12. 選用的浮點詞集(The optional Floating-Point word set)

12.1 簡介(Introduction)

參閱(See): A.12 選用的浮點詞集(The optional Floating-Point word set)

12.2 附加的專有名詞和記號(Additional terms and notation)

12.2.1 專有名詞的定義(Definition of terms)

浮點對齊位址(float-aligned address):: 一個浮點數字可以被存取的記憶體位置的位址.; The address of a memory location at which a floating-point number can be accessed.
雙浮點對齊位址(double-float-aligned address):: 一個 64 位元的 IEEE 雙精確浮點數字可以被存取的記憶體位置的位址.; The address of a memory location at which a 64-bit IEEE double-precision floating-point number can be accessed.
單浮點對齊位址(single-float-aligned address):: 一個 32 位元的 IEEE 單精確浮點數字可以被存取的記憶體位置的位址.; The address of a memory location at which a 32-bit IEEE single-precision floating-point number can be accessed.
IEEE 浮點數字(IEEE floating-point number):: 一個定義於 ANSI/IEEE 754-1985 的單或雙精確浮點數字.; A single- or double-precision floating-point number as defined in ANSI/IEEE 754-1985.

12.2.2 標記法(Notation)

12.2.2.1 數字標記法(Numeric notation)

下列的標記法是用來定義浮點數語法外部的說明.

The following notation is used to define the syntax of the external representation of floating-point numbers:

一個浮點數的每一個成分是用這個成分的名稱組成的規則定義的 (用尖括弧中的斜字體表示, 例如, <sign> 字元 := 加上一些連續的記號和亞字元);
記號可以是文字字元 (以粗體字, 例如, E) 或在尖括弧中的規則名 (例如,<digit>);
亞字元 * 是用來指定零或多個之前記號的出現 (例如, <digit>*);
包含於 [ 和 ] 中的記號是選用的 (例如, [<sign>]);
垂直的小節線從包含於大括弧中的一串記號中分隔選擇 (例如, { + | - }).

Each component of a floating-point number is defined with a rule consisting of the name of the component (italicized in angle-brackets, e.g.,<sign> characters := and a concatenation of tokens and metacharacters;
Tokens may be literal characters (in bold face, e.g.,E) or rule names in angle brackets (e.g.,<digit>);
The metacharacter * is used to specify zero or more occurrences of the preceding token (e.g.,<digit>*);
Tokens enclosed with [ and ] are optional (e.g.,[<sign>]);
Vertical bars separate choices from a list of tokens enclosed with braces (e.g.,{ + | - }).

12.2.2.2 堆疊標記法(Stack notation)

當浮點數堆疊是從資料堆疊分開時, 浮點數堆疊標記法是:

Floating-point stack notation when the floating-point stack is separate from the data stack is:

( F: 之前 -- 之後)

( F: before -- after )

12.3 附加的使用需求(Additional usage requirements)

12.3.1 字元型別(Data types)

將表格 12.1 加進表格 3.1.

Append table 12.1 to table 3.1.

表格 12.1 - 資料型別

符號      資料型別                        在堆疊上的大小
------    ---------                       -------------
r         浮點數                          實作自訂
f-addr    浮點對齊位址                    1 cell
sf-addr   單浮點對齊位址                  1 cell
df-addr   雙浮點對齊位址                  1 cell

Table 12.1 - Data Types

Symbol    Data type                       Size on stack
------    ---------                       -------------
r         floating-point number           implementation-defined
f-addr    float-aligned address           1 cell
sf-addr   single-float-aligned address    1 cell
df-addr   double-float-aligned address    1 cell

12.3.1.1 位址(Addresses)

浮點對齊位址的集合是實作自訂的對齊位址的子集. 增加一個浮點運算數目的大小到一個浮點對齊位址必須產生一個浮點對齊位址.

The set of float-aligned addresses is an implementation-defined subset of the set of aligned addresses. Adding the size of a floating-point number to a float-aligned address shall produce a float-aligned address.

雙浮點對齊位址的集合是實作自訂的對齊位址的子集. 增加一個 64 位元 IEEE 雙精確浮點運算數目的大小到一個雙浮點對齊位址必須產生一個雙浮點對齊位址.

The set of double-float-aligned addresses is an implementation-defined subset of the set of aligned addresses. Adding the size of a 64-bit IEEE double-precision floating-point number to a double-float-aligned address shall produce a double-float-aligned address.

單浮點對齊位址的集合是實作自訂的對齊位址的子集. 增加一個 32 位元 IEEE 單精確浮點運算數目的大小到一個單浮點對齊位址必須產生一個單浮點對齊位址.

The set of single-float-aligned addresses is an implementation-defined subset of the set of aligned addresses. Adding the size of a 32-bit IEEE single-precision floating-point number to a single-float-aligned address shall produce a single-float-aligned address.

12.3.1.2 浮點數目(Floating-point numbers)

一個浮點數目的內部表示法, 包含格式和有效的精確度及格式和指數的範圍, 是實作自訂的.

The internal representation of a floating-point number, including the format and precision of the significand and the format and range of the exponent, is implementation defined.

任何四捨五入或浮點數的捨去是實作自訂的.

Any rounding or truncation of floating-point numbers is implementation defined.

12.3.2 浮點運算(Floating-point operations)

四捨五入到最近的意思是調整浮點運算的結果成最接近結果的可表示值. 如果兩個最近的可表示值是相等地接近這個結果, 必須交付在最小有效位元是零的那一個.

Round to nearest means round the result of a floating-point operation to the representable value nearest the result. If the two nearest representable values are equally near the result, the one having zero as its least significant bit shall be delivered.

四捨五入到負無限意思是調整浮點運算的結果成最接近結果並且不大於結果的最接近值.

Round toward negative infinity means round the result of a floating-point operation to the representable value nearest to and no greater than the result.

12.3.3 浮點堆疊(Floating-point stack)

一個後進, 先出的列表必須用來作為所有浮點運算的操作.

A last in, first out list that shall be used by all floating-point operators.

浮點堆疊的寬度是實作自訂的. 預設的浮點堆疊必須從資料堆疊和返回堆疊中分開. 一個程式可以決定是否浮點運算數目被保留於資料堆疊, 利用傳送字串 FLOATING-STACK 給 ENVIRONMENT?.

The width of the floating-point stack is implementation-defined. By default the floating-point stack shall be separate from the data and return stacks. A program may determine whether floating-point numbers are kept on the data stack by passing the string FLOATING-STACK to ENVIRONMENT?.

浮點堆疊的大小必須至少六個元素.

The size of a floating-point stack shall be at least 6 items.

一個依靠浮點堆疊大於六個元素的程式有一個環境相依性.

