initial exp() implementation
(refout for log(1.5) changed due to using more accurate expected result)
This commit is contained in:
Jeff Wang
parent
277ae0acf3
commit
1a9bbcc1ce
227
src/decn/decn.c
227
src/decn/decn.c
@ -19,6 +19,8 @@
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// #define DEBUG_DIV
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#define DEBUG_LOG
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// #define DEBUG_LOG_ALL //even more verbose
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#define DEBUG_EXP
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// #define DEBUG_EXP_ALL //even more verbose
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#ifndef DESKTOP
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//#undef EXTRA_CHECKS
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@ -48,8 +50,8 @@ static const uint8_t num_digits_display = 16;
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__idata dec80 AccDecn, BDecn;
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__idata dec80 TmpDecn; //used by add_decn() and mult_decn()
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__idata dec80 Tmp2Decn; //used by div_decn() and ln_decn()
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__idata dec80 Tmp3Decn; //used by div_decn() and ln_decn()
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__idata dec80 Tmp2Decn; //used by recip_decn() and ln_decn()
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__idata dec80 Tmp3Decn; //used by recip_decn() and ln_decn()
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__idata dec80 Tmp4Decn; //used by div_decn() and ln_decn()
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__xdata char Buf[DECN_BUF_SIZE];
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@ -553,6 +555,8 @@ void add_decn(void){
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copy_decn(&AccDecn, &BDecn);
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return;
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}
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//save b for restoring later
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copy_decn(&TmpDecn, &BDecn);
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//handle cases where signs differ
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if (AccDecn.exponent < 0 && BDecn.exponent >= 0){
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// -acc, +x
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@ -562,23 +566,23 @@ void add_decn(void){
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printf("|-acc| > |+x|\n");
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#endif
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sub_mag();
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return;
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} else if (rel == -1){
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#ifdef DEBUG_ADD
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printf("|-acc| < |+x|\n");
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#endif
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copy_decn(&TmpDecn, &BDecn);
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copy_decn(&BDecn, &AccDecn);
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copy_decn(&AccDecn, &TmpDecn);
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sub_mag();
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return;
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} else { //equal
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#ifdef DEBUG_ADD
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printf("|-acc| == |+x|\n");
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#endif
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set_dec80_zero(&AccDecn);
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return;
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}
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//restore b
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copy_decn(&BDecn, &TmpDecn);
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return;
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} else if (AccDecn.exponent >= 0 && BDecn.exponent < 0){
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// +acc, -x
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rel = compare_magn();
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@ -587,23 +591,23 @@ void add_decn(void){
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printf("|+acc| > |-x|\n");
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#endif
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sub_mag();
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return;
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} else if (rel == -1){
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#ifdef DEBUG_ADD
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printf("|+acc| < |-x|\n");
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#endif
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copy_decn(&TmpDecn, &BDecn);
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copy_decn(&BDecn, &AccDecn);
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copy_decn(&AccDecn, &TmpDecn);
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sub_mag();
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return;
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} else { //equal
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#ifdef DEBUG_ADD
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printf("|+acc| == |-x|\n");
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#endif
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set_dec80_zero(&AccDecn);
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return;
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}
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//restore b
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copy_decn(&BDecn, &TmpDecn);
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return;
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}
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//signs must now be the same, begin adding
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//normalize
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@ -658,6 +662,9 @@ void add_decn(void){
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//track sign
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set_exponent(&AccDecn, curr_exp, rel); //rel==is_neg?
