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. 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 op‐
147 eration 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 if and only if x is finite i.e., not infinite and
183 not Float.nan .
184 Since 4.08.0
187 val is_infinite : float -> bool
191 is_infinite x is true if and only if x is Float.infinity or
194 Float.neg_infinity .
195 Since 4.08.0
198 val is_nan : float -> bool
202 is_nan x is true if and only if x is not a number (see Float.nan ).
205 Since 4.08.0
208 val is_integer : float -> bool
212 is_integer x is true if and only if x is an integer.
215 Since 4.08.0
218 val of_int : int -> float
222 Convert an integer to floating-point.
224 val to_int : float -> int
228 Truncate the given floating-point number to an integer. The result is
230 unspecified if the argument is nan or falls outside the range of repre‐
231 sentable integers.
232 val of_string : string -> float
236 Convert the given string to a float. The string is read in decimal (by
238 default) or in hexadecimal (marked by 0x or 0X ). The format of deci‐
239 mal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d
240 stands for a decimal digit. The format of hexadecimal floating-point
241 numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an
242 hexadecimal digit and d for a decimal digit. In both cases, at least
243 one of the integer and fractional parts must be given; the exponent
244 part is optional. The _ (underscore) character can appear anywhere in
245 the string and is ignored. Depending on the execution platforms, other
246 representations of floating-point numbers can be accepted, but should
247 not be relied upon.
248 Raises Failure if the given string is not a valid representation of a
251 float.
252 val of_string_opt : string -> float option
256 Same as of_string , but returns None instead of raising.
258 val to_string : float -> string
262 Return the string representation of a floating-point number.
264 type fpclass = fpclass =
267 | FP_normal (* Normal number, none of the below
268 *)
269 | FP_subnormal (* Number very close to 0.0, has reduced precision
270 *)
271 | FP_zero (* Number is 0.0 or -0.0
272 *)
273 | FP_infinite (* Number is positive or negative infinity
274 *)
275 | FP_nan (* Not a number: result of an undefined operation
276 *)
277 The five classes of floating-point numbers, as determined by the
280 Float.classify_float function.
281 val classify_float : float -> fpclass
285 Return the class of the given floating-point number: normal, subnormal,
287 zero, infinite, or not a number.
288 val pow : float -> float -> float
292 Exponentiation.
294 val sqrt : float -> float
298 Square root.
300 val exp : float -> float
304 Exponential.
306 val log : float -> float
310 Natural logarithm.
312 val log10 : float -> float
316 Base 10 logarithm.
318 val expm1 : float -> float
322 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
325 even if x is close to 0.0 .
326 val log1p : float -> float
330 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
333 cally-accurate results even if x is close to 0.0 .
334 val cos : float -> float
338 Cosine. Argument is in radians.
340 val sin : float -> float
344 Sine. Argument is in radians.
346 val tan : float -> float
350 Tangent. Argument is in radians.
352 val acos : float -> float
356 Arc cosine. The argument must fall within the range [-1.0, 1.0] . Re‐
358 sult is in radians and is between 0.0 and pi .
359 val asin : float -> float
363 Arc sine. The argument must fall within the range [-1.0, 1.0] . Re‐
365 sult is in radians and is between -pi/2 and pi/2 .
366 val atan : float -> float
370 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
372 val atan2 : float -> float -> float
376 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
379 used to determine the quadrant of the result. Result is in radians and
380 is between -pi and pi .
381 val hypot : float -> float -> float
385 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
388 hypotenuse of a right-angled triangle with sides of length x and y ,
389 or, equivalently, the distance of the point (x,y) to origin. If one of
390 x or y is infinite, returns infinity even if the other is nan .
391 val cosh : float -> float
395 Hyperbolic cosine. Argument is in radians.
397 val sinh : float -> float
401 Hyperbolic sine. Argument is in radians.
403 val tanh : float -> float
407 Hyperbolic tangent. Argument is in radians.
409 val trunc : float -> float
413 trunc x rounds x to the nearest integer whose absolute value is less
416 than or equal to x .
