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speedup log calculation by optimizing mulitplication by 1 + 10^-j

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This commit is contained in:
Jeff Wang 2019-10-05 01:04:04 -04:00
parent 06ca0b2829
commit 277ae0acf3
2 changed files with 10 additions and 69 deletions
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34
src/decn/decn.c
View File

@ -862,7 +862,6 @@ void ln_decn(void){
exp_t initial_exp;
#define B_j Tmp2Decn
#define NUM_TIMES Tmp3Decn
#define A_ARR_j Tmp4Decn
//check not negative or zero
if (AccDecn.exponent < 0 || decn_is_zero(&AccDecn)){
@ -878,9 +877,6 @@ void ln_decn(void){
decn_to_str_complete(&AccDecn);
printf("ln() accum scaled between 1,10: %s\n", Buf);
#endif
//get initial a_arr[0] = 2
set_dec80_zero(&A_ARR_j);
A_ARR_j.lsu[0] = 20;
//get initial estimate (accum = 10 - A)
copy_decn(&BDecn, &DECN_1);
BDecn.exponent = 1; //BDecn = 10
@ -902,12 +898,18 @@ void ln_decn(void){
copy_decn(&AccDecn, &B_j); //accum = b_j
k_j = 0;
while (!(AccDecn.exponent < 0)){ //while >= 0 (!negative) TODO: should just be >
uint8_t i;
copy_decn(&B_j, &AccDecn); //b_j = accum
//accum *= a_arr[i]
copy_decn(&BDecn, &A_ARR_j);
mult_decn();
//accum *= a_arr[j]
// since a_arr[j] is of the form 1 + 10^-j, just shift accum and add to self
copy_decn(&BDecn, &AccDecn);
for (i = 0; i < j; i++){
shift_right(&BDecn);
}
add_decn();
//accum -= 10
if (AccDecn.lsu[0] >= 10 && get_exponent(&AccDecn) > 0){ //accum.exponent is 1 while needs subtracting
// accum.exponent is 1 while needs subtracting
if (AccDecn.lsu[0] >= 10 && get_exponent(&AccDecn) > 0){
AccDecn.lsu[0] -= 10;
} else {
//set as negative to get out of while(), accum will get overwritten with b_j
@ -932,21 +934,6 @@ void ln_decn(void){
decn_to_str_complete(&B_j);
printf(" %u: num_times: %u, %s\n", j, NUM_TIMES.lsu[j], Buf);
#endif
//find next a_j (1 + 10^-j)
if (j == 0) {
//build value 1.1
set_dec80_zero(&A_ARR_j);
A_ARR_j.lsu[0] = 11;
} else {
//get next 1.000...1 value
shift_right(&A_ARR_j);
A_ARR_j.lsu[0] = 10;
}
#ifdef DEBUG_LOG
decn_to_str_complete(&A_ARR_j);
printf(" new a_j val: %s\n", Buf);
#endif
}
//build final value
@ -1020,7 +1007,6 @@ void ln_decn(void){
//try not to pollute namespace
#undef B_j
#undef NUM_TIMES
#undef A_ARR_j
#undef NUM_A_ARR
}

