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 the string representation of a floating-point number.
267 type fpclass = fpclass =
270 | FP_normal (* Normal number, none of the below
271 *)
272 | FP_subnormal (* Number very close to 0.0, has reduced precision
273 *)
274 | FP_zero (* Number is 0.0 or -0.0
275 *)
276 | FP_infinite (* Number is positive or negative infinity
277 *)
278 | FP_nan (* Not a number: result of an undefined operation
279 *)
280 The five classes of floating-point numbers, as determined by the
283 Float.classify_float function.
284 val classify_float : float -> fpclass
288 Return the class of the given floating-point number: normal, subnormal,
290 zero, infinite, or not a number.
291 val pow : float -> float -> float
295 Exponentiation.
297 val sqrt : float -> float
301 Square root.
303 val cbrt : float -> float
307 Cube root.
309 Since 4.13.0
312 val exp : float -> float
316 Exponential.
318 val exp2 : float -> float
322 Base 2 exponential function.
324 Since 4.13.0
327 val log : float -> float
331 Natural logarithm.
333 val log10 : float -> float
337 Base 10 logarithm.
339 val log2 : float -> float
343 Base 2 logarithm.
345 Since 4.13.0
348 val expm1 : float -> float
352 expm1 x computes exp x -. 1.0 , giving numerically-accurate results
355 even if x is close to 0.0 .
356 val log1p : float -> float
360 log1p x computes log(1.0 +. x) (natural logarithm), giving numeri‐
363 cally-accurate results even if x is close to 0.0 .
364 val cos : float -> float
368 Cosine. Argument is in radians.
370 val sin : float -> float
374 Sine. Argument is in radians.
376 val tan : float -> float
380 Tangent. Argument is in radians.
382 val acos : float -> float
386 Arc cosine. The argument must fall within the range [-1.0, 1.0] . Re‐
388 sult is in radians and is between 0.0 and pi .
389 val asin : float -> float
393 Arc sine. The argument must fall within the range [-1.0, 1.0] . Re‐
395 sult is in radians and is between -pi/2 and pi/2 .
396 val atan : float -> float
400 Arc tangent. Result is in radians and is between -pi/2 and pi/2 .
402 val atan2 : float -> float -> float
406 atan2 y x returns the arc tangent of y /. x . The signs of x and y are
409 used to determine the quadrant of the result. Result is in radians and
410 is between -pi and pi .
411 val hypot : float -> float -> float
415 hypot x y returns sqrt(x *. x + y *. y) , that is, the length of the
418 hypotenuse of a right-angled triangle with sides of length x and y ,
419 or, equivalently, the distance of the point (x,y) to origin. If one of
420 x or y is infinite, returns infinity even if the other is nan .
421 val cosh : float -> float
425 Hyperbolic cosine. Argument is in radians.
427 val sinh : float -> float
431 Hyperbolic sine. Argument is in radians.
433 val tanh : float -> float
437 Hyperbolic tangent. Argument is in radians.
439 val acosh : float -> float
443 Hyperbolic arc cosine. The argument must fall within the range [1.0,
445 inf] . Result is in radians and is between 0.0 and inf .
446 Since 4.13.0
449 val asinh : float -> float
453 Hyperbolic arc sine. The argument and result range over the entire
455 real line. Result is in radians.
456 Since 4.13.0
459 val atanh : float -> float
463 Hyperbolic arc tangent. The argument must fall within the range [-1.0,
465 1.0] . Result is in radians and ranges over the entire real line.
466 Since 4.13.0
469 val erf : float -> float
473 Error function. The argument ranges over the entire real line. The
475 result is always within [-1.0, 1.0] .
476 Since 4.13.0
479 val erfc : float -> float
483 Complementary error function ( erfc x = 1 - erf x ). The argument
485 ranges over the entire real line. The result is always within [-1.0,
486 1.0] .
487 Since 4.13.0
490 val trunc : float -> float
494 trunc x rounds x to the nearest integer whose absolute value is less
497 than or equal to x .
