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1.1 root 1: /*
2: * Copyright (c) 1980 Regents of the University of California.
3: * All rights reserved. The Berkeley software License Agreement
4: * specifies the terms and conditions for redistribution.
5: */
6:
7: #ifdef LIBC_SCCS
8: .asciz "@(#)atof.s 5.3 (Berkeley) 3/9/86"
9: #endif LIBC_SCCS
10:
11: #include "DEFS.h"
12:
13: /*
14: * atof: convert ascii to floating
15: *
16: * C usage:
17: *
18: * double atof (s)
19: * char *s;
20: *
21: * Register usage:
22: *
23: * r0-1: value being developed
24: * r2: first section: pointer to the next character
25: * second section: binary exponent
26: * r3: flags
27: * r4: first section: the current character
28: * second section: scratch
29: * r5: the decimal exponent
30: * r6-7: scratch
31: */
32: .set msign,0 # mantissa has negative sign
33: .set esign,1 # exponent has negative sign
34: .set decpt,2 # decimal point encountered
35:
36: ENTRY(atof, R6|R7)
37: /*
38: * Initialization
39: */
40: clrl r3 # All flags start out false
41: movl 4(ap),r2 # Address the first character
42: clrl r5 # Clear starting exponent
43: /*
44: * Skip leading white space
45: */
46: sk0: movzbl (r2)+,r4 # Fetch the next (first) character
47: cmpb $' ,r4 # Is it blank?
48: jeql sk0 # ...yes
49: cmpb r4,$8 # 8 is lowest of white-space group
50: jlss sk1 # Jump if char too low to be white space
51: cmpb r4,$13 # 13 is highest of white-space group
52: jleq sk0 # Jump if character is white space
53: sk1:
54: /*
55: * Check for a sign
56: */
57: cmpb $'+,r4 # Positive sign?
58: jeql cs1 # ... yes
59: cmpb $'-,r4 # Negative sign?
60: jneq cs2 # ... no
61: bisb2 $1<msign,r3 # Indicate a negative mantissa
62: cs1: movzbl (r2)+,r4 # Skip the character
63: cs2:
64: /*
65: * Accumulate digits, keeping track of the exponent
66: */
67: clrq r0 # Clear the accumulator
68: ad0: cmpb r4,$'0 # Do we have a digit?
69: jlss ad4 # ... no, too small
70: cmpb r4,$'9
71: jgtr ad4 # ... no, too large
72: /*
73: * We got a digit. Accumulate it
74: */
75: cmpl r1,$214748364 # Would this digit cause overflow?
76: jgeq ad1 # ... yes
77: /*
78: * Multiply (r0,r1) by 10. This is done by developing
79: * (r0,r1)*2 in (r6,r7), shifting (r0,r1) left three bits,
80: * and adding the two quadwords.
81: */
82: ashq $1,r0,r6 # (r6,r7)=(r0,r1)*2
83: ashq $3,r0,r0 # (r0,r1)=(r0,r1)*8
84: addl2 r6,r0 # Add low halves
85: adwc r7,r1 # Add high halves
86: /*
87: * Add in the digit
88: */
89: subl2 $'0,r4 # Get the digit value
90: addl2 r4,r0 # Add it into the accumulator
91: adwc $0,r1 # Possible carry into high half
92: jbr ad2 # Join common code
93: /*
94: * Here when the digit won't fit in the accumulator
95: */
96: ad1: incl r5 # Ignore the digit, bump exponent
97: /*
98: * If we have seen a decimal point, decrease the exponent by 1
99: */
100: ad2: jbc $decpt,r3,ad3 # Jump if decimal point not seen
101: decl r5 # Decrease exponent
102: ad3:
103: /*
104: * Fetch the next character, back for more
105: */
106: movzbl (r2)+,r4 # Fetch
107: jbr ad0 # Try again
108: /*
109: * Not a digit. Could it be a decimal point?
110: */
111: ad4: cmpb r4,$'. # If it's not a decimal point, either it's
112: jneq ad5 # the end of the number or the start of
113: # the exponent.
114: jbcs $decpt,r3,ad3 # If it IS a decimal point, we record that
115: # we've seen one, and keep collecting
116: # digits if it is the first one.
117: /*
118: * Check for an exponent
119: */
120: ad5: clrl r6 # Initialize the exponent accumulator
121:
122: cmpb r4,$'e # We allow both lower case e
123: jeql ex1 # ... and ...
