annotate ve.c @ 0:e0bbaa717f41 draft default tip

lol J
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Mon, 25 Nov 2013 11:56:30 -0500
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1 /* Copyright 1990-2011, Jsoftware Inc. All rights reserved. */
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2 /* License in license.txt. */
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3 /* */
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4 /* Verbs: Elementary Functions (Arithmetic, etc.) */
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5
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6 #include "j.h"
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7 #include "vasm.h"
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8
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9 #define DIVI(u,v) (u||v ? u/(D)v : 0.0)
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10 #define DIVBB(u,v) (v?u:u?inf:0.0)
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11
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12 #define TYMESBX(u,v) (u?v:0)
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13 #define TYMESXB(u,v) (v?u:0)
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14 #define TYMESID(u,v) (u ?u*v:0)
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15 #define TYMESDI(u,v) ( v?u*v:0)
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16 #define TYMESDD(u,v) (u&&v?u*v:0)
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17
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18 AOVF( plusII, I,I,I, PLUSVV, PLUS1V, PLUSV1)
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19 AOVF(minusII, I,I,I, MINUSVV,MINUS1V,MINUSV1)
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20 AOVF(tymesII, I,I,I, TYMESVV,TYMES1V,TYMESV1)
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21
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22 APFX( plusIO, D,I,I, PLUSO)
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23 APFX(minusIO, D,I,I, MINUSO)
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24 APFX(tymesIO, D,I,I, TYMESO)
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25
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26 AIFX( plusBB, I,B,B, + ) /* plusII */ AIFX( plusBD, D,B,D, + )
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27 /* plusII */ /* plusII */ AIFX( plusID, D,I,D, + )
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28 AIFX( plusDB, D,D,B, + ) AIFX( plusDI, D,D,I, +) ANAN( plusDD, D,D,D, PLUS)
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29 ANAN( plusZZ, Z,Z,Z, zplus )
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30
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31 AIFX(minusBB, I,B,B, - ) /* minusII */ AIFX(minusBD, D,B,D, - )
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32 /* minusII */ /* minusII */ AIFX(minusID, D,I,D, - )
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33 AIFX(minusDB, D,D,B, - ) AIFX(minusDI, D,D,I, -) ANAN(minusDD, D,D,D, MINUS)
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34 ANAN(minusZZ, Z,Z,Z, zminus)
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35
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36 /* andBB */ APFX(tymesBI, I,B,I, TYMESBX) APFX(tymesBD, D,B,D, TYMESBX)
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37 APFX(tymesIB, I,I,B, TYMESXB) /* tymesII */ APFX(tymesID, D,I,D, TYMESID)
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38 APFX(tymesDB, D,D,B, TYMESXB) APFX(tymesDI, D,D,I, TYMESDI) APFX(tymesDD, D,D,D, TYMESDD)
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39 ANAN(tymesZZ, Z,Z,Z, ztymes )
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40
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41 APFX( divBB, D,B,B, DIVBB) APFX( divBI, D,B,I, DIVI) APFX( divBD, D,B,D, DIV)
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42 APFX( divIB, D,I,B, DIVI ) APFX( divII, D,I,I, DIVI) APFX( divID, D,I,D, DIV)
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43 APFX( divDB, D,D,B, DIVI ) APFX( divDI, D,D,I, DIVI) ANAN( divDD, D,D,D, DIV)
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44 ANAN( divZZ, Z,Z,Z, zdiv )
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45
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46 /* orBB */ APFX( minBI, I,B,I, MIN) APFX( minBD, D,B,D, MIN)
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47 APFX( minIB, I,I,B, MIN) APFX( minII, I,I,I, MIN) APFX( minID, D,I,D, MIN)
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48 APFX( minDB, D,D,B, MIN) APFX( minDI, D,D,I, MIN) APFX( minDD, D,D,D, MIN)
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49 APFX( minSS, SB,SB,SB, SBMIN)
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50
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51 /* andBB */ APFX( maxBI, I,B,I, MAX) APFX( maxBD, D,B,D, MAX)
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52 APFX( maxIB, I,I,B, MAX) APFX( maxII, I,I,I, MAX) APFX( maxID, D,I,D, MAX)
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53 APFX( maxDB, D,D,B, MAX) APFX( maxDI, D,D,I, MAX) APFX( maxDD, D,D,D, MAX)
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54 APFX( maxSS, SB,SB,SB, SBMAX)
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55
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56
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57 static D jtremdd(J jt,D a,D b){D q,x,y;
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58 if(!a)R b;
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59 ASSERT(!INF(b),EVNAN);
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60 if(a==inf )R 0<=b?b:a;
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61 if(a==infm)R 0>=b?b:a;
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62 q=b/a; x=tfloor(q); y=tceil(q); R teq(x,y)?0:b-a*x;
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63 }
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64
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65 ANAN(remDD, D,D,D, remdd)
