;;; Copyright (c) 2004-2018 by Alex Shinn.
;; Adapted from SRFI 56.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; syntax
(define-syntax combine
(syntax-rules ()
((combine) 0)
((combine b1) b1)
((combine b1 b2 b3 ...)
(combine (+ (arithmetic-shift b1 8) b2) b3 ...))))
(define-syntax bytes-u8-set-all!
(syntax-rules ()
((_) bv off i)
((_ bv off i b1) (bytevector-u8-set! bv (+ off i) b1))
((_ bv off i b1 b2 b3 ...)
(begin
(bytevector-u8-set! bv (+ off i) b1)
(bytes-u8-set-all! bv off (+ i 1) b2 b3 ...)))))
(define-syntax bytevector-u8-set-all!
(syntax-rules ()
((_ bvapp iapp b1 ...)
(let ((bv bvapp)
(i iapp))
(bytes-u8-set-all! bv i 0 b1 ...)))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; reading floating point numbers
;; Inspired by Oleg's implementation from
;; http://okmij.org/ftp/Scheme/reading-IEEE-floats.txt
;; but removes mutations and magic numbers and allows for manually
;; specifying the endianness.
;;
;; See also
;; http://www.cs.auckland.ac.nz/~jham1/07.211/floats.html
;; and
;; http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html
;; as references to IEEE 754.
(define (bytevector-ieee-single-ref bytevector k endianness)
(define (mantissa expn b2 b3 b4)
(case expn
((255) ; special exponents
(if (zero? (combine b2 b3 b4)) (/ 1. 0.) (/ 0. 0.)))
((0) ; denormalized
(inexact (* (expt 2.0 (- 1 (+ 127 23))) (combine b2 b3 b4))))
(else
(inexact
(* (expt 2.0 (- expn (+ 127 23)))
(combine (+ b2 128) b3 b4)))))) ; hidden bit
(define (exponent b1 b2 b3 b4)
(if (> b2 127) ; 1st bit of b2 is low bit of expn
(mantissa (+ (* 2 b1) 1) (- b2 128) b3 b4)
(mantissa (* 2 b1) b2 b3 b4)))
(define (sign b1 b2 b3 b4)
(if (> b1 127) ; 1st bit of b1 is sign
(- (exponent (- b1 128) b2 b3 b4))
(exponent b1 b2 b3 b4)))
(let* ((b1 (bytevector-u8-ref bytevector (+ k 0)))
(b2 (bytevector-u8-ref bytevector (+ k 1)))
(b3 (bytevector-u8-ref bytevector (+ k 2)))
(b4 (bytevector-u8-ref bytevector (+ k 3))))
(if (eq? endianness 'big)
(sign b1 b2 b3 b4)
(sign b4 b3 b2 b1))))
(define (bytevector-ieee-single-native-ref bytevector k)
(bytevector-ieee-single-ref bytevector k (native-endianness)))
(define (bytevector-ieee-double-ref bytevector k endianness)
(define (mantissa expn b2 b3 b4 b5 b6 b7 b8)
(case expn
((255) ; special exponents
(if (zero? (combine b2 b3 b4 b5 b6 b7 b8)) (/ 1. 0.) (/ 0. 0.)))
((0) ; denormalized
(inexact (* (expt 2.0 (- 1 (+ 1023 52)))
(combine b2 b3 b4 b5 b6 b7 b8))))
(else
(inexact
(* (expt 2.0 (- expn (+ 1023 52)))
(combine (+ b2 16) b3 b4 b5 b6 b7 b8)))))) ; hidden bit
(define (exponent b1 b2 b3 b4 b5 b6 b7 b8)
(mantissa (bitwise-ior (arithmetic-shift b1 4) ; 7 bits
(arithmetic-shift b2 -4)) ; + 4 bits
(bitwise-and b2 #b1111)
b3 b4 b5 b6 b7 b8))
(define (sign b1 b2 b3 b4 b5 b6 b7 b8)
(if (> b1 127) ; 1st bit of b1 is sign
(- (exponent (- b1 128) b2 b3 b4 b5 b6 b7 b8))
(exponent b1 b2 b3 b4 b5 b6 b7 b8)))
(let* ((b1 (bytevector-u8-ref bytevector (+ k 0)))
(b2 (bytevector-u8-ref bytevector (+ k 1)))
(b3 (bytevector-u8-ref bytevector (+ k 2)))
(b4 (bytevector-u8-ref bytevector (+ k 3)))
(b5 (bytevector-u8-ref bytevector (+ k 4)))
(b6 (bytevector-u8-ref bytevector (+ k 5)))
(b7 (bytevector-u8-ref bytevector (+ k 6)))
(b8 (bytevector-u8-ref bytevector (+ k 7))))
(if (eq? endianness 'big)
(sign b1 b2 b3 b4 b5 b6 b7 b8)
(sign b8 b7 b6 b5 b4 b3 b2 b1))))
(define (bytevector-ieee-double-native-ref bytevector k)
(bytevector-ieee-double-ref bytevector k (native-endianness)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; writing floating point numbers
;; Underflow rounds down to zero as in IEEE-754, and overflow gets
;; written as +/- Infinity.