A program that depends on the floating-point stack being larger than six items has an environmental dependency.

12.3.4 環境的詢問(Environmental queries)

將表格 12.2 加進表格 3.5.

Append table 12.2 to table 3.5.

參閱(See): 3.2.6 環境的詢問(Environmental queries)

表格 12.2 - 環境詢問字串

字串            值     資料型別  常數?      意義
------          ---------------  ---------  -------
FLOATING        flag             no         浮點詞集存在
FLOATING-EXT    flag             no         浮點延伸詞集存在
FLOATING-STACK  n                yes        如果 n 是零, 浮點數目是保留在資料堆疊; 
                                            否則 n 是最大的分開的浮點堆疊的層數. 
MAX-FLOAT       r                yes        最大的可用浮點數目

Table 12.2 - Environmental query strings

String          Value data type  Constant?  Meaning
------          ---------------  ---------  -------
FLOATING        flag             no         floating-point word set present
FLOATING-EXT    flag             no         floating-point extensions word set present
FLOATING-STACK  n                yes        If n = zero, floating-point numbers are 
                                            kept on the data stack; otherwise n is 
                                            the maximum depth of the separate 
                                            floating-point stack.
MAX-FLOAT       r                yes        largest usable floating-point number

12.3.5 位址對齊(Address alignment)

由於一個 CREATE 出的詞傳回位址不必對齊任何特別的種類或浮點資料, 一個程式必須在存取在位址上的浮點資料前將位址對齊 (要浮點對齊, 單浮點對齊或雙浮點對齊).

Since the address returned by a CREATEd word is not necessarily aligned for any particular class of floating-point data, a program shall align the address (to be float aligned, single-float aligned, or double-float aligned) before accessing floating-point data at the address.

參閱(See): 3.3.3.1 位址對齊(Address alignment), A.12.3.5 位址對齊(Address alignment), 12.3.1.1 位址(Addresses).

12.3.6 變數(Variables)

一個程式可以對在資料空間中、由 FVARIABLE 傳回的記憶體定址. 這些區域可以是不連續地, 由後來的 , (comma) 或 ALLOT 配置的.

A program may address memory in data space regions made available by FVARIABLE. These regions may be non-contiguous with regions subsequently allocated with , (comma) or ALLOT.

參閱(See): 3.3.3.3 變數(Variables)

12.3.7 文字解譯器輸入數字轉換(Text interpreter input number conversion)

如果浮點詞集存在於詞典中, 並且目前的基底是十進位, 輸入數字轉換的演算法必須延伸成以下列格式認識浮點數字:

If the Floating-Point word set is present in the dictionary and the current base is DECIMAL, the input number-conversion algorithm shall be extended to recognize floating-point numbers in this form:

可轉換的字串 := <significand><exponent>

<significand> := [<sign>]<digits>[.<digits0>]
<exponent>    := E[<sign>]<digits0>
<sign>        := { + | - }
<digits>      := <digit><digits0>
<digits0>     := <digit>*
<digit>       := { 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 }

有一些以程式原始碼型式表示的正確的浮點數字的例子:

	1E   1.E   1.E0   +1.23E-1   -1.23E+1

Convertible string := <significand><exponent>

<significand> := [<sign>]<digits>[.<digits0>]
<exponent>    := E[<sign>]<digits0>
<sign>        := { + | - }
<digits>      := <digit><digits0>
<digits0>     := <digit>*
<digit>       := { 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 }

These are examples of valid representations of floating-point numbers in program source:

	1E   1.E   1.E0   +1.23E-1   -1.23E+1

參閱(See): 3.4.1.3 文字解譯器輸入數字轉換(Text interpreter input number conversion), A.12.3.7 文字解譯器輸入數字轉換(Text interpreter input number conversion), 12.6.1.0558 >FLOAT

12.4 附加的文件需求(Additional documentation requirements)

12.4.1 系統文件(System documentation)

12.4.1.1 實作自訂選項(Implementation-defined options)

浮點數字的格式和範圍 (12.3.1 資料型別, 12.6.1.2143 REPRESENT);
當浮點超過範圍時 12.6.1.2143 REPRESENT 的結果;
浮點數的四捨五入或捨去 (12.3.1.2 浮點數目);
浮點堆疊的大小 (12.3.3 浮點堆疊);
浮點堆疊的寬度 (12.3.3 浮點堆疊).

format and range of floating-point numbers (12.3.1 Data types, 12.6.1.2143 REPRESENT);
results of 12.6.1.2143 REPRESENT when float is out of range;
rounding or truncation of floating-point numbers (12.3.1.2 Floating-point numbers);
size of floating-point stack (12.3.3 Floating-point stack);
width of floating-point stack (12.3.3 Floating-point stack).

12.4.1.2 模稜兩可的情況(Ambiguous conditions)

DF@ 或 DF! 被用於一個非雙浮點對齊的位址;
F@ 或 F! 被用於一個非浮點對齊的位址;
浮點結果超過範圍 (例如, 在 12.6.1.1430 F/);
SF@ 或 SF! 被用於一個非單浮點對齊的位址;
BASE 不是十進位 (12.6.1.2143 REPRESENT, 12.6.2.1427 F., 12.6.2.1513 FE., 12.6.2.1613 FS.);
兩個參數都等於零 (12.6.2.1489 FATAN2);
對於 12.6.2.1625 FTAN 而言, 參數的 cosine 是零;
d 不能被精確地在浮點中展現 12.6.1.1130 D>F;
除以零 (12.6.1.1430 F/);
在轉換時, 指數過大 (12.6.2.1203 DF!, 12.6.2.1204 DF@, 12.6.2.2202 SF!, 12.6.2.2203 SF@);
FLOAT 小於一 (12.6.2.1477 FACOSH);
FLOAT 小於或等於負一 (12.6.2.1554 FLNP1);
FLOAT 小於或等於零 (12.6.2.1553 FLN, 12.6.2.1557 FLOG);
FLOAT 小於零 (12.6.2.1487 FASINH, 12.6.2.1618 FSQRT);
FLOAT 量值大於一 (12.6.2.1476 FACOS, 12.6.2.1486 FASIN, 12.6.2.1491 FATANH);
浮點數的整數部分不能由在 12.6.1.1470 F>D 中的 d 所展現;
字串大於書寫數字輸出區域 (12.6.2.1427 F., 12.6.2.1513 FE., 12.6.2.1613 FS.).

