440 lines
9.3 KiB
C
440 lines
9.3 KiB
C
/*
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(c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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See the copyright notice in the ACK home directory, in the file "Copyright".
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*/
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/* $Header$ */
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#include <ctype.h>
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#include "misc.h"
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/* The following tables can be computed with the following bc(1)
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program:
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obase=16
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scale=0
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define t(x){
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auto a, b, c
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a=2;b=1;c=2^32;n=1
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while(a<x) {
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b=a;n+=n;a*=a
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}
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n/=2
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a=b
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while(b<x) {
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a=b;b*=c;n+=32
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}
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n-=32
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b=a
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while(a<x) {
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b=a;a+=a;n+=1
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}
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n-=1
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x*=16^16
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b=x%a
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x/=a
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if(a<=(2*b)) x+=1
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obase=10
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n
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obase=16
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return(x)
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}
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for (i=1;i<28;i++) {
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t(10^i)
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}
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0
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for (i=1;i<20;i++) {
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t(10^(28*i))
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}
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0
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define r(x){
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auto a, b, c
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a=2;b=1;c=2^32;n=1
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while(a<x) {
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b=a;n+=n;a*=a
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}
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n/=2
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a=b
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while(b<x) {
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a=b;b*=c;n+=32
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}
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n-=32
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b=a
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while(a<x) {
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b=a;a+=a;n+=1
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}
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a=b
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a*=16^16
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b=a%x
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a/=x
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if(x<=(2*b)) a+=1
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obase=10
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-n
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obase=16
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return(a)
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}
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for (i=1;i<28;i++) {
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r(10^i)
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}
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0
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for (i=1;i<20;i++) {
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r(10^(28*i))
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}
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0
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*/
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static flt_arith s10pow[] = { /* representation of 10 ** i */
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{ 0, 0, 0x80000000, 0 },
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{ 0, 3, 0xA0000000, 0 },
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{ 0, 6, 0xC8000000, 0 },
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{ 0, 9, 0xFA000000, 0 },
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{ 0, 13, 0x9C400000, 0 },
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{ 0, 16, 0xC3500000, 0 },
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{ 0, 19, 0xF4240000, 0 },
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{ 0, 23, 0x98968000, 0 },
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{ 0, 26, 0xBEBC2000, 0 },
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{ 0, 29, 0xEE6B2800, 0 },
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{ 0, 33, 0x9502F900, 0 },
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{ 0, 36, 0xBA43B740, 0 },
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{ 0, 39, 0xE8D4A510, 0 },
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{ 0, 43, 0x9184E72A, 0 },
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{ 0, 46, 0xB5E620F4, 0x80000000 },
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{ 0, 49, 0xE35FA931, 0xA0000000 },
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{ 0, 53, 0x8E1BC9BF, 0x04000000 },
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{ 0, 56, 0xB1A2BC2E, 0xC5000000 },
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{ 0, 59, 0xDE0B6B3A, 0x76400000 },
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{ 0, 63, 0x8AC72304, 0x89E80000 },
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{ 0, 66, 0xAD78EBC5, 0xAC620000 },
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{ 0, 69, 0xD8D726B7, 0x177A8000 },
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{ 0, 73, 0x87867832, 0x6EAC9000 },
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{ 0, 76, 0xA968163F, 0x0A57B400 },
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{ 0, 79, 0xD3C21BCE, 0xCCEDA100 },
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{ 0, 83, 0x84595161, 0x401484A0 },
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{ 0, 86, 0xA56FA5B9, 0x9019A5C8 },
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{ 0, 89, 0xCECB8F27, 0xF4200F3A }
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};
