[wp34s] Converting to/from IEEE 754 Binary64 (Double Precision)
Message #1 Posted by David Maier on 15 June 2013, 7:14 p.m.
Here's a program to convert to/from IEEE 754 binary64 (double precision) format:
/* Program to convert to/from IEEE 754 binary64 (double precision) format
* Remarks:
* - XEQ A converts DP real numbers to IEEE 754 binary64 (double precision) format
* - XEQ B converts IEEE 754 binary64 (double precision) format numbers to DP real
* - XEQ 'IED' converts to DP real if the calculator is in integer mode, converts to IEEE 754 binary64 otherwise
* - Denormalized numbers (|x|<2.2250738585072014e-308 ) are supported. "Denorm" is shown as a warning in the alpha display.
* If |x|<5e-324, the number will be silently converted to 0.
* - +/- Infinity and NaN are supported. Since the WP-34S has "constants" for these values (see the Const catalog), large numbers
* are not considered to be infinite (see next note).
* - Numbers larger/smaller than +/- 1.7976931348623157e308 generate an Out of range error.
* - Negative 0 is supported. Since the sign may not be visible, depending on the setting of the global D (Danger) flag,
* "Neg 0" is shown in the alpha display
* - The calculator is set to integer sign-with-mantissa, word size 64 (sm64) mode and assumed to be in this mode when working with the
* IEEE 754 binary 64 format. Similarily, on the real side, the calculator is assumed to be in double precision mode.
*/
****LBL'IED'
WSIZE 64 // Operations are performed on sign-with-mantissa, word size 64 integers
SIGNMT
DBLON
INTM?
GTO B
**LBL A // Convert DP real to IEEE 754 binary64 format
LocR 001
CL[alpha]
x=0?
JMP ZeroF
SPEC? // Infinite or NaN
JMP SpecF
ENTER[^]
ABS
LOG[sub-2] // This is why we need to be in DP mode
FLOOR
# 10
2[^x]
DEC X
x<? Y // Punt if number is too large
ERR 08 // Note: Numbers too large for the format are not quietly replaced by infinity
+/-
MAX
STO .00 // Exponent in R.00: Denormalized: -1023; otherwise: -1022 to 1023
# 052
x[<->] Y
-
# 179 // Denormalized values are scaled by 2^1074 before rounding; otherwise, 2 ^ (52 - exponent)
# 6 // 1022 + 52 = 1074 = 179 * 6
[times]
MIN
2[^x]
[times]
ROUNDI
RCL .00
BASE 16 // x: exponent; y: mantissa, including sign
# 10 // Convert exponent
2[^x]
DEC X
+
CF .00 // Flag .00 set for denormalized value
x=0?
SF .00
SL 52
x[<->] Y
MASKR 52 // This removes the hidden bit, if any
+/- // Include sign in the mask
AND
OR // Insert exponent into result
FC? .00 // Warn if denormalized
RTN
"Denorm"
VW[alpha]+ X
RTN
ZeroF:: CF .01
x=-0? // Flag .01 set for negative 0
SF .01
BASE 16
FS? .01
SB 63
RTN
SpecF:: [infinity]? // Handle NaN here, infinity below
JMP InfF
BASE 16
MASKR 12 // Use 0x7FF8000000000000 for NaN
SL 51
[alpha]'NaN'
VW[alpha]+ X
RTN
InfF:: CF .01 // Flag .01 set for negative infinity
x<0?
SF .01
BASE 16
MASKR 11
SL 52
FS? .01
SB 63
RTN
**LBL B // Convert IEEE 754 binary64 format to DP real
LocR 001
CL[alpha]
x=0?
JMP ZeroI
ENTER[^] // Extract the exponent
CB 63
SR 52
# 11 // Are we special?
2[^x]
DEC X
x=? Y
JMP SpecI
DROP
CF .00 // Flag .00: denormalized
x=0?
SF .00
# 001 // Fix the minimum exponent
MAX
# 10
2[^x]
DEC X
-
x[<->] Y
MASKR 11
SL 52
NOT
AND
FC? .00 // Restore hidden bit if not denormalized
SB 52
DECM
x[<->] Y // Apply exponent
# 052
x[<->] Y
-
2[^x]
/
FC? .00 // Warn if denormalized
RTN
"Denorm"
VW[alpha]+ X
RTN
ZeroI:: CF .01 // +/- 0; flag .01 is negative zero
x=-0?
SF .01
DECM
FC? .01
RTN
"Neg 0" // Warn if negative (not visible if D flag not set)
0
+/-
VW[alpha]+ X
RTN
SpecI:: DROP // NaN or +/- infinity; don't need exponent
DROP
ENTER[^]
MASKR 52
AND
x=0? // Handle NaN here; infinity below
JMP InfI
DECM
# NaN
RTN
InfI:: DROP // +/- infinity; don't need mantissa
CF .01 // Flag .01 is negative infinity
x<0?
SF .01
DECM
# [infinity]
FS? .01
+/-
RTN
END
Edited: 15 June 2013, 8:18 p.m.
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