Here you go for 64 bit atom:
# With assembly
overhead 0.000000005 secs, precision 1000000 units of 6.00e-10 secs, CPU
freq 1667.00 MHz
mpn_sqr_basecase
1 0.000000016
2 0.000000043
3 0.000000104
4 0.000000176
5 0.000000249
6 0.000000334
7 0.000000432
8 0.000000544
9 0.000000670
10 0.000000851
11 0.000000959
12 0.000001124
13 0.000001303
14 0.000001502
15 0.000001706
16 0.000001924
17 0.000002155
18 0.000002408
19 0.000002655
20 0.000002926
21 0.000003210
22 0.000003506
23 0.000003815
24 0.000004168
25 0.000004486
26 0.000004834
27 0.000005197
28 0.000005582
29 0.000005963
30 0.000006364
31 0.000006780
32 0.000007218
33 0.000007680
34 0.000008165
35 0.000008640
36 0.000009172
37 0.000009645
38 0.000010181
39 0.000010713
40 0.000011275
41 0.000011846
42 0.000012410
43 0.000012982
44 0.000013582
45 0.000014193
46 0.000014788
47 0.000015444
48 0.000016123
49 0.000016774
50 0.000017411
51 0.000018119
52 0.000018854
53 0.000019580
54 0.000020291
55 0.000021061
56 0.000021824
57 0.000022595
58 0.000023358
59 0.000024153
60 0.000025000
61 0.000025832
62 0.000026639
63 0.000027487
64 0.000028409
65 0.000029348
66 0.000030227
67 0.000031156
68 0.000032106
69 0.000033036
70 0.000033928
71 0.000034871
72 0.000035875
73 0.000036875
74 0.000037832
75 0.000038847
76 0.000039891
77 0.000040949
78 0.000041962
79 0.000043022
80 0.000044379
81 0.000045477
82 0.000046551
83 0.000047666
84 0.000048805
85 0.000049956
86 0.000051057
87 0.000052227
88 0.000053429
89 0.000054624
90 0.000055804
91 0.000057026
92 0.000058271
93 0.000059531
94 0.000060736
95 0.000062011
96 0.000063312
97 0.000064619
98 0.000065906
99 0.000076595
100 0.000068600
make tuneup
./tuneup
Parameters for ./mpn/x86_64/atom/gmp-mparam.h
Using: CPU cycle counter, supplemented by microsecond getrusage()
speed_precision 1000000, speed_unittime 6.00e-10 secs, CPU freq 1667.00 MHz
DEFAULT_MAX_SIZE 1000, fft_max_size 50000
/* Generated by tuneup.c, 2014-02-18, gcc 4.6 */
#define MUL_KARATSUBA_THRESHOLD 10
#define MUL_TOOM3_THRESHOLD 66
#define MUL_TOOM4_THRESHOLD 169
#define MUL_TOOM8H_THRESHOLD 222
#define SQR_BASECASE_THRESHOLD 0 /* always (native) */
#define SQR_KARATSUBA_THRESHOLD 14
#define SQR_TOOM3_THRESHOLD 98
#define SQR_TOOM4_THRESHOLD 244
#define SQR_TOOM8_THRESHOLD 244
#define POWM_THRESHOLD 65
#define HGCD_THRESHOLD 208
#define GCD_DC_THRESHOLD 218
#define GCDEXT_DC_THRESHOLD 208
#define JACOBI_BASE_METHOD 3
#define DIVREM_1_NORM_THRESHOLD MP_SIZE_T_MAX /* never */
#define DIVREM_1_UNNORM_THRESHOLD MP_SIZE_T_MAX /* never */
#define MOD_1_NORM_THRESHOLD 0 /* always */
#define MOD_1_UNNORM_THRESHOLD 0 /* always */
#define USE_PREINV_DIVREM_1 1 /* native */
#define USE_PREINV_MOD_1 1
#define DIVEXACT_1_THRESHOLD 0 /* always */
#define MODEXACT_1_ODD_THRESHOLD 0 /* always (native) */
#define MOD_1_1_THRESHOLD 7
#define MOD_1_2_THRESHOLD 8
#define MOD_1_3_THRESHOLD 11
#define DIVREM_HENSEL_QR_1_THRESHOLD 126
