Split "mpfr.rkt" into "gmp.rkt" and "mpfr.rkt"
Fixed bigfloat functions that assumed (fixnum? x) means x fits in a _long (not true on Win64) Hopefully fixed dangling pointer errors that broke `math/bigfloat' on Win64. It apparently had no _long/_int mismatches, but GC on Win64 will run between creating an `_mpz' and using its value after passing it as an output argument to MPFR functions. That doesn't seem to happen on 64-bit Linux or Mac. No idea why, but Win64 exposed the problem so... that's good, I guess. Rewrote `rational->bigfloat' to not use GMP's rationals More/better bigfloat tests Added bigfloat stress test w/ weak leak detection Reenabled custodian shutdown callback that clears MPFR constants, because it seems to work now Removed `mpfr-available?' because it would only return non-#f
This commit is contained in:
Neil Toronto
parent
bd1a63a43a
commit
d935bc0643
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@ -8,8 +8,6 @@
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(require/typed
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"mpfr.rkt"
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;; Library stuffs
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[mpfr-available? (-> Boolean)]
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;; Parameters
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[bf-rounding-mode (Parameterof Rounding-Mode)]
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[bf-min-precision Exact-Positive-Integer]
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@ -48,7 +46,7 @@
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[bfsum ((Listof Bigfloat) -> Bigfloat)]
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[bfmax2 (Bigfloat Bigfloat -> Bigfloat)]
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[bfmin2 (Bigfloat Bigfloat -> Bigfloat)]
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[bfeqv? (Bigfloat Bigfloat -> Boolean)]
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[bf=? (Bigfloat Bigfloat -> Boolean)]
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[bflt? (Bigfloat Bigfloat -> Boolean)]
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[bflte? (Bigfloat Bigfloat -> Boolean)]
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[bfgt? (Bigfloat Bigfloat -> Boolean)]
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@ -126,7 +124,7 @@
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(: bfpred? (Bigfloat Bigfloat * -> Boolean))
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(define (bfpred? x . xs) (fold-binary-pred bfpred2? x xs))))
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(define-nary-pred bf= bfeqv?)
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(define-nary-pred bf= bf=?)
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(define-nary-pred bf< bflt?)
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(define-nary-pred bf<= bflte?)
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(define-nary-pred bf> bfgt?)
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@ -147,8 +145,6 @@
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(bf+ (flonum->bigfloat x1) (flonum->bigfloat x2)))
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(provide
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;; Library stuffs
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mpfr-available?
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;; Parameters
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bf-rounding-mode
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bf-min-precision
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166
collects/math/private/bigfloat/gmp.rkt
Normal file
166
collects/math/private/bigfloat/gmp.rkt
Normal file
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@ -0,0 +1,166 @@
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#lang racket/base
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(require (for-syntax racket/base)
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ffi/unsafe
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ffi/unsafe/define
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racket/runtime-path)
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(provide
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_mp_size_t
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_limb_t
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sizeof-limb_t
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gmp-limb-bits
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_mpz-pointer
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new-mpz
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integer->mpz
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mpz->integer)
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;; ===================================================================================================
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;; Setup
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(define-runtime-path libgmp-so
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(case (system-type)
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[(macosx) '(so "libgmp.10.dylib")]
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[(windows) '(so "libgmp-10.dll")]
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[else '(so "libgmp")]))
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(define gmp-lib (ffi-lib libgmp-so '("10" "3" "") #:fail (λ () #f)))
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(define-syntax-rule (get-gmp-fun name type)
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(get-ffi-obj name gmp-lib type (make-not-available name)))
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;; ===================================================================================================
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;; Types
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;; Size header, precision, sign, exponent, limb (a "digit" in an _mpz)
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(define _mp_size_t _long)
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(define _limb_t _ulong)
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(define _mp_bitcnt_t _ulong)
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(define sizeof-limb_t (ctype-sizeof _limb_t))
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;; Number of bits in a limb
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(define gmp-limb-bits (* 8 sizeof-limb_t))
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;; We don't support "nail" builds, which haven't worked since before GMP 4.3 anyway (a "nail" takes
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;; two bits from each limb, and is supposed to speed up carries between limbs on certain systems)
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;; GMP's big integers
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(define-cstruct _mpz ([alloc _int] [size _int] [limbs _pointer]))
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;; ALWAYS let GMP manage the memory pointed at by the limbs field in an _mpz. It likes to reallocate
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;; limbs, particularly when the _mpz is an output argument.
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;; This means that _mpz instances take up memory that Racket can't account for, so they should only
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;; be used as temporary values. Possibly permanent values should be either instances of _mpfr or
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;; Racket's own exact integers.
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(define mpz-init (get-gmp-fun '__gmpz_init (_fun _mpz-pointer -> _void)))
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(define mpz-init2 (get-gmp-fun '__gmpz_init2 (_fun _mpz-pointer _mp_bitcnt_t -> _void)))
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(define mpz-clear (get-gmp-fun '__gmpz_clear (_fun _mpz-pointer -> _void)))
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;; new-mpz : [_mp_bitcnt_t] -> _mpz-pointer
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;; Creates an _mpz that is managed by the garbage collector, but whose limbs are not, and which is
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;; not relocatable. These are always safe to pass to mpz_* functions.
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(define (new-mpz [bits 0])
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(define z (make-mpz 0 0 #f))
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;; Same as above, but don't let it move:
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;(define z (ptr-ref (malloc _mpz 'atomic-interior) _mpz))
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(if (= bits 0) (mpz-init z) (mpz-init2 z bits))
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(register-finalizer z (λ (z) (mpz-clear z)))
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z)
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;; ===================================================================================================
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;; Conversions
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(define mpz-get-si (get-gmp-fun '__gmpz_get_si (_fun _mpz-pointer -> _long)))
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(define mpz-fits-long? (get-gmp-fun '__gmpz_fits_slong_p (_fun _mpz-pointer -> _int)))
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;; integer->mpz : integer -> _mpz
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;; Converts a Racket integer to an _mpz.
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(define (integer->mpz n)
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(define abs-n (abs n))
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(define z (new-mpz (integer-length abs-n)))
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(define len (mpz-alloc z))
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(define limbs (mpz-limbs z))
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(let loop ([i 0])
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(when (i . < . len)
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(define bit (* i gmp-limb-bits))
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(ptr-set! limbs _limb_t i (bitwise-bit-field abs-n bit (+ bit gmp-limb-bits)))
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(loop (+ i 1))))
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(define size (ceiling (/ (integer-length abs-n) gmp-limb-bits)))
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(set-mpz-size! z (if (< n 0) (- size) size))
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z)
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;; size+limbs->integer : integer (listof integer) -> integer
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;; Converts a size (which may be negative) and a limb list into an integer.
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(define (size+limbs->integer size limbs)
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(define len (abs size))
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(define num
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(let loop ([i 0] [res 0])
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(cond [(i . < . len)
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(define v (ptr-ref limbs _limb_t i))
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(loop (+ i 1) (bitwise-ior res (arithmetic-shift v (* i gmp-limb-bits))))]
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[else res])))
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(if (negative? size) (- num) num))
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;; mpz->integer : _mpz -> integer
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;; Converts an mpz_t to a Racket integer.
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(define (mpz->integer z)
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(if (zero? (mpz-fits-long? z))
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(size+limbs->integer (mpz-size z) (mpz-limbs z))
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(mpz-get-si z)))
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;; ===================================================================================================
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;; Number Theoretic Functions
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;; http://gmplib.org/manual/Number-Theoretic-Functions.html#Number-Theoretic-Functions
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(define mpz-probab-prime-p
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(get-gmp-fun '__gmpz_probab_prime_p (_fun _mpz-pointer _int -> _int)))
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(define (probably-prime n [repetitions 10])
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(case (mpz-probab-prime-p (integer->mpz n) repetitions)
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[(0) 'composite]
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[(1) 'probably-prime]
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[(2) 'prime]))
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(define (prime? n)
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(case (probably-prime n)
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[(probably-prime prime) #t]
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[else #f]))
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(define mpz-nextprime
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(get-gmp-fun '__gmpz_nextprime (_fun _mpz-pointer _mpz-pointer -> _void)))
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(define (next-prime op)
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(define result (new-mpz))
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(mpz-nextprime result (integer->mpz op))
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(mpz->integer result))
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(define mpz-invert
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(get-gmp-fun '__gmpz_invert (_fun _mpz-pointer _mpz-pointer _mpz-pointer -> _void)))
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(define (mod-inverse n modulus)
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(define result (new-mpz))
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(mpz-invert result (integer->mpz n) (integer->mpz modulus))
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(mpz->integer result))
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(define mpz-jacobi
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(get-gmp-fun '__gmpz_jacobi (_fun _mpz-pointer _mpz-pointer -> _int)))
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(define (jacobi a b)
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(mpz-jacobi (integer->mpz a) (integer->mpz b)))
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(define mpz-legendre
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(get-gmp-fun '__gmpz_legendre (_fun _mpz-pointer _mpz-pointer -> _int)))
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(define (legendre a b)
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(mpz-legendre (integer->mpz a) (integer->mpz b)))
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(define mpz-remove
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(get-gmp-fun '__gmpz_remove (_fun _mpz-pointer _mpz-pointer _mpz-pointer -> _int)))
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(define (remove-factor z f)
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(define result (new-mpz))
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(define n (mpz-remove result (integer->mpz z) (integer->mpz f)))
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(define z/f (mpz->integer result))
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(values z/f n))
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@ -1,21 +1,20 @@
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#lang racket/base
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(require ffi/unsafe
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(require (for-syntax racket/base)
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ffi/unsafe
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ffi/unsafe/cvector
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ffi/unsafe/custodian
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ffi/unsafe/define
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racket/math
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racket/runtime-path
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racket/list
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racket/promise
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racket/serialize
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(for-syntax racket/base))
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(require (only-in rnrs/arithmetic/bitwise-6
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bitwise-first-bit-set))
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(only-in rnrs/arithmetic/bitwise-6
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bitwise-first-bit-set)
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"gmp.rkt"
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"utils.rkt")
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(provide
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;; Library stuffs
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mpfr-available?
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;; Parameters
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bf-rounding-mode
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bf-min-precision
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;; ===================================================================================================
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;; Setup/takedown
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;; All MPFR functions and constants are delayed so that libmpfr and libgmp are loaded on first use.
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;; This allows the `math' collection to export `math/bigfloat', and for `math/special-functions' to
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;; use MPFR for functions that don't have a Typed Racket implementation yet. On systems without MPFR,
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;; no exceptions will be raised unless a user tries to use those functions.
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(define-runtime-path libgmp-so
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(case (system-type)
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[(macosx) '(so "libgmp.10.dylib")]
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[(windows) '(so "libgmp-10.dll")]
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[else '(so "libgmp")]))
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(define-runtime-path libmpfr-so
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(case (system-type)
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[(macosx) '(so "libmpfr.4.dylib")]
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[(windows) '(so "libmpfr-4.dll")]
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[else '(so "libmpfr")]))
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(define gmp-lib (ffi-lib libgmp-so '("10" "3" "") #:fail (λ () #f)))
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(define mpfr-lib (ffi-lib libmpfr-so '("4" "1" "") #:fail (λ () #f)))
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(define-syntax-rule (get-gmp-fun name type)
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(get-ffi-obj name gmp-lib type (make-not-available name)))
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(define-syntax get-mpfr-fun
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(syntax-rules ()
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[(_ name type) (get-mpfr-fun name type (make-not-available name))]
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[(_ name type fail-thunk) (get-ffi-obj name mpfr-lib type fail-thunk)]))
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(define mpfr-free-cache (get-mpfr-fun 'mpfr_free_cache (_fun -> _void)))
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#;; This may be crashing Racket
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;; This may be crashing Racket
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(define mpfr-shutdown (register-custodian-shutdown
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mpfr-free-cache (λ (free) (free))))
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(define (mpfr-available?)
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(and gmp-lib mpfr-lib))
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;; ===================================================================================================
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;; Parameters: rounding mode, bit precision, printing
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;; Exponent min and max are not included; they can't be made into parameters, and if we tried they
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@ -97,8 +79,8 @@
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;; minimum precision (1 bit can't be rounded correctly)
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(define bf-min-precision 2)
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;; maximum precision (the number on 64-bit platforms is ridiculously large)
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(define bf-max-precision (- (expt 2 (- (* (ctype-sizeof _long) 8) 1)) 1))
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;; maximum precision (the number when longs are 64 bits is ridiculously large)
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(define bf-max-precision _long-max)
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(define bf-precision
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(make-parameter 128 (λ (p) (cond [(p . < . bf-min-precision) bf-min-precision]
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@ -111,20 +93,9 @@
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;; Rounding modes (not all of them, just the useful/well-supported ones)
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(define _rnd_t (_enum '(nearest zero up down)))
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;; Size header, precision, sign, exponent, limb (part of a bigint)
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(define _mp_size_t _long)
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(define _prec_t _long)
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(define _sign_t _int)
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(define _exp_t _long)
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(define _limb_t _ulong)
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;; Also the size of a union of _mp_size_t and _limb_t (which MPFR uses internally)
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(define sizeof-limb_t (ctype-sizeof _limb_t))
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;; Number of bits in a limb
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(define gmp-limb-bits (* 8 sizeof-limb_t))