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}
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//restore b
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copy_decn(&BDecn, &TmpDecn);
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}
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//AccDecn *= BDecn
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@ -752,10 +759,9 @@ void mult_decn(void){
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remove_leading_zeros(&AccDecn);
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}
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void div_decn(void){
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void recip_decn(void){
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#define CURR_RECIP Tmp2Decn //copy of x, holds current 1/x estimate
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#define X_COPY Tmp3Decn //holds copy of original x
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#define ACC_COPY Tmp4Decn //holds copy of original acc
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uint8_t i;
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exp_t initial_exp;
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//check divide by zero
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@ -771,8 +777,6 @@ void div_decn(void){
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//normalize
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remove_leading_zeros(&AccDecn);
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remove_leading_zeros(&BDecn);
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//store copy of acc for final multiply by 1/x
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copy_decn(&ACC_COPY, &AccDecn);
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//store copy of x
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copy_decn(&X_COPY, &BDecn);
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//get initial exponent of estimate for 1/x
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@ -834,30 +838,41 @@ void div_decn(void){
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//new_est(Accum) = recip + (1 - recip*x)*recip, where recip is current recip estimate
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copy_decn(&CURR_RECIP, &AccDecn);
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}
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//try not to pollute namespace
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#undef CURR_RECIP
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#undef X_COPY
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}
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inline void div_decn(void){
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#define ACC_COPY Tmp4Decn //holds copy of original acc
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//store copy of acc for final multiply by 1/x
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copy_decn(&ACC_COPY, &AccDecn);
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recip_decn();
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//Accum now holds 1/x, multiply by original acc to complete division
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copy_decn(&BDecn, &ACC_COPY);
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mult_decn();
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//try not to pollute namespace
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#undef CURR_RECIP
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#undef X_COPY
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#undef ACC_COPY
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}
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void ln_decn(void){
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//constants used for ln(x) and exp(x)
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#define NUM_A_ARR 9
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static const dec80 LN_A_ARR[NUM_A_ARR] = {
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{0, {69, 31, 47, 18, 5, 59, 94, 53, 9}},
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{0, {95, 31, 1, 79, 80, 43, 24, 86, 0}},
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{0, {99, 50, 33, 8, 53, 16, 80, 82, 84}},
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{0, {99, 95, 0, 33, 30, 83, 53, 31, 67}},
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{0, {99, 99, 50, 0, 33, 33, 8, 33, 33}},
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{0, {99, 99, 95, 0, 0, 33, 33, 29, 95}},
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{0, {99, 99, 99, 50, 0, 0, 33, 5, 35}},
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{0, {99, 99, 99, 95, 0, 0, 2, 76, 40}},
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{0, {99, 99, 99, 99, 50, 0, 15, 98, 65}},
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// {0, {99, 99, 99, 99, 95, 2, 19, 27, 11}},
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};
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static const dec80 LN_A_ARR[NUM_A_ARR] = {
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{-1 & 0x7fff, {69, 31, 47, 18, 5, 59, 94, 53, 9}},
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{-2 & 0x7fff, {95, 31, 1, 79, 80, 43, 24, 86, 0}},
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{-3 & 0x7fff, {99, 50, 33, 8, 53, 16, 80, 82, 84}},
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{-4 & 0x7fff, {99, 95, 0, 33, 30, 83, 53, 31, 67}},
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{-5 & 0x7fff, {99, 99, 50, 0, 33, 33, 8, 33, 33}},
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{-6 & 0x7fff, {99, 99, 95, 0, 0, 33, 33, 29, 95}},
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{-7 & 0x7fff, {99, 99, 99, 50, 0, 0, 33, 5, 35}},
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{-8 & 0x7fff, {99, 99, 99, 95, 0, 0, 2, 76, 40}},
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{-9 & 0x7fff, {99, 99, 99, 99, 50, 0, 15, 98, 65}},
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};
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void ln_decn(void){
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uint8_t j, k;
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exp_t initial_exp;
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#define B_j Tmp2Decn
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@ -946,6 +961,7 @@ void ln_decn(void){
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for (k = 0; k < NUM_TIMES.lsu[j]; k++){
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//accum += ln_a_arr[j];
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copy_decn(&BDecn, &LN_A_ARR[j]);
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BDecn.exponent = 0; //tracking exponent through shifts/saved initial exponent
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add_decn();
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}
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shift_right(&AccDecn);
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@ -1007,7 +1023,6 @@ void ln_decn(void){
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//try not to pollute namespace
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#undef B_j
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#undef NUM_TIMES
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#undef NUM_A_ARR
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}
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//inline void log10_decn(void){
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@ -1016,6 +1031,158 @@ void ln_decn(void){
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// div_decn();
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//}
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void exp_decn(void){
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uint8_t j, k;
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uint8_t need_recip;
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#define SAVED Tmp2Decn
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#define NUM_TIMES Tmp3Decn
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//check if negative
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if (AccDecn.exponent < 0){
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negate_decn(&AccDecn);
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need_recip = 1;
