1Float(3)                         OCaml library                        Float(3)
2
3
4

NAME

6       Float -  Floating-point arithmetic
7

Module

9       Module   Float
10

Documentation

12       Module Float
13        : sig end
14
15
16
17       Floating-point arithmetic
18
19       OCaml's floating-point numbers follow the IEEE 754 standard, using dou‐
20       ble precision (64 bits) numbers.  Floating-point operations never raise
21       an  exception  on overflow, underflow, division by zero, etc.  Instead,
22       special IEEE numbers are returned as appropriate, such as infinity  for
23       1.0  /.  0.0  , neg_infinity for -1.0 /. 0.0 , and nan ('not a number')
24       for 0.0 /. 0.0 .  These special numbers then propagate  through  float‐
25       ing-point  computations  as  expected: for instance, 1.0 /. infinity is
26       0.0 , and any arithmetic operation with nan as argument returns nan  as
27       result.
28
29
30       Since 4.07.0
31
32
33
34
35
36
37       val neg : float -> float
38
39       Unary negation.
40
41
42
43       val add : float -> float -> float
44
45       Floating-point addition.
46
47
48
49       val sub : float -> float -> float
50
51       Floating-point subtraction.
52
53
54
55       val mul : float -> float -> float
56
57       Floating-point multiplication.
58
59
60
61       val div : float -> float -> float
62
63       Floating-point division.
64
65
66
67       val rem : float -> float -> float
68
69
70       rem  a  b  returns the remainder of a with respect to b .  The returned
71       value is a -. n *. b , where n is the quotient a /. b  rounded  towards
72       zero to an integer.
73
74
75
76       val abs : float -> float
77
78
79       abs f returns the absolute value of f .
80
81
82
83       val infinity : float
84
85       Positive infinity.
86
87
88
89       val neg_infinity : float
90
91       Negative infinity.
92
93
94
95       val nan : float
96
97       A  special  floating-point  value  denoting  the result of an undefined
98       operation such as 0.0 /. 0.0 .  Stands for 'not a number'.  Any  float‐
99       ing-point operation with nan as argument returns nan as result.  As for
100       floating-point comparisons, = , < , <= , > and >= return false  and  <>
101       returns true if one or both of their arguments is nan .
102
103
104
105       val pi : float
106
107       The constant pi.
108
109
110
111       val max_float : float
112
113       The largest positive finite value of type float .
114
115
116
117       val min_float : float
118
119       The smallest positive, non-zero, non-denormalized value of type float .
120
121
122
123       val epsilon : float
124
125       The  difference  between  1.0  and  the  smallest exactly representable
126       floating-point number greater than 1.0 .
127
128
129
130       val of_int : int -> float
131
132       Convert an integer to floating-point.
133
134
135
136       val to_int : float -> int
137
138       Truncate the given floating-point number to an integer.  The result  is
139       unspecified if the argument is nan or falls outside the range of repre‐
140       sentable integers.
141
142
143
144       val of_string : string -> float
145
146       Convert the given string to a float.  The string is read in decimal (by
147       default)  or in hexadecimal (marked by 0x or 0X ).  The format of deci‐
148       mal floating-point numbers is [-] dd.ddd  (e|E)  [+|-]  dd  ,  where  d
149       stands  for  a decimal digit.  The format of hexadecimal floating-point
150       numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where  h  stands  for  an
151       hexadecimal  digit  and d for a decimal digit.  In both cases, at least
152       one of the integer and fractional parts must  be  given;  the  exponent
153       part  is optional.  The _ (underscore) character can appear anywhere in
154       the string and is ignored.  Depending on the execution platforms, other
155       representations  of  floating-point numbers can be accepted, but should
156       not be relied upon.  Raise Failure float_of_string if the given  string
157       is not a valid representation of a float.
158
159
160
161       val of_string_opt : string -> float option
162
163       Same as of_string , but returns None instead of raising.
164
165
166
167       val to_string : float -> string
168
169       Return the string representation of a floating-point number.
170
171
172       type fpclass = Pervasives.fpclass =
173        | FP_normal  (* Normal number, none of the below
174        *)
175        | FP_subnormal  (* Number very close to 0.0, has reduced precision
176        *)
177        | FP_zero  (* Number is 0.0 or -0.0
178        *)
179        | FP_infinite  (* Number is positive or negative infinity
180        *)
181        | FP_nan  (* Not a number: result of an undefined operation
182        *)
183
184
185       The  five  classes  of  floating-point  numbers,  as  determined by the
