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
97 expression 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
161 operation 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. Raise Failure "float_of_string" if the given
261 string is not a valid representation of a float.
262 val of_string_opt : string -> float option
266 Same as of_string , but returns None instead of raising.
268 val to_string : float -> string
272 Return the string representation of a floating-point number.
274 type fpclass = fpclass =
277 | FP_normal (* Normal number, none of the below
278 *)
279 | FP_subnormal (* Number very close to 0.0, has reduced precision
280 *)
281 | FP_zero (* Number is 0.0 or -0.0
282 *)
283 | FP_infinite (* Number is positive or negative infinity
284 *)
285 | FP_nan (* Not a number: result of an undefined operation
286 *)
287 The five classes of floating-point numbers, as determined by the
290 Float.classify_float function.
291 val classify_float : float -> fpclass
295 Return the class of the given floating-point number: normal, subnormal,
297 zero, infinite, or not a number.
298 val pow : float -> float -> float
302 Exponentiation.
304 val sqrt : float -> float
308 Square root.
310 val exp : float -> float
314 Exponential.
316 val log : float -> float
320 Natural logarithm.
322 val log10 : float -> float
326 Base 10 logarithm.
328 val expm1 : float -> float
332 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
335 even if x is close to 0.0 .
336 val log1p : float -> float
340 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
343 cally-accurate results even if x is close to 0.0 .
344 val cos : float -> float
348 Cosine. Argument is in radians.
350 val sin : float -> float
354 Sine. Argument is in radians.
356 val tan : float -> float
360 Tangent. Argument is in radians.
362 val acos : float -> float
366 Arc cosine. The argument must fall within the range [-1.0, 1.0] .
368 Result is in radians and is between 0.0 and pi .
369 val asin : float -> float
373 Arc sine. The argument must fall within the range [-1.0, 1.0] .
375 Result is in radians and is between -pi/2 and pi/2 .
376 val atan : float -> float
380 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
382 val atan2 : float -> float -> float
386 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
389 used to determine the quadrant of the result. Result is in radians and
390 is between -pi and pi .
391 val hypot : float -> float -> float
395 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
398 hypotenuse of a right-angled triangle with sides of length x and y ,
399 or, equivalently, the distance of the point (x,y) to origin. If one of
400 x or y is infinite, returns infinity even if the other is nan .
401 val cosh : float -> float
405 Hyperbolic cosine. Argument is in radians.
407 val sinh : float -> float
411 Hyperbolic sine. Argument is in radians.
413 val tanh : float -> float
417 Hyperbolic tangent. Argument is in radians.
419 val trunc : float -> float
423 trunc x rounds x to the nearest integer whose absolute value is less
426 than or equal to x .
427 Since 4.08.0
430 val round : float -> float
434 round x rounds x to the nearest integer with ties (fractional values of
437 0.5) rounded away from zero, regardless of the current rounding direc‐
438 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
439 returned.
440 Since 4.08.0
443 val ceil : float -> float
447 Round above to an integer value. ceil f returns the least integer
449 value greater than or equal to f . The result is returned as a float.
450 val floor : float -> float
454 Round below to an integer value. floor f returns the greatest integer
456 value less than or equal to f . The result is returned as a float.
457 val next_after : float -> float -> float
461 next_after x y returns the next representable floating-point value fol‐
464 lowing x in the direction of y . More precisely, if y is greater
465 (resp. less) than x , it returns the smallest (resp. largest) repre‐
466 sentable number greater (resp. less) than x . If x equals y , the
467 function returns y . If x or y is nan , a nan is returned. Note that
468 next_after max_float infinity = infinity and that next_after 0. infin‐
469 ity is the smallest denormalized positive number. If x is the smallest
470 denormalized positive number, next_after x 0. = 0.
471 Since 4.08.0
475 val copy_sign : float -> float -> float
479 copy_sign x y returns a float whose absolute value is that of x and
482 whose sign is that of y . If x is nan , returns nan . If y is nan ,
483 returns either x or -. x , but it is not specified which.
484 val sign_bit : float -> bool
488 sign_bit x is true iff the sign bit of x is set. For example sign_bit
491 1. and signbit 0. are false while sign_bit (-1.) and sign_bit (-0.)
492 are true .
493 Since 4.08.0
496 val frexp : float -> float * int
500 frexp f returns the pair of the significant and the exponent of f .
503 When f is zero, the significant x and the exponent n of f are equal to
504 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
505 <= x < 1.0 .
506 val ldexp : float -> int -> float
510 ldexp x n returns x *. 2 ** n .
513 val modf : float -> float * float
517 modf f returns the pair of the fractional and integral part of f .
520 type t = float
523 An alias for the type of floating-point numbers.
526 val compare : t -> t -> int
530 compare x y returns 0 if x is equal to y , a negative integer if x is
533 less than y , and a positive integer if x is greater than y . compare
534 treats nan as equal to itself and less than any other float value.
535 This treatment of nan ensures that compare defines a total ordering
536 relation.
537 val equal : t -> t -> bool
541 The equal function for floating-point numbers, compared using
543 Float.compare .
544 val min : t -> t -> t
548 min x y returns the minimum of x and y . It returns nan when x or y is
551 nan . Moreover min (-0.) (+0.) = -0.
552 Since 4.08.0
556 val max : float -> float -> float
560 max x y returns the maximum of x and y . It returns nan when x or y is
563 nan . Moreover max (-0.) (+0.) = +0.
564 Since 4.08.0
568 val min_max : float -> float -> float * float
572 min_max x y is (min x y, max x y) , just more efficient.
575 Since 4.08.0
578 val min_num : t -> t -> t
582 min_num x y returns the minimum of x and y treating nan as missing val‐
585 ues. If both x and y are nan , nan is returned. Moreover min_num
586 (-0.) (+0.) = -0.
587 Since 4.08.0
591 val max_num : t -> t -> t
595 max_num x y returns the maximum of x and y treating nan as missing val‐
598 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
599 (+0.) = +0.
600 Since 4.08.0
604 val min_max_num : float -> float -> float * float
608 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
611 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
612 y = (y, y) .
613 Since 4.08.0
616 val hash : t -> int
620 The hash function for floating-point numbers.
622 module Array : sig end
625 module ArrayLabels : sig end
630OCamldoc 2020-02-27 Float(3)