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;; We don't support "nail" builds, which haven't worked since before GMP 4.3 anyway (a "nail" takes
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;; two bits from each limb, and is supposed to speed up carries between limbs on certain systems)
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;; The "limbs" of a bigint are an array of _limb_t, where the element 0 is the length of the array
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;; in bytes. Entirely reasonable... except that MPFR's bigfloats point at *element 1* for the
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@ -147,9 +118,8 @@
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))
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(define (bigfloat-equal? x1 x2 _)
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(and (= (bigfloat-sign x1) (bigfloat-sign x2))
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(or (bfeqv? x1 x2)
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(and (bfnan? x1) (bfnan? x2)))))
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(or (and (bfnan? x1) (bfnan? x2))
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(bf=? x1 x2)))
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(define (canonicalize-sig+exp sig exp)
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(cond [(zero? sig) (values 0 0)]
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@ -164,16 +134,16 @@
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(define (bfcanonicalize x)
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(cond [(bfzero? x) (if (zero? (bigfloat-sign x)) (force 0.bf) (force -0.bf))]
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[(bfnan? x) (force +nan.bf)]
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[(bfinfinite? x) (if (bfnegative? x) (force -inf.bf) (force +inf.bf))]
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[(bfinfinite? x) (if (zero? (bigfloat-sign x)) (force +inf.bf) (force -inf.bf))]
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[else
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(let*-values ([(sig exp) (bigfloat-sig+exp x)]
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[(sig exp) (canonicalize-sig+exp sig exp)])
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(parameterize ([bf-precision (integer-length sig)])
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(bf sig exp)))]))
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(sig+exp->bigfloat sig exp)))]))
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(define (bigfloat-hash x recur-hash)
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(let*-values ([(sig exp) (bigfloat-sig+exp x)]
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[(sig exp) (canonicalize-sig+exp sig exp)])
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(let*-values ([(x) (bfcanonicalize x)]
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[(sig exp) (bigfloat-sig+exp x)])
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(recur-hash (vector (bigfloat-sign x) sig exp))))
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(define bigfloat-deserialize
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@ -193,7 +163,7 @@
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(unless (exact-integer? exp)
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(raise-argument-error 'bigfloat-deserialize "Integer" 2 p sig exp))
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(parameterize ([bf-precision p])
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(bf sig exp))]))
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(sig+exp->bigfloat sig exp))]))
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(define bigfloat-deserialize-info
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(make-deserialize-info
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@ -216,6 +186,7 @@
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;; mpfr_t: a multi-precision float with rounding (the main data type)
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(define-cstruct _mpfr ([prec _prec_t] [sign _sign_t] [exp _exp_t] [d (_gcable _mpfr_limbs)])
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#:property prop:custom-print-quotable 'never
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#:property prop:custom-write (λ (b port mode) (bigfloat-custom-write b port mode))
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#:property prop:equal+hash (list bigfloat-equal? bigfloat-hash bigfloat-hash)
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#:property prop:serializable bigfloat-serialize-info)
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@ -231,39 +202,25 @@
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(define (new-mpfr prec)
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(define n (add1 (quotient (- prec 1) gmp-limb-bits)))
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(define size (* sizeof-limb_t (+ n 1)))
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;; Allocate d so that it won't be traced (atomic) or moved (interior)
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;; Allocate d and x so they won't be traced (atomic) or moved (interior)
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(define d (make-cvector* (malloc size 'atomic-interior) _limb_t (+ n 1)))
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(define x (make-mpfr prec 1 0 d))
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;; Use a finalizer to keep a reference to d as long as x is alive (x's memory isn't traced because
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;; it's allocated using make-mpfr; this is equivalent to tracing through d only)
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;; The next five lines are like the one above, but malloc uses 'atomic-interior instead of 'atomic
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;(define x (ptr-ref (malloc (ctype-sizeof _mpfr) 'atomic-interior) _mpfr))
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;(set-mpfr-prec! x prec)
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;(set-mpfr-sign! x 1)
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;(set-mpfr-exp! x 0)
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;(set-mpfr-d! x d)
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;; Use a finalizer to keep a reference to d as long as x is alive (this is equivalent to tracing
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;; through d)
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(register-finalizer x (λ (x) d))
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(mpfr-set-nan x)
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x)
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;; We always create mpfr_ts using new-mpfr. In doing so, we assume that no mpfr_* function will ever
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;; try to reallocate limbs. This is a good assumption because an mpfr_t's precision is fixed from
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;; when it's allocated to when it's deallocated. (There's no reason to allocate new limbs for an
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;; mpfr_t without changing its precision.)
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;; Big integers, big rationals
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(define-cstruct _mpz ([alloc _int] [size _int] [limbs _pointer]))
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(define-cstruct _mpq ([num _mpz] [den _mpz]))
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||||
|
||||
;; BE CAREFUL WITH THESE. If you make one with make-mpz or make-mpq, DO NOT send it to a function
|
||||
;; that will reallocate its limbs. In particular, NEVER use it as an output argument. However, you
|
||||
;; can generally use it as an input argument.
|
||||
|
||||
;; MPFR memory management for mpz_t
|
||||
(define mpz-init (get-gmp-fun '__gmpz_init (_fun _mpz-pointer -> _void)))
|
||||
(define mpz-clear (get-gmp-fun '__gmpz_clear (_fun _mpz-pointer -> _void)))
|
||||
|
||||
;; raw-mpz : -> _mpz-pointer
|
||||
;; Creates an mpz_t that is managed by the garbage collector, but whose limbs are not. These are
|
||||
;; always safe to pass to mpz_* functions. We use them for output parameters.
|
||||
(define (raw-mpz)
|
||||
(define x (ptr-ref (malloc _mpz 'atomic-interior) _mpz))
|
||||
(mpz-init x)
|
||||
x)
|
||||
;; We always create _mpfr instances using new-mpfr. In doing so, we assume that no mpfr_* function
|
||||
;; will ever try to reallocate limbs. This is a good assumption because an _mpfr's precision is
|
||||
;; fixed from when it's allocated to when it's deallocated. (There's no reason to allocate new limbs
|
||||
;; for an _mpfr without changing its precision.)
|
||||
|
||||
;; ===================================================================================================
|
||||
;; Accessors
|
||||
|
|
@ -293,10 +250,9 @@
|
|||
;; bigfloat-sig+exp : bigfloat -> integer integer
|
||||
;; Returns the signed significand and exponent of a bigfloat.
|
||||
(define (bigfloat-sig+exp x)
|
||||
(define z (raw-mpz))
|
||||
(define z (new-mpz))
|
||||
(define exp (mpfr-get-z-2exp z x))
|
||||
(define sig (mpz->integer z))
|
||||
(mpz-clear z)
|
||||
(values sig exp))
|
||||
|
||||
;; bigfloat-significand : bigfloat -> integer
|
||||
|
|
@ -311,35 +267,14 @@
|
|||
(define mpfr-set-d (get-mpfr-fun 'mpfr_set_d (_fun _mpfr-pointer _double _rnd_t -> _void)))
|
||||
(define mpfr-set-si (get-mpfr-fun 'mpfr_set_si (_fun _mpfr-pointer _long _rnd_t -> _void)))
|
||||
(define mpfr-set-z (get-mpfr-fun 'mpfr_set_z (_fun _mpfr-pointer _mpz-pointer _rnd_t -> _void)))
|
||||
(define mpfr-set-q (get-mpfr-fun 'mpfr_set_q (_fun _mpfr-pointer _mpq-pointer _rnd_t -> _void)))
|
||||
(define mpfr-set-z-2exp
|
||||
(get-mpfr-fun 'mpfr_set_z_2exp (_fun _mpfr-pointer _mpz-pointer _exp_t _rnd_t -> _int)))
|
||||
|
||||
;; integer->size+limbs : integer -> (values integer (listof integer))
|
||||
;; Returns a cvector of limbs and the size of the limbs. The size is negated when n is negative.
|
||||
(define (integer->size+limbs n)
|
||||
;; +1 because GMP expects the last limb to be 0
|
||||
(define len (+ (ceiling (/ (integer-length (abs n)) gmp-limb-bits)) 1))
|
||||
(define limbs (make-cvector _limb_t len))
|
||||
(define an (abs n))
|
||||
(let loop ([i 0])
|
||||
(when (i . < . len)
|
||||
(define bit (* i gmp-limb-bits))
|
||||
(cvector-set! limbs i (bitwise-bit-field an bit (+ bit gmp-limb-bits)))
|
||||
(loop (+ i 1))))
|
||||
(define size (- len 1))
|
||||
(values (if (< n 0) (- size) size)
|
||||
(cvector-ptr limbs)))
|
||||
|
||||
;; integer->mpz : integer -> _mpz
|
||||
;; Converts an integer to an _mpz. DO NOT send the result of this as an output argument!
|
||||
(define (integer->mpz n)
|
||||
(let-values ([(size limbs) (integer->size+limbs n)])
|
||||
(make-mpz (abs size) size limbs)))
|
||||
|
||||
;; rational->mpq : rational -> _mpz
|
||||
;; Converts a rational to an _mpq. DO NOT send the result of this as an output argument!
|
||||
(define (rational->mpq r)
|
||||
(make-mpq (integer->mpz (numerator r))
|
||||
(integer->mpz (denominator r))))
|
||||
;; sig+exp->bigfloat integer integer -> bigfloat
|
||||
(define (sig+exp->bigfloat n e)
|
||||
(define y (new-mpfr (bf-precision)))
|
||||
(mpfr-set-z-2exp y (integer->mpz n) e (bf-rounding-mode))
|
||||
y)
|
||||
|
||||
;; flonum->bigfloat : float -> bigfloat
|
||||
;; Converts a Racket inexact real to a bigfloat; rounds if bf-precision < 53.
