#
#
# Nim's Runtime Library
# (c) Copyright 2012 Andreas Rumpf
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
# simple integer arithmetic with overflow checking
proc raiseOverflow {.compilerproc, noinline.} =
# a single proc to reduce code size to a minimum
sysFatal(OverflowError, "over- or underflow")
proc raiseDivByZero {.compilerproc, noinline.} =
sysFatal(DivByZeroError, "division by zero")
when defined(builtinOverflow):
# Builtin compiler functions for improved performance
when sizeof(clong) == 8:
proc addInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_saddl_overflow", nodecl, nosideeffect.}
proc subInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_ssubl_overflow", nodecl, nosideeffect.}
proc mulInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_smull_overflow", nodecl, nosideeffect.}
elif sizeof(clonglong) == 8:
proc addInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_saddll_overflow", nodecl, nosideeffect.}
proc subInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_ssubll_overflow", nodecl, nosideeffect.}
proc mulInt64Overflow[T: int64|int](a, b: T, c: var T): bool {.
importc: "__builtin_smulll_overflow", nodecl, nosideeffect.}
when sizeof(int) == 8:
proc addIntOverflow(a, b: int, c: var int): bool {.inline.} =
addInt64Overflow(a, b, c)
proc subIntOverflow(a, b: int, c: var int): bool {.inline.} =
subInt64Overflow(a, b, c)
proc mulIntOverflow(a, b: int, c: var int): bool {.inline.} =
mulInt64Overflow(a, b, c)
elif sizeof(int) == 4 and sizeof(cint) == 4:
proc addIntOverflow(a, b: int, c: var int): bool {.
importc: "__builtin_sadd_overflow", nodecl, nosideeffect.}
proc subIntOverflow(a, b: int, c: var int): bool {.
importc: "__builtin_ssub_overflow", nodecl, nosideeffect.}
proc mulIntOverflow(a, b: int, c: var int): bool {.
importc: "__builtin_smul_overflow", nodecl, nosideeffect.}
proc addInt64(a, b: int64): int64 {.compilerProc, inline.} =
if addInt64Overflow(a, b, result):
raiseOverflow()
proc subInt64(a, b: int64): int64 {.compilerProc, inline.} =
if subInt64Overflow(a, b, result):
raiseOverflow()
proc mulInt64(a, b: int64): int64 {.compilerproc, inline.} =
if mulInt64Overflow(a, b, result):
raiseOverflow()
else:
proc addInt64(a, b: int64): int64 {.compilerProc, inline.} =
result = a +% b
if (result xor a) >= int64(0) or (result xor b) >= int64(0):
return result
raiseOverflow()
proc subInt64(a, b: int64): int64 {.compilerProc, inline.} =
result = a -% b
if (result xor a) >= int64(0) or (result xor not b) >= int64(0):
return result
raiseOverflow()
#
# This code has been inspired by Python's source code.
# The native int product x*y is either exactly right or *way* off, being
# just the last n bits of the true product, where n is the number of bits
# in an int (the delivered product is the true product plus i*2**n for
# some integer i).
#
# The native float64 product x*y is subject to three
# rounding errors: on a sizeof(int)==8 box, each cast to double can lose
# info, and even on a sizeof(int)==4 box, the multiplication can lose info.
# But, unlike the native int product, it's not in *range* trouble: even
# if sizeof(int)==32 (256-bit ints), the product easily fits in the
# dynamic range of a float64. So the leading 50 (or so) bits of the float64
# product are correct.
#
# We check these two ways against each other, and declare victory if they're
# approximately the same. Else, because the native int product is the only
# one that can lose catastrophic amounts of information, it's the native int
# product that must have overflowed.
#
proc mulInt64(a, b: int64): int64 {.compilerproc.} =
var
resAsFloat, floatProd: float64
result = a *% b
floatProd = toBiggestFloat(a) # conversion
floatProd = floatProd * toBiggestFloat(b)
resAsFloat = toBiggestFloat(result)
