LAMMP 4.2.0
Lamina High-Precision Arithmetic Library
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宏定义 | 函数
mul_toom43.c 文件参考
#include "../../../include/lammp/impl/mparam.h"
#include "../../../include/lammp/impl/toom_interp.h"
+ mul_toom43.c 的引用(Include)关系图:

浏览源代码.

宏定义

#define a0   numa
 
#define a0a2   scratch
 
#define a1   (numa + n)
 
#define a1a3   asm1
 
#define a2   (numa + 2 * n)
 
#define a3   (numa + 3 * n)
 
#define as1   (dst + 4 * n + 4) /* n+1 */
 
#define as2   (dst + 3 * n + 3) /* n+1 */
 
#define asm1   (scratch + 3 * n + 3) /* n+1 */
 
#define asm2   (scratch + 4 * n + 4) /* n+1 */
 
#define b0   numb
 
#define b0b2   scratch
 
#define b1   (numb + n)
 
#define b1d   bsm1
 
#define b2   (numb + 2 * n)
 
#define bs1   dst /* n+1 */
 
#define bs2   (dst + 2 * n + 2) /* n+1 */
 
#define bsm1   (scratch + 2 * n + 2) /* n+1 */
 
#define bsm2   (dst + n + 1) /* n+1 */
 
#define lmmp_mul_n_(dst, numa, numb, n)
 Copyright (C) 2026 HJimmyK(Jericho Knox)
 
#define v0   dst /* 2n */
 
#define v1   (dst + 2 * n) /* 2n+1 */
 
#define v2   (scratch + 4 * n + 2) /* 2n+1 */
 
#define vinf   (dst + 5 * n) /* s+t */
 
#define vm1   (scratch) /* 2n+1 */
 
#define vm2   (scratch + 2 * n + 1) /* 2n+1 */
 

函数

void lmmp_mul_toom43_ (mp_ptr restrict dst, mp_srcptr restrict numa, mp_size_t na, mp_srcptr restrict numb, mp_size_t nb)
 

宏定义说明

◆ a0

#define a0   numa

◆ a0a2

#define a0a2   scratch

◆ a1

#define a1   (numa + n)

◆ a1a3

#define a1a3   asm1

◆ a2

#define a2   (numa + 2 * n)

◆ a3

#define a3   (numa + 3 * n)

◆ as1

#define as1   (dst + 4 * n + 4) /* n+1 */

◆ as2

#define as2   (dst + 3 * n + 3) /* n+1 */

◆ asm1

#define asm1   (scratch + 3 * n + 3) /* n+1 */

◆ asm2

#define asm2   (scratch + 4 * n + 4) /* n+1 */

◆ b0

#define b0   numb

◆ b0b2

#define b0b2   scratch

◆ b1

#define b1   (numb + n)

◆ b1d

#define b1d   bsm1

◆ b2

#define b2   (numb + 2 * n)

◆ bs1

#define bs1   dst /* n+1 */

◆ bs2

#define bs2   (dst + 2 * n + 2) /* n+1 */

◆ bsm1

#define bsm1   (scratch + 2 * n + 2) /* n+1 */

◆ bsm2

#define bsm2   (dst + n + 1) /* n+1 */

◆ lmmp_mul_n_

#define lmmp_mul_n_ (   dst,
  numa,
  numb,
  n 
)
值:
if ((n) < MUL_TOOM22_THRESHOLD) \
lmmp_mul_basecase_((dst), (numa), (n), (numb), (n)); \
else if ((n) < MUL_TOOM33_THRESHOLD) \
lmmp_mul_toom22_((dst), (numa), (n), (numb), (n)); \
else if ((n) < MUL_TOOM44_THRESHOLD) \
lmmp_mul_toom33_((dst), (numa), (n), (numb), (n)); \
else \
lmmp_mul_toom44_((dst), (numa), (n), (numb), (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
numb
#define numb
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 mul_toom43.c 第 21 行定义.