124: cmpb r4,$'E # upper-case E
125: jneq ex7
126: /*
127: * Does the exponent have a sign?
128: */
129: ex1: movzbl (r2)+,r4 # Get next character
130: cmpb r4,$'+ # Positive sign?
131: jeql ex2 # ... yes ...
132: cmpb r4,$'- # Negative sign?
133: jneq ex3 # ... no ...
134: bisb2 $1<esign,r3 # Indicate exponent is negative
135: ex2: movzbl (r2)+,r4 # Grab the next character
136: /*
137: * Accumulate exponent digits in r6
138: */
139: ex3: cmpb r4,$'0 # A digit is within the range
140: jlss ex4 # '0' through
141: cmpb r4,$'9 # '9',
142: jgtr ex4 # inclusive.
143: cmpl r6,$214748364 # Exponent outrageously large already?
144: jgeq ex2 # ... yes
145: moval (r6)[r6],r6 # r6 *= 5
146: movaw -'0(r4)[r6],r6 # r6 = r6 * 2 + r4 - '0'
147: jbr ex2 # Go 'round again
148: ex4:
149: /*
150: * Now get the final exponent and force it within a reasonable
151: * range so our scaling loops don't take forever for values
152: * that will ultimately cause overflow or underflow anyway.
153: * A tight check on over/underflow will be done by ldexp.
154: */
155: jbc $esign,r3,ex5 # Jump if exponent not negative
156: mnegl r6,r6 # If sign, negate exponent
157: ex5: addl2 r6,r5 # Add given exponent to calculated exponent
158: cmpl r5,$-100 # Absurdly small?
159: jgtr ex6 # ... no
160: movl $-100,r5 # ... yes, force within limit
161: ex6: cmpl r5,$100 # Absurdly large?
162: jlss ex7 # ... no
163: movl $100,r5 # ... yes, force within bounds
164: ex7:
165: /*
166: * Our number has now been reduced to a mantissa and an exponent.
167: * The mantissa is a 63-bit positive binary integer in r0,r1,
168: * and the exponent is a signed power of 10 in r5. The msign
169: * bit in r3 will be on if the mantissa should ultimately be
170: * considered negative.
171: *
172: * We now have to convert it to a standard format floating point
173: * number. This will be done by accumulating a binary exponent
174: * in r2, as we progressively get r5 closer to zero.
175: *
176: * Don't bother scaling if the mantissa is zero
177: */
178: movq r0,r0 # Mantissa zero?
179: jeql exit # ... yes
180:
181: clrl r2 # Initialize binary exponent
182: tstl r5 # Which way to scale?
183: jleq sd0 # Scale down if decimal exponent <= 0
184: /*
185: * Scale up by "multiplying" r0,r1 by 10 as many times as necessary,
186: * as follows:
187: *
188: * Step 1: Shift r0,r1 right as necessary to ensure that no
189: * overflow can occur when multiplying.
190: */
191: su0: cmpl r1,$429496729 # Compare high word to (2**31)/5
192: jlss su1 # Jump out if guaranteed safe
193: ashq $-1,r0,r0 # Else shift right one bit
194: incl r2 # bump exponent to compensate
195: jbr su0 # and go back to test again.
196: /*
197: * Step 2: Multiply r0,r1 by 5, by appropriate shifting and
198: * double-precision addition
199: */
200: su1: ashq $2,r0,r6 # (r6,r7) := (r0,r1) * 4
201: addl2 r6,r0 # Add low-order halves
202: adwc r7,r1 # and high-order halves
203: /*
204: * Step 3: Increment the binary exponent to take care of the final
205: * factor of 2, and go back if we still need to scale more.
206: */
207: incl r2 # Increment the exponent
208: sobgtr r5,su0 # and back for more (maybe)
209:
210: jbr cm0 # Merge to build final value
211:
212: /*
213: * Scale down. We must "divide" r0,r1 by 10 as many times
214: * as needed, as follows:
215: *
216: * Step 0: Right now, the condition codes reflect the state
217: * of r5. If it's zero, we are done.
218: */
219: sd0: jeql cm0 # If finished, build final number
220: /*
221: * Step 1: Shift r0,r1 left until the high-order bit (not counting
222: * the sign bit) is nonzero, so that the division will preserve
223: * as much precision as possible.