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66 ANAN(remZZ, Z,Z,Z, zrem )
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67
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68 static I jtremid(J jt,I a,D b){D r;I k;
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69 ASSERT(a&&-9e15<b&&b<9e15,EWOV);
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70 r=b-a*floor(b/a); k=(I)r;
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71 ASSERT(k==r,EWOV);
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72 R k;
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73 }
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74
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75 APFX(remID, I,I,D, remid)
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76
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77 static I remii(I a,I b){I r; R!a?b:(r=b%a,0<a?r+a*(0>r):r+a*(0<r));}
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78
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79 AHDR2(remII,I,I,I){I u,v;
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80 if(1==n) DO(m, *z++=remii(*x,*y); x++; y++; )
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81 else if(b)DO(m, u=*x++; if(0<=u&&!(u&(u-1))){--u; DO(n, *z++=u&*y++;);}
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82 else DO(n, *z++=remii( u,*y); y++;))
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83 else DO(m, v=*y++; DO(n, *z++=remii(*x, v); x++; ));
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84 }
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85
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86
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87 static I igcd1(I a,I b){R a?igcd1(b%a,a):b;}
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88
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89 static I jtigcd(J jt,I a,I b){
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90 if(a>IMIN&&b>IMIN){a=ABS(a); b=ABS(b);}
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91 else{
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92 if(a==b||!a||!b){jt->jerr=EWOV; R 0;}
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93 if(a==IMIN){b=ABS(b); a=-(a+b);}else{a=ABS(a); b=-(a+b);}
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94 }
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95 R a?igcd1(b%a,a):b;
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96 }
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97
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98 D jtdgcd(J jt,D a,D b){D a1,b1,t;
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99 a=ABS(a); b=ABS(b); if(a>b){t=a; a=b; b=t;}
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100 ASSERT(inf!=b,EVNAN);
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101 if(!a)R b;
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102 a1=a; b1=b;
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103 while(remdd(a1/jfloor(0.5+a1/a),b1)){t=a; a=remdd(a,b); b=t;}
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104 R a;
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105 } /* D.L. Forkes 1984; E.E. McDonnell 1992 */
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106 #if SY_64
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107 #if SY_WIN32
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108 static I jtilcm(J jt,I a,I b){C er=0;I b1,d,z;
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109 if(a&&b){RZ(d=igcd(a,b)); b1=b/d; TYMESVV(1L,&z,&a,&b1); if(er)jt->jerr=EWOV; R z;}else R 0;
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110 }
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111 #else
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112 static I jtilcm(J jt,I a,I b){LD z;I b1,d;
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113 if(a&&b){RZ(d=igcd(a,b)); b1=b/d; z=a*(LD)b1; if(z<IMIN||IMAX<z)jt->jerr=EWOV; R (I)z;}else R 0;
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114 }
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115 #endif
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116 #else
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117 static I jtilcm(J jt,I a,I b){D z;I b1,d;
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118 if(a&&b){RZ(d=igcd(a,b)); b1=b/d; z=a*(D)b1; if(z<IMIN||IMAX<z)jt->jerr=EWOV; R (I)z;}else R 0;
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119 }
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120 #endif
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121
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122 #define GCDIO(u,v) (dgcd((D)u,(D)v))
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123 #define LCMIO(u,v) (dlcm((D)u,(D)v))
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124
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125 static D jtdlcm(J jt,D a,D b){ASSERT(!(INF(a)||INF(b)),EVNAN); R a&&b?a*(b/dgcd(a,b)):0;}
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126
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127 APFX(gcdIO, D,I,I, GCDIO)
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128 APFX(gcdII, I,I,I, igcd )
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129 APFX(gcdDD, D,D,D, dgcd )
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130 APFX(gcdZZ, Z,Z,Z, zgcd )
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131
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132 APFX(lcmII, I,I,I, ilcm )
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133 APFX(lcmIO, D,I,I, LCMIO)
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134 APFX(lcmDD, D,D,D, dlcm )
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135 APFX(lcmZZ, Z,Z,Z, zlcm )
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136
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137
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138 #define GETD {d=*wv++; if(!d){z=0; break;}}
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139 #define INTDIVF(c,d) (0>c==0>d?c/d:c%d?c/d-1:c/d)
