change exponent from int16_t to int8_t to free up some space
This commit is contained in:
Jeff Wang
parent
836d4fc122
commit
fcf16153f6
@ -138,12 +138,16 @@ The keys on the original calculator map as follows:
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- The 3rd and subsequent presses negates the current exponent being entered.
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- `mode`: reserved for a future shift key
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## Floating Point
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The allowable range of exponents is +/-63. Trying to enter a number with a larger exponent will result in an error.
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## Turning off
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Hold `Shift` (the `mode` key on the physical calculator) and `0` at the same time to turn off. NOTE: There is no auto power off.
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# Bugs
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1. The calculator does not properly check for underflow or overflow.
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1. After division by 0, it's possible to negate `Error` to get an invalid number.
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1. The calculator does not properly check for underflow or overflow sometimes.
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1. Calculations with numbers with exponents near the max/min of +/-63 may give improper results, especially for division where intermediate results may go out of range, even if the result is in range.
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1. After division by 0 or over/underflow, it's possible to negate `Error` to get an invalid number. It's also possible to subtract `Error`.
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1. There are probably more bugs waiting to be discovered.
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# Internals
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@ -25,7 +25,7 @@ static void pop(){
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StackPtr++; //adjust pointer
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}
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void push_decn(const char* signif_str, int16_t exponent, uint8_t no_lift){
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void push_decn(const char* signif_str, int8_t exponent, uint8_t no_lift){
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if (!no_lift){
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StackPtr--;
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}
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@ -36,7 +36,7 @@ void clear_x(void){
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set_dec80_zero(&stack(STACK_X));
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}
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void set_x(const char* signif_str, int16_t exponent){
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void set_x(const char* signif_str, int8_t exponent){
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build_dec80(&stack(STACK_X), signif_str, exponent);
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}
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@ -16,10 +16,10 @@ extern "C" {
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void process_cmd(char cmd);
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void push_decn(const char* signif_str, int16_t exponent, uint8_t no_lift);
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void push_decn(const char* signif_str, int8_t exponent, uint8_t no_lift);
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void clear_x(void);
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void set_x(const char* signif_str, int16_t exponent);
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void set_x(const char* signif_str, int8_t exponent);
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__xdata dec80* get_x(void);
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__xdata dec80* get_y(void);
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@ -53,20 +53,20 @@ void copy_decn(dec80* dest, const dec80* src){
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}
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}
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int16_t get_exponent(const dec80* x){
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int16_t exponent = x->exponent;
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if (exponent & 0x4000){ //negative
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return exponent | 0x8000;
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int8_t get_exponent(const dec80* x){
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int8_t exponent = x->exponent;
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if (exponent & 0x40){ //negative
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return exponent | 0x80;
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} else { //positive
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return exponent & 0x7fff;
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return exponent & 0x7f;
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}
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}
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void set_exponent(dec80* acc, int16_t exponent, uint8_t num_is_neg){
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void set_exponent(dec80* acc, int8_t exponent, uint8_t num_is_neg){
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if (num_is_neg){
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exponent |= 0x8000;
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exponent |= 0x80;
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} else {
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exponent &= 0x7fff;
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exponent &= 0x7f;
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}
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acc->exponent = exponent;
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@ -103,7 +103,7 @@ static void shift_left(dec80* x){
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static void remove_leading_zeros(dec80* x){
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uint8_t digit100;
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uint8_t is_negative = (x->exponent < 0);
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int16_t exponent = get_exponent(x);
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int8_t exponent = get_exponent(x);
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//find first non-zero digit100
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for (digit100 = 0; digit100 < DEC80_NUM_LSU; digit100++){
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@ -133,7 +133,7 @@ static void remove_leading_zeros(dec80* x){
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set_exponent(x, exponent, is_negative);
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}
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void build_dec80(dec80* dest, const char* signif_str, int16_t exponent){
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void build_dec80(dec80* dest, const char* signif_str, int8_t exponent){
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enum {
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SIGN_ZERO,
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SIGN_ZERO_SEEN_POINT,
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@ -341,7 +341,7 @@ static uint8_t decn_is_zero(const dec80* x){
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uint8_t decn_is_nan(const dec80* x){
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uint8_t i;
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if (x->exponent != DEC80_NAN_EXP){
