1 //! Constants for the `f64` double-precision floating point type. 2 //! 3 //! *[See also the `f64` primitive type](primitive@f64).* 4 //! 5 //! Mathematically significant numbers are provided in the `consts` sub-module. 6 //! 7 //! For the constants defined directly in this module 8 //! (as distinct from those defined in the `consts` sub-module), 9 //! new code should instead use the associated constants 10 //! defined directly on the `f64` type. 11 12 #![allow(missing_docs)] 13 14 #[cfg(not(test))] 15 use crate::std::intrinsics; 16 #[cfg(not(test))] 17 use crate::std::sys::cmath; 18 19 #[allow(deprecated, deprecated_in_future)] 20 pub use core::f64::{ 21 consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP, 22 MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX, 23 }; 24 25 #[cfg(not(test))] 26 impl f64 { 27 /// Returns the largest integer less than or equal to `self`. 28 /// 29 /// # Examples 30 /// 31 /// ``` 32 /// let f = 3.7_f64; 33 /// let g = 3.0_f64; 34 /// let h = -3.7_f64; 35 /// 36 /// assert_eq!(f.floor(), 3.0); 37 /// assert_eq!(g.floor(), 3.0); 38 /// assert_eq!(h.floor(), -4.0); 39 /// ``` 40 #[rustc_allow_incoherent_impl] 41 #[must_use = "method returns a new number and does not mutate the original value"] 42 #[inline] 43 pub fn floor(self) -> f64 { 44 unsafe { intrinsics::floorf64(self) } 45 } 46 47 /// Returns the smallest integer greater than or equal to `self`. 48 /// 49 /// # Examples 50 /// 51 /// ``` 52 /// let f = 3.01_f64; 53 /// let g = 4.0_f64; 54 /// 55 /// assert_eq!(f.ceil(), 4.0); 56 /// assert_eq!(g.ceil(), 4.0); 57 /// ``` 58 #[doc(alias = "ceiling")] 59 #[rustc_allow_incoherent_impl] 60 #[must_use = "method returns a new number and does not mutate the original value"] 61 #[inline] 62 pub fn ceil(self) -> f64 { 63 unsafe { intrinsics::ceilf64(self) } 64 } 65 66 /// Returns the nearest integer to `self`. If a value is half-way between two 67 /// integers, round away from `0.0`. 68 /// 69 /// # Examples 70 /// 71 /// ``` 72 /// let f = 3.3_f64; 73 /// let g = -3.3_f64; 74 /// let h = -3.7_f64; 75 /// let i = 3.5_f64; 76 /// let j = 4.5_f64; 77 /// 78 /// assert_eq!(f.round(), 3.0); 79 /// assert_eq!(g.round(), -3.0); 80 /// assert_eq!(h.round(), -4.0); 81 /// assert_eq!(i.round(), 4.0); 82 /// assert_eq!(j.round(), 5.0); 83 /// ``` 84 #[rustc_allow_incoherent_impl] 85 #[must_use = "method returns a new number and does not mutate the original value"] 86 #[inline] 87 pub fn round(self) -> f64 { 88 unsafe { intrinsics::roundf64(self) } 89 } 90 91 /// Returns the nearest integer to a number. Rounds half-way cases to the number 92 /// with an even least significant digit. 93 /// 94 /// # Examples 95 /// 96 /// ``` 97 /// #![feature(round_ties_even)] 98 /// 99 /// let f = 3.3_f64; 100 /// let g = -3.3_f64; 101 /// let h = 3.5_f64; 102 /// let i = 4.5_f64; 103 /// 104 /// assert_eq!(f.round_ties_even(), 3.0); 105 /// assert_eq!(g.round_ties_even(), -3.0); 106 /// assert_eq!(h.round_ties_even(), 4.0); 107 /// assert_eq!(i.round_ties_even(), 4.0); 108 /// ``` 109 #[rustc_allow_incoherent_impl] 110 #[must_use = "method returns a new number and does not mutate the original value"] 111 #[inline] 112 pub fn round_ties_even(self) -> f64 { 113 unsafe { intrinsics::rintf64(self) } 114 } 115 116 /// Returns the integer part of `self`. 117 /// This means that non-integer numbers are always truncated towards zero. 118 /// 119 /// # Examples 120 /// 121 /// ``` 122 /// let f = 3.7_f64; 123 /// let g = 3.0_f64; 124 /// let h = -3.7_f64; 125 /// 126 /// assert_eq!(f.trunc(), 3.0); 127 /// assert_eq!(g.trunc(), 3.0); 128 /// assert_eq!