DF@ or DF! is used with an address that is not double-float aligned;
F@ or F! is used with an address that is not float aligned;
FLOATing point result out of range (e.g., in 12.6.1.1430 F/);
SF@ or SF! is used with an address that is not single-float aligned;
BASE is not decimal (12.6.1.2143 REPRESENT, 12.6.2.1427 F., 12.6.2.1513 FE., 12.6.2.1613 FS.);
both arguments equal zero (12.6.2.1489 FATAN2);
cosine of argument is zero for 12.6.2.1625 FTAN;
d can't be precisely represented as float in 12.6.1.1130 D>F;
dividing by zero (12.6.1.1430 F/);
exponent too big for conversion (12.6.2.1203 DF!, 12.6.2.1204 DF@, 12.6.2.2202 SF!, 12.6.2.2203 SF@);
FLOAT less than one (12.6.2.1477 FACOSH);
FLOAT less than or equal to minus-one (12.6.2.1554 FLNP1);
FLOAT less than or equal to zero (12.6.2.1553 FLN, 12.6.2.1557 FLOG);
FLOAT less than zero (12.6.2.1487 FASINH, 12.6.2.1618 FSQRT);
FLOAT magnitude greater than one (12.6.2.1476 FACOS, 12.6.2.1486 FASIN, 12.6.2.1491 FATANH);
Integer part of float can't be represented by d in 12.6.1.1470 F>D;
string larger than pictured-numeric output area (12.6.2.1427 F., 12.6.2.1513 FE., 12.6.2.1613 FS.).

12.4.1.3 其他的系統文件(Other system documentation)

沒有附加的需求(no additional requirements).

12.4.2 程式文件(Program documentation)

12.4.2.1 環境相依性(Environmental dependencies)

需要浮點堆疊大於六個元素 (12.3.3 浮點堆疊).

requiring the floating-point stack to be larger than six items (12.3.3 Floating-point stack).

12.4.2.2 其他程式文件(Other program documentation)

沒有附加的需求(no additional requirements).

12.5 遵守標準和命名(Compliance and labeling)

12.5.1 ANS Forth 系統(ANS Forth systems)

措辭 提供浮點詞集 必須被加到任何提供浮點詞集的標準系統的描述之中.

The phrase Providing the Floating-Point word set shall be appended to the label of any Standard System that provides all of the Floating-Point word set.

措辭 從浮點延伸詞集提供 name(s) 必須被加到任何提供部分浮點延伸詞集的標準系統的描述之中.

The phrase Providing name(s) from the Floating-Point Extensions word set shall be appended to the label of any Standard System that provides portions of the Floating-Point Extensions word set.

措辭 提供浮點延伸詞集 必須被加到任何提供所有浮點詞集和浮點延伸詞集的標準系統的描述之中.

The phrase Providing the Floating-Point Extensions word set shall be appended to the label of any Standard System that provides all of the Floating-Point and Floating-Point Extensions word sets.

12.5.2 ANS Forth 程式(ANS Forth programs)

措辭 需要浮點詞集 必須被加到任何需要系統提供浮點詞集的標準程式的描述之中.

The phrase Requiring the Floating-Point word set shall be appended to the label of Standard Programs that require the system to provide the Floating-Point word set.

措辭 需要浮點延伸詞集中的 name(s) 必須被加到任何需要系統提供部分浮點延伸詞集的標準程式的描述之中.

The phrase Requiring name(s) from the Floating-Point Extensions word set shall be appended to the label of Standard Programs that require the system to provide portions of the Floating-Point Extensions word set.

措辭 需要浮點延伸詞集 必須被加到任何需要系統提供所有浮點和浮點延伸詞集的標準程式的描述之中.

The phrase Requiring the Floating-Point Extensions word set shall be appended to the label of Standard Programs that require the system to provide all of the Floating-Point and Floating-Point Extensions word sets.

12.6 詞彙表(Glossary)

12.6.1 浮點詞(Floating-Point words)


12.6.1.0558 >FLOAT

到-浮點 FLOATING

	( c-addr u -- true | false ) ( F: -- r |  )  
	or ( c-addr u -- r true | false)

一個轉換由 c-addr 和 u 指定的字串到內部浮點表示法的嘗試. 如果這個字串用下列的語法展現了一個正確的浮點數字, 它的值 r 和 true 將會被傳回. 如果這個字串並未展現了一個正確的浮點數目, 只有假會被傳回.

一個空白的字串必須被當作是一個特別的情況, 展現了零.

一個可轉換字串的語法是 := <significand>[<exponent>]

<significand> := [<sign>]{<digits>[.<digits0>] |
.<digits> }
<exponent>    := <marker><digits0>
<marker>      := {<e-form> | <sign-form>}
<e-form>      := <e-char>[<sign-form>]
<sign-form>   := { + | - }
<e-char>      := { D | d | E | e }

參閱: A.12.6.1.0558 >FLOAT


12.6.1.0558 >FLOAT

to-float FLOATING

	( c-addr u -- true | false ) ( F: -- r |  )  
	or ( c-addr u -- r true | false)

An attempt is made to convert the string specified by c-addr and u to internal floating-point representation. If the string represents a valid floating-point number in the syntax below, its value r and true are returned. If the string does not represent a valid floating-point number only false is returned.

A string of blanks should be treated as a special case representing zero.

The syntax of a convertible string := <significand>[<exponent>]

<significand> := [<sign>]{<digits>[.<digits0>] |
.<digits> }
<exponent>    := <marker><digits0>
<marker>      := {<e-form> | <sign-form>}
<e-form>      := <e-char>[<sign-form>]
<sign-form>   := { + | - }
<e-char>      := { D | d | E | e }

See: A.12.6.1.0558 >FLOAT


12.6.1.1130 D>F

d-to-f FLOATING

	( d -- ) ( F: -- r ) 
        or ( d -- r )

r 是 d 的相等的浮點值. 如果 d 不能被精確地以一個浮點值表示, 將會有一個模稜兩可的情況存在.


12.6.1.1130 D>F

d-to-f FLOATING

	( d -- ) ( F: -- r ) 
        or ( d -- r )

r is the floating-point equivalent of d. An ambiguous condition exists if d cannot be precisely represented as a floating-point value.


12.6.1.1400 F!

f-儲存 FLOATING

	( f-addr -- ) ( F: r -- ) 
        or ( r f-addr -- )

將 r 存入 f-addr.


12.6.1.1400 F!

f-store FLOATING

	( f-addr -- ) ( F: r -- ) 
        or ( r f-addr -- )

Store r at f-addr.


12.6.1.1410 F*

f-星號 FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

將 r1 乘以 r2 得到 r3.


12.6.1.1410 F*

f-star FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

Multiply r1 by r2 giving r3.


12.6.1.1420 F+

f-加號 FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

將 r1 加進 r2 得到結果 r3.


