2.

+ 函数调用图: