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Diffstat (limited to 'tmac/62bit.tmac')
| -rw-r--r-- | tmac/62bit.tmac | 203 |
1 files changed, 203 insertions, 0 deletions
diff --git a/tmac/62bit.tmac b/tmac/62bit.tmac new file mode 100644 index 0000000..f1a593e --- /dev/null +++ b/tmac/62bit.tmac @@ -0,0 +1,203 @@ +.\" 62bit.tmac +.\" +.\" Copyright (C) 2003-2020 Free Software Foundation, Inc. +.\" Written by Werner Lemberg (wl@gnu.org) +.\" +.\" This file is part of groff. +.\" +.\" groff is free software; you can redistribute it and/or modify it +.\" under the terms of the GNU General Public License as published by +.\" the Free Software Foundation, either version 3 of the License, or +.\" (at your option) any later version. +.\" +.\" groff is distributed in the hope that it will be useful, but WITHOUT +.\" ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +.\" or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public +.\" License for more details. +.\" +.\" You should have received a copy of the GNU General Public License +.\" along with this program. If not, see +.\" <http://www.gnu.org/licenses/>. +.\" +.\" +.\" This file provides macros for addition, multiplication, and division +.\" of 62-bit signed integers. Its main application is to 'scale' +.\" 31-bit values--namely, to perform the operation 'a * b / c' +.\" accurately. +.\" +.\" Note that it is the duty of the user to check whether the input +.\" values fit within 31 bits (this is the range +.\" [-1073741824,1073741823]). +.\" +. +.do nr *groff_62bit_tmac_C \n[.cp] +.cp 0 +. +.if d add31to62 \ +. nx +. +. +.\" .add31to62 <x> <y> <z> +.\" +.\" Add a 31-bit signed integer to a signed 62-bit integer. Result is a +.\" signed 62-bit integer: +.\" +.\" <x> + (<y>h * 2^30 + <y>l) = <z>h * 2^30 + <z>l +.\" +.\" +.\" in: \n[<x>], \n[<y>h], \n[<y>l] +.\" +.\" out: \n[<z>h], \n[<z>l] +.\" +.\" Example: .add31to62 p q r +.\" +.\" -> input registers: \n[p], \n[qh], \n[ql] +.\" output registers: \n[rh], \n[rl] +.\" +.de1 add31to62 +. nr 62bit-lo2 (\\n[\\$2l]) +. nr 62bit-hi2 (\\n[\\$2h]) +. +. nr 62bit-i ((\\n[\\$1] + \\n[62bit-lo2]) / 1073741824) +. nr \\$3l ((\\n[\\$1] + \\n[62bit-lo2]) % 1073741824) +. +. ie ((\\n[62bit-lo2] > 0) & (\\n[\\$3l] < 0)) \{\ +. nr \\$3l +1073741824 +. nr 62bit-i -1 +. \} +. el \ +. if ((\\n[62bit-lo2] < 0) & (\\n[\\$3l] > 0)) \{\ +. nr \\$3l -1073741824 +. nr 62bit-i +1 +. \} +. +. nr \\$3h (\\n[62bit-hi2] + \\n[62bit-i]) +.. +. +. +.\" .mult31by31 <x> <y> <z> +.\" +.\" Multiply two 31-bit signed integers. Result is a 62-bit signed +.\" integer: +.\" +.\" <x> * <y> = <z>h * 2^30 + <z>l +.\" +.\" +.\" in: \n[<x>], \n[<y>] +.\" +.\" out: \n[<z>h], \n[<z>l] +.\" +.\" Example: .mult31by31 a b c +.\" +.\" -> input registers: \n[a], \n[b] +.