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static flt_arith big_10pow[] = { /* representation of 10 ** (28*i) */
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{ 0, 0, 0x80000000, 0 },
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{ 0, 93, 0x813F3978, 0xF8940984 },
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{ 0, 186, 0x82818F12, 0x81ED44A0 },
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{ 0, 279, 0x83C7088E, 0x1AAB65DB },
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{ 0, 372, 0x850FADC0, 0x9923329E },
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{ 0, 465, 0x865B8692, 0x5B9BC5C2 },
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{ 0, 558, 0x87AA9AFF, 0x79042287 },
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{ 0, 651, 0x88FCF317, 0xF22241E2 },
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{ 0, 744, 0x8A5296FF, 0xE33CC930 },
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{ 0, 837, 0x8BAB8EEF, 0xB6409C1A },
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{ 0, 930, 0x8D07E334, 0x55637EB3 },
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{ 0, 1023, 0x8E679C2F, 0x5E44FF8F },
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{ 0, 1116, 0x8FCAC257, 0x558EE4E6 },
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{ 0, 1209, 0x91315E37, 0xDB165AA9 },
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{ 0, 1302, 0x929B7871, 0xDE7F22B9 },
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{ 0, 1395, 0x940919BB, 0xD4620B6D },
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{ 0, 1488, 0x957A4AE1, 0xEBF7F3D4 },
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{ 0, 1581, 0x96EF14C6, 0x454AA840 },
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{ 0, 1674, 0x98678061, 0x27ECE4F5 },
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{ 0, 1767, 0x99E396C1, 0x3A3ACFF2 }
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};
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static flt_arith r_10pow[] = { /* representation of 10 ** -i */
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{ 0, 0, 0x80000000, 0 },
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{ 0, -4, 0xCCCCCCCC, 0xCCCCCCCD },
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{ 0, -7, 0xA3D70A3D, 0x70A3D70A },
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{ 0, -10, 0x83126E97, 0x8D4FDF3B },
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{ 0, -14, 0xD1B71758, 0xE219652C },
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{ 0, -17, 0xA7C5AC47, 0x1B478423 },
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{ 0, -20, 0x8637BD05, 0xAF6C69B6 },
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{ 0, -24, 0xD6BF94D5, 0xE57A42BC },
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{ 0, -27, 0xABCC7711, 0x8461CEFD },
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{ 0, -30, 0x89705F41, 0x36B4A597 },
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{ 0, -34, 0xDBE6FECE, 0xBDEDD5BF },
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{ 0, -37, 0xAFEBFF0B, 0xCB24AAFF },
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{ 0, -40, 0x8CBCCC09, 0x6F5088CC },
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{ 0, -44, 0xE12E1342, 0x4BB40E13 },
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{ 0, -47, 0xB424DC35, 0x095CD80F },
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{ 0, -50, 0x901D7CF7, 0x3AB0ACD9 },
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{ 0, -54, 0xE69594BE, 0xC44DE15B },
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{ 0, -57, 0xB877AA32, 0x36A4B449 },
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{ 0, -60, 0x9392EE8E, 0x921D5D07 },
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{ 0, -64, 0xEC1E4A7D, 0xB69561A5 },
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{ 0, -67, 0xBCE50864, 0x92111AEB },
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{ 0, -70, 0x971DA050, 0x74DA7BEF },
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{ 0, -74, 0xF1C90080, 0xBAF72CB1 },
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{ 0, -77, 0xC16D9A00, 0x95928A27 },
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{ 0, -80, 0x9ABE14CD, 0x44753B53 },
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{ 0, -84, 0xF79687AE, 0xD3EEC551 },
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{ 0, -87, 0xC6120625, 0x76589DDB },
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{ 0, -90, 0x9E74D1B7, 0x91E07E48 }
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};
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static flt_arith r_big_10pow[] = { /* representation of 10 ** -(28*i) */
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{ 0, 0, 0x80000000, 0 },
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{ 0, -94, 0xFD87B5F2, 0x8300CA0E },
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{ 0, -187, 0xFB158592, 0xBE068D2F },
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{ 0, -280, 0xF8A95FCF, 0x88747D94 },
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{ 0, -373, 0xF64335BC, 0xF065D37D },
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{ 0, -466, 0xF3E2F893, 0xDEC3F126 },
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{ 0, -559, 0xF18899B1, 0xBC3F8CA2 },
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{ 0, -652, 0xEF340A98, 0x172AACE5 },
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{ 0, -745, 0xECE53CEC, 0x4A314EBE },
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{ 0, -838, 0xEA9C2277, 0x23EE8BCB },
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{ 0, -931, 0xE858AD24, 0x8F5C22CA },
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{ 0, -1024, 0xE61ACF03, 0x3D1A45DF },
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{ 0, -1117, 0xE3E27A44, 0x4D8D98B8 },
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{ 0, -1210, 0xE1AFA13A, 0xFBD14D6E },
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{ 0, -1303, 0xDF82365C, 0x497B5454 },
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{ 0, -1396, 0xDD5A2C3E, 0xAB3097CC },
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{ 0, -1489, 0xDB377599, 0xB6074245 },
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{ 0, -1582, 0xD91A0545, 0xCDB51186 },
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{ 0, -1675, 0xD701CE3B, 0xD387BF48 },
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{ 0, -1768, 0xD4EEC394, 0xD6258BF8 }
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};
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#define BIGSZ (sizeof(big_10pow)/sizeof(big_10pow[0]))
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#define SMALLSZ (sizeof(s10pow)/sizeof(s10pow[0]))
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static
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add_exponent(e, exp)
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register flt_arith *e;
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{
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int neg = exp < 0;
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int divsz, modsz;
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flt_arith x;
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register int status = 0;
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if (neg) exp = -exp;
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divsz = exp / SMALLSZ;
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modsz = exp % SMALLSZ;
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if (!status) status = flt_status;
