1Float(3) OCaml library Float(3)
2
6 Float - Floating-point arithmetic
7
9 Module Float
10
12 Module Float
13 : sig end
14 Floating-point arithmetic
18 OCaml's floating-point numbers follow the IEEE 754 standard, using dou‐
19 ble precision (64 bits) numbers. Floating-point operations never raise
20 an exception on overflow, underflow, division by zero, etc. Instead,
21 special IEEE numbers are returned as appropriate, such as infinity for
22 1.0 /. 0.0 , neg_infinity for -1.0 /. 0.0 , and nan ('not a number')
23 for 0.0 /. 0.0 . These special numbers then propagate through float‐
24 ing-point computations as expected: for instance, 1.0 /. infinity is
25 0.0 , and any arithmetic operation with nan as argument returns nan as
26 result.
27 Since 4.07.0
30 val zero : float
37 The floating point 0.
39 Since 4.08.0
42 val one : float
46 The floating-point 1.
48 Since 4.08.0
51 val minus_one : float
55 The floating-point -1.
57 Since 4.08.0
60 val neg : float -> float
64 Unary negation.
66 val add : float -> float -> float
70 Floating-point addition.
72 val sub : float -> float -> float
76 Floating-point subtraction.
78 val mul : float -> float -> float
82 Floating-point multiplication.
84 val div : float -> float -> float
88 Floating-point division.
90 val fma : float -> float -> float -> float
94 fma x y z returns x * y + z , with a best effort for computing this ex‐
97 pression with a single rounding, using either hardware instructions
98 (providing full IEEE compliance) or a software emulation. Note: since
99 software emulation of the fma is costly, make sure that you are using
100 hardware fma support if performance matters.
101 Since 4.08.0
104 val rem : float -> float -> float
108 rem a b returns the remainder of a with respect to b . The returned
111 value is a -. n *. b , where n is the quotient a /. b rounded towards
112 zero to an integer.
113 val succ : float -> float
117 succ x returns the floating point number right after x i.e., the small‐
120 est floating-point number greater than x . See also Float.next_after .
121 Since 4.08.0
124 val pred : float -> float
128 pred x returns the floating-point number right before x i.e., the
131 greatest floating-point number smaller than x . See also
132 Float.next_after .
133 Since 4.08.0
136 val abs : float -> float
140 abs f returns the absolute value of f .
143 val infinity : float
147 Positive infinity.
149 val neg_infinity : float
153 Negative infinity.
155 val nan : float
159 A special floating-point value denoting the result of an undefined op‐
161 eration such as 0.0 /. 0.0 . Stands for 'not a number'. Any float‐
162 ing-point operation with nan as argument returns nan as result. As for
163 floating-point comparisons, = , < , <= , > and >= return false and <>
164 returns true if one or both of their arguments is nan .
165 val pi : float
169 The constant pi.
171 val max_float : float
175 The largest positive finite value of type float .
177 val min_float : float
181 The smallest positive, non-zero, non-denormalized value of type float .
183 val epsilon : float
187 The difference between 1.0 and the smallest exactly representable
189 floating-point number greater than 1.0 .
190 val is_finite : float -> bool
194 is_finite x is true iff x is finite i.e., not infinite and not
197 Float.nan .
198 Since 4.08.0
201 val is_infinite : float -> bool
205 is_infinite x is true iff x is Float.infinity or Float.neg_infinity .
208 Since 4.08.0
211 val is_nan : float -> bool
215 is_nan x is true iff x is not a number (see Float.nan ).
218 Since 4.08.0
221 val is_integer : float -> bool
225 is_integer x is true iff x is an integer.
228 Since 4.08.0
231 val of_int : int -> float
235 Convert an integer to floating-point.
237 val to_int : float -> int
241 Truncate the given floating-point number to an integer. The result is
243 unspecified if the argument is nan or falls outside the range of repre‐
244 sentable integers.
245 val of_string : string -> float
249 Convert the given string to a float. The string is read in decimal (by
251 default) or in hexadecimal (marked by 0x or 0X ). The format of deci‐
252 mal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d
253 stands for a decimal digit. The format of hexadecimal floating-point
254 numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an
255 hexadecimal digit and d for a decimal digit. In both cases, at least
256 one of the integer and fractional parts must be given; the exponent
257 part is optional. The _ (underscore) character can appear anywhere in
258 the string and is ignored. Depending on the execution platforms, other
259 representations of floating-point numbers can be accepted, but should
260 not be relied upon.
261 Raises Failure if the given string is not a valid representation of a
264 float.
265 val of_string_opt : string -> float option
269 Same as of_string , but returns None instead of raising.
271 val to_string : float -> string
275 Return the string representation of a floating-point number.
277 type fpclass = fpclass =
280 | FP_normal (* Normal number, none of the below
281 *)
282 | FP_subnormal (* Number very close to 0.0, has reduced precision
283 *)
284 | FP_zero (* Number is 0.0 or -0.0
285 *)
286 | FP_infinite (* Number is positive or negative infinity
287 *)
288 | FP_nan (* Not a number: result of an undefined operation
289 *)
290 The five classes of floating-point numbers, as determined by the
293 Float.classify_float function.
294 val classify_float : float -> fpclass
298 Return the class of the given floating-point number: normal, subnormal,
300 zero, infinite, or not a number.
