LAMMP 4.2.0
Lamina High-Precision Arithmetic Library
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宏定义 | 函数
mul_toom52.c 文件参考
#include "../../../include/lammp/impl/mparam.h"
#include "../../../include/lammp/impl/toom_interp.h"
+ mul_toom52.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 a4   (numa + 4 * 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 b1   (numb + n)
 
#define bs1   dst /* n+1 */
 
#define bs2   (dst + 2 * n + 2) /* n+1 */
 
#define bsm1   (scratch + 2 * n + 2) /* n */
 
#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_toom52_ (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)

◆ a4

#define a4   (numa + 4 * 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

◆ b1

#define b1   (numb + n)

◆ bs1

#define bs1   dst /* n+1 */

◆ bs2

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

◆ bsm1

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

◆ 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_toom52.c 第 21 行定义.

52 {
53 lmmp_param_assert(9 * na >= 20 * nb);
54 lmmp_param_assert(3 * nb >= na);
55 mp_size_t n, s, t;
56 enum toom6_flags flags;
57
58#define a0 numa
59#define a1 (numa + n)
60#define a2 (numa + 2 * n)
61#define a3 (numa + 3 * n)
62#define a4 (numa + 4 * n)
63#define b0 numb
64#define b1 (numb + n)
65
66 n = 1 + (2 * na >= 5 * nb ? (na - 1) / (mp_size_t)5 : (nb - 1) >> 1);
67 TEMP_S_DECL;
68 mp_ptr restrict scratch = SALLOC_TYPE(6 * n + 6, mp_limb_t);
69
70 s = na - 4 * n;
71 t = nb - n;
72
73 lmmp_debug_assert(0 < s && s <= n);
74 lmmp_debug_assert(0 < t && t <= n);
75
76 /* Ensures that 5 values of n+1 limbs each fits in the product area.
77 Borderline cases are na = 32, nb = 8, n = 7, and na = 36, bn = 9,
78 n = 8. */
79 lmmp_debug_assert(s + t >= 5);
80
81#define v0 dst /* 2n */
82#define vm1 (scratch) /* 2n+1 */
83#define v1 (dst + 2 * n) /* 2n+1 */
84#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
85#define v2 (scratch + 4 * n + 2) /* 2n+1 */
86#define vinf (dst + 5 * n) /* s+t */
87#define bs1 dst /* n+1 */
88#define bsm1 (scratch + 2 * n + 2) /* n */
89#define asm1 (scratch + 3 * n + 3) /* n+1 */
90#define asm2 (scratch + 4 * n + 4) /* n+1 */
91#define bsm2 (dst + n + 1) /* n+1 */
92#define bs2 (dst + 2 * n + 2) /* n+1 */
93#define as2 (dst + 3 * n + 3) /* n+1 */
94#define as1 (dst + 4 * n + 4) /* n+1 */
95
96
97#define a0a2 scratch
98#define a1a3 asm1
99
100 /* Compute as2 and asm2. */
101 flags = (enum toom6_flags)(toom6_vm2_neg & lmmp_toom_eval_pm2_(as2, asm2, 4, numa, n, s, a1a3));
102
103 /* Compute bs1 and bsm1. */
104 if (t == n) {
105 mp_limb_t cy;
106 if (lmmp_cmp_(b0, b1, n) < 0) {
107 cy = lmmp_add_n_sub_n_(bs1, bsm1, b1, b0, n);
108 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
109 } else {
110 cy = lmmp_add_n_sub_n_(bs1, bsm1, b0, b1, n);
111 }
112 bs1[n] = cy >> 1;
113 } else {
114 bs1[n] = lmmp_add_(bs1, b0, n, b1, t);
115 if (lmmp_zero_q_(b0 + t, n - t) && lmmp_cmp_(b0, b1, t) < 0) {
116 lmmp_sub_n_(bsm1, b1, b0, t);
117 lmmp_zero(bsm1 + t, n - t);
118 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
119 } else {
120 lmmp_sub_(bsm1, b0, n, b1, t);
121 }
122 }
123
124 /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
125 lmmp_add_(bs2, bs1, n + 1, b1, t);
126 if (flags & toom6_vm1_neg) {
127 bsm2[n] = lmmp_add_(bsm2, bsm1, n, b1, t);
128 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
129 } else {
130 bsm2[n] = 0;
131 if (t == n) {
132 if (lmmp_cmp_(bsm1, b1, n) < 0) {
