1Stdlib.Float(3) OCaml library Stdlib.Float(3)
2
6 Stdlib.Float - no description
7
9 Module Stdlib.Float
10
12 Module Float
13 : (module Stdlib__Float)
14 val zero : float
23 The floating point 0.
25 Since 4.08.0
28 val one : float
32 The floating-point 1.
34 Since 4.08.0
37 val minus_one : float
41 The floating-point -1.
43 Since 4.08.0
46 val neg : float -> float
50 Unary negation.
52 val add : float -> float -> float
56 Floating-point addition.
58 val sub : float -> float -> float
62 Floating-point subtraction.
64 val mul : float -> float -> float
68 Floating-point multiplication.
70 val div : float -> float -> float
74 Floating-point division.
76 val fma : float -> float -> float -> float
80 fma x y z returns x * y + z , with a best effort for computing this ex‐
83 pression with a single rounding, using either hardware instructions
84 (providing full IEEE compliance) or a software emulation.
85 On 64-bit Cygwin, 64-bit mingw-w64 and MSVC 2017 and earlier, this
87 function may be emulated owing to known bugs on limitations on these
88 platforms. Note: since software emulation of the fma is costly, make
89 sure that you are using hardware fma support if performance matters.
90 Since 4.08.0
93 val rem : float -> float -> float
97 rem a b returns the remainder of a with respect to b . The returned
100 value is a -. n *. b , where n is the quotient a /. b rounded towards
101 zero to an integer.
102 val succ : float -> float
106 succ x returns the floating point number right after x i.e., the small‐
109 est floating-point number greater than x . See also Float.next_after .
110 Since 4.08.0
113 val pred : float -> float
117 pred x returns the floating-point number right before x i.e., the
120 greatest floating-point number smaller than x . See also
121 Float.next_after .
122 Since 4.08.0
125 val abs : float -> float
129 abs f returns the absolute value of f .
132 val infinity : float
136 Positive infinity.
138 val neg_infinity : float
142 Negative infinity.
144 val nan : float
148 A special floating-point value denoting the result of an undefined op‐
150 eration such as 0.0 /. 0.0 . Stands for 'not a number'. Any float‐
151 ing-point operation with nan as argument returns nan as result. As for
152 floating-point comparisons, = , < , <= , > and >= return false and <>
153 returns true if one or both of their arguments is nan .
154 val pi : float
158 The constant pi.
160 val max_float : float
164 The largest positive finite value of type float .
166 val min_float : float
170 The smallest positive, non-zero, non-denormalized value of type float .
172 val epsilon : float
176 The difference between 1.0 and the smallest exactly representable
178 floating-point number greater than 1.0 .
179 val is_finite : float -> bool
183 is_finite x is true if and only if x is finite i.e., not infinite and
186 not Float.nan .
187 Since 4.08.0
190 val is_infinite : float -> bool
194 is_infinite x is true if and only if x is Float.infinity or
197 Float.neg_infinity .
198 Since 4.08.0
201 val is_nan : float -> bool
205 is_nan x is true if and only if x is not a number (see Float.nan ).
208 Since 4.08.0
211 val is_integer : float -> bool
215 is_integer x is true if and only if x is an integer.
218 Since 4.08.0
221 val of_int : int -> float
225 Convert an integer to floating-point.
227 val to_int : float -> int
231 Truncate the given floating-point number to an integer. The result is
233 unspecified if the argument is nan or falls outside the range of repre‐
234 sentable integers.
235 val of_string : string -> float
239 Convert the given string to a float. The string is read in decimal (by
241 default) or in hexadecimal (marked by 0x or 0X ). The format of deci‐
242 mal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d
243 stands for a decimal digit. The format of hexadecimal floating-point
244 numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an
245 hexadecimal digit and d for a decimal digit. In both cases, at least
246 one of the integer and fractional parts must be given; the exponent
247 part is optional. The _ (underscore) character can appear anywhere in
248 the string and is ignored. Depending on the execution platforms, other
249 representations of floating-point numbers can be accepted, but should
250 not be relied upon.
