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| author | rsc <devnull@localhost> | 2005-01-14 03:45:44 +0000 |
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| committer | rsc <devnull@localhost> | 2005-01-14 03:45:44 +0000 |
| commit | 78e51a8c6678b6e3dff3d619aa786669f531f4bc (patch) | |
| tree | 015e00fde4fc837fd31b705e18d17dc913829388 /man/man3/mp.html | |
| parent | 2634795b5f0053bc0ff08e5d7bbc0eda8efea061 (diff) | |
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diff --git a/man/man3/mp.html b/man/man3/mp.html new file mode 100644 index 00000000..86dc7455 --- /dev/null +++ b/man/man3/mp.html @@ -0,0 +1,441 @@ +<head> +<title>mp(3) - Plan 9 from User Space</title> +<meta content="text/html; charset=utf-8" http-equiv=Content-Type> +</head> +<body bgcolor=#ffffff> +<table border=0 cellpadding=0 cellspacing=0 width=100%> +<tr height=10><td> +<tr><td width=20><td> +<tr><td width=20><td><b>MP(3)</b><td align=right><b>MP(3)</b> +<tr><td width=20><td colspan=2> + <br> +<p><font size=+1><b>NAME </b></font><br> + +<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + mpsetminbits, mpnew, mpfree, mpbits, mpnorm, mpcopy, mpassign, + mprand, strtomp, mpfmt,mptoa, betomp, mptobe, letomp, mptole, + mptoui, uitomp, mptoi, itomp, uvtomp, mptouv, vtomp, mptov, mpdigdiv, + mpadd, mpsub, mpleft, mpright, mpmul, mpexp, mpmod, mpdiv, mpfactorial, + mpcmp, mpextendedgcd, + mpinvert, mpsignif, mplowbits0, mpvecdigmuladd, mpvecdigmulsub, + mpvecadd, mpvecsub, mpveccmp, mpvecmul, mpmagcmp, mpmagadd, mpmagsub, + crtpre, crtin, crtout, crtprefree, crtresfree – extended precision + arithmetic<br> + +</table> +<p><font size=+1><b>SYNOPSIS </b></font><br> + +<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + <tt><font size=+1>#include <u.h><br> + #include <libc.h><br> + #include <mp.h> + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* mpnew(int n) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpfree(mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpsetminbits(int n) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpbits(mpint *b, int n) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpnorm(mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* mpcopy(mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpassign(mpint *old, mpint *new) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* strtomp(char *buf, char **rptr, int base, mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>char* mptoa(mpint *b, int base, char *buf, int blen) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpfmt(Fmt*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* betomp(uchar *buf, uint blen, mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mptobe(mpint *b, uchar *buf, uint blen, uchar **bufp) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* letomp(uchar *buf, uint blen, mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mptole(mpint *b, uchar *buf, uint blen, uchar **bufp) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>uint mptoui(mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* uitomp(uint, mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mptoi(mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* itomp(int, mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* vtomp(vlong, mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>vlong mptov(mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* uvtomp(uvlong, mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>uvlong mptouv(mpint*) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpadd(mpint *b1, mpint *b2, mpint *sum) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpmagadd(mpint *b1, mpint *b2, mpint *sum) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpsub(mpint *b1, mpint *b2, mpint *diff) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpmagsub(mpint *b1, mpint *b2, mpint *diff) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpleft(mpint *b, int shift, mpint *res) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpright(mpint *b, int shift, mpint *res) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpmul(mpint *b1, mpint *b2, mpint *prod) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpexp(mpint *b, mpint *e, mpint *m, mpint *res) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpmod(mpint *b, mpint *m, mpint *remainder) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint + *remainder) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint* mpfactorial(ulong n) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpcmp(mpint *b1, mpint *b2) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpmagcmp(mpint *b1, mpint *b2) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x, mpint + *y) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpinvert(mpint *b, mpint *m, mpint *res) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpsignif(mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mplowbits0(mpint *b) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient) + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpvecadd(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit + *sum) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpvecsub(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit + *diff) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpvecdigmuladd(mpdigit *b, int n, mpdigit m, mpdigit *p) + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit + *p) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>int mpveccmp(mpdigit *a, int alen, mpdigit *b, int blen) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>CRTpre* crtpre(int nfactors, mpint **factors) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>CRTres* crtin(CRTpre *crt, mpint *x) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void crtout(CRTpre *crt, CRTres *r, mpint *x) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void crtprefree(CRTpre *cre) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void crtresfree(CRTres *res) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>mpint *mpzero, *mpone, *mptwo<br> + </font></tt> +</table> +<p><font size=+1><b>DESCRIPTION </b></font><br> + +<table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + +<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + These routines perform extended precision integer arithmetic. + The basic type is <tt><font size=+1>mpint</font></tt>, which points to an array of <tt><font size=+1>mpdigit</font></tt>s, + stored in little-endian order:<br> + <tt><font size=+1>typedef struct mpint mpint;<br> + struct mpint<br> + {<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + int sign; /* +1 or −1 */<br> + int size; /* allocated digits */<br> + int top; /* significant digits */<br> + mpdigit *p;<br> + char flags;<br> + + </table> + };<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + The sign of 0 is +1. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The size of <tt><font size=+1>mpdigit</font></tt> is architecture-dependent and defined in <tt><font size=+1>/$cputype/include/u.h</font></tt>. + <tt><font size=+1>Mpint</font></tt>s are dynamically allocated and must be explicitly freed. + Operations grow the array of digits as needed. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + In general, the result parameters are last in the argument list. + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + Routines that return an <tt><font size=+1>mpint</font></tt> will allocate the <tt><font size=+1>mpint</font></tt> if the result + parameter is <tt><font size=+1>nil</font></tt>. This includes <i>strtomp</i>, <i>itomp</i>, <i>uitomp</i>, and <i>btomp</i>. + These functions, in addition to <i>mpnew</i> and <i>mpcopy</i>, will return + <tt><font size=+1>nil</font></tt> if the allocation fails. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + Input and result parameters may point to the same <tt><font size=+1>mpint</font></tt>. The routines + check and copy where necessary. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpnew</i> creates an <tt><font size=+1>mpint</font></tt> with an initial allocation of <i>n</i> bits. If + <i>n</i> is zero, the allocation will be whatever was specified in the + last call to <i>mpsetminbits</i> or to the initial value, 1056. <i>Mpfree</i> + frees an <tt><font size=+1>mpint</font></tt>. <i>Mpbits</i> grows the allocation of <i>b</i> to fit at least + <i>n</i> bits. If <tt><font size=+1>b−>top</font></tt> doesn’t cover <i>n</i> bits it increases it to do so. + Unless + you are writing new basic operations, you can restrict yourself + to <tt><font size=+1>mpnew(0)</font></tt> and <tt><font size=+1>mpfree(b)</font></tt>. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpnorm</i> normalizes the representation by trimming any high order + zero digits. All routines except <tt><font size=+1>mpbits</font></tt> return normalized results. + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpcopy</i> creates a new <tt><font size=+1>mpint</font></tt> with the same value as <i>b</i> while <i>mpassign</i> + sets the value of <i>new</i> to be that of <i>old</i>. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mprand</i> creates an <i>n</i> bit random number using the generator <i>gen</i>. + <i>Gen</i> takes a pointer to a string of uchar’s and the number to fill + in. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Strtomp</i> and <i>mptoa</i> convert between ASCII and <tt><font size=+1>mpint</font></tt> representations + using the base indicated. Only the bases 10, 16, 32, and 64 are + supported. Anything else defaults to 16. <i>Strtomp</i> skips any leading + spaces or tabs. <i>Strtomp</i>’s scan stops when encountering a digit + not valid in the base. If <i>rptr</i> is not zero, <i>*rptr</i> is + set to point to the character immediately after the string converted. + If the parse pterminates before any digits are found, <i>strtomp</i> + return <tt><font size=+1>nil</font></tt>. <i>Mptoa</i> returns a pointer to the filled buffer. If the + parameter <i>buf</i> is <tt><font size=+1>nil</font></tt>, the buffer is allocated. <i>Mpfmt</i> can be used + with <a href="../man3/fmtinstall.html"><i>fmtinstall</i>(3)</a> and <a href="../man3/print.html"><i>print</i>(3)</a> to print hexadecimal + representations of <tt><font size=+1>mpint</font></tt>s. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mptobe</i> and <i>mptole</i> convert an <i>mpint</i> to a byte array. The former + creates a big endian representation, the latter a little endian + one. If the destination <i>buf</i> is not <tt><font size=+1>nil</font></tt>, it specifies the buffer + of length <i>blen</i> for the result. If the representation is less than + <i>blen</i> bytes, the rest of the buffer is zero filled. If <i>buf</i> is <tt><font size=+1>nil</font></tt>, + then a + buffer is allocated and a pointer to it is deposited in the location + pointed to by <i>bufp</i>. Sign is ignored in these conversions, i.e., + the byte array version is always positive. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Betomp</i>, and <i>letomp</i> convert from a big or little endian byte array + at <i>buf</i> of length <i>blen</i> to an <i>mpint</i>. If <i>b</i> is not <i>nil</i>, it refers + to a preallocated <i>mpint</i> for the result. If <i>b</i> is <tt><font size=+1>nil</font></tt>, a new integer + is allocated and returned as the result. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The integer conversions are:<br> + <i>mptoui</i><tt><font size=+1> mpint</font></tt>-><tt><font size=+1>unsigned int<br> + </font></tt><i>uitomp</i><tt><font size=+1> unsigned int</font></tt>-><tt><font size=+1>mpint<br> + </font></tt><i>mptoi</i><tt><font size=+1> mpint</font></tt>-><tt><font size=+1>int<br> + </font></tt><i>itomp</i><tt><font size=+1> int</font></tt>-><tt><font size=+1>mpint<br> + </font></tt><i>mptouv</i><tt><font size=+1> mpint</font></tt>-><tt><font size=+1>unsigned vlong<br> + </font></tt><i>uvtomp</i><tt><font size=+1> unsigned vlong</font></tt>-><tt><font size=+1>mpint<br> + </font></tt><i>mptov</i><tt><font size=+1> mpint</font></tt>-><tt><font size=+1>vlong<br> + </font></tt><i>vtomp</i><tt><font size=+1> vlong</font></tt>-><tt><font size=+1>mpint + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + When converting to the base integer types, if the integer is too + large, the largest integer of the appropriate sign and size is + returned. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The mathematical functions are:<br> + <i>mpadd</i><tt><font size=+1> sum = b1 + b2</font></tt>.<br> + <i>mpmagadd</i><tt><font size=+1> sum = abs(b1) + abs(b2)</font></tt>.<br> + <i>mpsub</i><tt><font size=+1> diff = b1 − b2</font></tt>.<br> + <i>mpmagsub</i><tt><font size=+1> diff = abs(b1) − abs(b2)</font></tt>.<br> + <i>mpleft</i><tt><font size=+1> res = b<<shift</font></tt>.<br> + <i>mpright</i><tt><font size=+1> res = b>>shift</font></tt>.<br> + <i>mpmul</i><tt><font size=+1> prod = b1*b2</font></tt>.<br> + <i>mpexp</i> if <i>m</i> is nil, <tt><font size=+1>res = b**e</font></tt>. Otherwise, <tt><font size=+1>res = b**e mod m</font></tt>.<br> + <i>mpmod</i><tt><font size=+1> remainder = b % m</font></tt>.<br> + <i>mpdiv</i><tt><font size=+1> quotient = dividend/divisor</font></tt>. <tt><font size=+1>remainder = dividend % divisor</font></tt>.<br> + <i>mpfactorial</i> returns factorial of <i>n</i>.<br> + <i>mpcmp</i> returns -1, 0, or +1 as <i>b1</i> is less than, equal to, or greater + than <i>b2</i>.