--- src/secure/lib/libcrypto/man/bn_internal.3 2004/09/02 09:26:58 1.2 +++ src/secure/lib/libcrypto/man/bn_internal.3 2004/12/18 21:34:10 1.3 @@ -1,12 +1,8 @@ -.rn '' }` -''' $RCSfile: bn_internal.3,v $$Revision: 1.2 $$Date: 2004/09/02 09:26:58 $ -''' -''' $Log: bn_internal.3,v $ -''' Revision 1.2 2004/09/02 09:26:58 asmodai -''' Commit manual pages after running 'man-update' and add new manual pages. -''' -''' -.de Sh +.\" Automatically generated by Pod::Man v1.37, Pod::Parser v1.14 +.\" +.\" Standard preamble: +.\" ======================================================================== +.de Sh \" Subsection heading .br .if t .Sp .ne 5 @@ -14,150 +10,98 @@ \fB\\$1\fR .PP .. -.de Sp +.de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. -.de Ip -.br -.ie \\n(.$>=3 .ne \\$3 -.el .ne 3 -.IP "\\$1" \\$2 -.. -.de Vb +.de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. -.de Ve +.de Ve \" End verbatim text .ft R - .fi .. -''' -''' -''' Set up \*(-- to give an unbreakable dash; -''' string Tr holds user defined translation string. -''' Bell System Logo is used as a dummy character. -''' +.\" Set up some character translations and predefined strings. \*(-- will +.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left +.\" double quote, and \*(R" will give a right double quote. | will give a +.\" real vertical bar. \*(C+ will give a nicer C++. Capital omega is used to +.\" do unbreakable dashes and therefore won't be available. \*(C` and \*(C' +.\" expand to `' in nroff, nothing in troff, for use with C<>. .tr \(*W-|\(bv\*(Tr +.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ -.ds -- \(*W- -.ds PI pi -.if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch -.if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch -.ds L" "" -.ds R" "" -''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of -''' \*(L" and \*(R", except that they are used on ".xx" lines, -''' such as .IP and .SH, which do another additional levels of -''' double-quote interpretation -.ds M" """ -.ds S" """ -.ds N" """"" -.ds T" """"" -.ds L' ' -.ds R' ' -.ds M' ' -.ds S' ' -.ds N' ' -.ds T' ' +. ds -- \(*W- +. ds PI pi +. if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch +. if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch +. ds L" "" +. ds R" "" +. ds C` "" +. ds C' "" 'br\} .el\{\ -.ds -- \(em\| -.tr \*(Tr -.ds L" `` -.ds R" '' -.ds M" `` -.ds S" '' -.ds N" `` -.ds T" '' -.ds L' ` -.ds R' ' -.ds M' ` -.ds S' ' -.ds N' ` -.ds T' ' -.ds PI \(*p +. ds -- \|\(em\| +. ds PI \(*p +. ds L" `` +. ds R" '' 'br\} -.\" If the F register is turned on, we'll generate -.\" index entries out stderr for the following things: -.\" TH Title -.\" SH Header -.\" Sh Subsection -.\" Ip Item -.\" X<> Xref (embedded -.\" Of course, you have to process the output yourself -.\" in some meaninful fashion. -.if \nF \{ -.de IX -.tm Index:\\$1\t\\n%\t"\\$2" +.\" +.\" If the F register is turned on, we'll generate index entries on stderr for +.\" titles (.TH), headers (.SH), subsections (.Sh), items (.Ip), and index +.\" entries marked with X<> in POD. Of course, you'll have to process the +.\" output yourself in some meaningful fashion. +.if \nF \{\ +. de IX +. tm Index:\\$1\t\\n%\t"\\$2" .. -.nr % 0 -.rr F +. nr % 0 +. rr F .\} -.TH bn_internal 3 "0.9.7d" "2/Sep/2004" "OpenSSL" -.UC -.if n .hy 0 +.\" +.\" For nroff, turn off justification. Always turn off hyphenation; it makes +.\" way too many mistakes in technical documents. +.hy 0 .if n .na -.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' -.de CQ \" put $1 in typewriter font -.ft CW -'if n "\c -'if t \\&\\$1\c -'if n \\&\\$1\c -'if n \&" -\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7 -'.ft R -.. -.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2 -. \" AM - accent mark definitions -.bd B 3 -. \" fudge factors for nroff and troff +.\" +.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). +.\" Fear. Run. Save yourself. No user-serviceable parts. +. \" fudge factors for nroff and troff .if n \{\ -. ds #H 0 -. ds #V .8m -. ds #F .3m -. ds #[ \f1 -. ds #] \fP +. ds #H 0 +. ds #V .8m +. ds #F .3m +. ds #[ \f1 +. ds #] \fP .\} .if t \{\ -. ds #H ((1u-(\\\\n(.fu%2u))*.13m) -. ds #V .6m -. ds #F 0 -. ds #[ \& -. ds #] \& +. ds #H ((1u-(\\\\n(.fu%2u))*.13m) +. ds #V .6m +. ds #F 0 +. ds #[ \& +. ds #] \& .\} -. \" simple accents for nroff and troff +. \" simple accents for nroff and troff .if n \{\ -. ds ' \& -. ds ` \& -. ds ^ \& -. ds , \& -. ds ~ ~ -. ds ? ? -. ds ! ! -. ds / -. ds q +. ds ' \& +. ds ` \& +. ds ^ \& +. ds , \& +. ds ~ ~ +. ds / .\} .if t \{\ -. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" -. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' -. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' -. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' -. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' -. ds ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10' -. ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m' -. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' -. ds q o\h'-\w'o'u*8/10'\s-4\v'.4m'\z\(*i\v'-.4m'\s+4\h'\w'o'u*8/10' +. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" +. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' +. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' +. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' +. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' +. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' .\} -. \" troff and (daisy-wheel) nroff accents +. \" troff and (daisy-wheel) nroff accents .ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V' .ds 8 \h'\*(#H'\(*b\h'-\*(#H' -.ds v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#] -.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u' -.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u' -.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#] .ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#] .ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H' .ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u' @@ -165,31 +109,27 @@ .ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#] .ds ae a\h'-(\w'a'u*4/10)'e .ds Ae A\h'-(\w'A'u*4/10)'E -.ds oe o\h'-(\w'o'u*4/10)'e -.ds Oe O\h'-(\w'O'u*4/10)'E -. \" corrections for vroff +. \" corrections for vroff .if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u' .if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u' -. \" for low resolution devices (crt and lpr) +. \" for low resolution devices (crt and lpr) .if \n(.H>23 .if \n(.V>19 \ \{\ -. ds : e -. ds 8 ss -. ds v \h'-1'\o'\(aa\(ga' -. ds _ \h'-1'^ -. ds . \h'-1'. -. ds 3 3 -. ds o a -. ds d- d\h'-1'\(ga -. ds D- D\h'-1'\(hy -. ds th \o'bp' -. ds Th \o'LP' -. ds ae ae -. ds Ae AE -. ds oe oe -. ds Oe OE +. ds : e +. ds 8 ss +. ds o a +. ds d- d\h'-1'\(ga +. ds D- D\h'-1'\(hy +. ds th \o'bp' +. ds Th \o'LP' +. ds ae ae +. ds Ae AE .\} .rm #[ #] #H #V #F C +.\" ======================================================================== +.\" +.IX Title "bn_internal 3" +.TH bn_internal 3 "2004-12-18" "0.9.7e" "OpenSSL" .SH "NAME" bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, @@ -200,7 +140,7 @@ bn_expand, bn_wexpand, bn_expand2, bn_fi bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM library internal functions .SH "SYNOPSIS" -.PP +.IX Header "SYNOPSIS" .Vb 9 \& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); \& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, @@ -212,15 +152,18 @@ library internal functions \& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, \& int num); .Ve +.PP .Vb 4 \& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); \& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); \& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); \& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); .Ve +.PP .Vb 1 \& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); .Ve +.PP .Vb 11 \& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, \& int nb); @@ -234,21 +177,25 @@ library internal functions \& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, \& int n2, BN_ULONG *tmp); .Ve +.PP .Vb 2 \& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); \& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); .Ve +.PP .Vb 3 \& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); \& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); \& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); .Ve +.PP .Vb 4 \& BIGNUM *bn_expand(BIGNUM *a, int bits); \& BIGNUM *bn_wexpand(BIGNUM *a, int n); \& BIGNUM *bn_expand2(BIGNUM *a, int n); \& void bn_fix_top(BIGNUM *a); .Ve +.PP .Vb 6 \& void bn_check_top(BIGNUM *a); \& void bn_print(BIGNUM *a); @@ -258,12 +205,13 @@ library internal functions \& void bn_set_low(BIGNUM *r, BIGNUM *a, int n); .Ve .SH "DESCRIPTION" +.IX Header "DESCRIPTION" This page documents the internal functions used by the OpenSSL -\fBBIGNUM\fR implementation. They are described here to facilitate +\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate debugging and extending the library. They are \fInot\fR to be used by applications. .Sh "The \s-1BIGNUM\s0 structure" -.PP +.IX Subsection "The BIGNUM structure" .Vb 7 \& typedef struct bignum_st \& { @@ -273,167 +221,144 @@ applications. \& int neg; /* sign */ \& } BIGNUM; .Ve +.PP The big number is stored in \fBd\fR, a \fImalloc()\fRed array of \fB\s-1BN_ULONG\s0\fRs, least significant first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits -in size (\fB\s-1BITS2\s0\fR), depending on the \*(L'number of bits\*(R' specified in -\f(CWopenssl/bn.h\fR. +in size (\fB\s-1BITS2\s0\fR), depending on the 'number of bits' specified in +\&\f(CW\*(C`openssl/bn.h\*(C'\fR. .PP -\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR -is the \*(L'last\*(R' entry being used, so for a value of 4, bn.d[0]=4 and +\&\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR +is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is -\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR. +\&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR. .PP Various routines in this library require the use of temporary -\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory +\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see -BN_CTX_start(3). +\&\fIBN_CTX_start\fR\|(3). .Sh "Low-level arithmetic operations" +.IX Subsection "Low-level arithmetic operations" These functions are implemented in C and for several platforms in assembly language: .PP -\fIbn_mul_words\fR\|(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word +bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result in \fBrp\fR, and returns the high word (carry). .PP -\fIbn_mul_add_words\fR\|(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR +bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places the result in \fBrp\fR, and returns the high word (carry). .PP -\fIbn_sqr_words\fR\|(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array -\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR -word-wise, and places the low and high bytes of the result in \fBrp\fR. +bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array +\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR +word\-wise, and places the low and high bytes of the result in \fBrp\fR. .PP -\fIbn_div_words\fR\|(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) +bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) by \fBd\fR and returns the result. .PP -\fIbn_add_words\fR\|(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word +bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the result in \fBrp\fR, and returns the high word (carry). .PP -\fIbn_sub_words\fR\|(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word +bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0 otherwise). .PP -\fIbn_mul_comba4\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and -\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the +bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and +\&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR. .PP -\fIbn_mul_comba8\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and -\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the +bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and +\&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR. .PP -\fIbn_sqr_comba4\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and -\fBb\fR and the 8 word array \fBr\fR. +bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and +\&\fBb\fR and the 8 word array \fBr\fR. .PP -\fIbn_sqr_comba8\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and -\fBb\fR and the 16 word array \fBr\fR. +bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and +\&\fBb\fR and the 16 word array \fBr\fR. .PP The following functions are implemented in C: .PP -\fIbn_cmp_words\fR\|(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR +bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and less than \fBb\fR. .PP -\fIbn_mul_normal\fR\|(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR +bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR. .PP -\fIbn_mul_low_normal\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word +bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of -\fBa\fR*\fBb\fR and places the result in \fBr\fR. +\&\fBa\fR*\fBb\fR and places the result in \fBr\fR. .PP -\fIbn_mul_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates +bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR (\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes -\fBa\fR*\fBb\fR and places the result in \fBr\fR. +\&\fBa\fR*\fBb\fR and places the result in \fBr\fR. .PP -\fIbn_mul_part_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR) +bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR) operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and -\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR. +\&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR. .PP -\fIbn_mul_low_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the -\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR +bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the +\&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR and \fBb\fR. .PP -\fIbn_mul_high\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the -\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word +bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the +\&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word array \fBtmp\fR. .PP -\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the +\&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8 words long, \fIbn_mul_recursive()\fR if they are larger than -\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word +\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word size, and \fIbn_mul_part_recursive()\fR for others that are larger than -\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR. +\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR. .PP -\fIbn_sqr_normal\fR\|(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array -\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR. +bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array +\&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR. .PP The implementations use the following macros which, depending on the architecture, may use \*(L"long long\*(R" C operations or inline assembler. -They are defined in \f(CWbn_lcl.h\fR. +They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR. .PP -\fImul\fR\|(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the +mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the low word of the result in \fBr\fR and the high word in \fBc\fR. .PP -\fImul_add\fR\|(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and +mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and places the low word of the result in \fBr\fR and the high word in \fBc\fR. .PP -\fIsqr\fR\|(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word +sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word of the result in \fBr0\fR and the high word in \fBr1\fR. .Sh "Size changes" -\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit +.IX Subsection "Size changes" +\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an -\fBn\fR word number. If the number has to be expanded, both macros +\&\fBn\fR word number. If the number has to be expanded, both macros call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise. .PP -The \fIbn_fix_top()\fR macro reduces \fBa->top\fR to point to the most +The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most significant non-zero word when \fBa\fR has shrunk. .Sh "Debugging" -\fIbn_check_top()\fR verifies that \f(CW((a)->top >= 0 && (a)->top -<= (a)->max)\fR. A violation will cause the program to abort. +.IX Subsection "Debugging" +\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top +<= (a)\->max)\*(C'\fR. A violation will cause the program to abort. .PP -\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR +\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR (in reverse order, i.e. most significant word first) to stderr. .PP -\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size. +\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size. This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only -\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR. +\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR. .PP If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR and \fIbn_set_max()\fR are defined as empty macros. .SH "SEE ALSO" -bn(3) - -.rn }` '' -.IX Title "bn_internal 3" -.IX Name "bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, -bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, -bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, -bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, -bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, -bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, -bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM -library internal functions" - -.IX Header "NAME" - -.IX Header "SYNOPSIS" - -.IX Header "DESCRIPTION" - -.IX Subsection "The \s-1BIGNUM\s0 structure" - -.IX Subsection "Low-level arithmetic operations" - -.IX Subsection "Size changes" - -.IX Subsection "Debugging" - .IX Header "SEE ALSO" - +\&\fIbn\fR\|(3)