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}
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//check if in range
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copy_decn(&SAVED, &AccDecn); //save = accum
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set_dec80_zero(&BDecn);
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BDecn.lsu[0] = 23;
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BDecn.lsu[1] = 02;
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BDecn.lsu[2] = 58;
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BDecn.lsu[2] = 51;
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BDecn.exponent = 2; //b = 230.25851
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negate_decn(&BDecn);
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add_decn(); //accum = x - 230.25851 (should be negative if in range)
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if (!(AccDecn.exponent < 0)){ //if not negative
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set_dec80_NaN(&AccDecn);
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return;
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}
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copy_decn(&AccDecn, &SAVED); //restore
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// //normalize
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// remove_leading_zeros(&AccDecn);
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//initial b = -10*ln(10)
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copy_decn(&BDecn, &DECN_LN_10); //b=ln(10)
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copy_decn(&SAVED, &AccDecn); //save = accum
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copy_decn(&AccDecn, &DECN_1);
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AccDecn.exponent = 1; //accum = 10
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mult_decn(); //accum = 10*ln(10)
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copy_decn(&BDecn, &AccDecn); //b = 10*ln(10)
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negate_decn(&BDecn); //b = -10*ln(10)
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copy_decn(&AccDecn, &SAVED); //restore
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//track number of times 10*ln(10) can be subtracted
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k = 0;
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while (!(AccDecn.exponent < 0)){ //while not negative
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copy_decn(&SAVED, &AccDecn); //save = accum
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//accum -= 10*ln10
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add_decn();
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k++;
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}
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//subtracted 1 time too many
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NUM_TIMES.exponent = (k - 1) * 10; //use exp to store number of times ln(10) subtracted
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copy_decn(&AccDecn, &SAVED); //restore
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#ifdef DEBUG_EXP
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decn_to_str_complete(&AccDecn);
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printf("exp() num_times for 10*ln(10): %s (%d)\n", Buf, NUM_TIMES.exponent);
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#endif
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//load b with -ln(10)
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copy_decn(&BDecn, &DECN_LN_10); //b = ln(10)
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negate_decn(&BDecn); //b = -ln(10)
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//track number of times ln(10) and then (1 + 10^-j) can be subtracted
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j = UINT8_MAX; //becomes 0 after incrementing to start (1 + 10^-j) series
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do {
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k = 0;
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while (!(AccDecn.exponent < 0)){ //while not negative
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copy_decn(&SAVED, &AccDecn); //save = accum
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//accum -= b (ln10, then ln(1 + 10^-j) series)
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add_decn();
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#ifdef DEBUG_EXP_ALL
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decn_to_str_complete(&AccDecn);
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printf(" %u: %s\n", k, Buf);
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// decn_to_str_complete(&BDecn);
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// printf("(%s)\n", Buf);
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#endif
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k++;
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#ifdef DEBUG_EXP
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assert(k != 255);
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#endif
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}
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//subtracted 1 time too many:
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if (j == UINT8_MAX){
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NUM_TIMES.exponent += k - 1;
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} else {
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NUM_TIMES.lsu[j] = k - 1;
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}
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copy_decn(&AccDecn, &SAVED); //restore
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#ifdef DEBUG_EXP
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decn_to_str_complete(&AccDecn);
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printf("exp() num_times for %d: %s (%d)\n", j, Buf, k-1);
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#endif
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//next j
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j++;
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if (j < NUM_A_ARR){
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//get next ln(1 + 10^-j) for subtraction
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copy_decn(&BDecn, &LN_A_ARR[j]);
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negate_decn(&BDecn);
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} else {
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break;
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}
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} while (1);
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//build final value
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// (currently accum = save = remainder)
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// calculate 1+remainder
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copy_decn(&BDecn, &DECN_1);
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add_decn();
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//get initial multiplier (10) for ln(10)
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copy_decn(&BDecn, &DECN_1);
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BDecn.exponent = 1; //BDecn = 10
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//do multiplies
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j = UINT8_MAX; //becomes 0 after incrementing to start (1 + 10^-j) series
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do {
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for (k = 0; k < (j==UINT8_MAX ? NUM_TIMES.exponent : NUM_TIMES.lsu[j]); k++){
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mult_decn();
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}
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#ifdef DEBUG_EXP
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decn_to_str_complete(&AccDecn);
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printf("exp() current val for %d: %s\n", j, Buf);
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#endif
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//next j
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j++;
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if (j < NUM_A_ARR){
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//get next multiplier (1 + 10^-j) for ln(1 + 10^-j)