|
||||
|
|
@ -352,51 +287,66 @@
|
|||
;; Converts a Racket integer to a bigfloat; rounds if necessary.
|
||||
(define (integer->bigfloat value)
|
||||
(define x (new-mpfr (bf-precision)))
|
||||
(if (fixnum? value)
|
||||
(if (_long? value)
|
||||
(mpfr-set-si x value (bf-rounding-mode))
|
||||
(mpfr-set-z x (integer->mpz value) (bf-rounding-mode)))
|
||||
x)
|
||||
|
||||
(define (round/mode q)
|
||||
(case (bf-rounding-mode)
|
||||
[(up) (ceiling q)]
|
||||
[(down) (floor q)]
|
||||
[(zero) (truncate q)]
|
||||
[else (round q)]))
|
||||
|
||||
(define (floor-log2 n) (max 0 (sub1 (integer-length n))))
|
||||
(define (ceiling-log2 n) (max 0 (integer-length (sub1 n))))
|
||||
|
||||
(define (log2-lower-bound q)
|
||||
(- (floor-log2 (numerator q))
|
||||
(ceiling-log2 (denominator q))))
|
||||
|
||||
(define (log2-upper-bound q)
|
||||
(- (ceiling-log2 (numerator q))
|
||||
(floor-log2 (denominator q))))
|
||||
|
||||
;; rational->bigfloat : rational -> bigfloat
|
||||
;; Converts a Racket rational to a bigfloat; rounds if necessary.
|
||||
(define (rational->bigfloat value)
|
||||
(define x (new-mpfr (bf-precision)))
|
||||
(mpfr-set-q x (rational->mpq value) (bf-rounding-mode))
|
||||
x)
|
||||
(define (rational->bigfloat q)
|
||||
(define bits (bf-precision))
|
||||
(define sgn-q (sgn q))
|
||||
(define abs-q (abs q))
|
||||
(define ipart (floor abs-q))
|
||||
(cond [(zero? sgn-q) (sig+exp->bigfloat 0 0)]
|
||||
[(zero? ipart)
|
||||
(define e-ub (- (log2-upper-bound abs-q) bits))
|
||||
(define e-lb (- (log2-lower-bound abs-q) bits))
|
||||
(let loop ([e e-ub])
|
||||
(define 2^-e (arithmetic-shift 1 (- e)))
|
||||
(define sig (round/mode (* sgn-q abs-q 2^-e)))
|
||||
(cond [(or (= e e-lb) (= bits (integer-length (abs sig))))
|
||||
(sig+exp->bigfloat sig e)]
|
||||
[else
|
||||
(loop (- e 1))]))]
|
||||
[else
|
||||
(define e (- (integer-length ipart) bits))
|
||||
(define 2^-e (cond [(e . < . 0) (arithmetic-shift 1 (- e))]
|
||||
[else (/ 1 (arithmetic-shift 1 e))]))
|
||||
(define sig (round/mode (* sgn-q abs-q 2^-e)))
|
||||
(sig+exp->bigfloat sig e)]))
|
||||
|
||||
;; real->bigfloat : real -> bigfloat
|
||||
;; Converts any real Racket value to a bigfloat; rounds if necessary.
|
||||
(define (real->bigfloat value)
|
||||
(cond [(inexact? value) (flonum->bigfloat value)]
|
||||
[(integer? value) (integer->bigfloat value)]
|
||||
[(rational? value) (rational->bigfloat value)]))
|
||||
[else (rational->bigfloat value)]))
|
||||
|
||||
;; ===================================================================================================
|
||||
;; Conversion from mpfr_t to Racket data types
|
||||
|
||||
(define mpfr-get-d (get-mpfr-fun 'mpfr_get_d (_fun _mpfr-pointer _rnd_t -> _double)))
|
||||
(define mpfr-get-z (get-mpfr-fun 'mpfr_get_z (_fun _mpz-pointer _mpfr-pointer _rnd_t -> _int)))
|
||||
(define mpz-get-si (get-mpfr-fun '__gmpz_get_si (_fun _mpz-pointer -> _long)))
|
||||
(define mpz-fits-long? (get-gmp-fun '__gmpz_fits_slong_p (_fun _mpz-pointer -> _int)))
|
||||
|
||||
;; size+limbs->integer : integer (listof integer) -> integer
|
||||
;; Converts a size (which may be negative) and a limb list into an integer.
|
||||
(define (size+limbs->integer size limbs)
|
||||
(define len (abs size))
|
||||
(define num
|
||||
(let loop ([i 0] [res 0])
|
||||
(cond [(i . < . len)
|
||||
(define v (ptr-ref limbs _limb_t i))
|
||||
(loop (+ i 1) (bitwise-ior res (arithmetic-shift v (* i gmp-limb-bits))))]
|
||||
[else res])))
|
||||
(if (negative? size) (- num) num))
|
||||
|
||||
;; mpz->integer : _mpz -> integer
|
||||
;; Converts an mpz_t to an integer.
|
||||
(define (mpz->integer z)
|
||||
(if (zero? (mpz-fits-long? z))
|
||||
(size+limbs->integer (mpz-size z) (mpz-limbs z))
|
||||
(mpz-get-si z)))
|
||||
|
||||
;; bigfloat->flonum : bigfloat -> float
|
||||
;; Converts a bigfloat to a Racket float; rounds if necessary.
|
||||
|
|
@ -407,10 +357,9 @@
|
|||
;; Converts a bigfloat to a Racket integer; rounds if necessary.
|
||||
(define (bigfloat->integer x)
|
||||
(unless (bfinteger? x) (raise-argument-error 'bigfloat->integer "bfinteger?" x))
|
||||
(define z (raw-mpz))
|
||||
(define z (new-mpz))
|
||||
(mpfr-get-z z x (bf-rounding-mode))
|
||||
(define res (mpz->integer z))
|
||||
(mpz-clear z)
|
||||
res)
|
||||
|
||||
;; bigfloat->rational : bigfloat -> rational
|
||||
|
|
@ -522,33 +471,23 @@
|
|||
|
||||
(define (bigfloat-custom-write x port mode)
|
||||
(write-string
|
||||
(if (mpfr-available?)