(h.trunc(), -3.0); 129 /// ``` 130 #[doc(alias = "truncate")] 131 #[rustc_allow_incoherent_impl] 132 #[must_use = "method returns a new number and does not mutate the original value"] 133 #[inline] 134 pub fn trunc(self) -> f64 { 135 unsafe { intrinsics::truncf64(self) } 136 } 137 138 /// Returns the fractional part of `self`. 139 /// 140 /// # Examples 141 /// 142 /// ``` 143 /// let x = 3.6_f64; 144 /// let y = -3.6_f64; 145 /// let abs_difference_x = (x.fract() - 0.6).abs(); 146 /// let abs_difference_y = (y.fract() - (-0.6)).abs(); 147 /// 148 /// assert!(abs_difference_x < 1e-10); 149 /// assert!(abs_difference_y < 1e-10); 150 /// ``` 151 #[rustc_allow_incoherent_impl] 152 #[must_use = "method returns a new number and does not mutate the original value"] 153 #[inline] 154 pub fn fract(self) -> f64 { 155 self - self.trunc() 156 } 157 158 /// Computes the absolute value of `self`. 159 /// 160 /// # Examples 161 /// 162 /// ``` 163 /// let x = 3.5_f64; 164 /// let y = -3.5_f64; 165 /// 166 /// let abs_difference_x = (x.abs() - x).abs(); 167 /// let abs_difference_y = (y.abs() - (-y)).abs(); 168 /// 169 /// assert!(abs_difference_x < 1e-10); 170 /// assert!(abs_difference_y < 1e-10); 171 /// 172 /// assert!(f64::NAN.abs().is_nan()); 173 /// ``` 174 #[rustc_allow_incoherent_impl] 175 #[must_use = "method returns a new number and does not mutate the original value"] 176 #[inline] 177 pub fn abs(self) -> f64 { 178 unsafe { intrinsics::fabsf64(self) } 179 } 180 181 /// Returns a number that represents the sign of `self`. 182 /// 183 /// - `1.0` if the number is positive, `+0.0` or `INFINITY` 184 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY` 185 /// - NaN if the number is NaN 186 /// 187 /// # Examples 188 /// 189 /// ``` 190 /// let f = 3.5_f64; 191 /// 192 /// assert_eq!(f.signum(), 1.0); 193 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0); 194 /// 195 /// assert!(f64::NAN.signum().is_nan()); 196 /// ``` 197 #[rustc_allow_incoherent_impl] 198 #[must_use = "method returns a new number and does not mutate the original value"] 199 #[inline] 200 pub fn signum(self) -> f64 { 201 if self.is_nan() { 202 Self::NAN 203 } else { 204 1.0_f64.copysign(self) 205 } 206 } 207 208 /// Returns a number composed of the magnitude of `self` and the sign of 209 /// `sign`. 210 /// 211 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise 212 /// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of 213 /// `sign` is returned. Note, however, that conserving the sign bit on NaN 214 /// across arithmetical operations is not generally guaranteed. 215 /// See [explanation of NaN as a special value](primitive@f32) for more info. 216 /// 217 /// # Examples 218 /// 219 /// ``` 220 /// let f = 3.5_f64; 221 /// 222 /// assert_eq!(f.copysign(0.42), 3.5_f64); 223 /// assert_eq!(f.copysign(-0.42), -3.5_f64); 224 /// assert_eq!((-f).copysign(0.42), 3.5_f64); 225 /// assert_eq!((-f).copysign(-0.42), -3.5_f64); 226 /// 227 /// assert!(f64::NAN.copysign(1.0).is_nan()); 228 /// ``` 229 #[rustc_allow_incoherent_impl] 230 #[must_use = "method returns a new number and does not mutate the original value"] 231 #[inline] 232 pub fn copysign(self, sign: f64) -> f64 { 233 unsafe { intrinsics::copysignf64(self, sign) } 234 } 235 236 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding 237 /// error, yielding a more accurate result than an unfused multiply-add. 238 /// 239 /// Using `mul_add` *may* be more performant than an unfused multiply-add if 240 /// the target architecture has a dedicated `fma` CPU instruction. However, 241 /// this is not always true, and will be heavily dependant on designing 242 /// algorithms with specific target hardware in mind. 243 /// 244 /// # Examples 245 /// 246 /// ``` 247 /// let m = 10.0_f64; 248 /// let x = 4.0_f64; 249 /// let b = 60.0_f64; 250 /// 251 /// // 100.0 252 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs(); 253 /// 254 /// assert!