301 val pow : float -> float -> float
305 Exponentiation.
307 val sqrt : float -> float
311 Square root.
313 val exp : float -> float
317 Exponential.
319 val log : float -> float
323 Natural logarithm.
325 val log10 : float -> float
329 Base 10 logarithm.
331 val expm1 : float -> float
335 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
338 even if x is close to 0.0 .
339 val log1p : float -> float
343 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
346 cally-accurate results even if x is close to 0.0 .
347 val cos : float -> float
351 Cosine. Argument is in radians.
353 val sin : float -> float
357 Sine. Argument is in radians.
359 val tan : float -> float
363 Tangent. Argument is in radians.
365 val acos : float -> float
369 Arc cosine. The argument must fall within the range [-1.0, 1.0] . Re‐
371 sult is in radians and is between 0.0 and pi .
372 val asin : float -> float
376 Arc sine. The argument must fall within the range [-1.0, 1.0] . Re‐
378 sult is in radians and is between -pi/2 and pi/2 .
379 val atan : float -> float
383 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
385 val atan2 : float -> float -> float
389 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
392 used to determine the quadrant of the result. Result is in radians and
393 is between -pi and pi .
394 val hypot : float -> float -> float
398 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
401 hypotenuse of a right-angled triangle with sides of length x and y ,
402 or, equivalently, the distance of the point (x,y) to origin. If one of
403 x or y is infinite, returns infinity even if the other is nan .
404 val cosh : float -> float
408 Hyperbolic cosine. Argument is in radians.
410 val sinh : float -> float
414 Hyperbolic sine. Argument is in radians.
416 val tanh : float -> float
420 Hyperbolic tangent. Argument is in radians.
422 val trunc : float -> float
426 trunc x rounds x to the nearest integer whose absolute value is less
429 than or equal to x .
430 Since 4.08.0
433 val round : float -> float
437 round x rounds x to the nearest integer with ties (fractional values of
440 0.5) rounded away from zero, regardless of the current rounding direc‐
441 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
442 returned.
443 Since 4.08.0
446 val ceil : float -> float
450 Round above to an integer value. ceil f returns the least integer
452 value greater than or equal to f . The result is returned as a float.
453 val floor : float -> float
457 Round below to an integer value. floor f returns the greatest integer
459 value less than or equal to f . The result is returned as a float.
460 val next_after : float -> float -> float
464 next_after x y returns the next representable floating-point value fol‐
467 lowing x in the direction of y . More precisely, if y is greater
468 (resp. less) than x , it returns the smallest (resp. largest) repre‐
469 sentable number greater (resp. less) than x . If x equals y , the
470 function returns y . If x or y is nan , a nan is returned. Note that
471 next_after max_float infinity = infinity and that next_after 0. infin‐
472 ity is the smallest denormalized positive number. If x is the smallest
473 denormalized positive number, next_after x 0. = 0.
474 Since 4.08.0
478 val copy_sign : float -> float -> float
482 copy_sign x y returns a float whose absolute value is that of x and
485 whose sign is that of y . If x is nan , returns nan . If y is nan ,
486 returns either x or -. x , but it is not specified which.
487 val sign_bit : float -> bool
491 sign_bit x is true iff the sign bit of x is set. For example sign_bit
494 1. and signbit 0. are false while sign_bit (-1.) and sign_bit (-0.)
495 are true .
496 Since 4.08.0
499 val frexp : float -> float * int
503 frexp f returns the pair of the significant and the exponent of f .
506 When f is zero, the significant x and the exponent n of f are equal to
507 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
508 <= x < 1.0 .
509 val ldexp : float -> int -> float
513 ldexp x n returns x *. 2 ** n .
516 val modf : float -> float * float
520 modf f returns the pair of the fractional and integral part of f .
523 type t = float
526 An alias for the type of floating-point numbers.
529 val compare : t -> t -> int
533 compare x y returns 0 if x is equal to y , a negative integer if x is
536 less than y , and a positive integer if x is greater than y . compare
537 treats nan as equal to itself and less than any other float value.
538 This treatment of nan ensures that compare defines a total ordering re‐
539 lation.
540 val equal : t -> t -> bool
544 The equal function for floating-point numbers, compared using
546 Float.compare .
547 val min : t -> t -> t
551 min x y returns the minimum of x and y . It returns nan when x or y is
554 nan . Moreover min (-0.) (+0.) = -0.
555 Since 4.08.0
559 val max : float -> float -> float
563 max x y returns the maximum of x and y . It returns nan when x or y is
566 nan . Moreover max (-0.) (+0.) = +0.
567 Since 4.08.0
571 val min_max : float -> float -> float * float
575 min_max x y is (min x y, max x y) , just more efficient.
578 Since 4.08.0
581 val min_num : t -> t -> t
585 min_num x y returns the minimum of x and y treating nan as missing val‐
588 ues. If both x and y are nan , nan is returned. Moreover min_num
589 (-0.) (+0.) = -0.
590 Since 4.08.0
594 val max_num : t -> t -> t
598 max_num x y returns the maximum of x and y treating nan as missing val‐
601 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
602 (+0.) = +0.
603 Since 4.08.0
607 val min_max_num : float -> float -> float * float
611 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
614 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
615 y = (y, y) .
616 Since 4.08.0
619 val hash : t -> int
623 The hash function for floating-point numbers.
625 module Array : sig end
628 module ArrayLabels : sig end
633OCamldoc 2021-01-26 Float(3)