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[smlnj] View of /sml/trunk/src/system/Basis/Implementation/real64.sml
 [smlnj] / sml / trunk / src / system / Basis / Implementation / real64.sml

# View of /sml/trunk/src/system/Basis/Implementation/real64.sml

Mon Sep 15 22:44:08 2003 UTC (17 years, 4 months ago) by mblume
File size: 10675 byte(s)
```fixed bug in Real.fromLargeInt
```
```(* real64.sml
*
* COPYRIGHT (c) 1995 AT&T Bell Laboratories.
*
*)

structure Real64Imp : REAL =
struct
structure I = InlineT.DfltInt

structure Math = Math64

infix 4 == !=
type real = real

fun *+(a:real,b,c) = a*b+c
fun *-(a:real,b,c) = a*b-c

val op == = InlineT.Real64.==
val op != = InlineT.Real64.!=

fun unordered(x:real,y) = Bool.not(x>y orelse x <= y)
fun ?= (x, y) = (x == y) orelse unordered(x, y)

fun isNormal x = (case Assembly.A.logb x
of ~1023 => false	(* 0.0 or subnormal *)
| 1024 => false	(* inf or nan *)
| _ => true
(* end case *))

val rbase = 1073741824.0	(* should be taken from CoreIntInf.base *)

(* The next three values are computed laboriously, partly to
* avoid problems with inaccurate string->float conversions
* in the compiler itself.
*)
val maxFinite = let
fun f(x,i) = if i=1023 then x else f(x*2.0, i + 1)
val y = f(1.0,0)
fun g(z, y, 0) = z
| g(z, y, i) = g (z+y, y*0.5, i - 1)
in
g(0.0,y,53)
end

val minNormalPos = let
fun f(x) = let
val y = x * 0.5
in
if isNormal y then f y else x
end
in
f 1.0
end

local
(* The x86 uses extended precision (80 bits) internally, therefore
* it is necessary to write out the result of r * 0.5 to get
* 64 bit precision.
*)
val mem = InlineT.PolyArray.array(1, minNormalPos)
val update = InlineT.PolyArray.update
val subscript = InlineT.PolyArray.chkSub
fun f () = let
val r = subscript(mem, 0)
val y = r * 0.5
in
update(mem, 0, y);
if subscript(mem, 0) == 0.0 then r else f ()
end
in
val minPos = f()
end

val posInf = maxFinite * maxFinite
val negInf = ~posInf

fun isFinite x = negInf < x andalso x < posInf
fun isNan x = Bool.not(x==x)
fun floor x = if x < 1073741824.0 andalso x >= ~1073741824.0
then Assembly.A.floor x
else if isNan x then raise General.Domain
else raise General.Overflow

fun ceil n = ~1 - floor (~1.0 - n)
fun trunc n = if n < 0.0 then ceil n else floor n
fun round x =
(* ties go to the nearest even number *)
let val fl = floor(x+0.5)
val cl = ceil(x-0.5)
in if fl=cl then fl
else if Word31Imp.andb(Word31Imp.fromInt fl,0w1) = 0w1 then cl else fl
end

(* This is the IEEE double-precision maxint *)
val maxInt = 4503599627370496.0

local
(* realround mode x returns x rounded to the nearest integer using the
* given rounding mode.
* May be applied to inf's and nan's.
