immutable class FLTD < $REAL{FLTD}, $FLT_FMT
****

________This_class_embodies_normal_arithmetic_(NOT_including_trigonometric)
___operations_on_a_floating_point_approximate_number_representation.___This
___has_been_chosn_to_be_the_single_32-bit_IEEE_754-1984_standard
___representation.___For_convenience_of_implementation,_most_of_the_operations
___are_done_in_terms_of_the_double_length_version_operations_for_portability.

________This_source_text_provides_for_optional_inclusion_of_logarithmic
___and_exponential_functions_as_a_group_using_the_LOG_EXP_FUNCTIONS_partial
___class.___Bessel,_gamma_and_erf_functions_may_additionally_be_included
___from_the_partial_class_MATH_FUNCTIONS.

___NOTE_1.___The_class_ANGLED_in_the_Geometric_section_of_this_library_has
________been_extracted_from_here_since_the_(inverse)_trigonometric_operations
________are_conversions_between_an_angle_domain_and_the_domain_of_numbers
________or_factors.

________2.___This_class_and_FLT_are_exceptions_to_the_general_rule_in
________the_required_library_that_immutable_classes_all_inherit_from_$BINARY.


Flattened version is here

Ancestors
$FLT_FMT $FMT $STR $REAL{_}
$IEEE_FLOAT{_} $LIMITED{_} $RATIONAL{_} $SIGNED{_}
$VALUE_ITERS{_} $LOG_OPS{_} $HASH $IS_EQ
$CONVERSION{_} $ROUNDING{_} $ARITHMETIC{_} $ADD_OPS{_}
$ZERO{_} $NFE{_} $TEXT $BINARY
$ORDERED{_} $IS_LT{_} $VALUE{_} $NIL
$IS_NIL



Public


Constants
const Decimal_Multiplier : SAME := 10.0d ;
****
const Max_Precision : CARD := 16 ;
**** digits for representation!
const Num_Bits : CARD := 64 ;
**** IEEE double size numbers
const digits : INT := 15 ;
**** No of decimal digits of precn
const epsilon : SAME := 2.2204460492503131e-16d ;
**** min x > 0.0 s.t, 1.0+x/=x
const half : SAME := 0.5d ;
**** used in rounding!
const mantissa_bits : INT := 53 ;
**** No of bits in the significand, including an implied bit.
const max_exp10 : INT := 308 ;
**** max x s.t 10^x is in range.
const max_exp : INT := 1024 ;
**** maximum permissible exponent
const min_exp10 : INT := -307 ;
const min_exp : INT := -1021 ;
const one : SAME := 1.0d ;
const zero : SAME := 0.0d ;
**** See $NFE.