|
||||
(cond [(bfzero? x) (if (= 0 (bigfloat-sign x)) "0.bf" "-0.bf")]
|
||||
[(bfrational? x)
|
||||
(define str (bigfloat->string x))
|
||||
(cond [(regexp-match #rx"\\.|e" str)
|
||||
(define exp (bigfloat-exponent x))
|
||||
(define prec (bigfloat-precision x))
|
||||
(if ((abs exp) . > . (* prec 2))
|
||||
(format "(bf \"~a\")" str)
|
||||
(format "(bf #e~a)" str))]
|
||||
[else (format "(bf ~a)" str)])]
|
||||
[(bfinfinite? x) (if (= 0 (bigfloat-sign x)) "+inf.bf" "-inf.bf")]
|
||||
[else "+nan.bf"])
|
||||
"#<bigfloat>")
|
||||
(cond [(bfzero? x) (if (= 0 (bigfloat-sign x)) "0.bf" "-0.bf")]
|
||||
[(bfrational? x)
|
||||
(define str (bigfloat->string x))
|
||||
(cond [(regexp-match #rx"\\.|e" str)
|
||||
(define exp (bigfloat-exponent x))
|
||||
(define prec (bigfloat-precision x))
|
||||
(if ((abs exp) . > . (* prec 2))
|
||||
(format "(bf \"~a\")" str)
|
||||
(format "(bf #e~a)" str))]
|
||||
[else (format "(bf ~a)" str)])]
|
||||
[(bfinfinite? x) (if (= 0 (bigfloat-sign x)) "+inf.bf" "-inf.bf")]
|
||||
[else "+nan.bf"])
|
||||
port))
|
||||
|
||||
;; ===================================================================================================
|
||||
;; Main bigfloat constructor
|
||||
|
||||
(define mpfr-set-z-2exp
|
||||
(get-mpfr-fun 'mpfr_set_z_2exp (_fun _mpfr-pointer _mpz-pointer _exp_t _rnd_t -> _int)))
|
||||
|
||||
(define (sig+exp->bigfloat n e)
|
||||
(define y (new-mpfr (bf-precision)))
|
||||
(mpfr-set-z-2exp y (integer->mpz n) e (bf-rounding-mode))
|
||||
y)
|
||||
|
||||
;; bf : (or real string) -> bigfloat
|
||||
;; : integer integer -> bigfloat
|
||||
(define bf
|
||||
|
|
@ -804,13 +743,13 @@
|
|||
(define mpfr-yn (get-mpfr-fun 'mpfr_yn (_fun _mpfr-pointer _long _mpfr-pointer _rnd_t -> _int)))
|
||||
|
||||
(define (bfbesj n x)
|
||||
(unless (fixnum? n) (raise-argument-error 'bfbesj "Fixnum" 0 n x))
|
||||
(unless (_long? n) (raise-argument-error 'bfbesj "_long?" 0 n x))
|
||||
(define y (new-mpfr (bf-precision)))
|
||||
(mpfr-jn y n x (bf-rounding-mode))
|
||||
y)
|
||||
|
||||
(define (bfbesy n x)
|
||||
(unless (fixnum? n) (raise-argument-error 'bfbesy "Fixnum" 0 n x))
|
||||
(unless (_long? n) (raise-argument-error 'bfbesy "_long?" 0 n x))
|
||||
(define y (new-mpfr (bf-precision)))
|
||||
(mpfr-yn y n x (bf-rounding-mode))
|
||||
y)
|
||||
|
|
@ -818,7 +757,7 @@
|
|||
(define mpfr-root (get-mpfr-fun 'mpfr_root (_fun _mpfr-pointer _mpfr-pointer _ulong _rnd_t -> _int)))
|
||||
|
||||
(define (bfroot x n)
|
||||
(unless (and (fixnum? n) (n . >= . 0)) (raise-argument-error 'bfroot "Nonnegative-Fixnum" 1 x n))
|
||||
(unless (and (_ulong? n) (n . >= . 0)) (raise-argument-error 'bfroot "_ulong?" 1 x n))
|
||||
(define y (new-mpfr (bf-precision)))
|
||||
(mpfr-root y x n (bf-rounding-mode))
|
||||
y)
|
||||
|
|
@ -908,7 +847,7 @@
|
|||
(begin (provide-2ary-pred name c-name) ...))
|
||||
|
||||
(provide-2ary-preds
|
||||
[bfeqv? 'mpfr_equal_p]
|
||||
[bf=? 'mpfr_equal_p]
|
||||
[bflt? 'mpfr_less_p]
|
||||
[bflte? 'mpfr_lessequal_p]
|
||||
[bfgt? 'mpfr_greater_p]
|
||||
|
|
@ -989,7 +928,7 @@
|
|||
|
||||
(define (epsilon.bf)
|
||||
(define p (bf-precision))
|
||||
(hash-ref! constant-hash (cons 'epsilon.bf p) (λ () (bfexpt (force 2.bf) (bf (- p))))))
|
||||
(hash-ref! constant-hash (cons 'epsilon.bf p) (λ () (bfexpt (force 2.bf) (bf (- 1 p))))))
|
||||
|
||||
(define (-max.bf) (bfnext (bf -inf.0)))
|
||||
(define (-min.bf) (bfprev (bf -0.0)))
|
||||
|
|
@ -1000,64 +939,3 @@
|
|||
(begin-for-syntax
|
||||
(set! 0ary-funs (list* #'phi.bf #'epsilon.bf #'-max.bf #'-min.bf #'+min.bf #'+max.bf
|
||||
0ary-funs)))
|
||||
|
||||
;; ===================================================================================================
|
||||
;; Number Theoretic Functions
|
||||
;; http://gmplib.org/manual/Number-Theoretic-Functions.html#Number-Theoretic-Functions
|
||||
|
||||
(define mpz-probab-prime-p
|
||||
(get-gmp-fun '__gmpz_probab_prime_p (_fun _mpz-pointer _int -> _int)))
|
||||
|
||||
(define (probably-prime n [repetitions 10])
|
||||
(case (mpz-probab-prime-p (integer->mpz n) repetitions)
|
||||
[(0) 'composite]
|
||||
[(1) 'probably-prime]
|
||||
[(2) 'prime]))
|
||||
|
||||
(define (prime? n)
|
||||
(case (probably-prime n)
|
||||
[(probably-prime prime) #t]
|
||||
[else #f]))
|
||||
|
||||
(define mpz-nextprime
|
||||
(get-gmp-fun '__gmpz_nextprime (_fun _mpz-pointer _mpz-pointer -> _void)))
|
||||
|
||||
(define (next-prime op)
|
||||
(define result (raw-mpz))
|
||||
(mpz-nextprime result (integer->mpz op))
|
||||
(begin0
|
||||
(mpz->integer result)
|
||||
(mpz-clear result)))
|
||||
|
||||
(define mpz-invert
|
||||
(get-gmp-fun '__gmpz_invert (_fun _mpz-pointer _mpz-pointer _mpz-pointer -> _void)))
|
||||
|
||||
(define (mod-inverse n modulus)
|
||||
(define result (raw-mpz))
|
||||
(mpz-invert result (integer->mpz n) (integer->mpz modulus))
|
||||
(begin0
|
||||
(mpz->integer result)
|
||||
(mpz-clear result)))
|
||||
|
||||
(define mpz-jacobi
|
||||
(get-gmp-fun '__gmpz_jacobi (_fun _mpz-pointer _mpz-pointer -> _int)))
|
||||
|
||||
(define (jacobi a b)
|
||||
(mpz-jacobi (integer->mpz a) (integer->mpz b)))
|
||||
|
||||
(define mpz-legendre
|
||||
(get-gmp-fun '__gmpz_legendre (_fun _mpz-pointer _mpz-pointer -> _int)))
|
||||
|
||||
(define (legendre a b)
|
||||
(mpz-legendre (integer->mpz a) (integer->mpz b)))
|
||||
|
||||
(define mpz-remove
|
||||
(get-gmp-fun '__gmpz_remove (_fun _mpz-pointer _mpz-pointer _mpz-pointer -> _int)))
|
||||
|
||||
(define (remove-factor z f)
|
||||
(define result (raw-mpz))
|
||||
(define n (mpz-remove result (integer->mpz z) (integer->mpz f)))
|
||||
(define z/f (mpz->integer result))
|
||||
(mpz-clear result)
|
||||
(values z/f n))
|
||||
|
||||
|
|
|
|||
|
|
@ -1,8 +1,24 @@
|
|||
#lang typed/racket/base
|
||||
#lang racket/base
|
||||
|
||||
(require (for-syntax racket/base racket/syntax syntax/strip-context))
|
||||
(require (for-syntax racket/base racket/syntax syntax/strip-context)
|
||||
typed/racket/base
|
||||
(only-in ffi/unsafe
|
||||
ctype-sizeof
|
||||
_long
|
||||
_ulong))
|
||||
|
||||
(provide req/prov-uniform-collection)
|
||||
(provide (all-defined-out))
|
||||
|
||||
(define (unsigned-max type) (- (expt 2 (* 8 (ctype-sizeof type))) 1))
|
||||
(define (signed-min type) (- (expt 2 (- (* 8 (ctype-sizeof type)) 1))))
|
||||
(define (signed-max type) (- (expt 2 (- (* 8 (ctype-sizeof type)) 1)) 1))
|
||||
|
||||
(define _long-min (signed-min _long))
|
||||
(define _long-max (signed-max _long))
|
||||
(define _ulong-max (unsigned-max _ulong))
|
||||
|
||||
(define (_ulong? n) (and (exact-integer? n) (<= 0 n _ulong-max)))
|
||||
(define (_long? n) (and (exact-integer? n) (<= _long-min n _long-max)))
|
||||
|
||||
(define-syntax (req/prov-uniform-collection stx)
|
||||
(syntax-case stx ()
|
||||
|
|
|
|||
|
|
@ -28,8 +28,7 @@ represented by the type @racket[Bigfloat].