12.6.1.1420 F+

f-plus FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

Add r1 to r2 giving the sum r3.


12.6.1.1425 F-

f-減號 FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

從 r1 減去 r2, 得到 r3.


12.6.1.1425 F-

f-minus FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

Subtract r2 from r1, giving r3.


12.6.1.1430 F/

f-除號 FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

將 r1 除以 r2, 得到商 r3. 如果 r2 是零, 或是商位於一個浮點數目的範圍之外, 將會有一個模稜兩可的情況存在.


12.6.1.1430 F/

f-slash FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

Divide r1 by r2, giving the quotient r3. An ambiguous condition exists if r2 is zero, or the quotient lies outside of the range of a floating-point number.


12.6.1.1440 F0<

f-zero-less-than FLOATING

	( -- flag ) ( F: r -- ) 
	or ( r -- flag )

如果 r 小於零, 則 flag 為真.


12.6.1.1440 F0<

f-zero-less-than FLOATING

	( -- flag ) ( F: r -- ) 
	or ( r -- flag )

flag is true if and only if r is less than zero.


12.6.1.1450 F0=

f-zero-equals FLOATING

	( -- flag ) ( F: r -- ) 
	or ( r -- flag )

如果 r 等於零, 則 flag 為真.


12.6.1.1450 F0=

f-zero-equals FLOATING

	( -- flag ) ( F: r -- ) 
	or ( r -- flag )

flag is true if and only if r is equal to zero.


12.6.1.1460 F<

f-less-than FLOATING

	( -- flag ) ( F: r1 r2 -- ) 
	or ( r1 r2 -- flag )

如果 r1 小於 r2, 則 flag 為真.


12.6.1.1460 F<

f-less-than FLOATING

	( -- flag ) ( F: r1 r2 -- ) 
	or ( r1 r2 -- flag )

flag is true

if and only if r1 is less than


12.6.1.1470 F>D

f-to-d FLOATING

	( -- d ) ( F: r -- ) 
	or ( r -- d )

d 是 r 的整數部分的雙單元有號整數等價值. r 的小數部分被丟棄. 如果 r 的整數部分不能被精確地以一個雙單元有號整數展現, 將會有一個模稜兩可的情況存在.


12.6.1.1460 F>D

f-to-d FLOATING

	( -- d ) ( F: r -- ) 
	or ( r -- d )

d is the double-cell signed-integer equivalent of the integer portion of r. The fractional portion of r is discarded. An ambiguous condition exists if the integer portion of r cannot be precisely represented as a double-cell signed integer.


12.6.1.1472 F@

f-fetch FLOATING

	( f-addr -- ) ( F: -- r )  
	or  ( f-addr -- r )

r 是儲存於 f-addr 的值.


12.6.1.1472 F@

f-fetch FLOATING

	( f-addr -- ) ( F: -- r )  
	or  ( f-addr -- r )

r is the value stored at f-addr.


12.6.1.1479 FALIGN

f-align FLOATING

	( -- )

如果資料空間指標不是浮點對齊的, 保留足夠的空間, 讓它是.


12.6.1.1479 FALIGN

f-align FLOATING

	( -- )

If the data-space pointer is not float aligned, reserve enough data space to make it so.


12.6.1.1483 FALIGNED

f-aligned FLOATING

	( addr -- f-addr )

f-addr 是第一個大於或等於 addr 的浮點對齊的位址.


12.6.1.1483 FALIGNED

f-aligned FLOATING

	( addr -- f-addr )

f-addr is the first float-aligned address greater than or equal to addr.


12.6.1.1492 FCONSTANT

f-constant FLOATING

	( "<spaces>name" -- ) ( F: r -- ) 
	or ( r "<spaces>name" -- )

跳過開頭的空白分界符號. 分析出由一個空白分界的 name. 為 name 創造一個有下列執行語義的定義.

name 被參考為一個 f-常數.

        name 執行: ( -- ) ( F: -- r ) 
			       or ( -- r )

將 r 放置於浮點堆疊.

參閱: A.12.6.1.1492 FCONSTANT , 3.4.1 分析.


12.6.1.1492 FCONSTANT

f-constant FLOATING

	( "<spaces>name" -- ) ( F: r -- ) 
	or ( r "<spaces>name" -- )

Skip leading space delimiters. Parse name delimited by a space. Create a definition for name with the execution semantics defined below.

name is referred to as an f-constant.

        name Execution: ( -- ) ( F: -- r ) 
			       or ( -- r )

Place r on the floating-point stack.

See: A.12.6.1.1492 FCONSTANT , 3.4.1 Parsing.


12.6.1.1497 FDEPTH

f-depth FLOATING

	( -- +n )

+n 是包含在預設分開的浮點堆疊上的數值數目. 如果浮點數目是保存於資料堆疊, +n 是目前包含於資料堆疊的可能的浮點數值的目前數目.


12.6.1.1497 FDEPTH

f-depth FLOATING

	( -- +n )

+n is the number of values contained on the default separate floating-point stack. If floating-point numbers are kept on the data stack, +n is the current number of possible floating-point values contained on the data stack.


12.6.1.1500 FDROP

f-drop
FLOATING

	( F: r -- ) 
	or ( r -- )

從浮點堆疊移除 r.


12.6.1.1500 FDROP

f-drop
FLOATING

	( F: r -- ) 
	or ( r -- )

Remove r from the floating-point stack.


12.6.1.1510 FDUP

f-dupe FLOATING

	( F: r -- r r ) 
	or ( r -- r r )

複製 r.


12.6.1.1510 FDUP

f-dupe FLOATING

	( F: r -- r r ) 
	or ( r -- r r )

Duplicate r.


12.6.1.1552 FLITERAL

f-literal FLOATING

        解譯: 這個詞的解譯語義是未定義的.

        編譯: ( F: r -- ) 
	or ( r -- )

將下列給予的執行時期語義加進目前的定義.

        執行時期: ( F: -- r ) 
	or ( -- r )

將 r 放置於浮點堆疊.

參閱: A.12.6.1.1552 FLITERAL


12.6.1.1552 FLITERAL

f-literal FLOATING

	Interpretation: Interpretation semantics for this word are undefined.

        Compilation: ( F: r -- ) 
	or ( r -- )

Append the run-time semantics given below to the current definition.

        Run-time: ( F: -- r ) 
	or ( -- r )

Place r on the floating-point stack.

See: A.12.6.1.1552 FLITERAL


12.6.1.1555 FLOAT+

FLOAT-plus FLOATING

	( f-addr1 -- f-addr2 )

將一個以位址單元為單位的浮點數目大小加進 f-addr1, 得到 f-addr2.