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if (j == 0){
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//set to 2
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BDecn.lsu[0] = 20;
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BDecn.exponent = 0;
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} else if (j == 1) {
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//set to 1.1
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BDecn.lsu[0] = 11;
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//exponent is already 0
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} else {
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//get next (1 + 10^-j)
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shift_right(&BDecn);
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BDecn.lsu[0] = 10;
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}
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} else {
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break;
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}
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} while (1);
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//take reciprocal if exp was negative
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if (need_recip){
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recip_decn();
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}
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//try not to pollute namespace
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#undef SAVED
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#undef NUM_TIMES
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}
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static void set_str_error(void){
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Buf[0] = 'E';
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Buf[1] = 'r';
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@ -64,18 +64,26 @@ void set_dec80_NaN(dec80* dest);
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uint8_t decn_is_nan(const dec80* x);
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void negate_decn(dec80* x);
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void add_decn(void);
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void mult_decn(void);
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void add_decn(void); //calculate AccDecn -= BDecn (BDecn is preserved)
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void mult_decn(void); //calculate AccDecn *= BDecn (BDecn is preserved)
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void recip_decn(void);
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void div_decn(void);
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void ln_decn(void);
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//inline void log10_decn(void);
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#define log10_decn() do { \
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ln_decn(); \
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copy_decn(&BDecn, &DECN_LN_10); \
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div_decn(); \
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} while(0);
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#define log10_decn() do { \
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ln_decn(); \
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copy_decn(&BDecn, &DECN_LN_10); \
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div_decn(); \
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} while(0);
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void exp_decn(void);
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//exp10_decn() = exp_decn(AccDecn * ln(10))
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#define exp10_decn() do { \
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copy_decn(&BDecn, &DECN_LN_10); \
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mult_decn(); \
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exp_decn(); \
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} while(0);
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//Buf should hold at least 18 + 4 + 5 + 1 = 28
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#define DECN_BUF_SIZE 28
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@ -68,16 +68,32 @@ static void log10_test(
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{
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build_dec80(x_str, x_exp);
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decn_to_str_complete(&AccDecn);
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printf(" a : %s\n", Buf);
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printf(" a : %s\n", Buf);
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log10_decn();
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decn_to_str_complete(&AccDecn);
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printf("ln(a): %s\n", Buf);
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printf("log(a): %s\n", Buf);
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build_decn_at(&diff, res_str, res_exp);
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take_diff();
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decn_to_str_complete(&diff);
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printf(" : %s\n\n", Buf);
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}
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static void exp_test(
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const char* x_str, int x_exp,
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const char* res_str, int res_exp)
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{
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build_dec80(x_str, x_exp);
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decn_to_str_complete(&AccDecn);
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printf(" a : %s\n", Buf);
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exp_decn();
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decn_to_str_complete(&AccDecn);
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printf("exp(a): %s\n", Buf);
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build_decn_at(&diff, res_str, res_exp);
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take_diff();
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decn_to_str_complete(&diff);
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printf(" : %s\n\n", Buf);
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}
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int main(void){
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// dec80 acc, b;
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@ -245,7 +261,29 @@ int main(void){
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//new acc for log test
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log10_test(
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"1.5", 0,
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"0.176091259", 0
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"0.176091259055681242", 0
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);
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//new acc for exp test
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exp_test(
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"4.4", 0,
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"81.4508686649681174", 0
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);
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//get new acc for exp test (calculate 3^201)
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// build_dec80("3", 0);
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// ln_decn();
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log_test(
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"3", 0,
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"1.09861228866810969", 0
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);
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build_decn_at(&BDecn, "201", 0);
|
||||
mult_decn(); //acc = 201*ln(3)
|
||||
int8_t exp_test_exp = decn_to_str(&AccDecn);
|
||||
exp_test(
|
||||
Buf, exp_test_exp,
|
||||
"7.96841966627624308", 95
|
||||
);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
@ -172,7 +172,7 @@ ln() exponent from initial: -9.
