emacs/lisp/float.elc

(provide (quote float))

(defconst exp-base 2 "\
Base of exponent in this floating point representation.")

(defconst mantissa-bits 24 "\
Number of significant bits in this floating point representation.")

(defconst decimal-digits 6 "\
Number of decimal digits expected to be accurate.")

(defconst expt-digits 2 "\
Maximum permitted digits in a scientific notation exponent.")

(defconst maxbit (1- mantissa-bits) "\
Number of highest bit")

(defconst mantissa-maxval (1- (ash 1 maxbit)) "\
Maximum permissable value of mantissa")

(defconst mantissa-minval (1- (ash 1 maxbit)) "\
Minimum permissable value of mantissa")

(defconst mantissa-half-minval (ash (ash 1 maxbit) -1))

(defconst floating-point-regexp "^[ 	]*\\(-?\\)\\([0-9]*\\)\\(\\.\\([0-9]*\\)\\|\\)\\(\\(\\([Ee]\\)\\(-?\\)\\([0-9][0-9]*\\)\\)\\|\\)[ 	]*$" "\
Regular expression to match floating point numbers.  Extract matches:
1 - minus sign
2 - integer part
4 - fractional part
8 - minus sign for power of ten
9 - power of ten
")

(defconst high-bit-mask (ash 1 maxbit) "\
Masks all bits except the high-order (sign) bit.")

(defconst second-bit-mask (ash 1 (1- maxbit)) "\
Masks all bits except the highest-order magnitude bit")

(setq _f0 (quote (0 . 1)))

(setq _f1/2 (quote (4194304 . -23)))

(setq _f1 (quote (4194304 . -22)))

(setq _f10 (quote (5242880 . -19)))

(setq powers-of-10 (make-vector (1+ decimal-digits) _f1))

(aset powers-of-10 1 _f10)

(aset powers-of-10 2 (quote (6553600 . -16)))

(aset powers-of-10 3 (quote (8192000 . -13)))

(aset powers-of-10 4 (quote (5120000 . -9)))

(aset powers-of-10 5 (quote (6400000 . -6)))

(aset powers-of-10 6 (quote (8000000 . -3)))

(setq all-decimal-digs-minval (aref powers-of-10 (1- decimal-digits)) highest-power-of-10 (aref powers-of-10 decimal-digits))

(defun fashl (fnum) (byte-code "Á@Â\"ASB‡" [fnum ash 1] 3))

(defun fashr (fnum) (byte-code "Á@Â\"ATB‡" [fnum ash -1] 3))

(defun normalize (fnum) (byte-code "@ÄVƒÅÆ@	\"!…Ç!‰ˆ‚‚:@ÄWƒ7@
V…4Ç!‰ˆ‚$‚:‰ˆ‡" [fnum second-bit-mask mantissa-half-minval _f0 0 zerop logand fashl] 7))

(defun abs (n) (byte-code "Á!ƒ
‚[‡" [n natnump] 2))

(defun fabs (fnum) (byte-code "ÁÂ@!AB!‡" [fnum normalize abs] 4))

(defun xor (a b) (byte-code "†	……
	?‡" [a b] 1))

(defun same-sign (a b) (byte-code "ÂÃ@!Ã	@!\"?‡" [a b xor natnump] 5))

(defun extract-match (str i) (byte-code "ÀÁÂ<C381>‡" [nil (byte-code "Â	!Ã	!O‡" [str i match-beginning match-end] 5) ((error (byte-code "À‡" [""] 1)))] 3))

(setq halfword-bits (/ mantissa-bits 2) masklo (1- (ash 1 halfword-bits)) maskhi (lognot masklo) round-limit (ash 1 (/ halfword-bits 2)))

(defun hihalf (n) (byte-code "ÃÄ	\"
[\"‡" [n maskhi halfword-bits ash logand] 4))

(defun lohalf (n) (byte-code "Â	\"‡" [n masklo logand] 3))

(defun f+ (a1 a2) "\
Returns the sum of two floating point numbers." (byte-code "	A
AVƒ	‚