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if (x->exponent & 0x7f != DEC80_NAN_EXP){
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return 0;
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}
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for (i = 0; i < DEC80_NUM_LSU; i++){
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@ -366,13 +366,13 @@ void set_dec80_NaN(dec80* dest){
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#endif
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void negate_decn(dec80* x){
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static const int16_t xor_val = -(0x7fff) - 1;
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static const int8_t xor_val = -(0x7f) - 1;
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(x->exponent) ^= xor_val;
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}
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int8_t compare_magn(const dec80* a, const dec80* b){ //a<b: -1, a==b: 0, a>b: 1
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uint8_t a_i, b_i;
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int16_t a_exp=0, b_exp=0;
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int8_t a_exp=0, b_exp=0;
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int8_t a_signif_b = 0; //a<b: -1, a==b: 0, a>b: 1
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static __xdata dec80 a_tmp, b_tmp;
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//copy
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@ -460,8 +460,8 @@ int8_t compare_decn(const dec80* a, const dec80* b){ //a<b: -1, a==b: 0, a>b: 1
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//acc and the number from which exponent was taken MUST be stripped of leading 0s first
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//rescales acc up to exponent (increase exponent of acc, while shifting right)
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//the actual value of acc->exponent remains unchanged
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static void _incr_exp(dec80* acc, int16_t exponent){
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int16_t curr_exp = get_exponent(acc);
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static void _incr_exp(dec80* acc, int8_t exponent){
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int8_t curr_exp = get_exponent(acc);
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#ifdef DEBUG_ADD
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uint8_t is_neg = (acc->exponent < 0);
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printf(" (is_neg,curr_exp,exponent)=(%d,%d,%d)\n",
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@ -612,7 +612,7 @@ void add_decn(dec80* acc, const dec80* x){
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}
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//may need to rescale number
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if (carry > 0){
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int16_t curr_exp = get_exponent(acc);
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int8_t curr_exp = get_exponent(acc);
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rel = (acc->exponent < 0); //is_neg?
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#ifdef DEBUG_ADD
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printf(" carry out: %d", carry);
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@ -639,7 +639,7 @@ void mult_decn(dec80* acc, const dec80* x){
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int8_t i, j;
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uint8_t carry = 0;
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uint8_t is_neg;
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int16_t new_exponent;
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int8_t new_exponent;
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//initialize values
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copy_decn(&tmp, x);
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set_dec80_zero(&acc_tmp);
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@ -647,7 +647,7 @@ void mult_decn(dec80* acc, const dec80* x){
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remove_leading_zeros(acc);
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remove_leading_zeros(&tmp);
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//store new sign
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if ((acc->exponent & 0x8000) ^ (tmp.exponent & 0x8000)){ //signs differ
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if ((acc->exponent & 0x80) ^ (tmp.exponent & 0x80)){ //signs differ
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is_neg = 1;
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} else {
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is_neg = 0;
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@ -709,8 +709,13 @@ void mult_decn(dec80* acc, const dec80* x){
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//add back carry to MSdigit in MSdigit100
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acc_tmp.lsu[0] += carry*10;
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}
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//set new exponent
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set_exponent(&acc_tmp, new_exponent, is_neg);
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//set new exponent, checking for over/underflow
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if (new_exponent < DEC80_MAX_EXP && new_exponent > DEC80_MIN_EXP){
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set_exponent(&acc_tmp, new_exponent, is_neg);
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} else {
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set_dec80_NaN(acc);
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return;
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}
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//copy back to acc
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copy_decn(acc, &acc_tmp);
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//normalize
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@ -721,7 +726,7 @@ void div_decn(dec80* acc, const dec80* x){
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static __xdata dec80 tmp; //copy of x, holds current 1/x estimate
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static __xdata dec80 acc_copy; //holds copy of original acc
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uint8_t i;
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int16_t initial_exp;
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int8_t initial_exp;
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//check divide by zero
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#ifdef EXTRA_CHECKS
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if (decn_is_zero(x)){
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@ -781,24 +786,28 @@ void div_decn(dec80* acc, const dec80* x){
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mult_decn(acc, &acc_copy);
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}
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static void set_str_error(char* buf){
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buf[0] = 'E';
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buf[1] = 'r';
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buf[2] = 'r';
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buf[3] = 'o';
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buf[4] = 'r';
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buf[5] = '\0';
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}
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//buf should hold at least 18 + 4 + 5 + 1 = 28
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int8_t decn_to_str(char* buf, const dec80* x){
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#define INSERT_DOT() buf[i++]='.'