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140 #define INTDIVC(c,d) (0>c!=0>d?c/d:c%d?c/d+1:c/d)
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141
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142 F2(jtintdiv){A z;B b,flr;I an,ar,*as,*av,c,d,j,k,m,n,p,p1,r,*s,wn,wr,*ws,*wv,*zv;
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143 RZ(a&&w);
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144 an=AN(a); ar=AR(a); as=AS(a); av=AV(a);
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145 wn=AN(w); wr=AR(w); ws=AS(w); wv=AV(w); b=ar>=wr; r=b?wr:ar; s=b?as:ws;
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146 ASSERT(!ICMP(as,ws,r),EVLENGTH);
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147 if(an&&wn){m=prod(r,s); n=prod(b?ar-r:wr-r,r+s);}else m=n=0;
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148 GA(z,INT,b?an:wn,b?ar:wr,s); zv=AV(z);
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149 d=wn?*wv:0; p=0<d?d:-d; p1=d==IMIN?p:p-1; flr=XMFLR==jt->xmode;
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150 if(!wr&&p&&!(p&p1)){
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151 k=0; j=1; while(p>j){++k; j<<=1;}
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152 switch((0<d?0:2)+(flr?0:1)){
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153 case 0: DO(n, *zv++=*av++>>k;); break;
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154 case 1: DO(n, c=*av++; *zv++=0< c?1+((c-1)>>k):(c+p1)>>k;); break;
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155 case 2: DO(n, c=*av++; *zv++=c>IMIN?-c>>k:-(-c>>k);); break;
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156 case 3: DO(n, c=*av++; *zv++=0<=c?-(c>>k):1+(-(1+c)>>k););
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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157 }}else if(flr){
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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158 if(1==n) DO(m, c=*av++; GETD; *zv++=INTDIVF(c,d); )
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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159 else if(b)DO(m, GETD; DO(n, c=*av++; *zv++=INTDIVF(c,d););)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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160 else DO(m, c=*av++; DO(n, GETD; *zv++=INTDIVF(c,d););)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
161 }else{
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
162 if(1==n) DO(m, c=*av++; GETD; *zv++=INTDIVC(c,d); )
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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163 else if(b)DO(m, GETD; DO(n, c=*av++; *zv++=INTDIVC(c,d););)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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164 else DO(m, c=*av++; DO(n, GETD; *zv++=INTDIVC(c,d););)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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165 }
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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166 R z?z:flr?floor1(divide(a,w)):ceil1(divide(a,w));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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167 } /* <.@% or >.@% on integers */
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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168
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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169
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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170 static F2(jtweight){RZ(a&&w); R df1(behead(over(AR(w)?w:reshape(a,w),one)),bsdot(slash(ds(CSTAR))));}
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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171
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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172 F1(jtbase1){A z;B*v;I c,d,m,n,p,r,*s,t,*x;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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173 RZ(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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174 n=AN(w); t=AT(w); r=AR(w); s=AS(w); c=r?*(s+r-1):1;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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175 ASSERT(t&DENSE,EVNONCE);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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176 if(c>(SY_64?63:31)||!(t&B01))R pdt(w,weight(sc(c),t&RAT+XNUM?cvt(XNUM,num[2]):num[2]));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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177 if(c)m=n/c; else RE(m=prod(r-1,s));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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178 GA(z,INT,m,r?r-1:0,s); x=m+AV(z); v=n+BAV(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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179 if(c)DO(m, p=0; d=1; DO(c, if(*--v)p+=d; d+=d;); *--x=p;)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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180 else memset(x-m,C0,m*SZI);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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diff changeset
181 R z;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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182 }
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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183