\" output registers: \n[ch], \n[cl] +.\" +.de1 mult31by31 +. nr 62bit-1 (\\n[\\$1]) +. nr 62bit-2 (\\n[\\$2]) +. +. nr 62bit-sign 1 +. if !\\n[62bit-1] \{\ +. nr 62bit-sign -(\\n[62bit-sign]) +. nr 62bit-1 -(\\n[62bit-1]) +. \} +. if !\\n[62bit-2] \{\ +. nr 62bit-sign -(\\n[62bit-sign]) +. nr 62bit-2 -(\\n[62bit-2]) +. \} +. +. nr 62bit-lo1 (\\n[62bit-1] % 32768) +. nr 62bit-hi1 (\\n[62bit-1] / 32768) +. nr 62bit-lo2 (\\n[62bit-2] % 32768) +. nr 62bit-hi2 (\\n[62bit-2] / 32768) +. +. nr 62bit-lo3 (\\n[62bit-lo1] * \\n[62bit-lo2] % 1073741824) +. nr 62bit-i1 (\\n[62bit-lo1] * \\n[62bit-hi2] % 1073741824) +. nr 62bit-i2 (\\n[62bit-lo2] * \\n[62bit-hi1] % 1073741824) +. nr 62bit-hi3 (\\n[62bit-hi1] * \\n[62bit-hi2] % 1073741824) +. +. nr 62bit-i1 (\\n[62bit-i1] + \\n[62bit-i2] % 1073741824) +. \" check carry overflow of 62bit-i1 + 62bit-i2 +. if (\\n[62bit-i1] < \\n[62bit-i2]) \ +. nr 62bit-hi3 +32768 +. +. nr 62bit-hi3 +(\\n[62bit-i1] / 32768) +. \" multiply by 32768 in small steps to avoid overflow +. nr 62bit-i 16 1 +. while \\n-[62bit-i] \ +. nr 62bit-i1 (\\n[62bit-i1] * 2 % 1073741824) +. +. nr 62bit-lo3 (\\n[62bit-lo3] + \\n[62bit-i1] % 1073741824) +. \" check carry overflow of 62bit-i1 + lo +. if (\\n[62bit-lo3] < \\n[62bit-i1]) \ +. nr 62bit-hi3 +1 +. +. if !\\n[62bit-sign] \{\ +. nr 62bit-lo3 -(\\n[62bit-lo3]) +. nr 62bit-hi3 -(\\n[62bit-hi3]) +. \} +. nr \\$3l \\n[62bit-lo3] +. nr \\$3h \\n[62bit-hi3] +.. +. +. +.\" .div62by31 <x> <y> <z> +.\" +.\" Divide a signed 62-bit integer by a 31-bit integer. Result is a +.\" 31-bit signed integer: +.\" +.\" (<x>h * 2^30 + <x>l) / <y> = <z> +.\" +.\" +.\" in: \n[<x>h], \n[<x>l], \n[<y>] +.\" +.\" out: \n[<z>] +.\" +.\" Example: .div62by31 foo bar baz +.\" +.\" -> input registers: \n[fooh] \n[fool] \n[bar] +.\" output register: \n[baz] +.\" +.de1 div62by31 +. nr 62bit-lo1 \\n[\\$1l] +. nr 62bit-hi1 \\n[\\$1h] +. nr 62bit-2 \\n[\\$2] +. nr 62bit-3 0 +. +. nr 62bit-sign 1 +. if ((\\n[62bit-lo1] < 0) : (\\n[62bit-hi1] < 0)) \{\ +. nr 62bit-sign -(\\n[62bit-sign]) +. nr 62bit-lo1 -(\\n[62bit-lo1]) +. nr 62bit-hi1 -(\\n[62bit-hi1]) +. \} +. if !\\n[62bit-2] \{\ +. nr 62bit-sign -(\\n[62bit-sign]) +. nr 62bit-2 -(\\n[62bit-2]) +. \} +. +. nr 62bit-i 31 1 +. while \\n-[62bit-i] \{\ +. nr 62bit-hi1 (\\n[62bit-hi1] * 2 % 1073741824) +. nr 62bit-3 (\\n[62bit-3] * 2) +. nr 62bit-hi1 +(\\n[62bit-lo1] / 536870912) +. +. if (\\n[62bit-hi1] >= \\n[62bit-2]) \{\ +. nr 62bit-hi1 -\\n[62bit-2] +. nr 62bit-3 +1 +. \} +. nr 62bit-lo1 (\\n[62bit-lo1] * 2 % 1073741824) +. \} +. +. if !\\n[62bit-sign] \ +. nr 62bit-3 -(\\n[62bit-3]) +. nr \\$3 \\n[62bit-3] +.. +. +.cp \n[*groff_62bit_tmac_C] +.do rr *groff_62bit_tmac_C +. +.\" Local Variables: +.\" mode: nroff +.\" fill-column: 72 +.\" End: +.\" vim: set filetype=groff textwidth=72: |