|
||||
ln(a): -22.3227534185273433
|
||||
: 1.E-16
|
||||
|
||||
a : 1.5
|
||||
a : 1.5
|
||||
ln() accum scaled between 1,10: 1.5
|
||||
ln() initial accum: 8.5 (1)
|
||||
0: num_times: 2, 4.
|
||||
@ -196,6 +196,83 @@ ln() remainder: 0.953729349636862
|
||||
0: ln() remainder: 1.8971199848858812
|
||||
ln() accum after summing: 1.8971199848858812
|
||||
ln() exponent from initial: 1.
|
||||
ln(a): 0.176091259055681285
|
||||
: 5.5681285E-11
|
||||
log(a): 0.176091259055681285
|
||||
: 4.3E-17
|
||||
|
||||
a : 4.4
|
||||
exp() num_times for 10*ln(10): 4.4 (0)
|
||||
exp() num_times for 255: 2.09741490700595432 (1)
|
||||
exp() num_times for 0: 0.017973365326118411 (3)
|
||||
exp() num_times for 1: 0.017973365326118411 (0)
|
||||
exp() num_times for 2: 0.0080230344729503282 (1)
|
||||
exp() num_times for 3: 2.703180828206292E-5 (8)
|
||||
exp() num_times for 4: 2.703180828206292E-5 (0)
|
||||
exp() num_times for 5: 7.0319082813962602E-6 (2)
|
||||
exp() num_times for 6: 3.191178139394649E-8 (7)
|
||||
exp() num_times for 7: 3.191178139394649E-8 (0)
|
||||
exp() num_times for 8: 1.9117815439416942E-9 (3)
|
||||
exp() current val for 255: 10.0000000191178154
|
||||
exp() current val for 0: 80.0000001529425232
|
||||
exp() current val for 1: 80.0000001529425232
|
||||
exp() current val for 2: 80.8000001544719485
|
||||
exp() current val for 3: 81.4486670861725846
|
||||
exp() current val for 4: 81.4486670861725846
|
||||
exp() current val for 5: 81.4502960676591747
|
||||
exp() current val for 6: 81.450866221442107
|
||||
exp() current val for 7: 81.450866221442107
|
||||
exp() current val for 8: 81.450868664968118
|
||||
exp(a): 81.450868664968118
|
||||
: 6.E-16
|
||||
|
||||
a : 3.
|
||||
ln() accum scaled between 1,10: 3.
|
||||
ln() initial accum: 7. (1)
|
||||
0: num_times: 1, 4.
|
||||
1: num_times: 5, 3.3694
|
||||
2: num_times: 3, 4.413961894
|
||||
3: num_times: 4, 4.2564024200762553
|
||||
4: num_times: 4, 2.5750519644445702
|
||||
5: num_times: 2, 5.7509346574136428
|
||||
6: num_times: 5, 7.5095341213443924
|
||||
7: num_times: 7, 5.0953727801950431
|
||||
8: num_times: 5, 0.953729349636862
|
||||
ln() remainder: 0.953729349636862
|
||||
8: ln() remainder: 5.0953729099644855
|
||||
7: ln() remainder: 7.509536940996642
|
||||
6: ln() remainder: 5.7509511941013168
|
||||
5: ln() remainder: 2.5750851194767976
|
||||
4: ln() remainder: 4.257308525280013
|
||||
3: ln() remainder: 4.4237321848621339
|
||||
2: ln() remainder: 3.4274724744366382
|
||||
1: ln() remainder: 5.1082562376599068
|
||||
0: ln() remainder: 1.2039728043259359
|
||||
ln() accum after summing: 1.2039728043259359
|
||||
ln() exponent from initial: 1.
