diff options
Diffstat (limited to 'src/algebra/sf.spad.pamphlet')
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 60 |
1 files changed, 34 insertions, 26 deletions
diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index c1a29b22..1b36780f 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -279,17 +279,25 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, == add MER ==> Record(MANTISSA:Integer,EXPONENT:Integer) - import %fmul: (%,%) -> % from Foreign Builtin - import %fadd: (%,%) -> % from Foreign Builtin - import %fsub: (%,%) -> % from Foreign Builtin - import %fdiv: (%,%) -> % from Foreign Builtin - import %fmin: (%,%) -> % from Foreign Builtin - import %fmax: (%,%) -> % from Foreign Builtin - import %feq: (%,%) -> Boolean from Foreign Builtin - import %flt: (%,%) -> Boolean from Foreign Builtin - import %fle: (%,%) -> Boolean from Foreign Builtin - import %fgt: (%,%) -> Boolean from Foreign Builtin - import %fge: (%,%) -> Boolean from Foreign Builtin + import %fminval: () -> % from Foreign Builtin + import %fmaxval: () -> % from Foreign Builtin + import %fbase: () -> PositiveInteger from Foreign Builtin + import %fprec: () -> PositiveInteger from Foreign Builtin + import %i2f: Integer -> % from Foreign Builtin + import %fabs: % -> % from Foreign Builtin + import %fneg: % -> % from Foreign Builtin + import %ftrunc: % -> Integer from Foreign Builtin + import %fmul: (%,%) -> % from Foreign Builtin + import %fadd: (%,%) -> % from Foreign Builtin + import %fsub: (%,%) -> % from Foreign Builtin + import %fdiv: (%,%) -> % from Foreign Builtin + import %fmin: (%,%) -> % from Foreign Builtin + import %fmax: (%,%) -> % from Foreign Builtin + import %feq: (%,%) -> Boolean from Foreign Builtin + import %flt: (%,%) -> Boolean from Foreign Builtin + import %fle: (%,%) -> Boolean from Foreign Builtin + import %fgt: (%,%) -> Boolean from Foreign Builtin + import %fge: (%,%) -> Boolean from Foreign Builtin manexp: % -> MER @@ -334,21 +342,21 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, -- complex to get the correct behaviour. --makeComplex(x: %):% == COMPLEX(x, 0$%)$Lisp - base() == FLOAT_-RADIX(0$%)$Lisp + base() == %fbase() mantissa x == manexp(x).MANTISSA exponent x == manexp(x).EXPONENT - precision() == FLOAT_-DIGITS(0$%)$Lisp + precision() == %fprec() bits() == base() = 2 => precision() base() = 16 => 4*precision() - wholePart(precision()*log2(base()::%))::PositiveInteger - max() == _$DoubleFloatMaximum$Lisp - min() == _$DoubleFloatMinimum$Lisp + wholePart(precision() * log2 %i2f base())::PositiveInteger + max() == %fmaxval() + min() == %fminval() order(a) == precision() + exponent a - 1 - 0 == FLOAT(0$Lisp,_$DoubleFloatMaximum$Lisp)$Lisp - 1 == FLOAT(1$Lisp,_$DoubleFloatMaximum$Lisp)$Lisp + 0 == %i2f(0@Integer) + 1 == %i2f(1@Integer) -- rational approximation to e accurate to 23 digits - exp1() == FLOAT(534625820200,_$DoubleFloatMaximum$Lisp)$Lisp / FLOAT(196677847971,_$DoubleFloatMaximum$Lisp)$Lisp + exp1() == %i2f(534625820200) / %i2f(196677847971) pi() == PI$Lisp coerce(x:%):OutputForm == outputForm x convert(x:%):InputForm == convert(x pretend DoubleFloat)$InputForm @@ -356,7 +364,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, x > y == %fgt(x,y) x <= y == %fle(x,y) x >= y == %fge(x,y) - - x == (-x)$Lisp + - x == %fneg x x + y == %fadd(x,y) x:% - y:% == %fsub(x,y) x:% * y:% == %fmul(x,y) @@ -369,7 +377,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, log10 x == checkComplex log(x)$Lisp x:% ** i:Integer == EXPT(x,i)$Lisp x:% ** y:% == checkComplex EXPT(x,y)$Lisp - coerce(i:Integer):% == FLOAT(i,_$DoubleFloatMaximum$Lisp)$Lisp + coerce(i:Integer):% == %i2f i exp x == EXP(x)$Lisp log x == checkComplex LN(x)$Lisp log2 x == checkComplex LOG2(x)$Lisp @@ -411,8 +419,8 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, Gamma x == Gamma(sfx)$SFSFUN pretend % Beta(x,y) == Beta(sfx,sfy)$SFSFUN pretend % - wholePart x == FIX(x)$Lisp - float(ma,ex,b) == ma*(b::%)**ex + wholePart x == %ftrunc x + float(ma,ex,b) == ma * %i2f(b)**ex convert(x:%):DoubleFloat == x pretend DoubleFloat convert(x:%):Float == convert(x pretend DoubleFloat)$Float rationalApproximation(x, d) == rationalApproximation(x, d, 10) @@ -435,15 +443,15 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, rationalApproximation(x, (precision() - 1)::NonNegativeInteger, base()) retract(x:%):Integer == - x = ((n := wholePart x)::%) => n + x = (%i2f(n := wholePart x)) => n error "Not an integer" retractIfCan(x:%):Union(Integer, "failed") == - x = ((n := wholePart x)::%) => n + x = (%i2f(n := wholePart x)) => n "failed" sign(x) == retract FLOAT_-SIGN(x,1)$Lisp - abs x == FLOAT_-SIGN(1,x)$Lisp + abs x == %fabs x |