(abs_difference < 1e-10); 255 /// ``` 256 #[rustc_allow_incoherent_impl] 257 #[must_use = "method returns a new number and does not mutate the original value"] 258 #[inline] 259 pub fn mul_add(self, a: f64, b: f64) -> f64 { 260 unsafe { intrinsics::fmaf64(self, a, b) } 261 } 262 263 /// Calculates Euclidean division, the matching method for `rem_euclid`. 264 /// 265 /// This computes the integer `n` such that 266 /// `self = n * rhs + self.rem_euclid(rhs)`. 267 /// In other words, the result is `self / rhs` rounded to the integer `n` 268 /// such that `self >= n * rhs`. 269 /// 270 /// # Examples 271 /// 272 /// ``` 273 /// let a: f64 = 7.0; 274 /// let b = 4.0; 275 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0 276 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0 277 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0 278 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0 279 /// ``` 280 #[rustc_allow_incoherent_impl] 281 #[must_use = "method returns a new number and does not mutate the original value"] 282 #[inline] 283 pub fn div_euclid(self, rhs: f64) -> f64 { 284 let q = (self / rhs).trunc(); 285 if self % rhs < 0.0 { 286 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }; 287 } 288 q 289 } 290 291 /// Calculates the least nonnegative remainder of `self (mod rhs)`. 292 /// 293 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in 294 /// most cases. However, due to a floating point round-off error it can 295 /// result in `r == rhs.abs()`, violating the mathematical definition, if 296 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`. 297 /// This result is not an element of the function's codomain, but it is the 298 /// closest floating point number in the real numbers and thus fulfills the 299 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)` 300 /// approximately. 301 /// 302 /// # Examples 303 /// 304 /// ``` 305 /// let a: f64 = 7.0; 306 /// let b = 4.0; 307 /// assert_eq!(a.rem_euclid(b), 3.0); 308 /// assert_eq!((-a).rem_euclid(b), 1.0); 309 /// assert_eq!(a.rem_euclid(-b), 3.0); 310 /// assert_eq!((-a).rem_euclid(-b), 1.0); 311 /// // limitation due to round-off error 312 /// assert!((-f64::EPSILON).rem_euclid(3.0) != 0.0); 313 /// ``` 314 #[doc(alias = "modulo", alias = "mod")] 315 #[rustc_allow_incoherent_impl] 316 #[must_use = "method returns a new number and does not mutate the original value"] 317 #[inline] 318 pub fn rem_euclid(self, rhs: f64) -> f64 { 319 let r = self % rhs; 320 if r < 0.0 { 321 r + rhs.abs() 322 } else { 323 r 324 } 325 } 326 327 /// Raises a number to an integer power. 328 /// 329 /// Using this function is generally faster than using `powf`. 330 /// It might have a different sequence of rounding operations than `powf`, 331 /// so the results are not guaranteed to agree. 332 /// 333 /// # Examples 334 /// 335 /// ``` 336 /// let x = 2.0_f64; 337 /// let abs_difference = (x.powi(2) - (x * x)).abs(); 338 /// 339 /// assert!(abs_difference < 1e-10); 340 /// ``` 341 #[rustc_allow_incoherent_impl] 342 #[must_use = "method returns a new number and does not mutate the original value"] 343 #[inline] 344 pub fn powi(self, n: i32) -> f64 { 345 unsafe { intrinsics::powif64(self, n) } 346 } 347 348 /// Raises a number to a floating point power. 349 /// 350 /// # Examples 351 /// 352 /// ``` 353 /// let x = 2.0_f64; 354 /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); 355 /// 356 /// assert!(abs_difference < 1e-10); 357 /// ``` 358 #[rustc_allow_incoherent_impl] 359 #[must_use = "method returns a new number and does not mutate the original value"] 360 #[inline] 361 pub fn powf(self, n: f64) -> f64 { 362 unsafe { intrinsics::powf64(self, n) } 363 } 364 365 /// Returns the square root of a number. 366 /// 367 /// Returns NaN if `self` is a negative number other than `-0.0`. 368 /// 369 /// # Examples 370 /// 371 /// ``` 372 /// let positive = 4.0_f64; 373 /// let negative = -4.0_f64; 374 /// let negative_zero = -0.0_f64; 375 /// 376 /// let abs_difference = (positive.sqrt() - 2.0).abs(); 377 /// 378 /// assert!(abs_difference < 1e-10); 379 /// assert!(negative.sqrt().is_nan()); 380 /// assert!(negative_zero.sqrt() == negative_zero); 381 /// ``` 382 #[rustc_allow_incoherent_impl] 383 #[must_use = "method returns a new number and does not mutate the original value"] 384 #[inline] 385 pub fn sqrt(self) -> f64 { 386 unsafe { intrinsics::sqrtf64(self) } 387 } 388 389 /// Returns `e^(self)`, (the exponential function). 390 /// 391 /// # Examples 392 /// 393 /// ``` 394 /// let one = 1.0_f64; 395 /// // e^1 396 /// let e = one.exp(); 397 /// 398 /// // ln(e) - 1 == 0 399 /// let abs_difference = (e.ln() - 1.0).abs(); 400 /// 401 /// assert!(abs_difference < 1e-10); 402 /// ``` 403 #[rustc_allow_incoherent_impl] 404 #[must_use = "method returns a new number and does not mutate the original value"] 405 #[inline] 406 pub fn exp(self) -> f64 { 407 unsafe { intrinsics::expf64(self) } 408 } 409 410 /// Returns `2^(self)`. 411 /// 412 /// # Examples 413 /// 414 /// ``` 415 /// let f = 2.0_f64; 416 /// 417 /// // 2^2 - 4 == 0 418 /// let abs_difference = (f.exp2() - 4.0).abs(); 419 /// 420 /// assert!(abs_difference < 1e-10); 421 /// ``` 422 #[rustc_allow_incoherent_impl] 423 #[must_use = "method returns a new number and does not mutate the original value"] 424 #[inline] 425 pub fn exp2(self) -> f64 { 426 unsafe { intrinsics::exp2f64(self) } 427 } 428 429 /// Returns the natural logarithm of the number. 430 /// 431 /// # Examples 432 /// 433 /// ``` 434 /// let one = 1.0_f64; 435 /// // e^1 436 /// let e = one.exp(); 437 /// 438 /// // ln(e) - 1 == 0 439 /// let abs_difference = (e.ln() - 1.0).abs(); 440 /// 441 /// assert!(abs_difference < 1e-10); 442 /// ``` 443 #[rustc_allow_incoherent_impl] 444 #[must_use = "method returns a new number and does not mutate the original value"] 445 #[inline] 446 pub fn ln(self) -> f64 { 447 crate::std::sys::log_wrapper(self, |n| unsafe { intrinsics::logf64(n) }) 448 } 449 450 /// Returns the logarithm of the number with respect to an arbitrary base. 451 /// 452 /// The result might not be correctly rounded owing to implementation details; 453 /// `self.log2()` can produce more accurate results for base 2, and 454 /// `self.log10()` can produce more accurate results for base 10. 455 /// 456 /// # Examples 457 /// 458 /// ``` 459 /// let twenty_five = 25.0_f64; 460 /// 461 /// // log5(25) - 2 == 0 462 /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs(); 463 /// 464 /// assert!(abs_difference < 1e-10); 465 /// ``` 466 #[rustc_allow_incoherent_impl] 467 #[must_use = "method returns a new number and does not mutate the original value"] 468 #[inline] 469 pub fn log(self, base: f64) -> f64 { 470 self.ln() / base.ln() 471 } 472 473 /// Returns the base 2 logarithm of the number. 