|
|||
|
||||
MPFR is free and license-compatible with commercial software. It is distributed with Racket
|
||||
for Windows and Mac OS X, is installed on most Linux systems, and is
|
||||
@hyperlink["http://www.mpfr.org/ports.html"]{easy to install} on all major platforms.
|
||||
See @secref{loading} for details.
|
||||
@hyperlink["http://www.mpfr.org/ports.html"]{easy to install} on major Unix-like platforms.
|
||||
|
||||
@local-table-of-contents[]
|
||||
|
||||
|
|
@ -709,21 +708,4 @@ Canonicalizing bigfloats won't change answers computed from them.
|
|||
(eval:result @racketresultfont{2}))]
|
||||
}
|
||||
|
||||
@section[#:tag "loading"]{Loading the MPFR Library}
|
||||
|
||||
The @racketmodname[math/bigfloat] library depends directly on external one library:
|
||||
MPFR, which on the filesystem is named something like @filepath{libmpfr.so}, but with a
|
||||
platform-specific suffix. MPFR itself depends on @hyperlink["http://gmplib.org/"]{GMP}, the
|
||||
GNU Multiple Precision Arithmetic Library, which on the filesystem is named something like
|
||||
@filepath{libgmp.so}.
|
||||
|
||||
@defproc[(mpfr-available?) Boolean]{
|
||||
If @racket[(mpfr-available?)] is @racket[#t], both MPFR and GMP have been loaded
|
||||
by the Racket runtime, and everything in @racketmodname[math/bigfloat] should work.
|
||||
|
||||
If @racket[(mpfr-available?)] is @racket[#t] and something doesn't work, it's likely an error
|
||||
in the foreign function interface. In that case, please email the author of this library or
|
||||
submit a bug report.
|
||||
}
|
||||
|
||||
@(close-eval untyped-eval)
|
||||
|
|
|
|||
35
collects/math/tests/bigfloat-stress-test.rkt
Normal file
35
collects/math/tests/bigfloat-stress-test.rkt
Normal file
|
|
@ -0,0 +1,35 @@
|
|||
#lang racket
|
||||
|
||||
(require math/bigfloat
|
||||
math/flonum
|
||||
math/special-functions
|
||||
math/private/bigfloat/bigfloat-hurwitz-zeta)
|
||||
|
||||
(collect-garbage)
|
||||
(collect-garbage)
|
||||
(collect-garbage)
|
||||
(define start-mem (current-memory-use))
|
||||
|
||||
(define num 60)
|
||||
|
||||
(for ([x (in-range 1 num)])
|
||||
(let ([x (* 0.25 x)])
|
||||
(printf "x = ~v~n" x)
|
||||
(for ([y (in-range 1 num)])
|
||||
(let ([y (* 0.25 y)])
|
||||
(define z (bigfloat->flonum (bfhurwitz-zeta (bf x) (bf y))))
|
||||
(define err (flulp-error (flhurwitz-zeta x y) z))
|
||||
(unless (err . <= . 5.0)
|
||||
(printf "hurwitz-zeta ~v ~v; error = ~v ulps~n" x y err))))))
|
||||
|
||||
(collect-garbage)
|
||||
(collect-garbage)
|
||||
(collect-garbage)
|
||||
(define end-mem (current-memory-use))
|
||||
|
||||
(define diff-mem (- end-mem start-mem))
|
||||
(when (diff-mem . > . (* 2 1024 1024))
|
||||
(printf "Significant higher memory use (more than 2MB):~n")
|
||||
(printf " start-mem = ~v~n" start-mem)
|
||||
(printf " end-mem = ~v~n" end-mem)
|
||||
(printf " difference = ~v~n" diff-mem))
|
||||
|
|
@ -1,11 +1,11 @@
|
|||
#lang typed/racket
|
||||
#lang racket
|
||||
|
||||
(require math/bigfloat
|
||||
math/flonum
|
||||
typed/rackunit)
|
||||
math/base
|
||||
rackunit)
|
||||
|
||||
;; ---------------------------------------------------------------------------------------------------
|
||||
;; Exact
|
||||
;; Exact tests
|
||||
|
||||
(check-= (bigfloat->integer (bf (expt 2 64)))
|
||||
(expt 2 64) 0)
|
||||
|
|
@ -51,12 +51,11 @@
|
|||
"987931636889230098793127736178215424999229576351482208269895"
|
||||
"1936680331825288693984964651058209392398294887933203625094431"))
|
||||
|
||||
;; truncates to 600 digits (many other numbers of digits, correct rounding makes it look wrong)
|
||||
(check-equal? (substring (bigfloat->string (bfexp (bf 1))) 0 600)
|
||||
;; truncates to 600 digits (with other numbers of digits, correct rounding makes it look wrong)
|
||||
(check-equal? (substring (bigfloat->string (bfexp 1.bf)) 0 600)
|
||||
e-truncated600))
|
||||
|
||||
;; ---------------------------------------------------------------------------------------------------
|
||||
;; Inexact
|
||||
;; Inexact tests
|
||||
|
||||
(check-= (bigfloat->rational (bfsqr (bf 22/7)))
|
||||
(/ (sqr 22) (sqr 7))
|
||||
|
|
@ -73,3 +72,401 @@
|
|||
(check-= (bigfloat->flonum (bfcbrt (bf 2)))
|
||||
(flexpt 2.0 #i1/3)
|
||||
epsilon.0)
|
||||
|
||||
;; Constants
|
||||
|
||||
(check-equal? pi.bf (bf #e3.141592653589793238462643383279502884195))
|
||||
(check-equal? gamma.bf (bf #e0.5772156649015328606065120900824024310432))
|
||||
(check-equal? catalan.bf (bf #e0.9159655941772190150546035149323841107734))
|
||||
(check-equal? log2.bf (bf #e0.6931471805599453094172321214581765680748))
|
||||
(check-equal? phi.bf (bf #e1.61803398874989484820458683436563811772))
|
||||
|
||||
;; Special values
|
||||
|
||||
(check-eqv? (bigfloat->flonum +nan.bf) +nan.0)
|
||||
(check-eqv? (bigfloat->flonum +inf.bf) +inf.0)
|
||||
(check-eqv? (bigfloat->flonum -inf.bf) -inf.0)
|
||||
(check-eqv? (bigfloat->flonum -0.bf) -0.0)
|
||||
(check-eqv? (bigfloat->flonum 0.bf) 0.0)
|
||||
(check-equal? (bf- +inf.bf) -inf.bf)
|
||||
(check-equal? (bf- -inf.bf) +inf.bf)
|
||||
(check-equal? (bf- +nan.bf) +nan.bf)
|
||||
(check-equal? (bf- 0.bf) -0.bf)
|
||||
(check-equal? (bf- -0.bf) 0.bf)
|
||||
|
||||
(for ([bits '(2 4 8 16 32 64 128 3 5 7 11 13 129)])
|
||||
(parameterize ([bf-precision bits])
|
||||
;; Epsilon
|
||||
(check-not-equal? (bf+ 1.bf epsilon.bf) 1.bf)
|
||||
(check-equal? (bf+ 1.bf (bf* (bf 0.5) epsilon.bf)) 1.bf)
|
||||
;; +max.bf/-max.bf
|
||||
(check-equal? (bf- +max.bf) -max.bf)
|
||||
(check-equal? (bf+ +max.bf (bf* epsilon.bf +max.bf)) +inf.bf)
|
||||
(check-equal? (bf- -max.bf (bf* epsilon.bf +max.bf)) -inf.bf)
|
||||
(check-equal? (- (bigfloat->ordinal +inf.bf) 1) (bigfloat->ordinal +max.bf))
|
||||
(check-equal? (+ (bigfloat->ordinal -inf.bf) 1) (bigfloat->ordinal -max.bf))
|
||||
(check-equal? (bfnext +max.bf) +inf.bf)
|
||||
(check-equal? (bfprev +inf.bf) +max.bf)
|
||||
(check-equal? (bfprev -max.bf) -inf.bf)
|
||||
(check-equal? (bfnext -inf.bf) -max.bf)
|
||||
;; +min.bf/-min.bf
|
||||
(check-equal? (bf- +min.bf) -min.bf)
|
||||
(check-equal? (bf* (bf 0.5) +min.bf) 0.bf)
|
||||
(check-equal? (bf* (bf 0.5) -min.bf) -0.bf)
|
||||
(check-equal? (bigfloat->ordinal +min.bf) 1)
|
||||
(check-equal? (bigfloat->ordinal -min.bf) -1)
|
||||
(check-equal? (bfprev +min.bf) 0.bf)
|
||||
(check-equal? (bfnext 0.bf) +min.bf)
|
||||