12.6.1.1555 FLOAT+

FLOAT-plus FLOATING

	( f-addr1 -- f-addr2 )

Add the size in address units of a floating-point number to f-addr1, giving f-addr2.


12.6.1.1556 FLOATS

FLOATING

	( n1 -- n2 )

n2 是以位址單元為單位的 n1 個浮點數目的大小.


12.6.1.1556 FLOATS

FLOATING

	( n1 -- n2 )

n2 is the size in address units of n1 floating-point numbers.


12.6.1.1558 FLOOR

FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

以 四捨五入到負無限的規則四捨五入 r1 到一個內部值, 得到 r2.


12.6.1.1558 FLOOR

FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

Round r1 to an integral value using the round toward negative infinity rule, giving r2.


12.6.1.1562 FMAX

f-max FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 是 r1 和 r2 中的較大者.


12.6.1.1562 FMAX

f-max FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 is the greater of r1 and r2.


12.6.1.1565 FMIN

f-min FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 是 r1 和 r2 中的較小者.


12.6.1.1565 FMIN

f-min FLOATING

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 is the lesser of r1 and r2.


12.6.1.1567 FNEGATE

f-negate FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是 r1 的否定值.


12.6.1.1567 FNEGATE

f-negate FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the negation of r1.


12.6.1.1600 FOVER

f-over FLOATING

	( F: r1 r2 -- r1 r2 r1 ) 
	or ( r1 r2 -- r1 r2 r1 )

將一份 r1 的複製品放置於浮點運算堆疊的上方.


12.6.1.1600 FOVER

f-over FLOATING

	( F: r1 r2 -- r1 r2 r1 ) 
	or ( r1 r2 -- r1 r2 r1 )

Place a copy of r1 on top of the floating-point stack.


12.6.1.1610 FROT

f-rote FLOATING

	( F: r1 r2 r3 -- r2 r3 r1 ) 
	or ( r1 r2 r3 -- r2 r3 r1 )

旋轉最上方三個浮點堆疊記錄.


12.6.1.1610 FROT

f-rote FLOATING

	( F: r1 r2 r3 -- r2 r3 r1 ) 
	or ( r1 r2 r3 -- r2 r3 r1 )

Rotate the top three floating-point stack entries.


12.6.1.1612 FROUND

f-round FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

用 四捨五入到最近 的規則四捨五入 r1 到一個整數值, 得到 r2.

參閱: 12.3.2 浮點運算


12.6.1.1612 FROUND

f-round FLOATING

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

Round r1 to an integral value using the round to nearest rule, giving r2.

See: 12.3.2 Floating-point operations


12.6.1.1620 FSWAP

f-swap FLOATING

	( F: r1 r2 -- r2 r1 ) 
	or ( r1 r2 -- r2 r1 )

交換在浮點堆疊最上方的兩個元素.


12.6.1.1620 FSWAP

f-swap FLOATING

	( F: r1 r2 -- r2 r1 ) 
	or ( r1 r2 -- r2 r1 )

Exchange the top two floating-point stack items.


12.6.1.1630 FVARIABLE

f-variable FLOATING

	( "<spaces>name" -- )

跳過開頭的空白分界符號. 分析出由一個空白分界的 name. 為 name 創造一個有下列執行語義的定義. 在資料空間的浮點對齊位址保留一個 FLOATS 位址單元.

name 被參考為一個 f-變數.

        name 執行: ( -- f-addr )

f-addr 是由當 FVARIABLE 創造 name 時保留的資料空間的位址. 一個程式負責用來初始化保留空間的內容.

參閱: A.12.6.1.1630 FVARIABLE , 3.4.1 分析.


12.6.1.1630 FVARIABLE

f-variable FLOATING

	( "<spaces>name" -- )

Skip leading space delimiters. Parse name delimited by a space. Create a definition for name with the execution semantics defined below. Reserve 1 FLOATS address units of data space at a float-aligned address.

name is referred to as an f-variable.

        name Execution: ( -- f-addr )

f-addr is the address of the data space reserved by FVARIABLE when it created name. A program is responsible for initializing the contents of the reserved space.

See: A.12.6.1.1630 FVARIABLE , 3.4.1 Parsing.


12.6.1.2143 REPRESENT

FLOATING

	( c-addr u -- n flag1 flag2 )  (F: r -- )  
	or ( r c-addr u -- n flag1 flag2 )

在 c-addr, 放置浮點數目 r 的有意義的延伸表示法的字元字串. 傳回以十進位為基底的指數 n, 符號 flag1, 和 flag2 為 正確的結果. 字元字串必須由最多 u 個有意義的有效數字組成, 包含一個十進元的部分, 加上由十進位點指到第一個數字的左邊, 並且只有在所有數字是零時, 第一個數字才能為零. 有效數字被以 四捨五入到最近值 的規則四捨五入到 u 個數字; 如果必要, n 會被調整成對應為有效數字的四捨五入量. 如果 flag2 是真則 r 是在實作自訂的浮點數目範圍. 如果 flag 為真, 則 r 為負數.

如果 BASE 之值不是十進位十時, 將會有模稜兩可的情況存在.

當 flag2 是假時, n 和 flag1 是實作自訂的, 如同 c-addr 的內容一樣. 在此情況下, 在 c-addr 的字串必須由書寫字元組成.

參閱: 3.2.1.2 數字轉換, 12.3.2 浮點操作, A.12.6.1.2143 REPRESENT


12.6.1.2143 REPRESENT

FLOATING

	( c-addr u -- n flag1 flag2 )  (F: r -- )  
	or ( r c-addr u -- n flag1 flag2 )

At c-addr, place the character-string external representation of the significand of the floating-point number r. Return the decimal-base exponent as n, the sign as flag1 and valid result as flag2. The character string shall consist of the u most significant digits of the significand represented as a decimal fraction with the implied decimal point to the left of the first digit, and the first digit zero only if all digits are zero. The significand is rounded to u digits following the round to nearest rule; n is adjusted, if necessary, to correspond to the rounded magnitude of the significand. If flag2 is true then r was in the implementation-defined range of floating-point numbers. If flag1 is true then r is negative.

An ambiguous condition exists if the value of BASE is not decimal ten.

When flag2 is false, n and flag1 are implementation defined, as are the contents of c-addr. Under these circumstances, the string at c-addr shall consist of graphic characters.