;; Break a real number down to a normalized mantissa and exponent.
;; Default base=2, mant-size=23 (52), exp-size=8 (11) for IEEE singles
;; (doubles).
;;
;; Note: This should never be used in practice, since it can be
;; implemented much faster in C. See decode-float in ChezScheme or
;; Gauche.
(define (call-with-mantissa&exponent num base mant-size exp-size proc)
(cond
((negative? num)
(call-with-mantissa&exponent (- num) base mant-size exp-size proc))
((zero? num) (proc 0 0))
(else
(let* ((bot (expt base mant-size))
(top (* base bot)))
(let loop ((n (inexact num)) (e 0))
(cond
((>= n top)
(loop (/ n base) (+ e 1)))
((< n bot)
(loop (* n base) (- e 1)))
(else
(proc (exact (round n)) e))))))))
(define (bytevector-ieee-single-set! bytevector k num endianness)
(define output
(if (eq? endianness 'big)
(lambda (b1 b2 b3 b4) (bytevector-u8-set-all! bytevector k b1 b2 b3 b4))
(lambda (b1 b2 b3 b4) (bytevector-u8-set-all! bytevector k b4 b3 b2 b1))))
(define (compute)
(call-with-mantissa&exponent num 2 23 8
(lambda (f e)
(let ((e0 (+ e 127 23)))
(cond
((negative? e0)
(let* ((f1 (exact (round (* f (expt 2 (- e0 1))))))
(b2 (bit-field f1 16 24)) ; mant:16-23
(b3 (bit-field f1 8 16)) ; mant:8-15
(b4 (bit-field f1 0 8))) ; mant:0-7
(output (if (negative? num) 128 0) b2 b3 b4)))
((> e0 255) ; infinity
(output (if (negative? num) 255 127) 128 0 0))
(else
(let* ((b0 (arithmetic-shift e0 -1))
(b1 (if (negative? num) (+ b0 128) b0)) ; sign + exp:1-7
(b2 (bitwise-ior
(if (odd? e0) 128 0) ; exp:0
(bit-field f 16 23))) ; + mant:16-23
(b3 (bit-field f 8 16)) ; mant:8-15
(b4 (bit-field f 0 8))) ; mant:0-7
(output b1 b2 b3 b4))))))))
(cond
((zero? num) (output 0 0 0 0))
((nan? num) (output #xff #xff #xff #xff))
(else (compute))))
(define (bytevector-ieee-single-native-set! bytevector k num)
(bytevector-ieee-single-set! bytevector k num (native-endianness)))
(define (bytevector-ieee-double-set! bytevector k num endianness)
(define output
(if (eq? endianness 'big)
(lambda (b1 b2 b3 b4 b5 b6 b7 b8)
(bytevector-u8-set-all! bytevector k b1 b2 b3 b4 b5 b6 b7 b8))
(lambda (b1 b2 b3 b4 b5 b6 b7 b8)
(bytevector-u8-set-all! bytevector k b8 b7 b6 b5 b4 b3 b2 b1))))
(define (compute)
(call-with-mantissa&exponent num 2 52 11
(lambda (f e)
(let ((e0 (+ e 1023 52)))
(cond
((negative? e0)
(let* ((f1 (exact (round (* f (expt 2 (- e0 1))))))
(b2 (bit-field f1 48 52))
(b3 (bit-field f1 40 48))
(b4 (bit-field f1 32 40))
(b5 (bit-field f1 24 32))
(b6 (bit-field f1 16 24))
(b7 (bit-field f1 8 16))
(b8 (bit-field f1 0 8)))
(output (if (negative? num) 128 0) b2 b3 b4 b5 b6 b7 b8)))
((> e0 4095) ; infinity
(output (if (negative? num) 255 127) 224 0 0 0 0 0 0))
(else
(let* ((b0 (bit-field e0 4 11))
(b1 (if (negative? num) (+ b0 128) b0))
(b2 (bitwise-ior (arithmetic-shift
(bit-field e0 0 4)
4)
(bit-field f 48 52)))
(b3 (bit-field f 40 48))
(b4 (bit-field f 32 40))
(b5 (bit-field f 24 32))
(b6 (bit-field f 16 24))
(b7 (bit-field f 8 16))
(b8 (bit-field f 0 8)))
(output b1 b2 b3 b4 b5 b6 b7 b8))))))))
(cond
((zero? num) (output 0 0 0 0 0 0 0 0))
((nan? num) (output #xff #xff #xff #xff #xff #xff #xff #xff))
(else (compute))))
(define (bytevector-ieee-double-native-set! bytevector k num)
(bytevector-ieee-double-set! bytevector k num (native-endianness)))
;; Local Variables:
;; eval: (put 'call-with-mantissa&exponent 'scheme-indent-function 4)
;; End: