diff options
Diffstat (limited to 'lib/pure/math.nim')
| -rw-r--r-- | lib/pure/math.nim | 254 |
1 files changed, 151 insertions, 103 deletions
diff --git a/lib/pure/math.nim b/lib/pure/math.nim index bea655a0e..ed7d2382f 100644 --- a/lib/pure/math.nim +++ b/lib/pure/math.nim @@ -57,13 +57,14 @@ import std/private/since {.push debugger: off.} # the user does not want to trace a part # of the standard library! -import bitops, fenv +import std/[bitops, fenv] +import system/countbits_impl when defined(nimPreviewSlimSystem): import std/assertions -when defined(c) or defined(cpp): +when not defined(js) and not defined(nimscript): # C proc c_isnan(x: float): bool {.importc: "isnan", header: "<math.h>".} # a generic like `x: SomeFloat` might work too if this is implemented via a C macro. @@ -77,6 +78,41 @@ when defined(c) or defined(cpp): importc: "frexpf", header: "<math.h>".} func c_frexp2(x: cdouble, exponent: var cint): cdouble {. importc: "frexp", header: "<math.h>".} + + type + div_t {.importc, header: "<stdlib.h>".} = object + quot: cint + rem: cint + ldiv_t {.importc, header: "<stdlib.h>".} = object + quot: clong + rem: clong + lldiv_t {.importc, header: "<stdlib.h>".} = object + quot: clonglong + rem: clonglong + + when cint isnot clong: + func divmod_c(x, y: cint): div_t {.importc: "div", header: "<stdlib.h>".} + when clong isnot clonglong: + func divmod_c(x, y: clonglong): lldiv_t {.importc: "lldiv", header: "<stdlib.h>".} + func divmod_c(x, y: clong): ldiv_t {.importc: "ldiv", header: "<stdlib.h>".} + func divmod*[T: SomeInteger](x, y: T): (T, T) {.inline.} = + ## Specialized instructions for computing both division and modulus. + ## Return structure is: (quotient, remainder) + runnableExamples: + doAssert divmod(5, 2) == (2, 1) + doAssert divmod(5, -3) == (-1, 2) + when T is cint | clong | clonglong: + when compileOption("overflowChecks"): + if y == 0: + raise new(DivByZeroDefect) + elif (x == T.low and y == -1.T): + raise new(OverflowDefect) + let res = divmod_c(x, y) + result[0] = res.quot + result[1] = res.rem + else: + result[0] = x div y + result[1] = x mod y func binom*(n, k: int): int = ## Computes the [binomial coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient). @@ -120,7 +156,7 @@ func fac*(n: int): int = {.push checks: off, line_dir: off, stack_trace: off.} -when defined(posix) and not defined(genode): +when defined(posix) and not defined(genode) and not defined(macosx): {.passl: "-lm".} const @@ -165,7 +201,7 @@ func isNaN*(x: SomeFloat): bool {.inline, since: (1,5,1).} = template fn: untyped = result = x != x when nimvm: fn() else: - when defined(js): fn() + when defined(js) or defined(nimscript): fn() else: result = c_isnan(x) when defined(js): @@ -184,13 +220,13 @@ when defined(js): let a = newFloat64Array(buffer) let b = newUint32Array(buffer) a[0] = x - asm """ + {.emit: """ function updateBit(num, bitPos, bitVal) { return (num & ~(1 << bitPos)) | (bitVal << bitPos); } `b`[1] = updateBit(`b`[1], 31, `sgn`); - `result` = `a`[0] - """ + `result` = `a`[0]; + """.} proc signbit*(x: SomeFloat): bool {.inline, since: (1, 5, 1).