474 /// 475 /// # Examples 476 /// 477 /// ``` 478 /// let four = 4.0_f64; 479 /// 480 /// // log2(4) - 2 == 0 481 /// let abs_difference = (four.log2() - 2.0).abs(); 482 /// 483 /// assert!(abs_difference < 1e-10); 484 /// ``` 485 #[rustc_allow_incoherent_impl] 486 #[must_use = "method returns a new number and does not mutate the original value"] 487 #[inline] 488 pub fn log2(self) -> f64 { 489 crate::std::sys::log_wrapper(self, crate::std::sys::log2f64) 490 } 491 492 /// Returns the base 10 logarithm of the number. 493 /// 494 /// # Examples 495 /// 496 /// ``` 497 /// let hundred = 100.0_f64; 498 /// 499 /// // log10(100) - 2 == 0 500 /// let abs_difference = (hundred.log10() - 2.0).abs(); 501 /// 502 /// assert!(abs_difference < 1e-10); 503 /// ``` 504 #[rustc_allow_incoherent_impl] 505 #[must_use = "method returns a new number and does not mutate the original value"] 506 #[inline] 507 pub fn log10(self) -> f64 { 508 crate::std::sys::log_wrapper(self, |n| unsafe { intrinsics::log10f64(n) }) 509 } 510 511 /// The positive difference of two numbers. 512 /// 513 /// * If `self <= other`: `0.0` 514 /// * Else: `self - other` 515 /// 516 /// # Examples 517 /// 518 /// ``` 519 /// let x = 3.0_f64; 520 /// let y = -3.0_f64; 521 /// 522 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs(); 523 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs(); 524 /// 525 /// assert!(abs_difference_x < 1e-10); 526 /// assert!(abs_difference_y < 1e-10); 527 /// ``` 528 #[rustc_allow_incoherent_impl] 529 #[must_use = "method returns a new number and does not mutate the original value"] 530 #[inline] 531 #[deprecated( 532 since = "1.10.0", 533 note = "you probably meant `(self - other).abs()`: \ 534 this operation is `(self - other).max(0.0)` \ 535 except that `abs_sub` also propagates NaNs (also \ 536 known as `fdim` in C). If you truly need the positive \ 537 difference, consider using that expression or the C function \ 538 `fdim`, depending on how you wish to handle NaN (please consider \ 539 filing an issue describing your use-case too)." 540 )] 541 pub fn abs_sub(self, other: f64) -> f64 { 542 unsafe { cmath::fdim(self, other) } 543 } 544 545 /// Returns the cube root of a number. 546 /// 547 /// # Examples 548 /// 549 /// ``` 550 /// let x = 8.0_f64; 551 /// 552 /// // x^(1/3) - 2 == 0 553 /// let abs_difference = (x.cbrt() - 2.0).abs(); 554 /// 555 /// assert!(abs_difference < 1e-10); 556 /// ``` 557 #[rustc_allow_incoherent_impl] 558 #[must_use = "method returns a new number and does not mutate the original value"] 559 #[inline] 560 pub fn cbrt(self) -> f64 { 561 unsafe { cmath::cbrt(self) } 562 } 563 564 /// Compute the distance between the origin and a point (`x`, `y`) on the 565 /// Euclidean plane. Equivalently, compute the length of the hypotenuse of a 566 /// right-angle triangle with other sides having length `x.abs()` and 567 /// `y.abs()`. 568 /// 569 /// # Examples 570 /// 571 /// ``` 572 /// let x = 2.0_f64; 573 /// let y = 3.0_f64; 574 /// 575 /// // sqrt(x^2 + y^2) 576 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); 577 /// 578 /// assert!(abs_difference < 1e-10); 579 /// ``` 580 #[rustc_allow_incoherent_impl] 581 #[must_use = "method returns a new number and does not mutate the original value"] 582 #[inline] 583 pub fn hypot(self, other: f64) -> f64 { 584 unsafe { cmath::hypot(self, other) } 585 } 586 587 /// Computes the sine of a number (in radians). 588 /// 589 /// # Examples 590 /// 591 /// ``` 592 /// let x = std::f64::consts::FRAC_PI_2; 593 /// 594 /// let abs_difference = (x.sin() - 1.0).abs(); 595 /// 596 /// assert!