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flt_mul(e, (neg ? r_10pow : s10pow) + modsz, &x);
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if (!status) status = flt_status;
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while (divsz >= BIGSZ) {
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flt_mul(&x, neg ? &r_big_10pow[BIGSZ-1] : &big_10pow[BIGSZ-1],&x);
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if (!status) status = flt_status;
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divsz -= BIGSZ-1;
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}
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flt_mul(&x, (neg ? r_big_10pow : big_10pow) + divsz, e);
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if (!status) status = flt_status;
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flt_status = status;
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}
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flt_str2flt(s, e)
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register char *s;
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register flt_arith *e;
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{
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register int c;
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int dotseen = 0;
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int digitseen = 0;
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int exp = 0;
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while (isspace(*s)) s++;
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flt_status = 0;
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e->flt_sign = 0;
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e->flt_exp = 0;
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e->m1 = e->m2 = 0;
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c = *s;
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switch(c) {
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case '-':
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e->flt_sign = 1;
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case '+':
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s++;
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}
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while (c = *s++, isdigit(c) || (c == '.' && ! dotseen++)) {
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if (c == '.') continue;
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digitseen = 1;
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if (e->m1 >= 0 && e->m1 <= 0x7FFFFFFF/5) {
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struct flt_mantissa a1;
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a1 = e->flt_mantissa;
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flt_b64_sft(&(e->flt_mantissa), -3);
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flt_b64_sft(&a1, -1);
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flt_b64_add(&(e->flt_mantissa), &a1);
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a1.flt_h_32 = 0;
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a1.flt_l_32 = c - '0';
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flt_b64_add(&(e->flt_mantissa), &a1);
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}
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else exp++;
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if (dotseen) exp--;
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}
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if (! digitseen) {
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flt_status = FLT_NOFLT;
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return;
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}
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if (c == 'E' || c == 'e') {
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int exp1 = 0;
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int sign = 1;
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switch(*s) {
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case '-':
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sign = -1;
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case '+':
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s++;
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}
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if (c = *s, isdigit(c)) {
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do {
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exp1 = 10 * exp1 + (c - '0');
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} while (c = *++s, isdigit(c));
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}
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exp += sign * exp1;
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}
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if (e->m1 == 0 && e->m2 == 0) return;
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e->flt_exp = 63;
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flt_nrm(e);
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add_exponent(e, exp);
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flt_chk(e);
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}
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#define NDIGITS 128
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static char *
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flt_ecvt(e, ndigit, decpt, sign)
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register flt_arith *e;
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int ndigit, *decpt, *sign;
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{
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/* Like ecvt(), but for extended precision */
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static char buf[NDIGITS+1];
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register char *p = buf;
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register char *pe;
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if (ndigit < 0) ndigit = 0;
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if (ndigit > NDIGITS) ndigit = NDIGITS;
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pe = &buf[ndigit];
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buf[0] = '\0';
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*sign = 0;
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if (e->flt_sign) {
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*sign = 1;
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e->flt_sign = 0;
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}
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*decpt = 0;
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if (e->m1 != 0) {
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register flt_arith *pp = &big_10pow[1];
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while (flt_cmp(e, &big_10pow[BIGSZ-1]) >= 0) {
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flt_mul(e,&r_big_10pow[BIGSZ-1],e);
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*decpt += (BIGSZ-1)*SMALLSZ;
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}
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while (flt_cmp(e,pp) >= 0) {
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pp++;
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}
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pp--;
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flt_mul(e,&r_big_10pow[pp-big_10pow],e);
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*decpt += (pp - big_10pow)*SMALLSZ;