133 lmmp_sub_n_(bsm2, b1, bsm1, n);
134 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
135 } else {
136 lmmp_sub_n_(bsm2, bsm1, b1, n);
137 }
138 } else {
139 if (lmmp_zero_q_(bsm1 + t, n - t) && lmmp_cmp_(bsm1, b1, t) < 0) {
140 lmmp_sub_n_(bsm2, b1, bsm1, t);
141 lmmp_zero(bsm2 + t, n - t);
142 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
143 } else {
144 lmmp_sub_(bsm2, bsm1, n, b1, t);
145 }
146 }
147 }
148
149 /* Compute as1 and asm1. */
150 flags = (enum toom6_flags)(flags ^ (toom6_vm1_neg & lmmp_toom_eval_pm1_(as1, asm1, 4, numa, n, s, a0a2)));
151
152 lmmp_debug_assert(as1[n] <= 4);
153 lmmp_debug_assert(bs1[n] <= 1);
154 lmmp_debug_assert(asm1[n] <= 2);
155 /* lmmp_debug_assert (bsm1[n] <= 1); */
156 lmmp_debug_assert(as2[n] <= 30);
157 lmmp_debug_assert(bs2[n] <= 2);
158 lmmp_debug_assert(asm2[n] <= 20);
159 lmmp_debug_assert(bsm2[n] <= 1);
160
161 /* vm1, 2n+1 limbs */
162 lmmp_mul_(vm1, asm1, n + 1, bsm1, n); /* W4 */
163
164 /* vm2, 2n+1 limbs */
165 lmmp_mul_n_(vm2, asm2, bsm2, n + 1); /* W2 */
166
167 /* v2, 2n+1 limbs */
168 lmmp_mul_n_(v2, as2, bs2, n + 1); /* W1 */
169
170 /* v1, 2n+1 limbs */
171 lmmp_mul_n_(v1, as1, bs1, n + 1); /* W3 */
172
173 /* vinf, s+t limbs */ /* W0 */
174 if (s > t)
175 lmmp_mul_(vinf, a4, s, b1, t);
176 else
177 lmmp_mul_(vinf, b1, t, a4, s);
178
179 /* v0, 2n limbs */
180 lmmp_mul_n_(v0, numa, numb, n); /* W5 */
181
182 lmmp_toom_interp6_(dst, n, flags, vm1, vm2, v2, t + s);
183 TEMP_S_FREE;
184#undef v0
185#undef vm1
186#undef v1
187#undef vm2
188#undef v2
189#undef vinf
190#undef bs1
191#undef bs2
192#undef bsm1
193#undef bsm2
194#undef asm1
195#undef asm2
196#undef as1
197#undef as2
198#undef a0a2
199#undef b0b2
200#undef a1a3
201#undef a0
202#undef a1
203#undef a2
204#undef a3
205#undef b0
206#undef b1
207#undef b2
208}
mp_ptr
mp_limb_t * mp_ptr
Definition lmmp.h:80
lmmp_zero
#define lmmp_zero(dst, n)
Definition lmmp.h:369
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_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_sub_
static mp_limb_t lmmp_sub_(mp_ptr dst, mp_srcptr numa, mp_size_t na, mp_srcptr numb, mp_size_t nb)
大数减法静态内联函数 [dst,na]=[numa,na]-[numb,nb]
Definition lmmpn.h:1064
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_sub_n_
mp_limb_t lmmp_sub_n_(mp_ptr dst, mp_srcptr numa, mp_srcptr numb, mp_size_t n)
无借位的n位减法 [dst,n] = [numa,n] - [numb,n]
Definition sub_n.c:80
lmmp_zero_q_
static int lmmp_zero_q_(mp_srcptr p, mp_size_t n)
大数判零函数（内联）
Definition lmmpn.h:1019
t
#define t
s
#define s
bs1
#define bs1
bs2
#define bs2
b0
#define b0
v0
#define v0
a4
#define a4
lmmp_mul_n_
#define lmmp_mul_n_(dst, numa, numb, n)
Copyright (C) 2026 HJimmyK(Jericho Knox)
Definition mul_toom52.c:21
b1
#define b1
bsm1
#define bsm1
as2
#define as2
v2
#define v2
vm1
#define vm1
asm2
#define asm2
bsm2
#define bsm2
a0a2
#define a0a2
asm1
#define asm1
vinf
#define vinf
as1
#define as1
v1
#define v1
a1a3
#define a1a3
vm2
#define vm2
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_eval_pm2_
int lmmp_toom_eval_pm2_(mp_ptr xp2, mp_ptr xm2, unsigned k, mp_srcptr xp, mp_size_t n, mp_size_t hn, mp_ptr tp)
通用高阶 Toom 求值：k次多项式在 x = +2 和 x = -2 处求值
Definition mul_toom_eval.c:117
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_pm1_
int lmmp_toom_eval_pm1_(mp_ptr xp1, mp_ptr xm1, unsigned k, mp_srcptr xp, mp_size_t n, mp_size_t hn, mp_ptr tp)
通用高阶 Toom 求值：k次多项式在 x = +1 和 x = -1 处求值
Definition mul_toom_eval.c:70