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uint8_t i = 0;
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uint8_t digit100;
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int16_t exponent = 0;
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int8_t exponent = 0;
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uint8_t trailing_zeros = 0;
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uint8_t use_sci = 0;
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static __xdata dec80 tmp;
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//handle corner case of NaN
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if (decn_is_nan(x)){
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buf[0] = 'E';
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buf[1] = 'r';
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buf[2] = 'r';
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buf[3] = 'o';
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buf[4] = 'r';
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buf[5] = '\0';
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set_str_error(buf);
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#ifdef DEBUG
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printf (" corner case NaN ");
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#endif
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@ -914,6 +923,10 @@ int8_t decn_to_str(char* buf, const dec80* x){
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#endif
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//print exponent
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if (use_sci){
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if (exponent > DEC80_MAX_EXP || exponent < DEC80_MIN_EXP){
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set_str_error(buf);
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return 0;
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}
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return exponent;
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} else {
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return 0;
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@ -16,15 +16,15 @@ extern "C" {
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#define DEC80_NUM_LSU 9
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//allow full range, but reserve -16384 for special numbers
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#define DEC80_MIN_EXP (-16383)
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#define DEC80_MAX_EXP 16383
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#define DEC80_NAN_EXP (-16383 - 1)
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//allow full range, but reserve -128 for special numbers
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#define DEC80_MIN_EXP (-63)
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#define DEC80_MAX_EXP 63
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#define DEC80_NAN_EXP (-63 - 1) //-64
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//decimal80 unpacked into 80 bits
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// for computation
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typedef struct {
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int16_t exponent; //MSBit is sign of dec80 number, bottom 15 bits are 2's Compl exponent
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int8_t exponent; //MSBit is sign of dec80 number, bottom 15 bits are 2's Compl exponent
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uint8_t lsu[DEC80_NUM_LSU]; //lsu[0] holds most-significant 2 digits (base 100)
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//implicit decimal point between (lsu[0]/10) and (lsu[0]%10)
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} dec80;
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@ -36,13 +36,13 @@ static const dec80 DECN_1 = {
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};
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//remove sign bit, and return 15 bit exponent sign-extended to 16 bits
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int16_t get_exponent(const dec80* x);
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int8_t get_exponent(const dec80* x);
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//void dec64to80(dec80* dest, const dec64* src);
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void copy_decn(dec80* dest, const dec80* src);
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void build_dec80(dec80* dest, const char* signif_str, int16_t exponent);
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void build_dec80(dec80* dest, const char* signif_str, int8_t exponent);
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void set_dec80_zero(dec80* dest);
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void set_dec80_NaN(dec80* dest);
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@ -80,7 +80,7 @@ int main(void){
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printf(" : %s\n\n", Buf);
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//new acc and b for divide test
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build_dec80(&acc, "3.14", 88);
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build_dec80(&acc, "3.14", 60);
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build_dec80(&b, "-1.5", -2);
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decn_to_str_complete(Buf, &acc);
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printf(" acc: %s\n", Buf);
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@ -89,8 +89,8 @@ int main(void){
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div_decn(&acc, &b);
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decn_to_str_complete(Buf, &acc);
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printf("acc/b: %s\n", Buf);
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printf(" : %s\n", "-2.09333333333333334E90");
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build_dec80(&diff, "-2.09333333333333334", 90);
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printf(" : %s\n", "-2.09333333333333334E62");
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build_dec80(&diff, "-2.09333333333333334", 62);
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negate_decn(&diff);
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add_decn(&diff, &acc);
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decn_to_str_complete(Buf, &diff);
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