#define RSH_DIVREM_HENSEL_QR_1_THRESHOLD 996
#define DIVREM_EUCLID_HENSEL_THRESHOLD 35
#define ROOTREM_THRESHOLD 6
#define GET_STR_DC_THRESHOLD 19
#define GET_STR_PRECOMPUTE_THRESHOLD 32
#define SET_STR_DC_THRESHOLD 244
#define SET_STR_PRECOMPUTE_THRESHOLD 344
#define MUL_FFT_FULL_THRESHOLD 2496
#define SQR_FFT_FULL_THRESHOLD 1760
#define MULLOW_BASECASE_THRESHOLD 0 /* always */
#define MULLOW_DC_THRESHOLD 10
#define MULLOW_MUL_THRESHOLD 2824
#define MULHIGH_BASECASE_THRESHOLD 8
#define MULHIGH_DC_THRESHOLD 8
#define MULHIGH_MUL_THRESHOLD 2324
#define MULMOD_2EXPM1_THRESHOLD 16
#define FAC_UI_THRESHOLD 8757
#define DC_DIV_QR_THRESHOLD 28
#define DC_DIVAPPR_Q_N_THRESHOLD 42
#define INV_DIV_QR_THRESHOLD 1258
#define INV_DIVAPPR_Q_N_THRESHOLD 42
#define DC_DIV_Q_THRESHOLD 73
#define INV_DIV_Q_THRESHOLD 2801
#define DC_DIVAPPR_Q_THRESHOLD 33
#define INV_DIVAPPR_Q_THRESHOLD 7881
#define DC_BDIV_QR_THRESHOLD 28
#define DC_BDIV_Q_THRESHOLD 34
/* fft_tuning -- autogenerated by tune-fft */
#define FFT_TAB \
{ { 4, 3 }, { 3, 2 }, { 3, 2 }, { 2, 1 }, { 1, 0 } }
#define MULMOD_TAB \
{ 4, 3, 3, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 }
#define FFT_N_NUM 19
#define FFT_MULMOD_2EXPP1_CUTOFF 128
/* Tuneup completed successfully, took 572 seconds */
# Without assembly
overhead 0.000000008 secs, precision 1000000 units of 1.00e-09 secs, CPU
freq 1000.00 MHz
mpn_sqr_basecase
1 0.000000040
2 0.000000084
3 0.000000149
4 0.000000236
5 0.000000378
6 0.000000508
7 0.000000668
8 0.000000842
9 0.000001040
10 0.000001249
11 0.000001488
12 0.000001741
13 0.000002018
14 0.000002306
15 0.000002625
16 0.000002957
17 0.000003313
18 0.000003680
19 0.000004077
20 0.000004488
21 0.000004923
22 0.000005382
23 0.000005845
24 0.000006348
25 0.000006849
26 0.000007388
27 0.000007956
28 0.000008512
29 0.000009132
30 0.000009751
31 0.000010385
32 0.000011036
33 0.000011738
34 0.000012449
35 0.000013149
36 0.000013864
37 0.000014627
38 0.000015402
39 0.000016197
40 0.000017003
41 0.000017849
42 0.000018702
43 0.000019588
44 0.000020462
45 0.000021399
46 0.000022335
47 0.000023287
48 0.000024238
49 0.000025282
50 0.000026268
51 0.000027313
52 0.000028397
53 0.000029439
54 0.000030557
55 0.000031669
56 0.000032792
57 0.000033939
58 0.000035110
59 0.000036298
60 0.000037513
61 0.000038740
62 0.000039990
63 0.000041257
64 0.000042553
65 0.000043857
66 0.000045186
67 0.000046532
68 0.000047906
69 0.000049290
70 0.000050698
71 0.000052123
72 0.000053577
73 0.000055039
74 0.000056526
75 0.000058031
76 0.000059562
77 0.000061106
78 0.000062671
79 0.000064261
80 0.000066405
81 0.000067486
82 0.000069628
83 0.000070793
84 0.000072995
85 0.000074184
86 0.000076376
87 0.000077648
88 0.000079847
89 0.000081197
90 0.000083384
91 0.000084821
92 0.000087068
93 0.000088526
94 0.000090765
95 0.000092308
96 0.000094551
97 0.000096172
98 0.000098405
99 0.000100112
100 0.000102405
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