186       Float.classify_float function.
187
188
189
190       val classify_float : float -> fpclass
191
192       Return the class of the given floating-point number: normal, subnormal,
193       zero, infinite, or not a number.
194
195
196
197       val pow : float -> float -> float
198
199       Exponentiation.
200
201
202
203       val sqrt : float -> float
204
205       Square root.
206
207
208
209       val exp : float -> float
210
211       Exponential.
212
213
214
215       val log : float -> float
216
217       Natural logarithm.
218
219
220
221       val log10 : float -> float
222
223       Base 10 logarithm.
224
225
226
227       val expm1 : float -> float
228
229
230       expm1  x  computes  exp  x -. 1.0 , giving numerically-accurate results
231       even if x is close to 0.0 .
232
233
234
235       val log1p : float -> float
236
237
238       log1p x computes log(1.0 +.  x)  (natural  logarithm),  giving  numeri‐
239       cally-accurate results even if x is close to 0.0 .
240
241
242
243       val cos : float -> float
244
245       Cosine.  Argument is in radians.
246
247
248
249       val sin : float -> float
250
251       Sine.  Argument is in radians.
252
253
254
255       val tan : float -> float
256
257       Tangent.  Argument is in radians.
258
259
260
261       val acos : float -> float
262
263       Arc  cosine.   The  argument  must  fall within the range [-1.0, 1.0] .
264       Result is in radians and is between 0.0 and pi .
265
266
267
268       val asin : float -> float
269
270       Arc sine.  The argument must  fall  within  the  range  [-1.0,  1.0]  .
271       Result is in radians and is between -pi/2 and pi/2 .
272
273
274
275       val atan : float -> float
276
277       Arc tangent.  Result is in radians and is between -pi/2 and pi/2 .
278
279
280
281       val atan2 : float -> float -> float
282
283
284       atan2 y x returns the arc tangent of y /. x .  The signs of x and y are
285       used to determine the quadrant of the result.  Result is in radians and
286       is between -pi and pi .
287
288
289
290       val hypot : float -> float -> float
291
292
293       hypot  x  y  returns sqrt(x *. x + y *. y) , that is, the length of the
294       hypotenuse of a right-angled triangle with sides of length x  and  y  ,
295       or, equivalently, the distance of the point (x,y) to origin.  If one of
296       x or y is infinite, returns infinity even if the other is nan .
297
298
299
300       val cosh : float -> float
301
302       Hyperbolic cosine.  Argument is in radians.
303
304
305
306       val sinh : float -> float
307
308       Hyperbolic sine.  Argument is in radians.
309
310
311
312       val tanh : float -> float
313
314       Hyperbolic tangent.  Argument is in radians.
315
316
317
318       val ceil : float -> float
319
320       Round above to an integer value.  ceil  f  returns  the  least  integer
321       value greater than or equal to f .  The result is returned as a float.
322
323
324
325       val floor : float -> float
326
327       Round  below to an integer value.  floor f returns the greatest integer
328       value less than or equal to f .  The result is returned as a float.
329
330
331
332       val copysign : float -> float -> float
333
334
335       copysign x y returns a float whose absolute value  is  that  of  x  and
336       whose  sign  is that of y .  If x is nan , returns nan .  If y is nan ,
337       returns either x or -. x , but it is not specified which.
338
339
340
341       val frexp : float -> float * int
342
343
344       frexp f returns the pair of the significant and the  exponent  of  f  .
345       When  f is zero, the significant x and the exponent n of f are equal to
346       zero.  When f is non-zero, they are defined by f = x *. 2 ** n and  0.5
347       <= x < 1.0 .
348
349
350
351       val ldexp : float -> int -> float
352
353
354       ldexp x n returns x *. 2 ** n .
355
356
357
358       val modf : float -> float * float
359
360
361       modf f returns the pair of the fractional and integral part of f .
362
363
364       type t = float
365
366
367       An alias for the type of floating-point numbers.
368
369
370
371       val compare : t -> t -> int
372
373
374       compare  x  y returns 0 if x is equal to y , a negative integer if x is
375       less than y , and a positive integer if x is greater than y .   compare
376       treats  nan  as  equal  to  itself and less than any other float value.
377       This treatment of nan ensures that compare  defines  a  total  ordering
378       relation.
379
380
381
382       val equal : t -> t -> bool
383
384       The   equal   function   for  floating-point  numbers,  compared  using
385       Float.compare .
386
387
388
389       val hash : t -> int
390
391       The hash function for floating-point numbers.
392
393
394       module Array : sig end
395
396
397
398
399
400
401
402OCamldoc                          2019-02-02                          Float(3)