*)
fun realround mode x = let
val saveMode = IEEEReal.getRoundingMode ()
in
IEEEReal.setRoundingMode mode;
(if x>=0.0 then x+maxInt-maxInt else x-maxInt+maxInt)
before IEEEReal.setRoundingMode saveMode
end
in
val realFloor = realround IEEEReal.TO_NEGINF
val realCeil = realround IEEEReal.TO_POSINF
val realTrunc = realround IEEEReal.TO_ZERO
end

val abs : real -> real = InlineT.Real64.abs
val fromInt : int -> real = InlineT.real

fun toInt IEEEReal.TO_NEGINF = floor
| toInt IEEEReal.TO_POSINF = ceil
| toInt IEEEReal.TO_ZERO = trunc
| toInt IEEEReal.TO_NEAREST = round

fun toLarge x = x
fun fromLarge _ x = x

fun sign x = if (x < 0.0) then ~1 else if (x > 0.0) then 1
else if isNan x then raise Domain else 0
fun signBit x = (* Bug: negative zero not handled properly *)
Assembly.A.scalb(x, ~(Assembly.A.logb x)) < 0.0

fun sameSign (x, y) = signBit x = signBit y

fun copySign(x,y) = (* may not work if x is Nan *)
if sameSign(x,y) then x else ~x

fun compare(x,y) =
if x<y then General.LESS
else if x>y then General.GREATER
else if x == y then General.EQUAL
else raise IEEEReal.Unordered

fun compareReal(x,y) =
if x<y then IEEEReal.LESS
else if x>y then IEEEReal.GREATER
else if x == y then IEEEReal.EQUAL
else IEEEReal.UNORDERED

(** This proably needs to be reorganized **)
fun class x =  (* does not distinguish between quiet and signalling NaN *)
if signBit x
then if x>negInf then if x == 0.0 then IEEEReal.ZERO
else if Assembly.A.logb x = ~1023
then IEEEReal.SUBNORMAL
else IEEEReal.NORMAL
else if x==x then IEEEReal.INF
else IEEEReal.NAN IEEEReal.QUIET
else if x<posInf then if x == 0.0 then IEEEReal.ZERO
else if Assembly.A.logb x = ~1023
then IEEEReal.SUBNORMAL
else IEEEReal.NORMAL
else if x==x then IEEEReal.INF
else IEEEReal.NAN IEEEReal.QUIET

val precision = 52

val two_to_the_neg_1000 =
let fun f(i,x) = if i=0 then x else f(i - 1, x*0.5)
in f(1000, 1.0)
end

(* AARGH!  Our version of logb gives a value that's one less than the
rest of the world's logb functions.
We should fix this systematically some time. *)

fun toManExp x =
case Assembly.A.logb x + 1
of ~1023 => if x==0.0 then {man=x,exp=0}
else let val {man=m,exp=e} = toManExp(x*1048576.0)
in { man = m, exp = e - 20 }
end
| 1024 => {man=x,exp=0}
| i => {man=Assembly.A.scalb(x, ~i),exp=i}

fun fromManExp {man=m,exp=e:int} =
if (m >= 0.5 andalso m <= 1.0  orelse m <= ~0.5 andalso m >= ~1.0)
then if e > 1020
then if e > 1050 then if m>0.0 then posInf else negInf
else let fun f(i,x) = if i=0 then x else f(i-1,x+x)
in f(e-1020,  Assembly.A.scalb(m,1020))
end
else if e < ~1020
then if e < ~1200 then 0.0
else let fun f(i,x) = if i=0 then x else f(i-1, x*0.5)
in f(1020-e, Assembly.A.scalb(m, ~1020))
end
else Assembly.A.scalb(m,e)  (* This is the common case! *)
else let val {man=m',exp=e'} = toManExp m
in fromManExp { man = m', exp = e'+ e }
end

fun fromLargeInt(x : IntInf.int) = let
val CoreIntInf.BI { negative, digits } = CoreIntInf.concrete x
val w2r = fromInt o InlineT.Word31.copyt_int31
fun calc [] = 0.0
| calc (d :: ds) = w2r d + rbase * calc ds
val m = calc digits
in
if negative then ~m else m
end

(* whole and split could be implemented more efficiently if we had
* control over the rounding mode; but for now we don't.
