531 lines
8.8 KiB
C
531 lines
8.8 KiB
C
/*
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* This file is part of the UCB release of Plan 9. It is subject to the license
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* terms in the LICENSE file found in the top-level directory of this
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* distribution and at http://akaros.cs.berkeley.edu/files/Plan9License. No
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* part of the UCB release of Plan 9, including this file, may be copied,
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* modified, propagated, or distributed except according to the terms contained
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* in the LICENSE file.
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*/
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#include <u.h>
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#include <libc.h>
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#include <jehanne/ctype.h>
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/*
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* This routine will convert to arbitrary precision
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* floating point entirely in multi-precision fixed.
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* The answer is the closest floating point number to
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* the given decimal number. Exactly half way are
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* rounded ala ieee rules.
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* Method is to scale input decimal between .500 and .999...
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* with external power of 2, then binary search for the
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* closest mantissa to this decimal number.
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* Nmant is is the required precision. (53 for ieee dp)
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* Nbits is the max number of bits/word. (must be <= 28)
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* Prec is calculated - the number of words of fixed mantissa.
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*/
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enum
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{
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Nbits = 28, // bits safely represented in a ulong
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Nmant = 53, // bits of precision required
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Bias = 1022,
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Prec = (Nmant+Nbits+1)/Nbits, // words of Nbits each to represent mantissa
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Sigbit = 1<<(Prec*Nbits-Nmant), // first significant bit of Prec-th word
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Ndig = 1500,
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One = (uint32_t)(1<<Nbits),
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Half = (uint32_t)(One>>1),
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Maxe = 310,
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Fsign = 1<<0, // found -
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Fesign = 1<<1, // found e-
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Fdpoint = 1<<2, // found .
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S0 = 0, // _ _S0 +S1 #S2 .S3
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S1, // _+ #S2 .S3
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S2, // _+# #S2 .S4 eS5
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S3, // _+. #S4
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S4, // _+#.# #S4 eS5
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S5, // _+#.#e +S6 #S7
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S6, // _+#.#e+ #S7
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S7, // _+#.#e+# #S7
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};
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static int xcmp(const char*, char*);
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static int fpcmp(char*, uint32_t*);
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static void frnorm(uint32_t*);
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static void divascii(char*, int*, int*, int*);
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static void mulascii(char*, int*, int*, int*);
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static void divby(char*, int*, int);
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typedef struct Tab Tab;
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struct Tab
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{
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int bp;
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int siz;
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char* cmp;
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};
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double
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jehanne_strtod(const char *as, const char **aas)
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{
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int na, ona, ex, dp, bp, c, i, flag, state;
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uint32_t low[Prec], hig[Prec], mid[Prec], num, den;
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double d;
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const char *s;
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char a[Ndig];
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flag = 0; // Fsign, Fesign, Fdpoint
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na = 0; // number of digits of a[]
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dp = 0; // na of decimal point
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ex = 0; // exonent
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state = S0;
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for(s=as;; s++) {
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c = *s;
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if(c >= '0' && c <= '9') {
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switch(state) {
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case S0:
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case S1:
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case S2:
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state = S2;
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break;
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case S3:
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case S4:
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state = S4;
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break;
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case S5:
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case S6:
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case S7:
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state = S7;
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ex = ex*10 + (c-'0');
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continue;
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}
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if(na == 0 && c == '0') {
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dp--;
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continue;
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}
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if(na < Ndig-50)
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a[na++] = c;
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continue;
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}
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switch(c) {
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case '\t':
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case '\n':
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case '\v':
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case '\f':
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case '\r':
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case ' ':
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if(state == S0)
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continue;
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break;
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case '-':
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if(state == S0)
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flag |= Fsign;
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else
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flag |= Fesign;
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case '+':
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if(state == S0)
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state = S1;
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else
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if(state == S5)
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state = S6;
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else
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break; // syntax
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continue;
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case '.':
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flag |= Fdpoint;
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dp = na;
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if(state == S0 || state == S1) {
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state = S3;
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continue;
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}
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if(state == S2) {
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state = S4;
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continue;
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}
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break;
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case 'e':
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case 'E':
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if(state == S2 || state == S4) {
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state = S5;
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continue;
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}
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break;
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}
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break;
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}
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/*
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* clean up return char-pointer
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*/
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switch(state) {
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case S0:
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if(xcmp(s, "nan") == 0) {
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if(aas != nil)
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*aas = s+3;