|
||||
ln(a): 1.09861228866810978
|
||||
: 9.E-17
|
||||
|
||||
a : 220.821070022290065
|
||||
exp() num_times for 10*ln(10): 13.5884116528259586 (90)
|
||||
exp() num_times for 255: 2.07548618785573036 (5)
|
||||
exp() num_times for 0: 0.68919182673583976 (2)
|
||||
exp() num_times for 1: 0.02202056810556574 (7)
|
||||
exp() num_times for 2: 0.0021199063992295744 (2)
|
||||
exp() num_times for 3: 1.2090573306250808E-4 (2)
|
||||
exp() num_times for 4: 2.0910732729199747E-5 (1)
|
||||
exp() num_times for 5: 9.108327285330872E-7 (2)
|
||||
exp() num_times for 6: 9.108327285330872E-7 (0)
|
||||
exp() num_times for 7: 1.0832773533062324E-8 (9)
|
||||
exp() num_times for 8: 8.327735830607254E-10 (1)
|
||||
exp() current val for 255: 1.00000000083277358E95
|
||||
exp() current val for 0: 4.00000000333109432E95
|
||||
exp() current val for 1: 7.79486840649136042E95
|
||||
exp() current val for 2: 7.95154526146183677E95
|
||||
exp() current val for 3: 7.96745630353002189E95
|
||||
exp() current val for 4: 7.96825304916037489E95
|
||||
exp() current val for 5: 7.96841241501818339E95
|
||||
exp() current val for 6: 7.96841241501818339E95
|
||||
exp() current val for 7: 7.9684195865922255E95
|
||||
exp() current val for 8: 7.96841966627642136E95
|
||||
exp(a): 7.96841966627642136E95
|
||||
: 1.7828E82
|
||||
|
||||
|
||||
1
src/decn/proto/.gitignore
vendored
1
src/decn/proto/.gitignore
vendored
@ -1,3 +1,4 @@
|
||||
div
|
||||
ln
|
||||
exp
|
||||
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
all: div ln
|
||||
all: div ln exp
|
||||
|
||||
div: div_mfp.cpp
|
||||
g++ -Wall div_mfp.cpp -o div -lgmp
|
||||
@ -6,3 +6,5 @@ div: div_mfp.cpp
|
||||
ln: ln_mfp.cpp
|
||||
g++ -Wall ln_mfp.cpp -o ln -lmpfr
|
||||
|
||||
exp: exp.cpp
|
||||
g++ -Wall exp.cpp -o exp -lmpfr
|
||||
|
||||
130
src/decn/proto/exp.cpp
Normal file
130
src/decn/proto/exp.cpp
Normal file
@ -0,0 +1,130 @@
|
||||
//prototype for exponential function
|
||||
// complement of ln() function based on HP Journal article
|
||||
// "Personal Calculator Algorithms IV: Logarithmic Functions"
|
||||
// (uses same set of constants)
|
||||
|
||||
#include <stdio.h>
|
||||
#include <iostream>
|
||||
#include <math.h>
|
||||
#include <boost/multiprecision/mpfr.hpp>
|
||||
using namespace boost::multiprecision;
|
||||
|
||||
// #define DEBUG
|
||||
// #define DEBUG_ALL
|
||||
|
||||
using std::cout;
|
||||
using std::endl;
|
||||
|
||||
static const int NUM_A_ARR = 9;
|
||||
mpfr_float a_arr[NUM_A_ARR];
|
||||
mpfr_float ln_a_arr[NUM_A_ARR];
|
||||
|
||||
static const unsigned int CALC_PRECISION = 18;
|
||||
|
||||
|
||||
int main(void){
|
||||
cout << std::scientific << std::setprecision(CALC_PRECISION);
|
||||
mpfr_float ln10 (10, CALC_PRECISION);
|
||||
ln10 = log( ln10 );
|
||||
cout << "ln(10):" << ln10 << endl;
|
||||
//initiallize a_arr and ln_a_arr
|
||||
for (int i = 0; i < NUM_A_ARR; i++){
|
||||
// a[i] = (1 + 10^-i)
|
||||
mpfr_float a(-i, CALC_PRECISION);