*)
fun whole x = if x>0.0
then if x > 0.5
then x-0.5+maxInt-maxInt
else whole(x+1.0)-1.0
else if x<0.0
then if x < ~0.5
then x+0.5-maxInt+maxInt
else whole(x-1.0)+1.0
else x

fun split x = let val w = whole x
val f = x-w
in if abs(f)==1.0
then {whole=w+f,frac=0.0}
else {whole=w, frac=f}
end

fun realMod x = let
val f = x - whole x
in
if abs f == 1.0 then 0.0 else f
end

fun rem(x,y) = y * #frac(split(x/y))

fun checkFloat x = if x>negInf andalso x<posInf then x
else if isNan x then raise General.Div
else raise General.Overflow

fun toLargeInt mode x =
if isNan x then raise Domain
else if x == posInf orelse x == negInf then raise Overflow
else let val (negative, x) =
if x < 0.0 then (true, ~x) else (false, x)
fun feven x = #frac (split (x / 2.0)) == 0.0
in
(* if the magnitute is less than 1.0, then
* we just have to figure out whether to return ~1, 0, or 1
*)
if x < 1.0 then
case mode of
IEEEReal.TO_ZERO => 0
| IEEEReal.TO_POSINF =>
if negative then 0 else 1
| IEEEReal.TO_NEGINF =>
if negative then ~1 else 0
| IEEEReal.TO_NEAREST =>
if x < 0.5 then 0
else if x > 0.5 then
if negative then ~1 else 1
else 0	(* 0 is even *)
else
* suitably adjusted according to fractional part
* and rounding mode: *)
let val { whole, frac } = split x
val start =
case mode of
IEEEReal.TO_NEGINF =>
if frac > 0.0 andalso negative then
whole + 1.0
else whole
| IEEEReal.TO_POSINF =>
if frac > 0.0 andalso not negative then
whole + 1.0
else whole
| IEEEReal.TO_ZERO => whole
| IEEEReal.TO_NEAREST =>
if frac > 0.5 then whole + 1.0
else if frac < 0.5 then whole
else if feven whole then whole
else whole + 1.0

(* Now, for efficiency, we construct the
* minimal whole number with
* all the significant bits.  First
* we get mantissa and exponent: *)
val { man, exp } = toManExp start
(* Then we adjust both to make sure the mantissa
* is whole: *)
if exp = 0 orelse #frac (split man) == 0.0 then
(man, exp)
else adjust (2.0 * man, exp - 1)
val (man, exp) = adjust (man, exp)

(* Now we can construct our bignum digits by
* repeated div/mod using the bignum base: *)
fun loop x =
if x == 0.0 then []
else
let val { whole, frac } = split (x / rbase)
val dig = InlineT.Word31.copyf_int31
(Assembly.A.floor
(frac * rbase))
in
dig :: loop whole
end
(* Now we make a bignum out of those digits: *)
val iman =
CoreIntInf.abstract
(CoreIntInf.BI { negative = negative,
digits = loop man })
in
(* Finally, we have to put the exponent back
* into the picture: *)
IntInfImp.<< (iman, InlineT.Word31.copyf_int31 exp)
end
end

fun nextAfter _ = raise Fail "Real.nextAfter unimplemented"

val min : real * real -> real = InlineT.Real64.min
val max : real * real -> real = InlineT.Real64.max
(*
fun min(x,y) = if x<y orelse isNan y then x else y
fun max(x,y) = if x>y orelse isNan y then x else y
*)

fun toDecimal _ = raise Fail "Real.toDecimal unimplemented"
fun fromDecimal _ = raise Fail "Real.fromDecimal unimplemented"

val fmt = RealFormat.fmtReal
val toString = fmt (StringCvt.GEN NONE)
val scan = NumScan.scanReal
val fromString = StringCvt.scanString scan

val ~ = InlineT.Real64.~
val op +  = InlineT.Real64.+
val op -  = InlineT.Real64.-
val op *  = InlineT.Real64.*
val op /  = InlineT.Real64./

val op >  = InlineT.Real64.>
val op <  = InlineT.Real64.<
val op >= = InlineT.Real64.>=
val op <= = InlineT.Real64.<=

end (* Real64 *)
```