# Fast path for normal case: small multiplicands, and no info
# is lost in either method.
if resAsFloat == floatProd: return result
# Somebody somewhere lost info. Close enough, or way off? Note
# that a != 0 and b != 0 (else resAsFloat == floatProd == 0).
# The difference either is or isn't significant compared to the
# true value (of which floatProd is a good approximation).
# abs(diff)/abs(prod) <= 1/32 iff
# 32 * abs(diff) <= abs(prod) -- 5 good bits is "close enough"
if 32.0 * abs(resAsFloat - floatProd) <= abs(floatProd):
return result
raiseOverflow()
proc negInt64(a: int64): int64 {.compilerProc, inline.} =
if a != low(int64): return -a
raiseOverflow()
proc absInt64(a: int64): int64 {.compilerProc, inline.} =
if a != low(int64):
if a >= 0: return a
else: return -a
raiseOverflow()
proc divInt64(a, b: int64): int64 {.compilerProc, inline.} =
if b == int64(0):
raiseDivByZero()
if a == low(int64) and b == int64(-1):
raiseOverflow()
return a div b
proc modInt64(a, b: int64): int64 {.compilerProc, inline.} =
if b == int64(0):
raiseDivByZero()
return a mod b
proc absInt(a: int): int {.compilerProc, inline.} =
if a != low(int):
if a >= 0: return a
else: return -a
raiseOverflow()
const
asmVersion = defined(I386) and (defined(vcc) or defined(wcc) or
defined(dmc) or defined(gcc) or defined(llvm_gcc))
# my Version of Borland C++Builder does not have
# tasm32, which is needed for assembler blocks
# this is why Borland is not included in the 'when'
when asmVersion and not defined(gcc) and not defined(llvm_gcc):
# assembler optimized versions for compilers that
# have an intel syntax assembler:
proc addInt(a, b: int): int {.compilerProc, asmNoStackFrame.} =
# a in eax, and b in edx
asm """
mov eax, ecx
add eax, edx
jno theEnd
call `raiseOverflow`
theEnd:
ret
"""
proc subInt(a, b: int): int {.compilerProc, asmNoStackFrame.} =
asm """
mov eax, ecx
sub eax, edx
jno theEnd
call `raiseOverflow`
theEnd:
ret
"""
proc negInt(a: int): int {.compilerProc, asmNoStackFrame.} =
asm """
mov eax, ecx
neg eax
jno theEnd
call `raiseOverflow`
theEnd:
ret
"""
proc divInt(a, b: int): int {.compilerProc, asmNoStackFrame.} =
asm """
mov eax, ecx
mov ecx, edx
xor edx, edx
idiv ecx
jno theEnd
call `raiseOverflow`
theEnd:
ret
"""
proc modInt(a, b: int): int {.compilerProc, asmNoStackFrame.} =
asm """
mov eax, ecx
mov ecx, edx
xor edx, edx
idiv ecx
jno theEnd
call `raiseOverflow`
theEnd:
mov eax, edx
ret
"""
proc mulInt(a, b: int): int {.compilerProc, asmNoStackFrame.} =
asm """
mov eax, ecx
mov ecx, edx
xor edx, edx
imul ecx
jno theEnd
call `raiseOverflow`
theEnd:
ret
"""
elif false: # asmVersion and (defined(gcc) or defined(llvm_gcc)):
proc addInt(a, b: int): int {.compilerProc, inline.} =
# don't use a pure proc here!
asm """
"addl %%ecx, %%eax\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
:"=a"(`result`)
:"a"(`a`), "c"(`b`)
"""
#".intel_syntax noprefix"
#/* Intel syntax here */
#".att_syntax"
proc subInt(a, b: int): int {.compilerProc, inline.} =
asm """ "subl %%ecx,%%eax\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
:"=a"(`result`)
:"a"(`a`), "c"(`b`)
"""
proc mulInt(a, b: int): int {.compilerProc, inline.} =
asm """ "xorl %%edx, %%edx\n"
"imull %%ecx\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
:"=a"(`result`)
:"a"(`a`), "c"(`b`)
:"%edx"
"""
proc negInt(a: int): int {.compilerProc, inline.} =
asm """ "negl %%eax\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
:"=a"(`result`)
:"a"(`a`)
"""
proc divInt(a, b: int): int {.compilerProc, inline.} =
asm """ "xorl %%edx, %%edx\n"
"idivl %%ecx\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
:"=a"(`result`)
:"a"(`a`), "c"(`b`)
:"%edx"
"""
proc modInt(a, b: int): int {.compilerProc, inline.} =
asm """ "xorl %%edx, %%edx\n"
"idivl %%ecx\n"
"jno 1\n"
"call _raiseOverflow\n"
"1: \n"
"movl %%edx, %%eax"
:"=a"(`result`)
:"a"(`a`), "c"(`b`)
:"%edx"
"""
when not declared(addInt) and defined(builtinOverflow):
proc addInt(a, b: int): int {.compilerProc, inline.} =
if addIntOverflow(a, b, result):
raiseOverflow()
when not declared(subInt) and defined(builtinOverflow):
proc subInt(a, b: int): int {.compilerProc, inline.} =
if subIntOverflow(a, b, result):
raiseOverflow()
when not declared(mulInt) and defined(builtinOverflow):
proc mulInt(a, b: int): int {.compilerProc, inline.} =
if mulIntOverflow(a, b, result):
raiseOverflow()