(abs_difference < 1e-10); 597 /// ``` 598 #[rustc_allow_incoherent_impl] 599 #[must_use = "method returns a new number and does not mutate the original value"] 600 #[inline] 601 pub fn sin(self) -> f64 { 602 unsafe { intrinsics::sinf64(self) } 603 } 604 605 /// Computes the cosine of a number (in radians). 606 /// 607 /// # Examples 608 /// 609 /// ``` 610 /// let x = 2.0 * std::f64::consts::PI; 611 /// 612 /// let abs_difference = (x.cos() - 1.0).abs(); 613 /// 614 /// assert!(abs_difference < 1e-10); 615 /// ``` 616 #[rustc_allow_incoherent_impl] 617 #[must_use = "method returns a new number and does not mutate the original value"] 618 #[inline] 619 pub fn cos(self) -> f64 { 620 unsafe { intrinsics::cosf64(self) } 621 } 622 623 /// Computes the tangent of a number (in radians). 624 /// 625 /// # Examples 626 /// 627 /// ``` 628 /// let x = std::f64::consts::FRAC_PI_4; 629 /// let abs_difference = (x.tan() - 1.0).abs(); 630 /// 631 /// assert!(abs_difference < 1e-14); 632 /// ``` 633 #[rustc_allow_incoherent_impl] 634 #[must_use = "method returns a new number and does not mutate the original value"] 635 #[inline] 636 pub fn tan(self) -> f64 { 637 unsafe { cmath::tan(self) } 638 } 639 640 /// Computes the arcsine of a number. Return value is in radians in 641 /// the range [-pi/2, pi/2] or NaN if the number is outside the range 642 /// [-1, 1]. 643 /// 644 /// # Examples 645 /// 646 /// ``` 647 /// let f = std::f64::consts::FRAC_PI_2; 648 /// 649 /// // asin(sin(pi/2)) 650 /// let abs_difference = (f.sin().asin() - std::f64::consts::FRAC_PI_2).abs(); 651 /// 652 /// assert!(abs_difference < 1e-10); 653 /// ``` 654 #[doc(alias = "arcsin")] 655 #[rustc_allow_incoherent_impl] 656 #[must_use = "method returns a new number and does not mutate the original value"] 657 #[inline] 658 pub fn asin(self) -> f64 { 659 unsafe { cmath::asin(self) } 660 } 661 662 /// Computes the arccosine of a number. Return value is in radians in 663 /// the range [0, pi] or NaN if the number is outside the range 664 /// [-1, 1]. 665 /// 666 /// # Examples 667 /// 668 /// ``` 669 /// let f = std::f64::consts::FRAC_PI_4; 670 /// 671 /// // acos(cos(pi/4)) 672 /// let abs_difference = (f.cos().acos() - std::f64::consts::FRAC_PI_4).abs(); 673 /// 674 /// assert!(abs_difference < 1e-10); 675 /// ``` 676 #[doc(alias = "arccos")] 677 #[rustc_allow_incoherent_impl] 678 #[must_use = "method returns a new number and does not mutate the original value"] 679 #[inline] 680 pub fn acos(self) -> f64 { 681 unsafe { cmath::acos(self) } 682 } 683 684 /// Computes the arctangent of a number. Return value is in radians in the 685 /// range [-pi/2, pi/2]; 686 /// 687 /// # Examples 688 /// 689 /// ``` 690 /// let f = 1.0_f64; 691 /// 692 /// // atan(tan(1)) 693 /// let abs_difference = (f.tan().atan() - 1.0).abs(); 694 /// 695 /// assert!(abs_difference < 1e-10); 696 /// ``` 697 #[doc(alias = "arctan")] 698 #[rustc_allow_incoherent_impl] 699 #[must_use = "method returns a new number and does not mutate the original value"] 700 #[inline] 701 pub fn atan(self) -> f64 { 702 unsafe { cmath::atan(self) } 703 } 704 705 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians. 706 /// 707 /// * `x = 0`, `y = 0`: `0` 708 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]` 709 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]` 710 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)` 711 /// 712 /// # Examples 713 /// 714 /// ``` 715 /// // Positive angles measured counter-clockwise 716 /// // from positive x axis 717 /// // -pi/4 radians (45 deg clockwise) 718 /// let x1 = 3.0_f64; 719 /// let y1 = -3.0_f64; 720 /// 721 /// // 3pi/4 radians (135 deg counter-clockwise) 722 /// let x2 = -3.0_f64; 723 /// let y2 = 3.0_f64; 724 /// 725 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f64::consts::FRAC_PI_4)).abs(); 726 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f64::consts::FRAC_PI_4)).abs(); 727 /// 728 /// assert!