48 {
49 lmmp_param_assert(4 * na >= 5 * nb);
50 lmmp_param_assert(3 * na <= 5 * nb);
51 mp_size_t n, s, t;
52 enum toom6_flags flags;
53 mp_limb_t cy;
54
55#define a0 numa
56#define a1 (numa + n)
57#define a2 (numa + 2 * n)
58#define a3 (numa + 3 * n)
59#define b0 numb
60#define b1 (numb + n)
61#define b2 (numb + 2 * n)
62
63 n = 1 + (3 * na >= 4 * nb ? (na - 1) >> 2 : (nb - 1) / (mp_size_t)3);
64 TEMP_S_DECL;
65 mp_limb_t* restrict scratch = SALLOC_TYPE(6 * n + 6, mp_limb_t);
66
67 s = na - 3 * n;
68 t = nb - 2 * n;
69
70 lmmp_debug_assert(0 < s && s <= n);
71 lmmp_debug_assert(0 < t && t <= n);
72
73 /* This is true whenever na >= 25 or nb >= 19, I think. It
74 guarantees that we can fit 5 values of size n+1 in the product
75 area. */
76 lmmp_debug_assert(s + t >= 5);
77
78#define v0 dst /* 2n */
79#define vm1 (scratch) /* 2n+1 */
80#define v1 (dst + 2 * n) /* 2n+1 */
81#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
82#define v2 (scratch + 4 * n + 2) /* 2n+1 */
83#define vinf (dst + 5 * n) /* s+t */
84#define bs1 dst /* n+1 */
85#define bsm1 (scratch + 2 * n + 2) /* n+1 */
86#define asm1 (scratch + 3 * n + 3) /* n+1 */
87#define asm2 (scratch + 4 * n + 4) /* n+1 */
88#define bsm2 (dst + n + 1) /* n+1 */
89#define bs2 (dst + 2 * n + 2) /* n+1 */
90#define as2 (dst + 3 * n + 3) /* n+1 */
91#define as1 (dst + 4 * n + 4) /* n+1 */
92
93 /* Total sccratch need is 6 * n + 3 + 1; we allocate one extra
94 limb, because products will overwrite 2n+2 limbs. */
95
96#define a0a2 scratch
97#define b0b2 scratch
98#define a1a3 asm1
99#define b1d bsm1
100
101 /* Compute as2 and asm2. */
102 flags = (enum toom6_flags)(toom6_vm2_neg & lmmp_toom_eval_dgr3_pm2_(as2, asm2, numa, n, s, a1a3));
103
104 /* Compute bs2 and bsm2. */
105 b1d[n] = lmmp_shl_(b1d, b1, n, 1); /* 2b1 */
106 cy = lmmp_shl_(b0b2, b2, t, 2); /* 4b2 */
107 cy += lmmp_add_n_(b0b2, b0b2, b0, t); /* 4b2 + b0 */
108 if (t != n)
109 cy = lmmp_add_1_(b0b2 + t, b0 + t, n - t, cy);
110 b0b2[n] = cy;
111
112 if (lmmp_cmp_(b0b2, b1d, n + 1) < 0) {
113 lmmp_add_n_sub_n_(bs2, bsm2, b1d, b0b2, n + 1);
114 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
115 } else {
116 lmmp_add_n_sub_n_(bs2, bsm2, b0b2, b1d, n + 1);
117 }
118
119
120 /* Compute as1 and asm1. */
121 flags = (enum toom6_flags)(flags ^ (toom6_vm1_neg & lmmp_toom_eval_dgr3_pm1_(as1, asm1, numa, n, s, a0a2)));
122
123 /* Compute bs1 and bsm1. */
124 bsm1[n] = lmmp_add_(bsm1, b0, n, b2, t);
125 if (bsm1[n] == 0 && lmmp_cmp_(bsm1, b1, n) < 0) {
126 cy = lmmp_add_n_sub_n_(bs1, bsm1, b1, bsm1, n);
127 bs1[n] = cy >> 1;
128 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
129 } else {
130 cy = lmmp_add_n_sub_n_(bs1, bsm1, bsm1, b1, n);
131 bs1[n] = bsm1[n] + (cy >> 1);
132 bsm1[n] -= cy & 1;
133 }
134
135 lmmp_debug_assert(as1[n] <= 3);
136 lmmp_debug_assert(bs1[n] <= 2);
137 lmmp_debug_assert(asm1[n] <= 1);
138 lmmp_debug_assert(bsm1[n] <= 1);
139 lmmp_debug_assert(as2[n] <= 14);
140 lmmp_debug_assert(bs2[n] <= 6);
141 lmmp_debug_assert(asm2[n] <= 9);
142 lmmp_debug_assert(bsm2[n] <= 4);