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pp = &s10pow[1];
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while (pp < &s10pow[SMALLSZ] && flt_cmp(e, pp) >= 0) pp++;
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pp--;
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flt_mul(e, &r_10pow[pp-s10pow], e);
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*decpt += pp - s10pow;
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if (flt_cmp(e, &s10pow[0]) < 0) {
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while (flt_cmp(e, &r_big_10pow[BIGSZ-1]) < 0) {
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flt_mul(e,&big_10pow[BIGSZ-1],e);
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*decpt -= (BIGSZ-1)*SMALLSZ;
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}
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pp = &r_big_10pow[1];
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while(flt_cmp(e,pp) < 0) pp++;
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pp--;
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flt_mul(e,&big_10pow[pp-r_big_10pow],e);
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*decpt -= (pp - r_big_10pow)*SMALLSZ;
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/* here, value >= 10 ** -28 */
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flt_mul(e, &s10pow[1], e);
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(*decpt)--;
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pp = &r_10pow[0];
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while(flt_cmp(e, pp) < 0) pp++;
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flt_mul(e, &s10pow[pp-r_10pow], e);
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*decpt -= pp - r_10pow;
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}
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(*decpt)++; /* because now value in [1.0, 10.0) */
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}
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while (p <= pe) {
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if (e->flt_exp >= 0 && e->m1 != 0) {
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flt_arith x;
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x.m2 = 0; x.flt_exp = e->flt_exp;
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x.flt_sign = 1;
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x.m1 = (e->m1 >> 1) & 0x7FFFFFFF;
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x.m1 = x.m1>>(30-e->flt_exp);
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*p++ = (x.m1) + '0';
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if (x.m1) {
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x.m1 = x.m1 << (31-e->flt_exp);
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flt_add(e, &x, e);
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}
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}
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else *p++ = '0';
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flt_mul(e, &s10pow[1], e);
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}
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if (pe >= buf) {
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p = pe;
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*p += 5; /* round of at the end */
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while (*p > '9') {
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*p = '0';
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if (p > buf) ++*--p;
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else {
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*p = '1';
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++*decpt;
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}
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}
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*pe = '\0';
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}
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return buf;
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}
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flt_flt2str(e, buf, bufsize)
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flt_arith *e;
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char *buf;
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{
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#define NDIG 20
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int sign, dp;
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register int i;
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register char *s1;
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char Xbuf[NDIG+12];
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register char *s = Xbuf;
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flt_arith e1;
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e1 = *e;
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flt_status = 0;
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s1 = flt_ecvt(&e1,NDIG,&dp,&sign);
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if (sign)
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*s++ = '-';
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*s++ = *s1++;
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*s++ = '.';
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for (i = NDIG-1; i > 0; i--) {
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if (*s1) *s++ = *s1++;
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else *s++ = '0';
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}
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if (e->m1 | e->m2) {
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--dp ;
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}
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if (dp != 0) {
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*s++ = 'e';
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if ( dp<0 ) {
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*s++ = '-' ; dp= -dp ;
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} else {
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*s++ = '+' ;
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}
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s1 = &Xbuf[NDIG+12];
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*--s1 = '\0';
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do {
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*--s1 = dp % 10 + '0';
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dp /= 10;
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} while (dp != 0);
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while (*s1) *s++ = *s1++;
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}
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*s++ = '\0';
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if (s - Xbuf > bufsize) {
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flt_status = FLT_BTSM;
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return;
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}
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s = Xbuf;
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s1 = buf;
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do {
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*s1++ = *s;
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} while (*s++);
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}
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