|
||||
a = pow(10, a);
|
||||
a_arr[i] = a + 1;
|
||||
ln_a_arr[i] = log(a_arr[i]);
|
||||
cout << i << endl;
|
||||
cout << " a:" << a_arr[i] << endl;
|
||||
cout << " ln(a):" << ln_a_arr[i] << endl;
|
||||
}
|
||||
cout << endl << endl ;
|
||||
//loop through values to test
|
||||
for (mpfr_float x(0.0001, CALC_PRECISION); x < 230.0; x += 0.015625){
|
||||
// for (mpfr_float x(230, CALC_PRECISION); x < 230.01; x += 0.015625){
|
||||
//build mpf values
|
||||
mpfr_float accum(x, CALC_PRECISION);
|
||||
mpfr_float save (0, CALC_PRECISION);
|
||||
mpfr_float_1000 actual;
|
||||
actual = exp(x);
|
||||
|
||||
int num_times_ln10;
|
||||
int num_times[NUM_A_ARR];
|
||||
int k_j = 0;
|
||||
//track number of times 10*ln(10) subtracted
|
||||
while (accum > 0){
|
||||
save = accum;
|
||||
accum -= 10*ln10;
|
||||
k_j++;
|
||||
}
|
||||
num_times_ln10 = (k_j - 1) * 10;
|
||||
accum = save; //restore
|
||||
//track number of times ln(10) subtracted
|
||||
k_j = 0;
|
||||
while (accum > 0){
|
||||
save = accum;
|
||||
accum -= ln10;
|
||||
k_j++;
|
||||
}
|
||||
num_times_ln10 += k_j - 1;
|
||||
accum = save; //restore
|
||||
#ifdef DEBUG
|
||||
printf(" 10: num_times: %d, ", num_times_ln10);
|
||||
cout << accum << endl;
|
||||
#endif
|
||||
//track number of times ln_a_arr[j] subtracted
|
||||
for (int j = 0; j < NUM_A_ARR; j++){
|
||||
k_j = 0;
|
||||
while (accum > 0){
|
||||
save = accum;
|
||||
accum -= ln_a_arr[j];
|
||||
#ifdef DEBUG_ALL
|
||||
printf(" %d: ", k_j);
|
||||
cout << accum << endl;
|
||||
#endif
|
||||
k_j++;
|
||||
}
|
||||
num_times[j] = k_j - 1;
|
||||
accum = save; //restore
|
||||
#ifdef DEBUG
|
||||
printf(" %d: num_times: %d, ", j, num_times[j]);
|
||||
cout << accum << endl;
|
||||
#endif
|
||||
}
|
||||
|
||||
//build final value
|
||||
accum = 1+save; //initialize product to 1+remainder
|
||||
//multiplies for ln(10)
|
||||
for (int k = 0; k < num_times_ln10; k++){
|
||||
accum *= 10;
|
||||
}
|
||||
//multiplies for ln(1 + 10^-j)
|
||||
for (int j = 0; j < NUM_A_ARR; j++){
|
||||
for (int k = 0; k < num_times[j]; k++){
|
||||
accum *= a_arr[j];
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//calculate relative error
|
||||
mpfr_float_1000 calc, diff;
|
||||
calc = accum;
|
||||
diff = abs((actual - calc)/actual);
|
||||
|
||||
#ifdef DEBUG_ALL
|
||||
if (1){
|
||||
#else
|
||||
if (diff > 5e-17){
|
||||
#endif
|
||||
cout << x << ": ";
|
||||
cout << std::setprecision(18) << accum << ", ";
|
||||
#ifdef DEBUG_ALL
|
||||
cout << actual << ", ";
|
||||
#endif
|
||||
cout << diff << endl;
|
||||
}
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
@ -80,7 +80,7 @@ int main(void){
|
||||
//calculate relative error
|
||||
mpfr_float_1000 calc, diff;
|
||||
calc = accum;
|
||||
diff = (actual - calc)/actual;
|
||||
diff = abs((actual - calc)/actual);
|
||||
|
||||
if (diff > 5e-17){
|
||||
cout << x << ": ";
|
||||
|
||||
Loading…
Reference in New Issue
Block a user