# Platform independent versions of the above (slower!)
when not declared(addInt):
proc addInt(a, b: int): int {.compilerProc, inline.} =
result = a +% b
if (result xor a) >= 0 or (result xor b) >= 0:
return result
raiseOverflow()
when not declared(subInt):
proc subInt(a, b: int): int {.compilerProc, inline.} =
result = a -% b
if (result xor a) >= 0 or (result xor not b) >= 0:
return result
raiseOverflow()
when not declared(negInt):
proc negInt(a: int): int {.compilerProc, inline.} =
if a != low(int): return -a
raiseOverflow()
when not declared(divInt):
proc divInt(a, b: int): int {.compilerProc, inline.} =
if b == 0:
raiseDivByZero()
if a == low(int) and b == -1:
raiseOverflow()
return a div b
when not declared(modInt):
proc modInt(a, b: int): int {.compilerProc, inline.} =
if b == 0:
raiseDivByZero()
return a mod b
when not declared(mulInt):
#
# This code has been inspired by Python's source code.
# The native int product x*y is either exactly right or *way* off, being
# just the last n bits of the true product, where n is the number of bits
# in an int (the delivered product is the true product plus i*2**n for
# some integer i).
#
# The native float64 product x*y is subject to three
# rounding errors: on a sizeof(int)==8 box, each cast to double can lose
# info, and even on a sizeof(int)==4 box, the multiplication can lose info.
# But, unlike the native int product, it's not in *range* trouble: even
# if sizeof(int)==32 (256-bit ints), the product easily fits in the
# dynamic range of a float64. So the leading 50 (or so) bits of the float64
# product are correct.
#
# We check these two ways against each other, and declare victory if
# they're approximately the same. Else, because the native int product is
# the only one that can lose catastrophic amounts of information, it's the
# native int product that must have overflowed.
#
proc mulInt(a, b: int): int {.compilerProc.} =
var
resAsFloat, floatProd: float
result = a *% b
floatProd = toFloat(a) * toFloat(b)
resAsFloat = toFloat(result)
# Fast path for normal case: small multiplicands, and no info
# is lost in either method.
if resAsFloat == floatProd: return result
# Somebody somewhere lost info. Close enough, or way off? Note
# that a != 0 and b != 0 (else resAsFloat == floatProd == 0).
# The difference either is or isn't significant compared to the
# true value (of which floatProd is a good approximation).
# abs(diff)/abs(prod) <= 1/32 iff
# 32 * abs(diff) <= abs(prod) -- 5 good bits is "close enough"
if 32.0 * abs(resAsFloat - floatProd) <= abs(floatProd):
return result
raiseOverflow()
# We avoid setting the FPU control word here for compatibility with libraries
# written in other languages.
proc raiseFloatInvalidOp {.noinline.} =
sysFatal(FloatInvalidOpError, "FPU operation caused a NaN result")
proc nanCheck(x: float64) {.compilerProc, inline.} =
if x != x: raiseFloatInvalidOp()
proc raiseFloatOverflow(x: float64) {.noinline.} =
if x > 0.0:
sysFatal(FloatOverflowError, "FPU operation caused an overflow")
else:
sysFatal(FloatUnderflowError, "FPU operations caused an underflow")
proc infCheck(x: float64) {.compilerProc, inline.} =
if x != 0.0 and x*0.5 == x: raiseFloatOverflow(x)