251 Raises Failure if the given string is not a valid representation of a
254 float.
255 val of_string_opt : string -> float option
259 Same as of_string , but returns None instead of raising.
261 val to_string : float -> string
265 Return a string representation of a floating-point number.
267 This conversion can involve a loss of precision. For greater control
269 over the manner in which the number is printed, see Printf .
270 This function is an alias for string_of_float .
272 type fpclass = fpclass =
275 | FP_normal (* Normal number, none of the below
276 *)
277 | FP_subnormal (* Number very close to 0.0, has reduced precision
278 *)
279 | FP_zero (* Number is 0.0 or -0.0
280 *)
281 | FP_infinite (* Number is positive or negative infinity
282 *)
283 | FP_nan (* Not a number: result of an undefined operation
284 *)
285 The five classes of floating-point numbers, as determined by the
288 Float.classify_float function.
289 val classify_float : float -> fpclass
293 Return the class of the given floating-point number: normal, subnormal,
295 zero, infinite, or not a number.
296 val pow : float -> float -> float
300 Exponentiation.
302 val sqrt : float -> float
306 Square root.
308 val cbrt : float -> float
312 Cube root.
314 Since 4.13.0
317 val exp : float -> float
321 Exponential.
323 val exp2 : float -> float
327 Base 2 exponential function.
329 Since 4.13.0
332 val log : float -> float
336 Natural logarithm.
338 val log10 : float -> float
342 Base 10 logarithm.
344 val log2 : float -> float
348 Base 2 logarithm.
350 Since 4.13.0
353 val expm1 : float -> float
357 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
360 even if x is close to 0.0 .
361 val log1p : float -> float
365 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
368 cally-accurate results even if x is close to 0.0 .
369 val cos : float -> float
373 Cosine. Argument is in radians.
375 val sin : float -> float
379 Sine. Argument is in radians.
381 val tan : float -> float
385 Tangent. Argument is in radians.
387 val acos : float -> float
391 Arc cosine. The argument must fall within the range [-1.0, 1.0] . Re‐
393 sult is in radians and is between 0.0 and pi .
394 val asin : float -> float
398 Arc sine. The argument must fall within the range [-1.0, 1.0] . Re‐
400 sult is in radians and is between -pi/2 and pi/2 .
401 val atan : float -> float
405 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
407 val atan2 : float -> float -> float
411 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
414 used to determine the quadrant of the result. Result is in radians and
415 is between -pi and pi .
416 val hypot : float -> float -> float
420 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
423 hypotenuse of a right-angled triangle with sides of length x and y ,
424 or, equivalently, the distance of the point (x,y) to origin. If one of
425 x or y is infinite, returns infinity even if the other is nan .
426 val cosh : float -> float
430 Hyperbolic cosine. Argument is in radians.
432 val sinh : float -> float
436 Hyperbolic sine. Argument is in radians.
438 val tanh : float -> float
442 Hyperbolic tangent. Argument is in radians.
444 val acosh : float -> float
448 Hyperbolic arc cosine. The argument must fall within the range [1.0,
450 inf] . Result is in radians and is between 0.0 and inf .
451 Since 4.13.0
454 val asinh : float -> float
458 Hyperbolic arc sine. The argument and result range over the entire
460 real line. Result is in radians.
461 Since 4.13.0
464 val atanh : float -> float
468 Hyperbolic arc tangent. The argument must fall within the range [-1.0,
470 1.0] . Result is in radians and ranges over the entire real line.
471 Since 4.13.0
474 val erf : float -> float
478 Error function. The argument ranges over the entire real line. The
480 result is always within [-1.0, 1.0] .
481 Since 4.13.0
484 val erfc : float -> float
488 Complementary error function ( erfc x = 1 - erf x ). The argument
490 ranges over the entire real line. The result is always within [-1.0,
491 1.0] .
492 Since 4.13.0
495 val trunc : float -> float
499 trunc x rounds x to the nearest integer whose absolute value is less
502 than or equal to x .
503 Since 4.08.0
506 val round : float -> float
510 round x rounds x to the nearest integer with ties (fractional values of
513 0.5) rounded away from zero, regardless of the current rounding direc‐
514 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
515 returned.
516 On 64-bit mingw-w64, this function may be emulated owing to a bug in
518 the C runtime library (CRT) on this platform.
519 Since 4.08.0
522 val ceil : float -> float
526 Round above to an integer value. ceil f returns the least integer
528 value greater than or equal to f . The result is returned as a float.
529 val floor : float -> float
533 Round below to an integer value. floor f returns the greatest integer
535 value less than or equal to f . The result is returned as a float.
536 val next_after : float -> float -> float
540 next_after x y returns the next representable floating-point value fol‐
543 lowing x in the direction of y . More precisely, if y is greater
544 (resp. less) than x , it returns the smallest (resp. largest) repre‐
545 sentable number greater (resp. less) than x . If x equals y , the
546 function returns y . If x or y is nan , a nan is returned. Note that
547 next_after max_float infinity = infinity and that next_after 0. infin‐
548 ity is the smallest denormalized positive number. If x is the smallest
549 denormalized positive number, next_after x 0. = 0.
550 Since 4.08.0
554 val copy_sign : float -> float -> float
558 copy_sign x y returns a float whose absolute value is that of x and
561 whose sign is that of y . If x is nan , returns nan . If y is nan ,
562 returns either x or -. x , but it is not specified which.
563 val sign_bit : float -> bool
567 sign_bit x is true if and only if the sign bit of x is set. For exam‐
570 ple sign_bit 1. and signbit 0. are false while sign_bit (-1.) and
571 sign_bit (-0.) are true .
572 Since 4.08.0
575 val frexp : float -> float * int
579 frexp f returns the pair of the significant and the exponent of f .
582 When f is zero, the significant x and the exponent n of f are equal to
583 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
584 <= x < 1.0 .
585 val ldexp : float -> int -> float
589 ldexp x n returns x *. 2 ** n .
592 val modf : float -> float * float
596 modf f returns the pair of the fractional and integral part of f .
599 type t = float
602 An alias for the type of floating-point numbers.
605 val compare : t -> t -> int
609 compare x y returns 0 if x is equal to y , a negative integer if x is
612 less than y , and a positive integer if x is greater than y . compare
613 treats nan as equal to itself and less than any other float value.
614 This treatment of nan ensures that compare defines a total ordering re‐
615 lation.
616 val equal : t -> t -> bool
620 The equal function for floating-point numbers, compared using
622 Float.compare .
623 val min : t -> t -> t
627 min x y returns the minimum of x and y . It returns nan when x or y is
630 nan . Moreover min (-0.) (+0.) = -0.
631 Since 4.08.0
635 val max : float -> float -> float
639 max x y returns the maximum of x and y . It returns nan when x or y is
642 nan . Moreover max (-0.) (+0.) = +0.
643 Since 4.08.0
647 val min_max : float -> float -> float * float
651 min_max x y is (min x y, max x y) , just more efficient.
654 Since 4.08.0
657 val min_num : t -> t -> t
661 min_num x y returns the minimum of x and y treating nan as missing val‐
664 ues. If both x and y are nan , nan is returned. Moreover min_num
665 (-0.) (+0.) = -0.
666 Since 4.08.0
670 val max_num : t -> t -> t
674 max_num x y returns the maximum of x and y treating nan as missing val‐
677 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
678 (+0.) = +0.
679 Since 4.08.0
683 val min_max_num : float -> float -> float * float
687 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
690 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
691 y = (y, y) .
692 Since 4.08.0
695 val hash : t -> int
699 The hash function for floating-point numbers.
701 module Array : sig end
704 Float arrays with packed representation.
707 module ArrayLabels : sig end
710 Float arrays with packed representation (labeled functions).
713OCamldoc 2023-01-23 Stdlib.Float(3)