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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184 F2(jtbase2){I ar,*as,at,c,t,wr,*ws,wt;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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185 RZ(a&&w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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186 at=AT(a); ar=AR(a); as=AS(a);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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187 wt=AT(w); wr=AR(w); ws=AS(w); c=wr?*(ws+wr-1):1; t=maxtype(at,wt);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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188 ASSERT(at&DENSE&&wt&DENSE,EVNONCE);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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189 if(!(t&at))RZ(a=cvt(t,a));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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190 if(!(t&wt))RZ(w=cvt(t,w));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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191 R 1>=ar?pdt(w,weight(sc(c),a)):rank2ex(w,rank2ex(sc(c),a,0L,0L,1L,jtweight),0L,1L,1L,jtpdt);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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192 }
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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193
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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194 F1(jtabase1){A d,z;B*zv;I c,n,p,r,t,*v,x;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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195 RZ(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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196 n=AN(w); r=AR(w); t=AT(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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197 ASSERT(t&DENSE,EVNONCE);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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198 if(!n||t&B01)R reshape(over(shape(w),n?one:zero),w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
199 if(!(t&INT)){
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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200 d=df2(num[2],maximum(one,aslash(CMAX,mag(ravel(w)))),atop(ds(CFLOOR),ds(CLOG)));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
201 RZ(z=abase2(reshape(increm(d),num[2]),w));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
202 R t&FL&&equ(irs1(z,0L,1L,jthead),lt(w,zero))?irs1(z,0L,1L,jtbehead):z;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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203 }
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
204 c=x=0; v=AV(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
205 DO(n, p=*v++; if(p==IMIN){c=SY_64?64:32; break;} x=x<p?p:x<-p?-p:x;);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
206 if(!c)while(x){x>>=1; ++c;}
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
207 c=MAX(1,c);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
208 GA(z,B01,n*c,1+r,AS(w)); *(r+AS(z))=c;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
209 v=n+AV(w); zv=AN(z)+BAV(z);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
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210 DO(n, x=*--v; DO(c, *--zv=(B)(x&1); x>>=1;));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
211 R z;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
212 }
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
213
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
214 F2(jtabase2){A z;I an,ar,at,wn,wr,wt,zn;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
215 RZ(a&&w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
216 an=AN(a); ar=AR(a); at=AT(a);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
217 wn=AN(w); wr=AR(w); wt=AT(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
218 ASSERT(at&DENSE&&wt&DENSE,EVNONCE);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
219 if(!ar)R residue(a,w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
220 if(1==ar&&at&B01+INT&&wt&B01+INT){I*av,d,r,*u,*wv,x,*zv;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
221 RZ(coerce2(&a,&w,INT));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
222 RE(zn=mult(an,wn)); GA(z,INT,zn,1+wr,AS(w)); *(wr+AS(z))=an;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
223 av=an+AV(a); wv=wn+AV(w); zv=zn+AV(z);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
224 if(2==an&&!av[-2]&&0<(d=av[-1])){I d1,j,k;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
225 k=0; j=1; while(d>j){++k; j<<=1;} d1=d-1;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
226 if(d==j)DO(wn, x=*--wv; *--zv=x&d1; *--zv=x>>k;)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
227 else DO(wn, x=*--wv; if(0<=x){*--zv=x%d; *--zv=x/d;}else{*--zv=d+x%d; *--zv=-1+x/d;})
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
228 }else DO(wn, x=*--wv; u=av; DO(an, d=*--u; *--zv=r=remii(d,x); x=d?(x-r)/d:0;););
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
229 R z;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
230 }else{PROLOG;A y,*zv;C*u,*yv;I k;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
231 F2RANK(1,0,jtabase2,0);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
232 k=bp(at); u=an*k+CAV(a);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
233 GA(y,at, 1, 0,0); yv=CAV(y);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
234 GA(z,BOX,an,1,0); zv=an+AAV(z);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
235 DO(an, MC(yv,u-=k,k); RZ(w=divide(minus(w,*--zv=residue(y,w)),y)););
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
236 EPILOG(ope(z));
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
237 }}
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
238
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
239 F1(jtintmod2){A z;B*b,*v;I k=SZI,mask,m,n,q,r,*u,*wi;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
240 RZ(w);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
241 n=AN(w); q=n/k; r=n%k; v=BAV(w)+!liln*(k-1);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
242 GA(z,B01,n,AR(w),AS(w)); u=AV(z);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
243 b=(B*)&mask; DO(k, b[i]=1;);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
244 b=(B*)&m; DO(q, DO(k, b[i]=*v; v+=k;); *u++=mask&m;)
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
245 b=(B*)u; wi=AV(w)+q*k; DO(r, *b++=1&*wi++?1:0;);
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
246 R z;
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
diff changeset
247 }