	A
AVƒ
‚	Ä	
\"…,Å!Å!‰ˆÆ@Ç@AAZ\"\\AB!*‡" [f1 a1 a2 f2 same-sign fashr normalize ash] 9))

(defun f- (a1 &optional a2) "\
Returns the difference of two floating point numbers." (byte-code "ƒ
Â	Ã!\"‚Ä	@[	AB!‡" [a2 a1 f+ f- normalize] 5))

(defun f* (a1 a2) "\
Returns the product of two floating point numbers." (byte-code "É	!@É!@Ê	\"?ËÌÍÎ!Î
!\"!ÎÍÌ!Î
!\"!ÎÍÎ!Ì
!\"!#ËÍÌ!Ì
!\"ÌÍÌ!Î
!\"!ÌÍÎ!Ì
!\"!Ì
!$Î
!V…cT‰ˆÏƒo[‚qËÉ	!AÉ!A#B!-‡" [i1 a1 i2 a2 sign prodlo prodhi round-limit mantissa-bits fabs same-sign + hihalf * lohalf normalize] 38))

(defun f/ (a1 a2) "\
Returns the quotient of two floating point numbers." (byte-code "È@!ƒÉÊË	E\"‚vSÌÍ	!@Í!@Î	\"?Ï
!…Z
ZÌWƒ@ÐÑ\"‰‚LÐÑ\"T
Z‰ˆÐ
Ñ\"
S‰ˆ‚(ˆÒƒf[‚gÓÍ	!AÍ!AS#B!-‡" [a2 a1 bits maxbit quotient dividend divisor sign zerop signal arith-error "attempt to divide by zero" 0 fabs same-sign natnump ash 1 normalize -] 17))

(defun f% (a1 a2) "\
Returns the remainder of first floating point number divided by second." (byte-code "ÂÃÄÅ	\"!	\"\"‡" [a1 a2 f- f* ftrunc f/] 7))

(defun f= (a1 a2) "\
Returns t if two floating point numbers are equal, nil otherwise." (byte-code "Â	\"‡" [a1 a2 equal] 3))

(defun f> (a1 a2) "\
Returns t if first floating point number is greater than second,
nil otherwise." (byte-code "Ä@!…	@ÅWƒ‚L@ÅV…	@ÅXƒ$‚L@ÅX…/Ä	@!ƒ6ÂLÆA	A\"ƒGA	AV‚L@	@V‡" [a1 a2 t nil natnump 0 /=] 5))

(defun f>= (a1 a2) "\
Returns t if first floating point number is greater than or equal to 
second, nil otherwise." (byte-code "Â	\"†Ã	\"‡" [a1 a2 f> f=] 4))

(defun f< (a1 a2) "\
Returns t if first floating point number is less than second,
nil otherwise." (byte-code "Â	\"?‡" [a1 a2 f>=] 3))

(defun f<= (a1 a2) "\
Returns t if first floating point number is less than or equal to
second, nil otherwise." (byte-code "Â	\"?‡" [a1 a2 f>] 3))

(defun f/= (a1 a2) "\
Returns t if first floating point number is not equal to second,
nil otherwise." (byte-code "Â	\"?‡" [a1 a2 f=] 3))

(defun fmin (a1 a2) "\
Returns the minimum of two floating point numbers." (byte-code "Â	\"ƒ‚	‡" [a1 a2 f<] 3))

(defun fmax (a1 a2) "\
Returns the maximum of two floating point numbers." (byte-code "Â	\"ƒ‚	‡" [a1 a2 f>] 3))

(defun fzerop (fnum) "\
Returns t if the floating point number is zero, nil otherwise." (byte-code "@ÁU‡" [fnum 0] 2))

(defun floatp (fnum) "\
Returns t if the arg is a floating point number, nil otherwise." (byte-code ":…Á@!…ÁA!‡" [fnum integerp] 3))

(defun f (int) "\
Convert the integer argument to floating point, like a C cast operator." (byte-code "ÁÂB!‡" [int normalize 0] 3))