(check-equal? (bfnext -min.bf) -0.bf)
|
||||
(check-equal? (bfprev 0.bf) -min.bf)
|
||||
))
|
||||
|
||||
;; Integer conversion
|
||||
|
||||
(check-equal? (bigfloat->rational (integer->bigfloat 0)) 0)
|
||||
|
||||
(for ([mode (in-list '(nearest up down zero))])
|
||||
(define eps (if (eq? mode 'nearest) (bf* (bf 0.5) epsilon.bf) epsilon.bf))
|
||||
(parameterize ([bf-rounding-mode mode])
|
||||
(for* ([s (in-list '(-1 1))]
|
||||
[i (in-range 1000)])
|
||||
(define n (* s (expt 10 i)))
|
||||
(define n0 (bigfloat->integer (integer->bigfloat n)))
|
||||
(define err (bf (relative-error n0 n)))
|
||||
(unless (err . bf<= . eps)
|
||||
(printf "bad integer conversion: mode = ~v n = ~v~n" mode n))
|
||||
(check-true (err . bf<= . eps)))))
|
||||
|
||||
;; Rational conversion
|
||||
|
||||
(for ([mode (in-list '(nearest up down zero))])
|
||||
(parameterize ([bf-rounding-mode mode])
|
||||
(for* ([i (in-range -37 37)]
|
||||
[j (in-range 1 37)])
|
||||
(define q0 (bigfloat->rational (rational->bigfloat (/ i j))))
|
||||
(define q1 (bigfloat->rational (bf/ (bf i) (bf j))))
|
||||
(unless (equal? q0 q1)
|
||||
(printf "bad rational conversion: mode = ~v q = ~v/~v~n" mode i j))
|
||||
(check-equal? q0 q1))))
|
||||
|
||||
;; Flonum conversion
|
||||
|
||||
(for ([mode (in-list '(nearest up down zero))])
|
||||
(parameterize ([bf-rounding-mode mode])
|
||||
(for* ([i (in-range -37 37)]
|
||||
[j (in-range 1 37)])
|
||||
(define x (fl (/ i j)))
|
||||
(define x0 (bigfloat->flonum (flonum->bigfloat x)))
|
||||
(unless (equal? x x0)
|
||||
(printf "bad flonum conversion: mode = ~v x = ~v~n" mode x))
|
||||
(check-equal? x x0))))
|
||||
|
||||
;; String conversion
|
||||
|
||||
(for ([mode (in-list '(nearest up down zero))])
|
||||
(parameterize ([bf-rounding-mode mode])
|
||||
(for* ([i (in-range -37 37)]
|
||||
[j (in-range 1 37)])
|
||||
(define q (rational->bigfloat (/ i j)))
|
||||
(define q0 (string->bigfloat (bigfloat->string q)))
|
||||
(unless (equal? q q0)
|
||||
(printf "bad string conversion: mode = ~v q = ~v/~v~n" mode i j))
|
||||
(check-equal? q q0))))
|
||||
|
||||
(parameterize ([bf-precision 53])
|
||||
(for ([f+xs+ys
|
||||
(list
|
||||
(list
|
||||
bfsqr
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +inf.bf +inf.bf 1.bf 0.bf 0.bf 0.bf 0.bf 1.bf +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfsqrt
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +max.bf
|
||||
+inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -0.bf 0.bf
|
||||
(bf "4.8811524304081624e-161614249") 1.bf (bf "1.4486472022088012e161614248")
|
||||
+inf.bf +nan.bf))
|
||||
(list
|
||||
bfcbrt
|
||||
(list -inf.bf
|
||||
-max.bf -1.bf -min.bf
|
||||
-0.bf 0.bf
|
||||
+min.bf 1.bf +max.bf
|
||||
+inf.bf +nan.bf)
|
||||
(list -inf.bf
|
||||
(bf "-1.2802902004094324e107742832") -1.bf (bf "-6.1993798416193228e-107742833")
|
||||
-0.bf 0.bf
|
||||
(bf "6.1993798416193228e-107742833") 1.bf (bf "1.2802902004094324e107742832")
|
||||
+inf.bf +nan.bf))
|
||||
(list
|
||||
bf-
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +inf.bf +max.bf 1.bf +min.bf 0.bf -0.bf -min.bf -1.bf -max.bf -inf.bf +nan.bf))
|
||||
(list
|
||||
bf/
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -0.bf (bf "-4.7651298097759032e-323228497") -1.bf -inf.bf -inf.bf
|
||||
+inf.bf +inf.bf 1.bf (bf "4.7651298097759032e-323228497") 0.bf +nan.bf))
|
||||
(list
|
||||
bfabs
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +inf.bf +max.bf 1.bf +min.bf 0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bflog
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf
|
||||
(bf #e-744261117.95489299) 0.bf (bf #e744261117.26174581) +inf.bf +nan.bf))
|
||||
(list
|
||||
bflog2
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf
|
||||
(bf -1073741824) 0.bf (bf 1073741823) +inf.bf +nan.bf))
|
||||
(list
|
||||
bflog10
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf
|
||||
(bf #e-323228496.62295526) 0.bf (bf #e323228496.32192528) +inf.bf +nan.bf))
|
||||
(list
|
||||
bflog1p
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf
|
||||
1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf -inf.bf -min.bf -0.bf 0.bf +min.bf
|
||||
(bf #e0.69314718055994529) (bf #e744261117.26174581) +inf.bf +nan.bf))
|
||||
(list
|
||||
bfexp
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list 0.bf 0.bf (bf #e0.36787944117144233) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e2.7182818284590451) +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfexp2
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list 0.bf 0.bf (bf #e0.5) 1.bf 1.bf 1.bf 1.bf 2.bf +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfexp10
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list 0.bf 0.bf (bf #e0.1) 1.bf 1.bf 1.bf 1.bf 10.bf +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfexpm1
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -1.bf -1.bf (bf #e-0.63212055882855767) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e1.7182818284590453) +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfsin
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e-0.8414709848078965) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e0.8414709848078965) +nan.bf +nan.bf))
|
||||
(list
|
||||
bfcos
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e0.54030230586813977) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e0.54030230586813977) +nan.bf +nan.bf))
|
||||
(list
|
||||
bftan
|
||||
(list -inf.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e-1.5574077246549023) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e1.5574077246549023) +nan.bf +nan.bf))
|
||||
(list
|
||||
bfcsc
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e-1.1883951057781212) -inf.bf -inf.bf
|
||||
+inf.bf +inf.bf (bf #e1.1883951057781212) +nan.bf +nan.bf))
|
||||
(list
|
||||
bfsec
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e1.8508157176809257) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e1.8508157176809257) +nan.bf +nan.bf))
|
||||
(list
|
||||
bfcot
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf (bf #e-0.64209261593433076) -inf.bf -inf.bf
|
||||
+inf.bf +inf.bf (bf #e0.64209261593433076) +nan.bf +nan.bf))
|
||||
(list
|
||||
bfasin
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf (bf #e-1.5707963267948966) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e1.5707963267948966) +nan.bf +nan.bf +nan.bf))