See: 3.2.1.2 Digit conversion, 12.3.2 Floating-point operations, A.12.6.1.2143 REPRESENT

12.6.2 浮點延伸詞(Floating-Point extension words)


12.6.2.1203 DF!

d-f-store FLOATING EXT

	( df-addr -- ) ( F: r -- ) 
	or ( r df-addr -- )

以一個 64 位元的 IEEE 雙精確浮點數字的方式將浮點數目 r 存入 df-addr. 如果內部表示法 r 的有效位數比 IEEE 雙精確格式有更多的精確度, 它將會被以 四捨五入到最近值 規則來四捨五入. 如果 r 的指數部分大於能以 IEEE 雙精確格式容納時, 將會有模稜兩可的情況存在.

參閱: 12.3.1.1 位址, 12.3.2 浮點運算.


12.6.2.1203 DF!

d-f-store FLOATING EXT

	( df-addr -- ) ( F: r -- ) 
	or ( r df-addr -- )

Store the floating-point number r as a 64-bit IEEE double-precision number at df-addr. If the significand of the internal representation of r has more precision than the IEEE double-precision format, it will be rounded using the round to nearest rule. An ambiguous condition exists if the exponent of r is too large to be accommodated in IEEE double-precision format.

See: 12.3.1.1 Addresses, 12.3.2 Floating-point operations.


12.6.2.1204 DF@

d-f-fetch FLOATING EXT

	( df-addr -- ) ( F: -- r ) 
	or ( df-addr -- r )

取得儲存於 df-addr 的一個 64 位元的 IEEE 雙精確浮點數字, 到浮點堆疊以內部表示法成為 r. 如果 IEEE 的雙精確有效數字比內部表示法有更多的精確度, 它將會被用 四捨五入到最接近 的規則來四捨五入成內部表示法. 如果 IEEE 的雙精確表示法的指數部分大於能以內部表示法容納時, 將會有模稜兩可的情況存在.

參閱: 12.3.1.1 位址, 12.3.2 浮點運算.


12.6.2.1204 DF@

d-f-fetch FLOATING EXT

	( df-addr -- ) ( F: -- r ) 
	or ( df-addr -- r )

Fetch the 64-bit IEEE double-precision number stored at df-addr to the floating-point stack as r in the internal representation. If the IEEE double-precision significand has more precision than the internal representation it will be rounded to the internal representation using the round to nearest rule. An ambiguous condition exists if the exponent of the IEEE double-precision representation is too large to be accommodated by the internal representation.

See: 12.3.1.1 Addresses, 12.3.2 Floating-point operations.


12.6.2.1205 DFALIGN

d-f-align FLOATING EXT

	( -- )

如果資料空間指標不是雙浮點對齊的, 保留足夠的空間, 讓它是.

參閱: 12.3.1.1 位址


12.6.2.1205 DFALIGN

d-f-align FLOATING EXT

	( -- )

If the data-space pointer is not double-float aligned, reserve enough data space to make it so.

See: 12.3.1.1 Addresses


12.6.2.1207 DFALIGNED

d-f-aligned FLOATING EXT

	( addr -- df-addr )

df-addr 是第一個大於或等於 addr 的雙浮點對齊的位址.

參閱: 12.3.1.1 位址


12.6.2.1207 DFALIGNED

d-f-aligned FLOATING EXT

	( addr -- df-addr )

df-addr is the first double-float-aligned address greater than or equal to addr.

See: 12.3.1.1 Addresses


12.6.2.1208 DFLOAT+

d-float-plus FLOATING EXT

	( df-addr1 -- df-addr2 )

將一個以位址單元為單位的 64 位元的 IEEE 雙精確浮點數字大小加進 df-addr1, 得到 df-addr2.

參閱: 12.3.1.1 位址


12.6.2.1208 DFLOAT+

d-float-plus FLOATING EXT

	( df-addr1 -- df-addr2 )

Add the size in address units of a 64-bit IEEE double-precision number to df-addr1, giving df-addr2.

See: 12.3.1.1 Addresses


2.6.2.1209 DFLOATS

d-floats FLOATING EXT

	( n1 -- n2 )

n2 是以位址單元為單位的 n1 個 64 位元的 IEEE 雙精確數目的大小.


2.6.2.1209 DFLOATS

d-floats FLOATING EXT

	( n1 -- n2 )

n2 is the size in address units of n1 64-bit IEEE double-precision numbers.


12.6.2.1415 F**

f-star-star FLOATING EXT

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

將 r1 增加指數 r2, 得到結果 r3.


12.6.2.1415 F**

f-star-star FLOATING EXT

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

Raise r1 to the power r2, giving the product r3.


12.6.2.1427 F.

f-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

用浮點表示法顯示有一個後緣空白的浮點堆疊最上方的數字:

	[-] <digits>.<digits0>

如果 BASE 的值不是 (十進位) 十或字元字串表現的大小超過書寫數字輸出字串緩衝區的大小, 將會出現模稜兩可的情況.

參閱: 12.6.1.0558 >FLOAT , A.12.6.1.1427 F.


12.6.2.1427 F.

f-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

Display, with a trailing space, the top number on the floating-point stack using fixed-point notation:

	[-] <digits>.<digits0>

An ambiguous condition exists if the value of BASE is not (decimal) ten or if the character string representation exceeds the size of the pictured numeric output string buffer.

See: 12.6.1.0558 >FLOAT , A.12.6.1.1427 F.


12.6.2.1474 FABS

f-abs FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是 r1 的絕對值.


12.6.2.1474 FABS

f-abs FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the absolute value of r1.


12.6.2.1476 FACOS

f-a-cos FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是餘弦是 r1 的首要弧度角度. 如果 |r1| 大於一時, 將會出現模稜兩可的情況.


12.6.2.1476 FACOS

f-a-cos FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the principal radian angle whose cosine is r1. An ambiguous condition exists if |r1| is greater than one.


12.6.2.1477 FACOSH

f-a-cosh FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是雙曲餘弦值是 r1 的浮點值. 如果 r1 小於一時, 將會出現模稜兩可的情況.


12.6.2.1477 FACOSH

f-a-cosh FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the floating-point value whose hyperbolic cosine is r1. An ambiguous condition exists if r1 is less than one.


12.6.2.1484 FALOG

f-a-log FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

將十提升指數 r1, 得到 r2.


12.6.2.1484 FALOG

f-a-log FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

Raise ten to the power r1, giving r2.


12.6.2.1486 FASIN

f-a-sine FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是正弦是 r1 的首要弧度角度. 如果 |r1| 大於一時, 將會出現模稜兩可的情況.


12.6.2.1486 FASIN

f-a-sine FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the principal radian angle whose sine is r1. An ambiguous condition exists if |r1| is greater than one.


12.6.2.1487 FASINH

f-a-cinch FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是雙曲正弦是 r1 的浮點值. 如果 r1 小於零時, 將會出現模稜兩可的情況.


12.6.2.1487 FASINH

f-a-cinch FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the floating-point value whose hyperbolic sine is r1. An ambiguous condition exists if r1 is less than zero.


12.6.2.1488 FATAN

f-a-tan FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是正切值是 r1 的首要弧度角度.


12.6.2.1488 FATAN

f-a-tan FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the principal radian angle whose tangent is r1.


12.6.2.1489 FATAN2

f-a-tan-two FLOATING EXT

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 是正切是 r1/r2 的首要弧度角度. 如果 r1 和 r2 是零時, 將會出現模稜兩可的情況.

參閱: A.12.6.2.1489 FATAN2


12.6.2.1489 FATAN2

f-a-tan-two FLOATING EXT

	( F: r1 r2 -- r3 ) 
	or ( r1 r2 -- r3 )

r3 is the radian angle whose tangent is r1/r2. An ambiguous condition exists if r1 and r2 are zero.

See: A.12.6.2.1489 FATAN2


12.6.2.1491 FATANH

f-a-tan-h FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是雙曲正切是 r1 的浮點值. 如果 r1 是在 -1E0 到 1E0 的範圍之外時, 將會有模稜兩可的情況存在.


12.6.2.1491 FATANH

f-a-tan-h FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the floating-point value whose hyperbolic tangent is r1. An ambiguous condition exists if r1 is outside the range of -1E0 to 1E0.


12.6.2.1493 FCOS

f-cos FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的餘弦值.


12.6.2.1493 FCOS

f-cos FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the cosine of the radian angle r1.


12.6.2.1494 FCOSH

f-cosh FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的雙曲餘弦值.


12.6.2.1494 FCOSH

f-cosh FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the hyperbolic cosine of r1.


12.6.2.1513 FE.

f-e-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

用工程表示法顯示有一個後緣空白的浮點堆疊最上方的數字, 它的有效數字是大於或等於 1.0 並且小於 1000.0 並且十進位指數值是三的乘數.

如果 BASE 的值不是 (十進位) 十或字元字串表現的大小超過書寫數字輸出字串緩衝區的大小, 將會出現模稜兩可的情況.

參閱: 12.3.2 浮點操作, 12.6.1.2143 REPRESENT


12.6.2.1513 FE.

f-e-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

Display, with a trailing space, the top number on the floating-point stack using engineering notation, where the significand is greater than or equal to 1.0 and less than 1000.0 and the decimal exponent is a multiple of three.

An ambiguous condition exists if the value of BASE is not (decimal) ten or if the character string representation exceeds the size of the pictured numeric output string buffer.

See: 12.3.2 Floating-point operations, 12.6.1.2143 REPRESENT


12.6.2.1515 FEXP

f-e-x-p FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

以指數 r1 提升 e, 得到 r2.


12.6.2.1515 FEXP

f-e-x-p FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

Raise e to the power r1, giving r2.


12.6.2.1516 FEXPM1

f-e-x-p-m-one FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

以指數 r1 提升 e, 並且減去一, 得到 r2.

參閱: A.12.6.2.1516 FEXPM1


12.6.2.1516 FEXPM1

f-e-x-p-m-one FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

Raise e to the power r1 and subtract one, giving r2.

See: A.12.6.2.1516 FEXPM1


12.6.2.1553 FLN

f-l-n FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是 r1 的自然對數. 如果 r1 是小於或等於零, 將會有一個模稜兩可的情況存在.


12.6.2.1553 FLN

f-l-n FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the natural logarithm of r1. An ambiguous condition exists if r1 is less than or equal to zero.


12.6.2.1554 FLNP1

f-l-n-p-one FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是量 r1 加一的自然對數. 如果 r1 小於或等於負一時, 將會有一個模稜兩可的情況存在.

參閱: A.12.6.2.1554 FLNP1


12.6.2.1554 FLNP1

f-l-n-p-one FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the natural logarithm of the quantity r1 plus one. An ambiguous condition exists if r1 is less than or equal to negative one.

See: A.12.6.2.1554 FLNP1


12.6.2.1557 FLOG

f-log FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是 r1 的十基底的對數. 如果 r1 小於或等於零時, 將會有一個模稜兩可的情況存在.


12.6.2.1557 FLOG

f-log FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the base-ten logarithm of r1. An ambiguous condition exists if r1 is less than or equal to zero.


12.6.2.1613 FS.

f-s-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

用科學表示法顯示有一個後緣空白的浮點堆疊最上方的數字:

	<significand><exponent>

而:

	<significand>  :=  [-]<digit>.<digits0>
	<exponent>     :=  E[-]<digits>

如果 BASE 的值不是 (十進位) 十或字元字串表現的大小超過書寫數字輸出字串緩衝區的大小, 將會出現模稜兩可的情況.

參閱: 12.3.2 浮點運算, 12.6.1.2143 REPRESENT


12.6.2.1613 FS.

f-s-dot FLOATING EXT

	( -- ) ( F: r -- ) 
	or ( r -- )

Display, with a trailing space, the top number on the floating-point stack in scientific notation:

	<significand><exponent>

where:

	<significand>  :=  [-]<digit>.<digits0>
	<exponent>     :=  E[-]<digits>

An ambiguous condition exists if the value of BASE is not (decimal) ten or if the character string representation exceeds the size of the pictured numeric output string buffer.

See: 12.3.2 Floating-point operations, 12.6.1.2143 REPRESENT


12.6.2.1614 FSIN

f-sine FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的正弦值.


12.6.2.1614 FSIN

f-sine FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the sine of the radian angle r1.


12.6.2.1616 FSINCOS

f-sine-cos FLOATING EXT

	( F: r1 -- r2 r3 ) 
	or ( r1 -- r2 r3 )

r2 是弧度角度 r1 的正弦值. r3 是弧度角度 r1 的餘弦值.

參閱: A.12.6.2.1489 FATAN2


12.6.2.1616 FSINCOS

f-sine-cos FLOATING EXT

	( F: r1 -- r2 r3 ) 
	or ( r1 -- r2 r3 )

r2 is the sine of the radian angle r1. r3 is the cosine of the radian angle r1.

See: A.12.6.2.1489 FATAN2


12.6.2.1617 FSINH

f-cinch FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的雙曲正弦值.


12.6.2.1617 FSINH

f-cinch FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the hyperbolic sine of r1.


12.6.2.1618 FSQRT

f-square-root FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是 r1 的平方根. 如果 r1 小於零, 將會有一個模稜兩可的情況存在.


12.6.2.1618 FSQRT

f-square-root FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the square root of r1. An ambiguous condition exists if r1 is less than zero.


12.6.2.1625 FTAN

f-tan FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的正切值. 如果 cos(r1) 是零, 將會有一個模稜兩可的情況存在.