(abs_difference_1 < 1e-10); 729 /// assert!(abs_difference_2 < 1e-10); 730 /// ``` 731 #[rustc_allow_incoherent_impl] 732 #[must_use = "method returns a new number and does not mutate the original value"] 733 #[inline] 734 pub fn atan2(self, other: f64) -> f64 { 735 unsafe { cmath::atan2(self, other) } 736 } 737 738 /// Simultaneously computes the sine and cosine of the number, `x`. Returns 739 /// `(sin(x), cos(x))`. 740 /// 741 /// # Examples 742 /// 743 /// ``` 744 /// let x = std::f64::consts::FRAC_PI_4; 745 /// let f = x.sin_cos(); 746 /// 747 /// let abs_difference_0 = (f.0 - x.sin()).abs(); 748 /// let abs_difference_1 = (f.1 - x.cos()).abs(); 749 /// 750 /// assert!(abs_difference_0 < 1e-10); 751 /// assert!(abs_difference_1 < 1e-10); 752 /// ``` 753 #[doc(alias = "sincos")] 754 #[rustc_allow_incoherent_impl] 755 #[inline] 756 pub fn sin_cos(self) -> (f64, f64) { 757 (self.sin(), self.cos()) 758 } 759 760 /// Returns `e^(self) - 1` in a way that is accurate even if the 761 /// number is close to zero. 762 /// 763 /// # Examples 764 /// 765 /// ``` 766 /// let x = 1e-16_f64; 767 /// 768 /// // for very small x, e^x is approximately 1 + x + x^2 / 2 769 /// let approx = x + x * x / 2.0; 770 /// let abs_difference = (x.exp_m1() - approx).abs(); 771 /// 772 /// assert!(abs_difference < 1e-20); 773 /// ``` 774 #[rustc_allow_incoherent_impl] 775 #[must_use = "method returns a new number and does not mutate the original value"] 776 #[inline] 777 pub fn exp_m1(self) -> f64 { 778 unsafe { cmath::expm1(self) } 779 } 780 781 /// Returns `ln(1+n)` (natural logarithm) more accurately than if 782 /// the operations were performed separately. 783 /// 784 /// # Examples 785 /// 786 /// ``` 787 /// let x = 1e-16_f64; 788 /// 789 /// // for very small x, ln(1 + x) is approximately x - x^2 / 2 790 /// let approx = x - x * x / 2.0; 791 /// let abs_difference = (x.ln_1p() - approx).abs(); 792 /// 793 /// assert!(abs_difference < 1e-20); 794 /// ``` 795 #[doc(alias = "log1p")] 796 #[rustc_allow_incoherent_impl] 797 #[must_use = "method returns a new number and does not mutate the original value"] 798 #[inline] 799 pub fn ln_1p(self) -> f64 { 800 unsafe { cmath::log1p(self) } 801 } 802 803 /// Hyperbolic sine function. 804 /// 805 /// # Examples 806 /// 807 /// ``` 808 /// let e = std::f64::consts::E; 809 /// let x = 1.0_f64; 810 /// 811 /// let f = x.sinh(); 812 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)` 813 /// let g = ((e * e) - 1.0) / (2.0 * e); 814 /// let abs_difference = (f - g).abs(); 815 /// 816 /// assert!(abs_difference < 1e-10); 817 /// ``` 818 #[rustc_allow_incoherent_impl] 819 #[must_use = "method returns a new number and does not mutate the original value"] 820 #[inline] 821 pub fn sinh(self) -> f64 { 822 unsafe { cmath::sinh(self) } 823 } 824 825 /// Hyperbolic cosine function. 826 /// 827 /// # Examples 828 /// 829 /// ``` 830 /// let e = std::f64::consts::E; 831 /// let x = 1.0_f64; 832 /// let f = x.cosh(); 833 /// // Solving cosh() at 1 gives this result 834 /// let g = ((e * e) + 1.0) / (2.0 * e); 835 /// let abs_difference = (f - g).abs(); 836 /// 837 /// // Same result 838 /// assert!(abs_difference < 1.0e-10); 839 /// ``` 840 #[rustc_allow_incoherent_impl] 841 #[must_use = "method returns a new number and does not mutate the original value"] 842 #[inline] 843 pub fn cosh(self) -> f64 { 844 unsafe { cmath::cosh(self) } 845 } 846 847 /// Hyperbolic tangent function. 