417 Since 4.08.0
420 val round : float -> float
424 round x rounds x to the nearest integer with ties (fractional values of
427 0.5) rounded away from zero, regardless of the current rounding direc‐
428 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
429 returned.
430 Since 4.08.0
433 val ceil : float -> float
437 Round above to an integer value. ceil f returns the least integer
439 value greater than or equal to f . The result is returned as a float.
440 val floor : float -> float
444 Round below to an integer value. floor f returns the greatest integer
446 value less than or equal to f . The result is returned as a float.
447 val next_after : float -> float -> float
451 next_after x y returns the next representable floating-point value fol‐
454 lowing x in the direction of y . More precisely, if y is greater
455 (resp. less) than x , it returns the smallest (resp. largest) repre‐
456 sentable number greater (resp. less) than x . If x equals y , the
457 function returns y . If x or y is nan , a nan is returned. Note that
458 next_after max_float infinity = infinity and that next_after 0. infin‐
459 ity is the smallest denormalized positive number. If x is the smallest
460 denormalized positive number, next_after x 0. = 0.
461 Since 4.08.0
465 val copy_sign : float -> float -> float
469 copy_sign x y returns a float whose absolute value is that of x and
472 whose sign is that of y . If x is nan , returns nan . If y is nan ,
473 returns either x or -. x , but it is not specified which.
474 val sign_bit : float -> bool
478 sign_bit x is true if and only if the sign bit of x is set. For exam‐
481 ple sign_bit 1. and signbit 0. are false while sign_bit (-1.) and
482 sign_bit (-0.) are true .
483 Since 4.08.0
486 val frexp : float -> float * int
490 frexp f returns the pair of the significant and the exponent of f .
493 When f is zero, the significant x and the exponent n of f are equal to
494 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
495 <= x < 1.0 .
496 val ldexp : float -> int -> float
500 ldexp x n returns x *. 2 ** n .
503 val modf : float -> float * float
507 modf f returns the pair of the fractional and integral part of f .
510 type t = float
513 An alias for the type of floating-point numbers.
516 val compare : t -> t -> int
520 compare x y returns 0 if x is equal to y , a negative integer if x is
523 less than y , and a positive integer if x is greater than y . compare
524 treats nan as equal to itself and less than any other float value.
525 This treatment of nan ensures that compare defines a total ordering re‐
526 lation.
527 val equal : t -> t -> bool
531 The equal function for floating-point numbers, compared using
533 Float.compare .
534 val min : t -> t -> t
538 min x y returns the minimum of x and y . It returns nan when x or y is
541 nan . Moreover min (-0.) (+0.) = -0.
542 Since 4.08.0
546 val max : float -> float -> float
550 max x y returns the maximum of x and y . It returns nan when x or y is
553 nan . Moreover max (-0.) (+0.) = +0.
554 Since 4.08.0
558 val min_max : float -> float -> float * float
562 min_max x y is (min x y, max x y) , just more efficient.
565 Since 4.08.0
568 val min_num : t -> t -> t
572 min_num x y returns the minimum of x and y treating nan as missing val‐
575 ues. If both x and y are nan , nan is returned. Moreover min_num
576 (-0.) (+0.) = -0.
577 Since 4.08.0
581 val max_num : t -> t -> t
585 max_num x y returns the maximum of x and y treating nan as missing val‐
588 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
589 (+0.) = +0.
590 Since 4.08.0
594 val min_max_num : float -> float -> float * float
598 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
601 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
602 y = (y, y) .
603 Since 4.08.0
606 val hash : t -> int
610 The hash function for floating-point numbers.
612 module Array : sig end
615 Float arrays with packed representation.
618 module ArrayLabels : sig end
621 Float arrays with packed representation (labeled functions).
624OCamldoc 2021-07-22 Stdlib.Float(3)