45
src/decn/decn_test_refout.txt
View File

@ -68,23 +68,14 @@ acc/b: 0.666666666666666672
ln() accum scaled between 1,10: 1.55
ln() initial accum: 8.45 (0)
0: num_times: 2, 3.8
new a_j val: 1.1
1: num_times: 5, 0.14838
new a_j val: 1.01
2: num_times: 0, 1.4838
new a_j val: 1.001
3: num_times: 1, 4.852838
new a_j val: 1.0001
4: num_times: 4, 8.5417938638869182
new a_j val: 1.00001
5: num_times: 8, 5.4219722571346027
new a_j val: 1.000001
6: num_times: 5, 4.2198936704010812
new a_j val: 1.0000001
7: num_times: 4, 2.1989475835876253
new a_j val: 1.00000001
8: num_times: 2, 1.9894761756657718
new a_j val: 1.000000001
ln() remainder: 1.9894761756657718
8: ln() remainder: 2.1989476075668969
7: ln() remainder: 4.2198945607568002
@ -104,23 +95,14 @@ ln(a): -1.8643301620628904
ln() accum scaled between 1,10: 1.
ln() initial accum: 9. (2)
0: num_times: 3, 2.
new a_j val: 1.1
1: num_times: 2, 3.2
new a_j val: 1.01
2: num_times: 3, 2.668632
new a_j val: 1.001
3: num_times: 2, 6.72971932632
new a_j val: 1.0001
4: num_times: 6, 7.3225796749329481
new a_j val: 1.00001
5: num_times: 7, 3.2288226738783197
new a_j val: 1.000001
6: num_times: 3, 2.2882936035502779
new a_j val: 1.0000001
7: num_times: 2, 2.8829396120902148
new a_j val: 1.00000001
8: num_times: 2, 8.8293965974900732
new a_j val: 1.000000001
ln() remainder: 8.8293965974900732
8: ln() remainder: 2.882939649749327
7: ln() remainder: 2.2882938649749879
@ -140,23 +122,14 @@ ln(a): 2.30258509299404576
ln() accum scaled between 1,10: 1.1
ln() initial accum: 8.9 (11)
0: num_times: 3, 1.2
new a_j val: 1.1
1: num_times: 1, 3.2
new a_j val: 1.01
2: num_times: 3, 2.668632
new a_j val: 1.001
3: num_times: 2, 6.72971932632
new a_j val: 1.0001
4: num_times: 6, 7.3225796749329481
new a_j val: 1.00001
5: num_times: 7, 3.2288226738783197
new a_j val: 1.000001
6: num_times: 3, 2.2882936035502779
new a_j val: 1.0000001
7: num_times: 2, 2.8829396120902148
new a_j val: 1.00000001
8: num_times: 2, 8.8293965974900732
new a_j val: 1.000000001
ln() remainder: 8.8293965974900732
8: ln() remainder: 2.882939649749327
7: ln() remainder: 2.2882938649749879
@ -176,23 +149,14 @@ ln(a): 23.1211611097447817
ln() accum scaled between 1,10: 2.02
ln() initial accum: 7.98 (-9)
0: num_times: 2, 1.92
new a_j val: 1.1
1: num_times: 2, 2.232
new a_j val: 1.01
2: num_times: 2, 2.668632
new a_j val: 1.001
3: num_times: 2, 6.72971932632
new a_j val: 1.0001
4: num_times: 6, 7.3225796749329481
new a_j val: 1.00001
5: num_times: 7, 3.2288226738783197
new a_j val: 1.000001
6: num_times: 3, 2.2882936035502779
new a_j val: 1.0000001
7: num_times: 2, 2.8829396120902148
new a_j val: 1.00000001
8: num_times: 2, 8.8293965974900732
new a_j val: 1.000000001
ln() remainder: 8.8293965974900732
8: ln() remainder: 2.882939649749327
7: ln() remainder: 2.2882938649749879
@ -212,23 +176,14 @@ ln(a): -22.3227534185273433
ln() accum scaled between 1,10: 1.5
ln() initial accum: 8.5 (1)
0: num_times: 2, 4.
new a_j val: 1.1
1: num_times: 5, 3.3694
new a_j val: 1.01
2: num_times: 3, 4.413961894
new a_j val: 1.001
3: num_times: 4, 4.2564024200762553
new a_j val: 1.0001
4: num_times: 4, 2.5750519644445702
new a_j val: 1.00001
5: num_times: 2, 5.7509346574136428
new a_j val: 1.000001
6: num_times: 5, 7.5095341213443924
new a_j val: 1.0000001
7: num_times: 7, 5.0953727801950431
new a_j val: 1.00000001
8: num_times: 5, 0.953729349636862
new a_j val: 1.000000001
ln() remainder: 0.953729349636862
8: ln() remainder: 5.0953729099644855
7: ln() remainder: 7.509536940996642