|
||||
(list
|
||||
bfacos
|
||||
(list -inf.bf -max.bf
|
||||
-1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf
|
||||
+max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf
|
||||
(bf #e3.1415926535897931) (bf #e1.5707963267948966) (bf #e1.5707963267948966)
|
||||
(bf #e1.5707963267948966) (bf #e1.5707963267948966) 0.bf
|
||||
+nan.bf +nan.bf +nan.bf))
|
||||
(list
|
||||
bfatan
|
||||
(list -inf.bf -max.bf
|
||||
-1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf
|
||||
+max.bf +inf.bf +nan.bf)
|
||||
(list (bf #e-1.5707963267948966) (bf #e-1.5707963267948966)
|
||||
(bf #e-0.78539816339744828) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e0.78539816339744828)
|
||||
(bf #e1.5707963267948966) (bf #e1.5707963267948966) +nan.bf))
|
||||
(list
|
||||
bfsinh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -inf.bf -inf.bf (bf #e-1.1752011936438014) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e1.1752011936438014) +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfcosh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +inf.bf +inf.bf (bf #e1.5430806348152437) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e1.5430806348152437) +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bftanh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -1.bf -1.bf (bf #e-0.76159415595576485) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e0.76159415595576485) 1.bf 1.bf +nan.bf))
|
||||
(list
|
||||
bfcsch
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -0.bf -0.bf (bf #e-0.85091812823932156) -inf.bf -inf.bf
|
||||
+inf.bf +inf.bf (bf #e0.85091812823932156) 0.bf 0.bf +nan.bf))
|
||||
(list
|
||||
bfsech
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list 0.bf 0.bf (bf #e0.64805427366388535) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e0.64805427366388535) 0.bf 0.bf +nan.bf))
|
||||
(list
|
||||
bfcoth
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -1.bf -1.bf (bf #e-1.3130352854993312) -inf.bf -inf.bf
|
||||
+inf.bf +inf.bf (bf #e1.3130352854993312) 1.bf 1.bf +nan.bf))
|
||||
(list
|
||||
bfasinh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -inf.bf (bf #e-744261117.95489299) (bf #e-0.88137358701954305) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e0.88137358701954305) (bf #e744261117.95489299) +inf.bf +nan.bf))
|
||||
(list
|
||||
bfacosh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf
|
||||
+max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf +nan.bf +nan.bf +nan.bf 0.bf
|
||||
(bf #e744261117.95489299) +inf.bf +nan.bf))
|
||||
(list
|
||||
bfatanh
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf -inf.bf -min.bf -0.bf 0.bf +min.bf +inf.bf +nan.bf +nan.bf +nan.bf))
|
||||
(list
|
||||
bfeint
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf
|
||||
1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf (bf #e-744261117.37767732)
|
||||
(bf #e1.8951178163559368) +inf.bf +inf.bf +nan.bf))
|
||||
(list
|
||||
bfli2
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list -inf.bf (bf -276962305333851100) (bf #e-0.8224670334241132) -min.bf -0.bf
|
||||
0.bf +min.bf (bf #e1.6449340668482264) (bf -276962305333851100) -inf.bf +nan.bf))
|
||||
(list
|
||||
bfgamma
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf 1.bf +max.bf +inf.bf
|
||||
+nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf +inf.bf +inf.bf 1.bf +inf.bf +inf.bf
|
||||
+nan.bf))
|
||||
(list
|
||||
bfpsi0
|
||||
(list -inf.bf -1.bf -min.bf -0.bf 0.bf +min.bf
|
||||
1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +inf.bf +inf.bf -inf.bf -inf.bf
|
||||
(bf #e-0.57721566490153287) +inf.bf +nan.bf))
|
||||
(list
|
||||
bfzeta
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf 0.bf (bf #e-0.083333333333333329) (bf #e-0.5) (bf #e-0.5)
|
||||
(bf #e-0.5) (bf #e-0.5) +inf.bf 1.bf 1.bf +nan.bf))
|
||||
(list
|
||||
bferf
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf
|
||||
+nan.bf)
|
||||
(list -1.bf -1.bf (bf #e-0.84270079294971489) (bf "-2.6884366029284653e-323228497") -0.bf
|
||||
0.bf (bf "2.6884366029284653e-323228497") (bf #e0.84270079294971489) 1.bf 1.bf
|
||||
+nan.bf))
|
||||
(list
|
||||
bferfc
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +max.bf +inf.bf +nan.bf)
|
||||
(list 2.bf 2.bf (bf #e1.8427007929497148) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e0.15729920705028513) 0.bf 0.bf +nan.bf))
|
||||
(list
|
||||
bfbesj0
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list 0.bf (bf #e0.76519768655796661) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e0.76519768655796661) 0.bf +nan.bf))
|
||||
(list
|
||||
bfbesj1
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list 0.bf (bf #e-0.4400505857449335) -0.bf -0.bf
|
||||
0.bf 0.bf (bf #e0.4400505857449335) 0.bf +nan.bf))
|
||||
(list
|
||||
(λ (x) (bfbesj 0 x))
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list 0.bf (bf #e0.76519768655796661) 1.bf 1.bf
|
||||
1.bf 1.bf (bf #e0.76519768655796661) 0.bf +nan.bf))
|
||||
(list
|
||||
(λ (x) (bfbesj 1 x))
|
||||
(list -inf.bf -1.bf -min.bf -0.bf
|
||||
0.bf +min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list 0.bf (bf #e-0.4400505857449335) -0.bf -0.bf
|
||||
0.bf 0.bf (bf #e0.4400505857449335) 0.bf +nan.bf))
|
||||
(list
|
||||
bfbesy0
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf
|
||||
(bf #e-473811343.56828988) (bf #e0.088256964215676956) 0.bf +nan.bf))
|
||||
(list
|
||||
bfbesy1
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf
|
||||
1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf -inf.bf
|
||||
(bf #e-0.78121282130028868) 0.bf +nan.bf))
|
||||
(list
|
||||
(λ (x) (bfbesy 0 x))
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf
|
||||
+min.bf 1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf
|
||||
(bf #e-473811343.56828988) (bf #e0.088256964215676956) 0.bf +nan.bf))
|
||||
(list
|
||||
(λ (x) (bfbesy 1 x))
|
||||
(list -inf.bf -max.bf -1.bf -min.bf -0.bf 0.bf +min.bf
|
||||
1.bf +inf.bf +nan.bf)
|
||||
(list +nan.bf +nan.bf +nan.bf +nan.bf -inf.bf -inf.bf -inf.bf
|
||||
(bf #e-0.78121282130028868) 0.bf +nan.bf)))])
|
||||
(match-define (list f xs ys) f+xs+ys)
|
||||
(for ([x (in-list xs)]
|
||||
[y (in-list ys)])
|
||||
(define y0 (f x))
|
||||
(unless (equal? y y0)
|
||||
(printf "f = ~a x = ~v y = ~v~n" f x y))
|
||||
(check-equal? y0 y))))
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user