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| -rw-r--r-- | sicp.org | 48 |
1 files changed, 36 insertions, 12 deletions
@@ -62,19 +62,43 @@ and will evaluate to ~0~. again and again. *** 7 +The following list show the tolerance value and the corresponding +square root of 0.1 computed with that tolerance value. + +#+BEGIN_EXAMPLE +((0.001 . 0.316245562280389) +(1.0e-4 . 0.316245562280389) +(1.0e-5 . 0.31622776651756745) +(1.0000000000000002e-6 . 0.31622776651756745) +(1.0000000000000002e-7 . 0.31622776651756745) +(1.0000000000000002e-8 . 0.31622776651756745) +(1.0000000000000003e-9 . 0.31622776651756745) +1.0000000000000003e-10 . 0.31622776601683794) +#+END_EXAMPLE + +Guile's =sqrt= function says the square root of 0.1 is +0.31622776601683794: #+BEGIN_SRC scheme -$ guile scheme@(guile-user)> (sqrt 0.1) -$1 = 0.31622776601683794 +$7 = 0.31622776601683794 #+END_SRC -#+BEGIN_EXAMPLE - 0.31622776601683794 -0.0001 = 0.316245562280389 -0.00001 = 0.31622776651756745 -0.000001 = 0.31622776651756745 -0.0000001 = 0.31622776651756745 -0.00000001 = 0.31622776651756745 -0.000000001 = 0.31622776651756745 -0.0000000001 = 0.31622776601683794 -#+END_EXAMPLE +From above, it can be observed that the only when the tolerance value +for the =good-enough?= function is ~1.0e-10, does the square root of +0.1 produced by our custom square root function matches the value +produced by Guile's =sqrt= function. + +If the =good-enough?= is changed such that it returns =true= if the +difference between the present guess and the previous guess is less +than or equal to 0.001, the sqrt function yields 0.31622776651756745 +for sqrt(0.1). + +#+BEGIN_SRC scheme +scheme@(guile-user)> (sqrt-sicp-alt 0.1) +$9 = 0.31622776651756745 +#+END_SRC + +0.31622776651756745 is more precise than 0.316245562280389 (which is +the answer returned by the custom sqrt function that uses the ol' +=good-enough= function) but not as precise as the answer returned by +the guile's sqrt function. |