} = ## Returns true if `x` is negative, false otherwise. @@ -235,7 +271,6 @@ func classify*(x: float): FloatClass = ## Classifies a floating point value. ## ## Returns `x`'s class as specified by the `FloatClass enum<#FloatClass>`_. - ## Doesn't work with `--passc:-ffast-math`. runnableExamples: doAssert classify(0.3) == fcNormal doAssert classify(0.0) == fcZero @@ -244,6 +279,7 @@ func classify*(x: float): FloatClass = doAssert classify(5.0e-324) == fcSubnormal # JavaScript and most C compilers have no classify: + if isNan(x): return fcNan if x == 0.0: if 1.0 / x == Inf: return fcZero @@ -252,7 +288,6 @@ func classify*(x: float): FloatClass = if x * 0.5 == x: if x > 0.0: return fcInf else: return fcNegInf - if x != x: return fcNan if abs(x) < MinFloatNormal: return fcSubnormal return fcNormal @@ -326,68 +361,8 @@ func nextPowerOfTwo*(x: int): int = result = result or (result shr 1) result += 1 + ord(x <= 0) -func sum*[T](x: openArray[T]): T = - ## Computes the sum of the elements in `x`. - ## - ## If `x` is empty, 0 is returned. - ## - ## **See also:** - ## * `prod func <#prod,openArray[T]>`_ - ## * `cumsum func <#cumsum,openArray[T]>`_ - ## * `cumsummed func <#cumsummed,openArray[T]>`_ - runnableExamples: - doAssert sum([1, 2, 3, 4]) == 10 - doAssert sum([-4, 3, 5]) == 4 - - for i in items(x): result = result + i - -func prod*[T](x: openArray[T]): T = - ## Computes the product of the elements in `x`. - ## - ## If `x` is empty, 1 is returned. - ## - ## **See also:** - ## * `sum func <#sum,openArray[T]>`_ - ## * `fac func <#fac,int>`_ - runnableExamples: - doAssert prod([1, 2, 3, 4]) == 24 - doAssert prod([-4, 3, 5]) == -60 - - result = T(1) - for i in items(x): result = result * i - -func cumsummed*[T](x: openArray[T]): seq[T] = - ## Returns the cumulative (aka prefix) summation of `x`. - ## - ## If `x` is empty, `@[]` is returned. - ## - ## **See also:** - ## * `sum func <#sum,openArray[T]>`_ - ## * `cumsum func <#cumsum,openArray[T]>`_ for the in-place version - runnableExamples: - doAssert cumsummed([1, 2, 3, 4]) == @[1, 3, 6, 10] - - let xLen = x.len - if xLen == 0: - return @[] - result.setLen(xLen) - result[0] = x[0] - for i in 1 ..< xLen: result[i] = result[i - 1] + x[i] -func cumsum*[T](x: var openArray[T]) = - ## Transforms `x` in-place (must be declared as `var`) into its - ## cumulative (aka prefix) summation. - ## - ## **See also:** - ## * `sum func <#sum,openArray[T]>`_ - ## * `cumsummed func <#cumsummed,openArray[T]>`_ for a version which - ## returns a cumsummed sequence - runnableExamples: - var a = [1, 2, 3, 4] - cumsum(a) - doAssert a == @[1, 3, 6, 10] - for i in 1 ..< x.len: x[i] = x[i - 1] + x[i] when not defined(js): # C func sqrt*(x: float32): float32 {.importc: "sqrtf", header: "<math.h>".} @@ -853,6 +828,14 @@ else: # JS doAssert -6.5 mod 2.5 == -1.5 doAssert 6.5 mod -2.5 == 1.5 doAssert -6.5 mod -2.5 == -1.5 + + func divmod*[T:SomeInteger](num, denom: T): (T, T) = + runnableExamples: + doAssert divmod(5, 2) == (2, 1) + doAssert divmod(5, -3) == (-1, 2) + result[0] = num div denom + result[1] = num mod denom + func round*[T: float32|float64](x: T, places: int): T = ## Decimal rounding on a binary floating point number. @@ -1133,6 +1116,69 @@ func sgn*[T: SomeNumber](x: T): int {.inline.} = {.pop.} {.pop.