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goto retnan;
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}
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case S1:
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if(xcmp(s, "infinity") == 0) {
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if(aas != nil)
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*aas = s+8;
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goto retinf;
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}
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if(xcmp(s, "inf") == 0) {
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if(aas != nil)
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*aas = s+3;
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goto retinf;
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}
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case S3:
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if(aas != nil)
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*aas = as;
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goto ret0; // no digits found
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case S6:
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s--; // back over +-
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case S5:
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s--; // back over e
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break;
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}
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if(aas != nil)
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*aas = s;
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if(flag & Fdpoint)
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while(na > 0 && a[na-1] == '0')
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na--;
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if(na == 0)
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goto ret0; // zero
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a[na] = 0;
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if(!(flag & Fdpoint))
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dp = na;
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if(flag & Fesign)
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ex = -ex;
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dp += ex;
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if(dp < -Maxe-Nmant/3) /* actually -Nmant*jehanne_log(2)/jehanne_log(10), but Nmant/3 close enough */
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goto ret0; // underflow by exp
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else
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if(dp > +Maxe)
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goto retinf; // overflow by exp
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/*
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* normalize the decimal ascii number
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* to range .[5-9][0-9]* e0
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*/
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bp = 0; // binary exponent
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while(dp > 0)
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divascii(a, &na, &dp, &bp);
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while(dp < 0 || a[0] < '5')
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mulascii(a, &na, &dp, &bp);
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a[na] = 0;
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/*
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* very small numbers are represented using
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* bp = -Bias+1. adjust accordingly.
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*/
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if(bp < -Bias+1){
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ona = na;
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divby(a, &na, -bp-Bias+1);
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if(na < ona){
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jehanne_memmove(a+ona-na, a, na);
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jehanne_memset(a, '0', ona-na);
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na = ona;
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}
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a[na] = 0;
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bp = -Bias+1;
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}
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/* close approx by naive conversion */
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num = 0;
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den = 1;
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for(i=0; i<9 && (c=a[i]); i++) {
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num = num*10 + (c-'0');
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den *= 10;
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}
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low[0] = jehanne_umuldiv(num, One, den);
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hig[0] = jehanne_umuldiv(num+1, One, den);
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for(i=1; i<Prec; i++) {
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low[i] = 0;
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hig[i] = One-1;
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}
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/* binary search for closest mantissa */
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for(;;) {
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/* mid = (hig + low) / 2 */
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c = 0;
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for(i=0; i<Prec; i++) {
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mid[i] = hig[i] + low[i];
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if(c)
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mid[i] += One;
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c = mid[i] & 1;
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mid[i] >>= 1;
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}
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frnorm(mid);
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/* compare */
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c = fpcmp(a, mid);
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if(c > 0) {
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c = 1;
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for(i=0; i<Prec; i++)
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if(low[i] != mid[i]) {
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c = 0;
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low[i] = mid[i];
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}
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if(c)
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break; // between mid and hig
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continue;
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}
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if(c < 0) {
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for(i=0; i<Prec; i++)
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hig[i] = mid[i];
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continue;
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}
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/* only hard part is if even/odd roundings wants to go up */
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c = mid[Prec-1] & (Sigbit-1);
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if(c == Sigbit/2 && (mid[Prec-1]&Sigbit) == 0)
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mid[Prec-1] -= c;
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break; // exactly mid
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}
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/* normal rounding applies */
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c = mid[Prec-1] & (Sigbit-1);
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mid[Prec-1] -= c;
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if(c >= Sigbit/2) {
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mid[Prec-1] += Sigbit;
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frnorm(mid);
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}
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d = 0;
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for(i=0; i<Prec; i++)
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d = d*One + mid[i];
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if(flag & Fsign)
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d = -d;
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d = jehanne_ldexp(d, bp - Prec*Nbits);
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return d;
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ret0:
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return 0;
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retnan:
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return jehanne_NaN();
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retinf:
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if(flag & Fsign)
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return jehanne_Inf(-1);
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return jehanne_Inf(+1);
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}
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static void
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frnorm(uint32_t *f)
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{
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int i, c;
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c = 0;
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for(i=Prec-1; i>0; i--) {
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f[i] += c;
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c = f[i] >> Nbits;
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f[i] &= One-1;
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}
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f[0] += c;
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}
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static int
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fpcmp(char *a, uint32_t* f)
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{
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uint32_t tf[Prec];
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int i, d, c;
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for(i=0; i<Prec; i++)
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tf[i] = f[i];
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for(;;) {
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/* tf *= 10 */
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for(i=0; i<Prec; i++)
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tf[i] = tf[i]*10;
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frnorm(tf);
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d = (tf[0] >> Nbits) + '0';