224: */
225: tstl r1 # Is the entire high-order half zero?
226: jneq sd2 # ...no, go shift one bit at a time
227: ashq $30,r0,r0 # ...yes, shift left 30,
228: subl2 $30,r2 # decrement the exponent to compensate,
229: # and now it's known to be safe to shift
230: # at least once more.
231: sd1: ashq $1,r0,r0 # Shift (r0,r1) left one, and
232: decl r2 # decrement the exponent to compensate
233: sd2: jbc $30,r1,sd1 # If the high-order bit is off, go shift
234: /*
235: * Step 2: Divide the high-order part of (r0,r1) by 5,
236: * giving a quotient in r1 and a remainder in r7.
237: */
238: sd3: movl r1,r6 # Copy the high-order part
239: clrl r7 # Zero-extend to 64 bits
240: ediv $5,r6,r1,r7 # Divide (cannot overflow)
241: /*
242: * Step 3: Divide the low-order part of (r0,r1) by 5,
243: * using the remainder from step 2 for rounding.
244: * Note that the result of this computation is unsigned,
245: * so we have to allow for the fact that an ordinary division
246: * by 5 could overflow. We make allowance by dividing by 10,
247: * multiplying the quotient by 2, and using the remainder
248: * to adjust the modified quotient.
249: */
250: addl3 $2,r0,r6 # Dividend is low part of (r0,r1) plus
251: adwc $0,r7 # 2 for rounding plus
252: # (2**32) * previous remainder
253: ediv $10,r6,r0,r6 # r0 := quotient, r6 := remainder.
254: addl2 r0,r0 # Make r0 result of dividing by 5
255: cmpl r6,$5 # If remainder is 5 or greater,
256: jlss sd4 # increment the adjustted quotient.
257: incl r0
258: /*
259: * Step 4: Increment the decimal exponent, decrement the binary
260: * exponent (to make the division by 5 into a division by 10),
261: * and back for another iteration.
262: */
263: sd4: decl r2 # Binary exponent
264: aoblss $0,r5,sd2
265: /*
266: * We now have the following:
267: *
268: * r0: low-order half of a 64-bit integer
269: * r1: high-order half of the same 64-bit integer
270: * r2: a binary exponent
271: *
272: * Our final result is the integer represented by (r0,r1)
273: * multiplied by 2 to the power contained in r2.
274: * We will transform (r0,r1) into a floating-point value,
275: * set the sign appropriately, and let ldexp do the
276: * rest of the work.
277: *
278: * Step 1: if the high-order bit (excluding the sign) of
279: * the high-order half (r1) is 1, then we have 63 bits of
280: * fraction, too many to convert easily. However, we also
281: * know we won't need them all, so we will just throw the
282: * low-order bit away (and adjust the exponent appropriately).
283: */
284: cm0: jbc $30,r1,cm1 # jump if no adjustment needed
285: ashq $-1,r0,r0 # lose the low-order bit
286: incl r2 # increase the exponent to compensate
287: /*
288: * Step 2: split the 62-bit number in (r0,r1) into two
289: * 31-bit positive quantities
290: */
291: cm1: ashq $1,r0,r0 # put the high-order bits in r1
292: # and a 0 in the bottom of r0
293: rotl $-1,r0,r0 # right-justify the bits in r0
294: # moving the 0 from the ashq
295: # into the sign bit.
296: /*
297: * Step 3: convert both halves to floating point
298: */
299: cvtld r0,r6 # low-order part in r6-r7
300: cvtld r1,r0 # high-order part in r0-r1
301: /*
302: * Step 4: multiply the high order part by 2**31 and combine them
303: */
304: muld2 two31,r0 # multiply
305: addd2 r6,r0 # combine
306: /*
307: * Step 5: if appropriate, negate the floating value
308: */
309: jbc $msign,r3,cm2 # Jump if mantissa not signed
310: mnegd r0,r0 # If negative, make it so
311: /*
312: * Step 6: call ldexp to complete the job
313: */
314: cm2: pushl r2 # Put exponent in parameter list
315: movd r0,-(sp) # and also mantissa
316: calls $3,_ldexp # go combine them
317:
318: exit:
319: ret
320:
321: .align 2
322: two31: .word 0x5000 # 2 ** 31
323: .word 0 # (=2147483648)
324: .word 0 # in floating-point
325: .word 0 # (so atof doesn't have to convert it)
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