Features
abs : SAME
card : CARD
ceiling : SAME
copysign(other : SAME) : SAME
cos:SAME
create(val : CARD) : SAME
**** This routine returns the value of val converted to a floating point
___representation.
create(val : FIELD) : SAME
****
__This_routine_returns_the_value_of_val_converted_to_a_floating_point
___representation.
create(val : FLT) : SAME
**** This routine returns the value of val converted to a floating point representation.
create(val : FLTD) : SAME
**** This routine returns the value of val. It is provided to ensure
___symmetry_of_arithmetic_conversion/creation_routines.
create(val : INT) : SAME
**** This routine returns the value of val converted to a floating point
___representation.
create(val : INTI) : SAME
create(val : RAT) : SAME
cube_root : SAME
div(other : SAME) : SAME
double_inv_pi : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_twice_the_inverse_of_pi.___Built-in_to_this
___implementation.
double_sqrt_pi : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_twice_the_inverse_of_the_square_root_of_pi.___Built-in_to
___this_implementation.
e : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_the_mathematical_natural_logarithm_base.___Built-in_to
___this_implementation.
exp : SAME
**** This routine returns the exponential e^self. Built-in.
field : FIELD
floor : SAME
flt : FLT
fltd : FLTD
get_representation(out sign : BOOL,out exp : INT,out mantissa_lo,out mantissa_hi : CARD)
half_pi : SAME
****
__This_is_a_'routine'_returning_the_implementation-dependent
___approximation_to_pi/2.___Built-in_to_this_implementation.
infinity : SAME
**** This routine returns the representation of infinity -- which is
___implementation-dependent.___Built-in_to_this_implementation.
int : INT
inti : INTI
inv_pi : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_the_inverse_of_pi.___Built-in_to_this_implementation.
inv_sqrt_2 : SAME
****
__This_is_a_'routine'_returning_the_implementation-dependent
__approximation_to_one_divided_by_the_square-root_of_2.___Built-in_to_this
__implementation.
is_eq(other : SAME) : BOOL
**** This routine returns tru if and only if self and other have the same
___value.___Built-in_to_this_implementation.
is_finite : BOOL
**** This routine returns true if and only if self is zero, subnormal
___or_normal.___Built-in_to_this_implementation.
is_inf : BOOL
**** This routine returns true if and only if self is infinite. Built-in
___to_this_implementation.
is_lt(other : SAME) : BOOL
**** This rouitne returns true if and only if other is less than self. Built-in to this implementation.
is_normal : BOOL
**** This routine returns true if and only if self is a normalised number. Built-in to this implementation.
is_subnormal : BOOL
**** This routine returns true if and only if self is an un-normalised
___number.___Built-in_to_this_implementation.
is_zero : BOOL
**** This routine returns true if and only if self is zero. Built-in to
___this_implementation.
log10_e : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_e.log10.
log2_e : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_e.log2.
log : SAME
**** This routine returns the natural logarithm of self. Built-in.
log_10 : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_the_natural_logarithm_of_10.
log_2 : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_the_natural_logarithm_of_2.
max_normal : SAME
**** This routine returns the largest normalized positive number
___in_this_class.___Built-in_to_this_implementation.
max_subnormal : SAME
**** This routine returns the largest un-normalized positive number
___in_this_class.___Built-in_to_this_implementation.
min_normal : SAME
****
__This_routine_returns_the_smallest_normalized_positive_number
___in_this_class.___Built-in_to_this_implementation.
min_subnormal : SAME
**** This routine returns the smallest un-normalized positive number
___in_this_class.___Built-in_to_this_implementation.
minus(other : SAME) : SAME
mod(other : SAME) : SAME
negate : SAME
nextdown : SAME
nextup : SAME
pi : SAME
**** This is a 'routine' returning the implementation-dependent
___approximation_to_the_mathematical_number_pi.___Built-in_to_this
___implementation.
plus(other : SAME) : SAME
pow(arg : SAME) : SAME
**** This routine returns self raised to the arg'th power. Note that
___self.pow(0.0)_=_1.0_for_all_self.___Built-in.
quarter_pi : SAME
****
__This_is_a_'routine'_returning_the_implementation-dependent
___approximation_to_pi/4.___Built-in_to_this_implementation.
quiet_NaN(sig : INT) : SAME
**** This routine returns the representation which is interpreted by
___the_IEEE_arithmetic_model_as_being_a_quiet_(ie_non-interrupting)_NaN.
___The_argument_is_not_used_in_this_implementation.
Built-in to this implementation.
rat : RAT
remainder(other : SAME) : SAME
round : SAME
scale_by(exp : INT) : SAME
signalling_NaN(sig : INT) : SAME
**** This routine returns the representation which is interpreted by
___the_IEEE_arithmetic_model_as_a_signalling_(ie_interrupt_generating)_NaN.
___The_argument_is_unused_in_this_implementation.___Built-in_to_this
___implementation.
signbit_set : BOOL
**** This routine returns true if and only if the sign bit of self is
___set.___Built-in_to_this_implementation.
sin:SAME
sqrt : SAME
sqrt_2 : SAME
****
__This_is_a_'routine'_returning_the_implementation-dependent
___approximation_to_the_square_root_of_2.___Built-in_to_this_implementation.
tan:SAME
times(other : SAME) : SAME
truncate : SAME
unbiassed_exponent : INT

Iters


Private

const asize : CARD := 8 ;
****---------------???????? FUDGE!!
cos_approx(x2, xn:SAME, n:CARD):SAME
**** n+2-th and later terms of Tayler series. x2=x^2, xn=(+-1) x^n/n!
cos_approx:SAME
cuberoot : SAME
**** This routine returns the cube root of self. It is provided
___to_avoid_the_circularity_in_cube_and_cube-root_pre-requisites!__Built-in
___to_this_implementation.
next_down : SAME
**** This routine returns the next lower representable number from self.
___Note_that_this_version_has_NO_pre_requisites_in_order_to_prevent
___circularity_between_the_public_versions_of_nextup_and_nextdown.__Built-in
___to_this_implementation.
next_up : SAME
**** This private routine returns the next higher representable number
___from_self.___Note_that_this_version_has_NO_pre_requisites_in_order_to
___prevent_circularity_between_the_public_versions_of_nextup_and_nextdown.
___Built-in_to_this_implementation.
sin_approx(x2, xn:SAME, n:CARD):SAME
**** n+2-th and later terms of Tayler series. x2=x^2, xn=(+-1) x^n/n!
sin_approx:SAME
square_root : SAME
**** This private routine returns the square root of self. It is provided
___to_avoid_the_circularity_in_square_and_square-root_pre-requisites!
___Built-in_to_this_implementation.

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