◆ 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_toom52_()

void lmmp_mul_toom52_ ( mp_ptr restrict  dst,
mp_srcptr restrict  numa,
mp_size_t  na,
mp_srcptr restrict  numb,
mp_size_t  nb 
)

在文件 mul_toom52.c 第 52 行定义.

52 {
53 lmmp_param_assert(9 * na >= 20 * nb);
54 lmmp_param_assert(3 * nb >= na);
55 mp_size_t n, s, t;
56 enum toom6_flags flags;
57
58#define a0 numa
59#define a1 (numa + n)
60#define a2 (numa + 2 * n)
61#define a3 (numa + 3 * n)
62#define a4 (numa + 4 * n)
63#define b0 numb
64#define b1 (numb + n)
65
66 n = 1 + (2 * na >= 5 * nb ? (na - 1) / (mp_size_t)5 : (nb - 1) >> 1);
67 TEMP_S_DECL;
68 mp_ptr restrict scratch = SALLOC_TYPE(6 * n + 6, mp_limb_t);
69
70 s = na - 4 * n;
71 t = nb - n;
72
73 lmmp_debug_assert(0 < s && s <= n);
74 lmmp_debug_assert(0 < t && t <= n);
75
76 /* Ensures that 5 values of n+1 limbs each fits in the product area.
77 Borderline cases are na = 32, nb = 8, n = 7, and na = 36, bn = 9,
78 n = 8. */
79 lmmp_debug_assert(s + t >= 5);
80
81#define v0 dst /* 2n */
82#define vm1 (scratch) /* 2n+1 */
83#define v1 (dst + 2 * n) /* 2n+1 */
84#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
85#define v2 (scratch + 4 * n + 2) /* 2n+1 */
86#define vinf (dst + 5 * n) /* s+t */
87#define bs1 dst /* n+1 */
88#define bsm1 (scratch + 2 * n + 2) /* n */
89#define asm1 (scratch + 3 * n + 3) /* n+1 */
90#define asm2 (scratch + 4 * n + 4) /* n+1 */
91#define bsm2 (dst + n + 1) /* n+1 */
92#define bs2 (dst + 2 * n + 2) /* n+1 */
93#define as2 (dst + 3 * n + 3) /* n+1 */
94#define as1 (dst + 4 * n + 4) /* n+1 */
95
96
97#define a0a2 scratch
98#define a1a3 asm1
99
100 /* Compute as2 and asm2. */
101 flags = (enum toom6_flags)(toom6_vm2_neg & lmmp_toom_eval_pm2_(as2, asm2, 4, numa, n, s, a1a3));
102
103 /* Compute bs1 and bsm1. */
104 if (t == n) {
105 mp_limb_t cy;
106 if (lmmp_cmp_(b0, b1, n) < 0) {
107 cy = lmmp_add_n_sub_n_(bs1, bsm1, b1, b0, n);
108 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
109 } else {
110 cy = lmmp_add_n_sub_n_(bs1, bsm1, b0, b1, n);
111 }
112 bs1[n] = cy >> 1;
113 } else {
114 bs1[n] = lmmp_add_(bs1, b0, n, b1, t);
115 if (lmmp_zero_q_(b0 + t, n - t) && lmmp_cmp_(b0, b1, t) < 0) {
116 lmmp_sub_n_(bsm1, b1, b0, t);
117 lmmp_zero(bsm1 + t, n - t);
118 flags = (enum toom6_flags)(flags ^ toom6_vm1_neg);
119 } else {
120 lmmp_sub_(bsm1, b0, n, b1, t);
121 }
122 }
123
124 /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