} +func sum*[T](x: openArray[T]): T = + ## Computes the sum of the elements in `x`. + ## + ## If `x` is empty, 0 is returned. + ## + ## **See also:** + ## * `prod func <#prod,openArray[T]>`_ + ## * `cumsum func <#cumsum,openArray[T]>`_ + ## * `cumsummed func <#cumsummed,openArray[T]>`_ + runnableExamples: + doAssert sum([1, 2, 3, 4]) == 10 + doAssert sum([-4, 3, 5]) == 4 + + for i in items(x): result = result + i + +func prod*[T](x: openArray[T]): T = + ## Computes the product of the elements in `x`. + ## + ## If `x` is empty, 1 is returned. + ## + ## **See also:** + ## * `sum func <#sum,openArray[T]>`_ + ## * `fac func <#fac,int>`_ + runnableExamples: + doAssert prod([1, 2, 3, 4]) == 24 + doAssert prod([-4, 3, 5]) == -60 + + result = T(1) + for i in items(x): result = result * i + +func cumsummed*[T](x: openArray[T]): seq[T] = + ## Returns the cumulative (aka prefix) summation of `x`. + ## + ## If `x` is empty, `@[]` is returned. + ## + ## **See also:** + ## * `sum func <#sum,openArray[T]>`_ + ## * `cumsum func <#cumsum,openArray[T]>`_ for the in-place version + runnableExamples: + doAssert cumsummed([1, 2, 3, 4]) == @[1, 3, 6, 10] + + let xLen = x.len + if xLen == 0: + return @[] + result.setLen(xLen) + result[0] = x[0] + for i in 1 ..< xLen: result[i] = result[i - 1] + x[i] + +func cumsum*[T](x: var openArray[T]) = + ## Transforms `x` in-place (must be declared as `var`) into its + ## cumulative (aka prefix) summation. + ## + ## **See also:** + ## * `sum func <#sum,openArray[T]>`_ + ## * `cumsummed func <#cumsummed,openArray[T]>`_ for a version which + ## returns a cumsummed sequence + runnableExamples: + var a = [1, 2, 3, 4] + cumsum(a) + doAssert a == @[1, 3, 6, 10] + + for i in 1 ..< x.len: x[i] = x[i - 1] + x[i] + func `^`*[T: SomeNumber](x: T, y: Natural): T = ## Computes `x` to the power of `y`. ## @@ -1184,40 +1230,42 @@ func gcd*[T](x, y: T): T = swap x, y abs x -func gcd*(x, y: SomeInteger): SomeInteger = - ## Computes the greatest common (positive) divisor of `x` and `y`, - ## using the binary GCD (aka Stein's) algorithm. - ## - ## **See also:** - ## * `gcd func <#gcd,T,T>`_ for a float version - ## * `lcm func <#lcm,T,T>`_ - runnableExamples: - doAssert gcd(12, 8) == 4 - doAssert gcd(17, 63) == 1 - - when x is SomeSignedInt: - var x = abs(x) - else: - var x = x - when y is SomeSignedInt: - var y = abs(y) - else: - var y = y - - if x == 0: - return y - if y == 0: - return x - - let shift = countTrailingZeroBits(x or y) - y = y shr countTrailingZeroBits(y) - while x != 0: - x = x shr countTrailingZeroBits(x) - if y > x: - swap y, x - x -= y - y shl shift - +when useBuiltins: + ## this func uses bitwise comparisons from C compilers, which are not always available. + func gcd*(x, y: SomeInteger): SomeInteger = + ## Computes the greatest common (positive) divisor of `x` and `y`, + ## using the binary GCD (aka Stein's) algorithm. + ## + ## **See also:** + ## * `gcd func <#gcd,T,T>`_ for a float version + ## * `lcm func <#lcm,T,T>`_ + runnableExamples: + doAssert gcd(12, 8) == 4 + doAssert gcd(17, 63) == 1 + + when x is SomeSignedInt: + var x = abs(x) + else: + var x = x + when y is SomeSignedInt: + var y = abs(y) + else: + var y = y + + if x == 0: + return y + if y == 0: + return x + + let shift = countTrailingZeroBits(x or y) + y = y shr countTrailingZeroBits(y) + while x != 0: + x = x shr countTrailingZeroBits(x) + if y > x: + swap y, x + x -= y + y shl shift + func gcd*[T](x: openArray[T]): T {.since: (1, 1).} = ## Computes the greatest common (positive) divisor of the elements of `x`. ## |