848 /// 849 /// # Examples 850 /// 851 /// ``` 852 /// let e = std::f64::consts::E; 853 /// let x = 1.0_f64; 854 /// 855 /// let f = x.tanh(); 856 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` 857 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2)); 858 /// let abs_difference = (f - g).abs(); 859 /// 860 /// assert!(abs_difference < 1.0e-10); 861 /// ``` 862 #[rustc_allow_incoherent_impl] 863 #[must_use = "method returns a new number and does not mutate the original value"] 864 #[inline] 865 pub fn tanh(self) -> f64 { 866 unsafe { cmath::tanh(self) } 867 } 868 869 /// Inverse hyperbolic sine function. 870 /// 871 /// # Examples 872 /// 873 /// ``` 874 /// let x = 1.0_f64; 875 /// let f = x.sinh().asinh(); 876 /// 877 /// let abs_difference = (f - x).abs(); 878 /// 879 /// assert!(abs_difference < 1.0e-10); 880 /// ``` 881 #[doc(alias = "arcsinh")] 882 #[rustc_allow_incoherent_impl] 883 #[must_use = "method returns a new number and does not mutate the original value"] 884 #[inline] 885 pub fn asinh(self) -> f64 { 886 let ax = self.abs(); 887 let ix = 1.0 / ax; 888 (ax + (ax / (Self::hypot(1.0, ix) + ix))) 889 .ln_1p() 890 .copysign(self) 891 } 892 893 /// Inverse hyperbolic cosine function. 894 /// 895 /// # Examples 896 /// 897 /// ``` 898 /// let x = 1.0_f64; 899 /// let f = x.cosh().acosh(); 900 /// 901 /// let abs_difference = (f - x).abs(); 902 /// 903 /// assert!(abs_difference < 1.0e-10); 904 /// ``` 905 #[doc(alias = "arccosh")] 906 #[rustc_allow_incoherent_impl] 907 #[must_use = "method returns a new number and does not mutate the original value"] 908 #[inline] 909 pub fn acosh(self) -> f64 { 910 if self < 1.0 { 911 Self::NAN 912 } else { 913 (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln() 914 } 915 } 916 917 /// Inverse hyperbolic tangent function. 918 /// 919 /// # Examples 920 /// 921 /// ``` 922 /// let e = std::f64::consts::E; 923 /// let f = e.tanh().atanh(); 924 /// 925 /// let abs_difference = (f - e).abs(); 926 /// 927 /// assert!(abs_difference < 1.0e-10); 928 /// ``` 929 #[doc(alias = "arctanh")] 930 #[rustc_allow_incoherent_impl] 931 #[must_use = "method returns a new number and does not mutate the original value"] 932 #[inline] 933 pub fn atanh(self) -> f64 { 934 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() 935 } 936 937 /// Gamma function. 938 /// 939 /// # Examples 940 /// 941 /// ``` 942 /// #![feature(float_gamma)] 943 /// let x = 5.0f64; 944 /// 945 /// let abs_difference = (x.gamma() - 24.0).abs(); 946 /// 947 /// assert!(abs_difference <= f64::EPSILON); 948 /// ``` 949 #[rustc_allow_incoherent_impl] 950 #[must_use = "method returns a new number and does not mutate the original value"] 951 #[inline] 952 pub fn gamma(self) -> f64 { 953 unsafe { cmath::tgamma(self) } 954 } 955 956 /// Natural logarithm of the absolute value of the gamma function 957 /// 958 /// The integer part of the tuple indicates the sign of the gamma function. 959 /// 960 /// # Examples 961 /// 962 /// ``` 963 /// #![feature(float_gamma)] 964 /// let x = 2.0f64; 965 /// 966 /// let abs_difference = (x.ln_gamma().0 - 0.0).abs(); 967 /// 968 /// assert!(abs_difference <= f64::EPSILON); 969 /// ``` 970 #[rustc_allow_incoherent_impl] 971 #[must_use = "method returns a new number and does not mutate the original value"] 972 #[inline] 973 pub fn ln_gamma(self) -> (f64, i32) { 974 let mut signgamp: i32 = 0; 975 let x = unsafe { cmath::lgamma_r(self, &mut signgamp) }; 976 (x, signgamp) 977 } 978 } 979