143
144 /* vm1, 2n+1 limbs */
145 lmmp_mul_n_(vm1, asm1, bsm1, n + 1); /* W4 */
146
147 /* vm2, 2n+1 limbs */
148 lmmp_mul_n_(vm2, asm2, bsm2, n + 1); /* W2 */
149
150 /* v2, 2n+1 limbs */
151 lmmp_mul_n_(v2, as2, bs2, n + 1); /* W1 */
152
153 /* v1, 2n+1 limbs */
154 lmmp_mul_n_(v1, as1, bs1, n + 1); /* W3 */
155
156 /* vinf, s+t limbs */ /* W0 */
157 if (s > t)
158 lmmp_mul_(vinf, a3, s, b2, t);
159 else
160 lmmp_mul_(vinf, b2, t, a3, s);
161
162 /* v0, 2n limbs */
163 lmmp_mul_n_(v0, numa, numb, n); /* W5 */
164
165 lmmp_toom_interp6_(dst, n, flags, vm1, vm2, v2, t + s);
166
167 TEMP_S_FREE;
168#undef v0
169#undef vm1
170#undef v1
171#undef vm2
172#undef v2
173#undef vinf
174#undef bs1
175#undef bs2
176#undef bsm1
177#undef bsm2
178#undef asm1
179#undef asm2
180#undef as1
181#undef as2
182#undef a0a2
183#undef b0b2
184#undef a1a3
185#undef b1d
186#undef a0
187#undef a1
188#undef a2
189#undef a3
190#undef b0
191#undef b1
192#undef b2
193}
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_add_
static mp_limb_t lmmp_add_(mp_ptr dst, mp_srcptr numa, mp_size_t na, mp_srcptr numb, mp_size_t nb)
大数加法静态内联函数 [dst,na]=[numa,na]+[numb,nb]
Definition lmmpn.h:1050
lmmp_cmp_
static int lmmp_cmp_(mp_srcptr numa, mp_srcptr numb, mp_size_t n)
大数比较函数（内联）
Definition lmmpn.h:996
lmmp_add_1_
static mp_limb_t lmmp_add_1_(mp_ptr dst, mp_srcptr numa, mp_size_t na, mp_limb_t x)
大数加单精度数静态内联函数 [dst,na]=[numa,na]+x
Definition lmmpn.h:1103
lmmp_mul_
void lmmp_mul_(mp_ptr dst, mp_srcptr numa, mp_size_t na, mp_srcptr numb, mp_size_t nb)
不等长大数乘法操作 [dst,na+nb] = [numa,na] * [numb,nb]
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_add_n_sub_n_
mp_limb_t lmmp_add_n_sub_n_(mp_ptr dsta, mp_ptr dstb, mp_srcptr numa, mp_srcptr numb, mp_size_t n)
同时执行n位加法和减法 ([dsta,n],[dstb,n]) = ([numa,n]+[numb,n],[numa,n]-[numb,n])
Definition add_n_sub_n.c:20
lmmp_add_n_
mp_limb_t lmmp_add_n_(mp_ptr dst, mp_srcptr numa, mp_srcptr numb, mp_size_t n)
无进位的n位加法 [dst,n] = [numa,n] + [numb,n]
Definition add_n.c:81
t
#define t
s
#define s
bs1
#define bs1
bs2
#define bs2
b0
#define b0
v0
#define v0
a3
#define a3
lmmp_mul_n_
#define lmmp_mul_n_(dst, numa, numb, n)
Copyright (C) 2026 HJimmyK(Jericho Knox)
Definition mul_toom43.c:21
b1
#define b1
bsm1
#define bsm1
as2
#define as2
v2
#define v2
vm1
#define vm1
b0b2
#define b0b2
asm2
#define asm2
bsm2
#define bsm2
a0a2
#define a0a2
asm1
#define asm1
b2
#define b2
vinf
#define vinf
as1
#define as1
v1
#define v1
a1a3
#define a1a3
vm2
#define vm2
b1d
#define b1d
scratch
#define scratch
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
lmmp_toom_interp6_
void lmmp_toom_interp6_(mp_ptr dst, mp_size_t n, enum toom6_flags flags, mp_ptr w4, mp_ptr w2, mp_ptr w1, mp_size_t w0n)
Toom插值计算（6点插值）：用于Toom-43和Toom-52 乘法算法
Definition mul_toom_interp6.c:49
toom6_flags
toom6_flags
Copyright (C) 2026 HJimmyK(Jericho Knox)
Definition toom_interp.h:22
toom6_vm2_neg
@ toom6_vm2_neg
Definition toom_interp.h:22
toom6_vm1_neg
@ toom6_vm1_neg
Definition toom_interp.h:22
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

