100 lines
3.9 KiB
Nim
100 lines
3.9 KiB
Nim
# Stint
|
|
# Copyright 2018 Status Research & Development GmbH
|
|
# Licensed under either of
|
|
#
|
|
# * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
|
|
# * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
|
|
#
|
|
# at your option. This file may not be copied, modified, or distributed except according to those terms.
|
|
|
|
import ../datatypes
|
|
|
|
# ############################################################
|
|
#
|
|
# Extended precision primitives on GCC & Clang (all CPU archs)
|
|
#
|
|
# ############################################################
|
|
|
|
const
|
|
newerNim = (NimMajor, NimMinor) > (1, 6)
|
|
noExplicitPtrDeref = defined(cpp) or newerNim
|
|
|
|
static:
|
|
doAssert GCC_Compatible
|
|
doAssert sizeof(int) == 8
|
|
|
|
func div2n1n_128*(q, r: var uint64, n_hi, n_lo, d: uint64) {.inline.}=
|
|
## Division uint128 by uint64
|
|
## Warning ⚠️ :
|
|
## - if n_hi == d, quotient does not fit in an uint64 and will throw SIGFPE on some platforms
|
|
## - if n_hi > d result is undefined
|
|
var dblPrec {.noinit.}: uint128
|
|
{.emit:[dblPrec, " = (unsigned __int128)", n_hi," << 64 | (unsigned __int128)",n_lo,";"].}
|
|
|
|
# Don't forget to dereference the var param in C mode
|
|
when noExplicitPtrDeref:
|
|
{.emit:[q, " = (NU64)(", dblPrec," / ", d, ");"].}
|
|
{.emit:[r, " = (NU64)(", dblPrec," % ", d, ");"].}
|
|
else:
|
|
{.emit:["*",q, " = (NU64)(", dblPrec," / ", d, ");"].}
|
|
{.emit:["*",r, " = (NU64)(", dblPrec," % ", d, ");"].}
|
|
|
|
func mul_128*(hi, lo: var uint64, a, b: uint64) {.inline.} =
|
|
## Extended precision multiplication
|
|
## (hi, lo) <- a*b
|
|
block:
|
|
var dblPrec {.noinit.}: uint128
|
|
{.emit:[dblPrec, " = (unsigned __int128)", a," * (unsigned __int128)", b,";"].}
|
|
|
|
# Don't forget to dereference the var param in C mode
|
|
when noExplicitPtrDeref:
|
|
{.emit:[hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:[lo, " = (NU64)", dblPrec,";"].}
|
|
else:
|
|
{.emit:["*",hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:["*",lo, " = (NU64)", dblPrec,";"].}
|
|
|
|
func muladd1_128*(hi, lo: var uint64, a, b, c: uint64) {.inline.} =
|
|
## Extended precision multiplication + addition
|
|
## (hi, lo) <- a*b + c
|
|
##
|
|
## Note: 0xFFFFFFFF_FFFFFFFF² -> (hi: 0xFFFFFFFFFFFFFFFE, lo: 0x0000000000000001)
|
|
## so adding any c cannot overflow
|
|
##
|
|
## This is constant-time on most hardware
|
|
## See: https://www.bearssl.org/ctmul.html
|
|
block:
|
|
var dblPrec {.noinit.}: uint128
|
|
{.emit:[dblPrec, " = (unsigned __int128)", a," * (unsigned __int128)", b, " + (unsigned __int128)",c,";"].}
|
|
|
|
# Don't forget to dereference the var param in C mode
|
|
when noExplicitPtrDeref:
|
|
{.emit:[hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:[lo, " = (NU64)", dblPrec,";"].}
|
|
else:
|
|
{.emit:["*",hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:["*",lo, " = (NU64)", dblPrec,";"].}
|
|
|
|
func muladd2_128*(hi, lo: var uint64, a, b, c1, c2: uint64) {.inline.}=
|
|
## Extended precision multiplication + addition + addition
|
|
## This is constant-time on most hardware except some specific one like Cortex M0
|
|
## (hi, lo) <- a*b + c1 + c2
|
|
##
|
|
## Note: 0xFFFFFFFF_FFFFFFFF² -> (hi: 0xFFFFFFFFFFFFFFFE, lo: 0x0000000000000001)
|
|
## so adding 0xFFFFFFFFFFFFFFFF leads to (hi: 0xFFFFFFFFFFFFFFFF, lo: 0x0000000000000000)
|
|
## and we have enough space to add again 0xFFFFFFFFFFFFFFFF without overflowing
|
|
block:
|
|
var dblPrec {.noinit.}: uint128
|
|
{.emit:[
|
|
dblPrec, " = (unsigned __int128)", a," * (unsigned __int128)", b,
|
|
" + (unsigned __int128)",c1," + (unsigned __int128)",c2,";"
|
|
].}
|
|
|
|
# Don't forget to dereference the var param in C mode
|
|
when noExplicitPtrDeref:
|
|
{.emit:[hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:[lo, " = (NU64)", dblPrec,";"].}
|
|
else:
|
|
{.emit:["*",hi, " = (NU64)(", dblPrec," >> ", 64'u64, ");"].}
|
|
{.emit:["*",lo, " = (NU64)", dblPrec,";"].}
|