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tf[0] &= One-1;
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/* compare next digit */
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c = *a;
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if(c == 0) {
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if('0' < d)
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return -1;
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if(tf[0] != 0)
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goto cont;
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for(i=1; i<Prec; i++)
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if(tf[i] != 0)
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goto cont;
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return 0;
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}
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if(c > d)
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return +1;
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if(c < d)
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return -1;
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a++;
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cont:;
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}
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}
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static void
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_divby(char *a, int *na, int b)
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{
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int n, c;
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char *p;
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p = a;
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n = 0;
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while(n>>b == 0) {
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c = *a++;
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if(c == 0) {
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while(n) {
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c = n*10;
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if(c>>b)
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break;
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n = c;
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}
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goto xx;
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}
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n = n*10 + c-'0';
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(*na)--;
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}
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for(;;) {
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c = n>>b;
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n -= c<<b;
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*p++ = c + '0';
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c = *a++;
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if(c == 0)
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break;
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n = n*10 + c-'0';
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}
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(*na)++;
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xx:
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while(n) {
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n = n*10;
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c = n>>b;
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n -= c<<b;
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*p++ = c + '0';
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(*na)++;
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}
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*p = 0;
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}
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static void
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divby(char *a, int *na, int b)
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{
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while(b > 9){
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_divby(a, na, 9);
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a[*na] = 0;
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b -= 9;
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}
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if(b > 0)
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_divby(a, na, b);
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}
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static Tab tab1[] =
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{
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1, 0, "",
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3, 1, "7",
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6, 2, "63",
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9, 3, "511",
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13, 4, "8191",
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16, 5, "65535",
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19, 6, "524287",
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23, 7, "8388607",
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26, 8, "67108863",
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27, 9, "134217727",
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};
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static void
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divascii(char *a, int *na, int *dp, int *bp)
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{
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int b, d;
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Tab *t;
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d = *dp;
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if(d >= nelem(tab1))
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d = nelem(tab1)-1;
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t = tab1 + d;
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b = t->bp;
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if(jehanne_memcmp(a, t->cmp, t->siz) > 0)
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d--;
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*dp -= d;
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*bp += b;
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divby(a, na, b);
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}
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static void
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mulby(char *a, char *p, char *q, int b)
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{
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int n, c;
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n = 0;
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*p = 0;
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for(;;) {
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q--;
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if(q < a)
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break;
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c = *q - '0';
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c = (c<<b) + n;
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n = c/10;
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c -= n*10;
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p--;
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*p = c + '0';
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}
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while(n) {
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c = n;
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n = c/10;
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c -= n*10;
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p--;
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*p = c + '0';
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}
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}
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static Tab tab2[] =
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{
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1, 1, "", // dp = 0-0
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3, 3, "125",
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6, 5, "15625",
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9, 7, "1953125",
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13, 10, "1220703125",
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16, 12, "152587890625",
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19, 14, "19073486328125",
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23, 17, "11920928955078125",
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26, 19, "1490116119384765625",
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27, 19, "7450580596923828125", // dp 8-9
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};
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static void
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mulascii(char *a, int *na, int *dp, int *bp)
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{
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char *p;
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int d, b;
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Tab *t;
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d = -*dp;
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if(d >= nelem(tab2))
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d = nelem(tab2)-1;
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t = tab2 + d;
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b = t->bp;
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if(jehanne_memcmp(a, t->cmp, t->siz) < 0)
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d--;
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p = a + *na;
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*bp -= b;
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*dp += d;
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*na += d;
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mulby(a, p+d, p, b);
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}
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|
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static int
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xcmp(const char *a, char *b)
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{
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int c1, c2;
|
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while(c1 = *b++) {
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c2 = *a++;
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if(isupper(c2))
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c2 = jehanne_tolower(c2);
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if(c1 != c2)
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return 1;
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}
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return 0;
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}
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