498 Since 4.08.0
501 val round : float -> float
505 round x rounds x to the nearest integer with ties (fractional values of
508 0.5) rounded away from zero, regardless of the current rounding direc‐
509 tion. If x is an integer, +0. , -0. , nan , or infinite, x itself is
510 returned.
511 On 64-bit mingw-w64, this function may be emulated owing to a bug in
513 the C runtime library (CRT) on this platform.
514 Since 4.08.0
517 val ceil : float -> float
521 Round above to an integer value. ceil f returns the least integer
523 value greater than or equal to f . The result is returned as a float.
524 val floor : float -> float
528 Round below to an integer value. floor f returns the greatest integer
530 value less than or equal to f . The result is returned as a float.
531 val next_after : float -> float -> float
535 next_after x y returns the next representable floating-point value fol‐
538 lowing x in the direction of y . More precisely, if y is greater
539 (resp. less) than x , it returns the smallest (resp. largest) repre‐
540 sentable number greater (resp. less) than x . If x equals y , the
541 function returns y . If x or y is nan , a nan is returned. Note that
542 next_after max_float infinity = infinity and that next_after 0. infin‐
543 ity is the smallest denormalized positive number. If x is the smallest
544 denormalized positive number, next_after x 0. = 0.
545 Since 4.08.0
549 val copy_sign : float -> float -> float
553 copy_sign x y returns a float whose absolute value is that of x and
556 whose sign is that of y . If x is nan , returns nan . If y is nan ,
557 returns either x or -. x , but it is not specified which.
558 val sign_bit : float -> bool
562 sign_bit x is true if and only if the sign bit of x is set. For exam‐
565 ple sign_bit 1. and signbit 0. are false while sign_bit (-1.) and
566 sign_bit (-0.) are true .
567 Since 4.08.0
570 val frexp : float -> float * int
574 frexp f returns the pair of the significant and the exponent of f .
577 When f is zero, the significant x and the exponent n of f are equal to
578 zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5
579 <= x < 1.0 .
580 val ldexp : float -> int -> float
584 ldexp x n returns x *. 2 ** n .
587 val modf : float -> float * float
591 modf f returns the pair of the fractional and integral part of f .
594 type t = float
597 An alias for the type of floating-point numbers.
600 val compare : t -> t -> int
604 compare x y returns 0 if x is equal to y , a negative integer if x is
607 less than y , and a positive integer if x is greater than y . compare
608 treats nan as equal to itself and less than any other float value.
609 This treatment of nan ensures that compare defines a total ordering re‐
610 lation.
611 val equal : t -> t -> bool
615 The equal function for floating-point numbers, compared using
617 Float.compare .
618 val min : t -> t -> t
622 min x y returns the minimum of x and y . It returns nan when x or y is
625 nan . Moreover min (-0.) (+0.) = -0.
626 Since 4.08.0
630 val max : float -> float -> float
634 max x y returns the maximum of x and y . It returns nan when x or y is
637 nan . Moreover max (-0.) (+0.) = +0.
638 Since 4.08.0
642 val min_max : float -> float -> float * float
646 min_max x y is (min x y, max x y) , just more efficient.
649 Since 4.08.0
652 val min_num : t -> t -> t
656 min_num x y returns the minimum of x and y treating nan as missing val‐
659 ues. If both x and y are nan , nan is returned. Moreover min_num
660 (-0.) (+0.) = -0.
661 Since 4.08.0
665 val max_num : t -> t -> t
669 max_num x y returns the maximum of x and y treating nan as missing val‐
672 ues. If both x and y are nan nan is returned. Moreover max_num (-0.)
673 (+0.) = +0.
674 Since 4.08.0
678 val min_max_num : float -> float -> float * float
682 min_max_num x y is (min_num x y, max_num x y) , just more efficient.
685 Note that in particular min_max_num x nan = (x, x) and min_max_num nan
686 y = (y, y) .
687 Since 4.08.0
690 val hash : t -> int
694 The hash function for floating-point numbers.
696 module Array : sig end
699 Float arrays with packed representation.
702 module ArrayLabels : sig end
705 Float arrays with packed representation (labeled functions).
708OCamldoc 2022-07-22 Stdlib.Float(3)