<br> + <i>mpmagcmp</i> the same as <i>mpcmp</i> but ignores the sign and just compares + magnitudes. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpextendedgcd</i> computes the greatest common denominator, <i>d</i>, of + <i>a</i> and <i>b</i>. It also computes <i>x</i> and <i>y</i> such that <tt><font size=+1>a*x + b*y = d</font></tt>. Both + <i>a</i> and <i>b</i> are required to be positive. If called with negative arguments, + it will return a gcd of 0. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpinverse</i> computes the multiplicative inverse of <i>b</i> <tt><font size=+1>mod</font></tt> <i>m</i>. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Mpsignif</i> returns the bit offset of the left most 1 bit in <i>b</i>. <i>Mplowbits0</i> + returns the bit offset of the right most 1 bit. For example, for + 0x14, <i>mpsignif</i> would return 4 and <i>mplowbits0</i> would return 2. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The remaining routines all work on arrays of <tt><font size=+1>mpdigit</font></tt> rather than + <tt><font size=+1>mpint</font></tt>’s. They are the basis of all the other routines. They are + separated out to allow them to be rewritten in assembler for each + architecture. There is also a portable C version for each one.<br> + <i>mpdigdiv</i><tt><font size=+1> quotient = dividend[0:1] / divisor</font></tt>.<br> + <i>mpvecadd</i><tt><font size=+1> sum[0:alen] = a[0:alen−1] + b[0:blen−1]</font></tt>. We assume alen + >= blen and that sum has room for alen+1 digits.<br> + <i>mpvecsub</i><tt><font size=+1> diff[0:alen−1] = a[0:alen−1] − b[0:blen−1]</font></tt>. We assume + that alen >= blen and that diff has room for alen digits.<br> + <i>mpvecdigmuladd</i><tt><font size=+1> p[0:n] += m * b[0:n−1]</font></tt>. This multiplies a an array + of digits times a scalar and adds it to another array. We assume + p has room for n+1 digits.<br> + <i>mpvecdigmulsub</i><tt><font size=+1> p[0:n] −= m * b[0:n−1]</font></tt>. This multiplies a an array + of digits times a scalar and subtracts it fromo another array. + We assume p has room for n+1 digits. It returns +1 is the result + is positive and -1 if negative.<br> + <i>mpvecmul</i><tt><font size=+1> p[0:alen*blen] = a[0:alen−1] * b[0:blen−1]</font></tt>. We assume + that p has room for alen*blen+1 digits.<br> + <i>mpveccmp</i> This returns -1, 0, or +1 as a - b is negative, 0, or + positive. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>mptwo</i>, <i>mpone</i> and <i>mpzero</i> are the constants 2, 1 and 0. These cannot + be freed.<br> + <p><font size=+1><b>Chinese remainder theorem </b></font><br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + When computing in a non-prime modulus, <i>n,</i> it is possible to perform + the computations on the residues modulo the prime factors of <i>n</i> + instead. Since these numbers are smaller, multiplication and exponentiation + can be much faster. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Crtin</i> computes the residues of <i>x</i> and returns them in a newly allocated + structure:<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + <tt><font size=+1>typedef struct CRTres CRTres; <br> + {<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + int n; // number of residues<br> + mpint *r[n]; // residues<br> + + </table> + };<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + + </table> + <i>Crtout</i> takes a residue representation of a number and converts + it back into the number. It also frees the residue structure. + + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Crepre</i> saves a copy of the factors and precomputes the constants + necessary for converting the residue form back into a number modulo + the product of the factors. It returns a newly allocated structure + containing values. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + <i>Crtprefree</i> and <i>crtresfree</i> free <i>CRTpre</i> and <i>CRTres</i> structures respectively.<br> + +</table> +<p><font size=+1><b>SOURCE </b></font><br> + +<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + <tt><font size=+1>/usr/local/plan9/src/libmp<br> + </font></tt> +</table> + +<td width=20> +<tr height=20><td> +</table> +<!-- TRAILER --> +<table border=0 cellpadding=0 cellspacing=0 width=100%> +<tr height=15><td width=10><td><td width=10> +<tr><td><td> +<center> +<a href="../../"><img src="../../dist/spaceglenda100.png" alt="Space Glenda" border=1></a> +</center> +</table> +<!-- TRAILER --> +</body></html> |