(defun int-to-hex-string (int) "\
Convert the integer argument to a C-style hexadecimal string." (byte-code "ÄÅÆÇX…#	È
ÉÊ\"Ë\"H!PÌ\\‰ˆ‚ˆ	+‡" [shiftval str hex-chars int -20 "0x" "0123456789ABCDEF" 0 char-to-string logand lsh 15 4] 8))

(defun ftrunc (fnum) "\
Truncate the fractional part of a floating point number." (byte-code "ÅA!ƒ‚=A	[XƒÆ‚=@AÇÅ!ƒ/ÈÈ\"[\"‚9ÈÈ[\"[\"[B!*‡" [fnum maxbit t mant exp natnump (0 . 1) normalize ash] 9))

(defun fint (fnum) "\
Convert the floating point number to integer, with truncation, 
like a C cast operator." (byte-code "È	!@AYƒ
‚$[Xƒ ‚$É
\"+‡" [tf fnum tint texp mantissa-bits mantissa-maxval mantissa-minval t ftrunc ash] 4))

(defun float-to-string (fnum &optional sci) "\
Convert the floating point number to a decimal string.
Optional second argument non-nil means use scientific notation." (byte-code "Ó	!	@ÔWÔÔÕÔÖ		\"ƒ\"ׂe
Ø\"ƒfÙÚ
\"‰\"…G\\‰ˆ‚*ˆÙÚ\"‰\"…cT‰ˆ‚H‚œÛÜ
\"‰\"…ƒZ‰ˆ‚fˆÛ\"…œÜ\"S‰ˆ‚„ˆÚÜ\"
\"Ý!‰ˆÞÛß\"\"ƒÅà!T‰‚Ëà!‰ˆá!‰ˆâY…ÞT‰)ˆƒùã
ÔäOå
äÞOæá!%‰‚Y
SYƒ 
Zç!…

×PS‰ˆ‚
)‚Y
ÔWƒK
[èZç!…A
×
PS‰ˆ‚,
ˆé
P‰)‚Y

ÔTOå
TÞOQ‰ˆ
ƒd
ê
P‚e

.‡" [value fnum sign power result str temp pow10 _f1 _f0 highest-power-of-10 decimal-digits _f10 all-decimal-digs-minval int _f1/2 sci zeroes t fabs 0 "" f= "0" f>= f<= f* f> f/ ftrunc nil f- fint int-to-string 1000000 concat 1 "." "E" natnump 2 "0." "-"] 28))

(defun string-to-float (str) "\
Convert the string to a floating point number.
Accepts a decimal string in scientific notation, 
with exponent preceded by either E or e.
Only the 6 most significant digits of the integer and fractional parts
are used; only the first two digits of the exponent are used.
Negative signs preceding both the decimal number and the exponent
are recognized." (byte-code "×	Ø#ƒ)
ÉÙÚ	Û\"Ú	Ü\"PÝÚ	Þ\"ß\"ØÉG
Z‰ˆ
GW…>
HàU…KT‰ˆ‚0ˆ
Z
ÉO‰ˆ
G
Vƒs

HáY
Ø
O‰‚|


GZ\\‰ˆâãä
!ƒ‹Þ‚ŒØ\\ƒ–å‚—Þ\"!.Ú	æ\"ÝÚ	ç\"ß\"Ø
ØØÙãäØG^O!ƒÐå‚ÑÞ\"
\\‰
ˆ
ØW…è
[
艈é

\"ê

\"‰ˆØV…
ë#S‰ˆ‚ûˆëH#.\")‚+
‡" [floating-point-regexp str power int-subst fract-subst digit-string mant-sign leading-0s round-up nil decimal-digits expt-subst expt-sign expt chunks tens exponent _f1 func expt-digits highest-power-of-10 powers-of-10 _f0 string-match 0 f* extract-match 2 4 equal 1 "-" 48 53 f * string-to-int -1 9 8 f/ / % funcall] 23))