125 lmmp_add_(bs2, bs1, n + 1, b1, t);
126 if (flags & toom6_vm1_neg) {
127 bsm2[n] = lmmp_add_(bsm2, bsm1, n, b1, t);
128 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
129 } else {
130 bsm2[n] = 0;
131 if (t == n) {
132 if (lmmp_cmp_(bsm1, b1, n) < 0) {
133 lmmp_sub_n_(bsm2, b1, bsm1, n);
134 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
135 } else {
136 lmmp_sub_n_(bsm2, bsm1, b1, n);
137 }
138 } else {
139 if (lmmp_zero_q_(bsm1 + t, n - t) && lmmp_cmp_(bsm1, b1, t) < 0) {
140 lmmp_sub_n_(bsm2, b1, bsm1, t);
141 lmmp_zero(bsm2 + t, n - t);
142 flags = (enum toom6_flags)(flags ^ toom6_vm2_neg);
143 } else {
144 lmmp_sub_(bsm2, bsm1, n, b1, t);
145 }
146 }
147 }
148
149 /* Compute as1 and asm1. */
150 flags = (enum toom6_flags)(flags ^ (toom6_vm1_neg & lmmp_toom_eval_pm1_(as1, asm1, 4, numa, n, s, a0a2)));
151
152 lmmp_debug_assert(as1[n] <= 4);
153 lmmp_debug_assert(bs1[n] <= 1);
154 lmmp_debug_assert(asm1[n] <= 2);
155 /* lmmp_debug_assert (bsm1[n] <= 1); */
156 lmmp_debug_assert(as2[n] <= 30);
157 lmmp_debug_assert(bs2[n] <= 2);
158 lmmp_debug_assert(asm2[n] <= 20);
159 lmmp_debug_assert(bsm2[n] <= 1);
160
161 /* vm1, 2n+1 limbs */
162 lmmp_mul_(vm1, asm1, n + 1, bsm1, n); /* W4 */
163
164 /* vm2, 2n+1 limbs */
165 lmmp_mul_n_(vm2, asm2, bsm2, n + 1); /* W2 */
166
167 /* v2, 2n+1 limbs */
168 lmmp_mul_n_(v2, as2, bs2, n + 1); /* W1 */
169
170 /* v1, 2n+1 limbs */
171 lmmp_mul_n_(v1, as1, bs1, n + 1); /* W3 */
172
173 /* vinf, s+t limbs */ /* W0 */
174 if (s > t)
175 lmmp_mul_(vinf, a4, s, b1, t);
176 else
177 lmmp_mul_(vinf, b1, t, a4, s);
178
179 /* v0, 2n limbs */
180 lmmp_mul_n_(v0, numa, numb, n); /* W5 */
181
182 lmmp_toom_interp6_(dst, n, flags, vm1, vm2, v2, t + s);
183 TEMP_S_FREE;
184#undef v0
185#undef vm1
186#undef v1
187#undef vm2
188#undef v2
189#undef vinf
190#undef bs1
191#undef bs2
192#undef bsm1
193#undef bsm2
194#undef asm1
195#undef asm2
196#undef as1
197#undef as2
198#undef a0a2
199#undef b0b2
200#undef a1a3
201#undef a0
202#undef a1
203#undef a2
204#undef a3
205#undef b0
206#undef b1
207#undef b2
208}

引用了 a0a2, a1a3, a4, as1, as2, asm1, asm2, b0, b1, bs1, bs2, bsm1, bsm2, lmmp_add_(), lmmp_add_n_sub_n_(), lmmp_cmp_(), lmmp_debug_assert, lmmp_mul_(), lmmp_mul_n_, lmmp_param_assert, lmmp_sub_(), lmmp_sub_n_(), lmmp_toom_eval_pm1_(), lmmp_toom_eval_pm2_(), lmmp_toom_interp6_(), lmmp_zero, lmmp_zero_q_(), 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: