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
83 expression with a single rounding, using either hardware instructions
84 (providing full IEEE compliance) or a software emulation. Note: since
85 software emulation of the fma is costly, make sure that you are using
86 hardware fma support if performance matters.
87 Since 4.08.0
90 val rem : float -> float -> float
94 rem a b returns the remainder of a with respect to b . The returned
97 value is a -. n *. b , where n is the quotient a /. b rounded towards
98 zero to an integer.
99 val succ : float -> float
103 succ x returns the floating point number right after x i.e., the small‐
106 est floating-point number greater than x . See also Float.next_after .
107 Since 4.08.0
110 val pred : float -> float
114 pred x returns the floating-point number right before x i.e., the
117 greatest floating-point number smaller than x . See also
118 Float.next_after .
119 Since 4.08.0
122 val abs : float -> float
126 abs f returns the absolute value of f .
129 val infinity : float
133 Positive infinity.
135 val neg_infinity : float
139 Negative infinity.
141 val nan : float
145 A special floating-point value denoting the result of an undefined
147 operation such as 0.0 /. 0.0 . Stands for 'not a number'. Any float‐
148 ing-point operation with nan as argument returns nan as result. As for
149 floating-point comparisons, = , < , <= , > and >= return false and <>
150 returns true if one or both of their arguments is nan .
151 val pi : float
155 The constant pi.
157 val max_float : float
161 The largest positive finite value of type float .
163 val min_float : float
167 The smallest positive, non-zero, non-denormalized value of type float .
169 val epsilon : float
173 The difference between 1.0 and the smallest exactly representable
175 floating-point number greater than 1.0 .
176 val is_finite : float -> bool
180 is_finite x is true iff x is finite i.e., not infinite and not
183 Float.nan .
184 Since 4.08.0
187 val is_infinite : float -> bool
191 is_infinite x is true iff x is Float.infinity or Float.neg_infinity .
194 Since 4.08.0
197 val is_nan : float -> bool
201 is_nan x is true iff x is not a number (see Float.nan ).
204 Since 4.08.0
207 val is_integer : float -> bool
211 is_integer x is true iff x is an integer.
214 Since 4.08.0
217 val of_int : int -> float
221 Convert an integer to floating-point.
223 val to_int : float -> int
227 Truncate the given floating-point number to an integer. The result is
229 unspecified if the argument is nan or falls outside the range of repre‐
230 sentable integers.
231 val of_string : string -> float
235 Convert the given string to a float. The string is read in decimal (by
237 default) or in hexadecimal (marked by 0x or 0X ). The format of deci‐
238 mal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d
239 stands for a decimal digit. The format of hexadecimal floating-point
240 numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an
241 hexadecimal digit and d for a decimal digit. In both cases, at least
242 one of the integer and fractional parts must be given; the exponent
243 part is optional. The _ (underscore) character can appear anywhere in
244 the string and is ignored. Depending on the execution platforms, other
245 representations of floating-point numbers can be accepted, but should
246 not be relied upon. Raise Failure float_of_string if the given string
247 is not a valid representation of a float.
248 val of_string_opt : string -> float option
252 Same as of_string , but returns None instead of raising.
254 val to_string : float -> string
258 Return the string representation of a floating-point number.
260 type fpclass = fpclass =
263 | FP_normal (* Normal number, none of the below
264 *)
265 | FP_subnormal (* Number very close to 0.0, has reduced precision
266 *)
267 | FP_zero (* Number is 0.0 or -0.0
268 *)
269 | FP_infinite (* Number is positive or negative infinity
270 *)
271 | FP_nan (* Not a number: result of an undefined operation
272 *)
273 The five classes of floating-point numbers, as determined by the
276 Float.classify_float function.
277 val classify_float : float -> fpclass
281 Return the class of the given floating-point number: normal, subnormal,
283 zero, infinite, or not a number.
284 val pow : float -> float -> float
288 Exponentiation.
290 val sqrt : float -> float
294 Square root.
296 val exp : float -> float
300 Exponential.
302 val log : float -> float
306 Natural logarithm.
308 val log10 : float -> float
312 Base 10 logarithm.
314 val expm1 : float -> float
318 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
321 even if x is close to 0.0 .
322 val log1p : float -> float
326 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
329 cally-accurate results even if x is close to 0.0 .
330 val cos : float -> float
334 Cosine. Argument is in radians.
336 val sin : float -> float
340 Sine. Argument is in radians.
342 val tan : float -> float
346 Tangent. Argument is in radians.
348 val acos : float -> float
352 Arc cosine. The argument must fall within the range [-1.0, 1.0] .
354 Result is in radians and is between 0.0 and pi .
355 val asin : float -> float
359 Arc sine. The argument must fall within the range [-1.0, 1.0] .
361 Result is in radians and is between -pi/2 and pi/2 .
362 val atan : float -> float
366 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
368 val atan2 : float -> float -> float
372 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
375 used to determine the quadrant of the result. Result is in radians and
376 is between -pi and pi .
377 val hypot : float -> float -> float
381 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
384 hypotenuse of a right-angled triangle with sides of length x and y ,
385 or, equivalently, the distance of the point (x,y) to origin. If one of
386 x or y is infinite, returns infinity even if the other is nan .
387 val cosh : float -> float
391 Hyperbolic cosine. Argument is in radians.
393 val sinh : float -> float
397 Hyperbolic sine. Argument is in radians.
399 val tanh : float -> float
403 Hyperbolic tangent. Argument is in radians.
405 val trunc : float -> float
409 trunc x rounds x to the nearest integer whose absolute value is less
412 than or equal to x .
413 Since 4.08.0
416 val round : float -> float
420 round x rounds x to the nearest integer with ties (fractional values of
423 0.5) rounded away from zero, regardless of the current rounding direc‐
424 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
425 returned.
426 Since 4.08.0
429 val ceil : float -> float
433 Round above to an integer value. ceil f returns the least integer
435 value greater than or equal to f . The result is returned as a float.
436 val floor : float -> float
440 Round below to an integer value. floor f returns the greatest integer
442 value less than or equal to f . The result is returned as a float.
443 val next_after : float -> float -> float
447 next_after x y returns the next representable floating-point value fol‐
450 lowing x in the direction of y . More precisely, if y is greater
451 (resp. less) than x , it returns the smallest (resp. largest) repre‐
452 sentable number greater (resp. less) than x . If x equals y , the
453 function returns y . If x or y is nan , a nan is returned. Note that
454 next_after max_float infinity = infinity and that next_after 0. infin‐
455 ity is the smallest denormalized positive number. If x is the smallest
456 denormalized positive number, next_after x 0. = 0.
457 Since 4.08.0
461 val copy_sign : float -> float -> float
465 copy_sign x y returns a float whose absolute value is that of x and
468 whose sign is that of y . If x is nan , returns nan . If y is nan ,
469 returns either x or -. x , but it is not specified which.
470 val sign_bit : float -> bool
474 sign_bit x is true iff the sign bit of x is set. For example sign_bit
477 1. and signbit 0. are false while sign_bit (-1.) and sign_bit (-0.)
478 are true .
479 Since 4.08.0
482 val frexp : float -> float * int
486 frexp f returns the pair of the significant and the exponent of f .
489 When f is zero, the significant x and the exponent n of f are equal to
490 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
491 <= x < 1.0 .
492 val ldexp : float -> int -> float
496 ldexp x n returns x *. 2 ** n .
499 val modf : float -> float * float
503 modf f returns the pair of the fractional and integral part of f .
506 type t = float
509 An alias for the type of floating-point numbers.
512 val compare : t -> t -> int
516 compare x y returns 0 if x is equal to y , a negative integer if x is
519 less than y , and a positive integer if x is greater than y . compare
520 treats nan as equal to itself and less than any other float value.
521 This treatment of nan ensures that compare defines a total ordering
522 relation.
523 val equal : t -> t -> bool
527 The equal function for floating-point numbers, compared using
529 Float.compare .
530 val min : t -> t -> t
534 min x y returns the minimum of x and y . It returns nan when x or y is
537 nan . Moreover min (-0.) (+0.) = -0.
538 Since 4.08.0
542 val max : float -> float -> float
546 max x y returns the maximum of x and y . It returns nan when x or y is
549 nan . Moreover max (-0.) (+0.) = +0.
550 Since 4.08.0
554 val min_max : float -> float -> float * float
558 min_max x y is (min x y, max x y) , just more efficient.
561 Since 4.08.0
564 val min_num : t -> t -> t
568 min_num x y returns the minimum of x and y treating nan as missing val‐
571 ues. If both x and y are nan , nan is returned. Moreover min_num
572 (-0.) (+0.) = -0.
573 Since 4.08.0
577 val max_num : t -> t -> t
581 max_num x y returns the maximum of x and y treating nan as missing val‐
584 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
585 (+0.) = +0.
586 Since 4.08.0
590 val min_max_num : float -> float -> float * float
594 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
597 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
598 y = (y, y) .
599 Since 4.08.0
602 val hash : t -> int
606 The hash function for floating-point numbers.
608 module Array : sig end
611 module ArrayLabels : sig end
616OCamldoc 2019-07-30 Stdlib.Float(3)