12.6.2.1625 FTAN

f-tan FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the tangent of the radian angle r1. An ambiguous condition exists if cos(r1) is zero.


12.6.2.1626 FTANH

f-tan-h FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 是弧度角度 r1 的雙曲正切值.


12.6.2.1626 FTANH

f-tan-h FLOATING EXT

	( F: r1 -- r2 ) 
	or ( r1 -- r2 )

r2 is the hyperbolic tangent of r1.


12.6.2.1640 F~

f-近似值 FLOATING EXT
(

	( -- flag ) ( F: r1 r2 r3 -- ) 
	or ( r1 r2 r3 -- flag )

如果 r3 是正數, (r1 減 r2) 的絕對值小於 r3, flag 是真.

如果 r3 是零, 如果實作相依的 r1 和 r2 編碼完全相同, flag 為真. (如果正零和負零有不同的編碼, 它們是不相等的.)

如果 r3 是負數, 如果 (r1 減 r2) 的絕對值小於 r3 的絕對值乘以 r1 和 r2 的絕對值的總和, flag 是真.

參閱: A.12.6.2.1640 F~


12.6.2.1640 F~

f-proximate FLOATING EXT
(

	( -- flag ) ( F: r1 r2 r3 -- ) 
	or ( r1 r2 r3 -- flag )

If r3 is positive, flag is true if the absolute value of (r1 minus r2) is less than r3.

If r3 is zero, flag is true if the implementation-dependent encoding of r1 and r2 are exactly identical (positive and negative zero are unequal if they have distinct encodings).

If r3 is negative, flag is true if the absolute value of (r1 minus r2) is less than the absolute value of r3 times the sum of the absolute values of r1 and r2.

See: A.12.6.2.1640 F~


12.6.2.2035 PRECISION

FLOATING EXT

	( -- u )

傳回目前使用於 F., FE., 或 FS. 的有效數字數目為 u.


12.6.2.2035 PRECISION

FLOATING EXT

	( -- u )

Return the number of significant digits currently used by F., FE., or FS. as u.


12.6.2.2200 SET-PRECISION

FLOATING EXT

	( u -- )

設定目前使用於 F., FE., 或 FS. 的有效數字數目成 u.


12.6.2.2200 SET-PRECISION

FLOATING EXT

	( u -- )

Set the number of significant digits currently used by F., FE., or FS. to u.


12.6.2.2202 SF!

s-f-store FLOATING EXT

	( sf-addr -- ) ( F: r -- ) 
	or ( r sf-addr -- )

以一個 32 位元的 IEEE 單精確浮點數字的方式將浮點數目 r 存入 sf-addr. 如果內部表示法 r 的有效位數比 IEEE 單精確格式有更多的精確度, 它將會被以 四捨五入到最近值 規則來四捨五入. 如果 r 的指數部分大於能以 IEEE 單精確格式容納時, 將會有模稜兩可的情況存在.

參閱: 12.3.1.1 位址, 12.3.2 浮點運算.


12.6.2.2202 SF!

s-f-store FLOATING EXT

	( sf-addr -- ) ( F: r -- ) 
	or ( r sf-addr -- )

Store the floating-point number r as a 32-bit IEEE single-precision number at sf-addr. If the significand of the internal representation of r has more precision than the IEEE single-precision format, it will be rounded using the round to nearest rule. An ambiguous condition exists if the exponent of r is too large to be accommodated by the IEEE single-precision format.

See: 12.3.1.1 Addresses, 12.3.2 Floating-point operations.


12.6.2.2203 SF@

s-f-fetch FLOATING EXT

	( sf-addr -- ) ( F: -- r ) 
	or ( sf-addr -- r )

取得儲存於 sf-addr 的一個 32 位元的 IEEE 單精確浮點數字, 到浮點堆疊以內部表示法成為 r. 如果 IEEE 的單精確有效數字比內部表示法有更多的精確度, 它將會被用 四捨五入到最接近 的規則來四捨五入成內部表示法. 如果 IEEE 的單精確表示法的指數部分大於能以內部表示法容納時, 將會有模稜兩可的情況存在.

參閱: 12.3.1.1 位址, 12.3.2 浮點運算.


12.6.2.2203 SF@

s-f-fetch FLOATING EXT

	( sf-addr -- ) ( F: -- r ) 
	or ( sf-addr -- r )

Fetch the 32-bit IEEE single-precision number stored at sf-addr to the floating-point stack as r in the internal representation. If the IEEE single-precision significand has more precision than the internal representation, it will be rounded to the internal representation using the round to nearest rule. An ambiguous condition exists if the exponent of the IEEE single-precision representation is too large to be accommodated by the internal representation.

See: 12.3.1.1 Addresses, 12.3.2 Floating-point operations.


12.6.2.2204 SFALIGN

s-f-align FLOATING EXT

	( -- )

如果資料空間指標不是單浮點對齊的, 保留足夠的空間, 讓它是.

參閱: 12.3.1.1 位址


12.6.2.2204 SFALIGN

s-f-align FLOATING EXT

	( -- )

If the data-space pointer is not single-float aligned, reserve enough data space to make it so.

See: 12.3.1.1 Addresses


12.6.2.2206 SFALIGNED

s-f-aligned FLOATING EXT

	( addr -- sf-addr )

sf-addr 是第一個大於或等於 addr 的單浮點對齊的位址.

參閱: 12.3.1.1 位址


12.6.2.2206 SFALIGNED

s-f-aligned FLOATING EXT

	( addr -- sf-addr )

sf-addr is the first single-float-aligned address greater than or equal to addr.

See: 12.3.1.1 Addresses


12.6.2.2207 SFLOAT+

s-float-plus FLOATING EXT

	( sf-addr1 -- sf-addr2 )

將一個以位址單元為單位的 32 位元的 IEEE 單精確浮點數字大小加進 sf-addr1, 得到 sf-addr2.

參閱: 12.3.1.1 位址


12.6.2.2207 SFLOAT+

s-float-plus FLOATING EXT

	( sf-addr1 -- sf-addr2 )

Add the size in address units of a 32-bit IEEE single-precision number to sf-addr1, giving sf-addr2.

See: 12.3.1.1 Addresses


12.6.2.2208 SFLOATS

s-floats FLOATING EXT

	( n1 -- n2 )

n2 是以位址單元為單位的 n1 個 32 位元的 IEEE 單精確數目的大小.

參閱: 12.3.1.1 位址


12.6.2.2208 SFLOATS

s-floats FLOATING EXT

	( n1 -- n2 )

n2 is the size in address units of n1 32-bit IEEE single-precision numbers.

See: 12.3.1.1 Addresses

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