◆ v0

#define v0   dst /* 2n */

◆ v1

#define v1   (dst + 2 * n) /* 2n+1 */

◆ v2

#define v2   (scratch + 4 * n + 2) /* 2n+1 */

◆ vinf

#define vinf   (dst + 5 * n) /* s+t */

◆ vm1

#define vm1   (scratch) /* 2n+1 */

◆ vm2

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

函数说明

◆ lmmp_mul_toom43_()

void lmmp_mul_toom43_ ( mp_ptr restrict  dst,
mp_srcptr restrict  numa,
mp_size_t  na,
mp_srcptr restrict  numb,
mp_size_t  nb 
)

在文件 mul_toom43.c 第 48 行定义.

48 {
49 lmmp_param_assert(4 * na >= 5 * nb);
50 lmmp_param_assert(3 * na <= 5 * nb);
51 mp_size_t n, s, t;
52 enum toom6_flags flags;
53 mp_limb_t cy;
54
55#define a0 numa
56#define a1 (numa + n)
57#define a2 (numa + 2 * n)
58#define a3 (numa + 3 * n)
59#define b0 numb
60#define b1 (numb + n)
61#define b2 (numb + 2 * n)
62
63 n = 1 + (3 * na >= 4 * nb ? (na - 1) >> 2 : (nb - 1) / (mp_size_t)3);
64 TEMP_S_DECL;
65 mp_limb_t* restrict scratch = SALLOC_TYPE(6 * n + 6, mp_limb_t);
66
67 s = na - 3 * n;
68 t = nb - 2 * n;
69
70 lmmp_debug_assert(0 < s && s <= n);
71 lmmp_debug_assert(0 < t && t <= n);
72
73 /* This is true whenever na >= 25 or nb >= 19, I think. It
74 guarantees that we can fit 5 values of size n+1 in the product
75 area. */
76 lmmp_debug_assert(s + t >= 5);
77
78#define v0 dst /* 2n */
79#define vm1 (scratch) /* 2n+1 */
80#define v1 (dst + 2 * n) /* 2n+1 */
81#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
82#define v2 (scratch + 4 * n + 2) /* 2n+1 */
83#define vinf (dst + 5 * n) /* s+t */
84#define bs1 dst /* n+1 */
85#define bsm1 (scratch + 2 * n + 2) /* n+1 */
86#define asm1 (scratch + 3 * n + 3) /* n+1 */
87#define asm2 (scratch + 4 * n + 4) /* n+1 */
88#define bsm2 (dst + n + 1) /* n+1 */
89#define bs2 (dst + 2 * n + 2) /* n+1 */
90#define as2 (dst + 3 * n + 3) /* n+1 */
91#define as1 (dst + 4 * n + 4) /* n+1 */
92
93 /* Total sccratch need is 6 * n + 3 + 1; we allocate one extra
94 limb, because products will overwrite 2n+2 limbs. */
95
96#define a0a2 scratch
97#define b0b2 scratch
98#define a1a3 asm1
99#define b1d bsm1
100
101 /* Compute as2 and asm2. */
102 flags = (enum toom6_flags)(toom6_vm2_neg & lmmp_toom_eval_dgr3_pm2_(as2, asm2, numa, n, s, a1a3));
103
104 /* Compute bs2 and bsm2. */
105 b1d[n] = lmmp_shl_(b1d, b1, n, 1); /* 2b1 */
106 cy = lmmp_shl_(b0b2, b2, t, 2); /* 4b2 */
107 cy += lmmp_add_n_(b0b2, b0b2, b0, t); /* 4b2 + b0 */
108 if (t != n)
109 cy = lmmp_add_1_(b0b2 + t, b0 + t, n - t, cy);
110 b0b2[n] = cy;
111
112 if (lmmp_cmp_(b0b2, b1d, n + 1) < 0) {
113 lmmp_add_n_sub_n_(bs2, bsm2, b1d, b0b2, n + 1);
114 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
115 } else {
116 lmmp_add_n_sub_n_(bs2, bsm2, b0b2, b1d, n + 1);
117 }
118
119
120 /* Compute as1 and asm1. */
121 flags = (enum toom6_flags)(flags ^ (toom6_vm1_neg & lmmp_toom_eval_dgr3_pm1_(as1, asm1, numa, n, s, a0a2)));
122
123 /* Compute bs1 and bsm1. */
124 bsm1[n] = lmmp_add_(bsm1, b0, n, b2, t);
125 if (bsm1[n] == 0 && lmmp_cmp_(bsm1, b1, n) < 0) {
126 cy = lmmp_add_n_sub_n_(bs1, bsm1, b1, bsm1, n);
127 bs1[n] = cy >> 1;
128 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
129 } else {
130 cy = lmmp_add_n_sub_n_(bs1, bsm1, bsm1, b1, n);
131 bs1[n] = bsm1[n] + (cy >> 1);
132 bsm1[n] -= cy & 1;
133 }
134
135 lmmp_debug_assert(as1[n] <= 3);
136 lmmp_debug_assert(bs1[n] <= 2);
137 lmmp_debug_assert(asm1[n] <= 1);
138 lmmp_debug_assert(bsm1[n] <= 1);
139 lmmp_debug_assert(as2[n] <= 14);
140 lmmp_debug_assert(bs2[n] <= 6);
141 lmmp_debug_assert(asm2[n] <= 9);
142 lmmp_debug_assert(bsm2[n] <= 4);
143
144 /* vm1, 2n+1 limbs */
145 lmmp_mul_n_(vm1, asm1, bsm1, n + 1); /* W4 */
146
147 /* vm2, 2n+1 limbs */
148 lmmp_mul_n_(vm2, asm2, bsm2, n + 1); /* W2 */
149
150 /* v2, 2n+1 limbs */
151 lmmp_mul_n_(v2, as2, bs2, n + 1); /* W1 */
152
153 /* v1, 2n+1 limbs */
154 lmmp_mul_n_(v1, as1, bs1, n + 1); /* W3 */
155
156 /* vinf, s+t limbs */ /* W0 */
157 if (s > t)
158 lmmp_mul_(vinf, a3, s, b2, t);
159 else
160 lmmp_mul_(vinf, b2, t, a3, s);
161
162 /* v0, 2n limbs */
163 lmmp_mul_n_(v0, numa, numb, n); /* W5 */
164
165 lmmp_toom_interp6_(dst, n, flags, vm1, vm2, v2, t + s);
166
167 TEMP_S_FREE;
168#undef v0
169#undef vm1
170#undef v1
171#undef vm2
172#undef v2
173#undef vinf
174#undef bs1
175#undef bs2
176#undef bsm1
177#undef bsm2
178#undef asm1
179#undef asm2
180#undef as1
181#undef as2
182#undef a0a2
183#undef b0b2
184#undef a1a3
185#undef b1d
186#undef a0
187#undef a1
188#undef a2
189#undef a3
190#undef b0
191#undef b1
192#undef b2
193}

引用了 a0a2, a1a3, a3, as1, as2, asm1, asm2, b0, b0b2, b1, b1d, b2, bs1, bs2, bsm1, bsm2, lmmp_add_(), lmmp_add_1_(), lmmp_add_n_(), lmmp_add_n_sub_n_(), lmmp_cmp_(), lmmp_debug_assert, lmmp_mul_(), lmmp_mul_n_, lmmp_param_assert, lmmp_shl_(), lmmp_toom_eval_dgr3_pm1_(), lmmp_toom_eval_dgr3_pm2_(), lmmp_toom_interp6_(), n, numb, s, SALLOC_TYPE, scratch, t, TEMP_S_DECL, TEMP_S_FREE, toom6_vm1_neg, toom6_vm2_neg, v0, v1, v2, vinf, vm1 , 以及 vm2.

+ 函数调用图: