Inadvertently substituted d0 for d2. Fix.

No change in conclusion -- there was no convenient cancellation or
anything as a consequence of this.

diff --git a/src/runtime/arith.scm b/src/runtime/arith.scm
index 6c766891cc00c0c72969c91acd19fc6e4acfa61d..b417b4843c210ba1a10c6783a70298ce8dd26776 100644 (file)
--- a/src/runtime/arith.scm
+++ b/src/runtime/arith.scm
@@ -2113,13 +2113,13 @@ USA.
          ;; relative error d2, then we get
          ;;
          ;;     (1 + d2)/[(1 + (1 + d0) e^{-x})(1 + d1)]
-         ;;     = (1 + d0)/[1 + e^{-x} + d0 e^{-x}
+         ;;     = (1 + d2)/[1 + e^{-x} + d0 e^{-x}
          ;;                     + d1 + d1 e^{-x} + d0 d1 e^{-x}]
-         ;;     = (1 + d0)/[(1 + e^{-x})(1 + d0 e^{-x}/(1 + e^{-x})
+         ;;     = (1 + d2)/[(1 + e^{-x})(1 + d0 e^{-x}/(1 + e^{-x})
          ;;                                 + d1/(1 + e^{-x})
          ;;                                 + d0 d1 e^{-x}/(1 + e^{-x}))].
-         ;;     = (1 + d0)/[(1 + e^{-x})(1 + d')]
-         ;;     = [1/(1 + e^{-x})] (1 + d0)/(1 + d')
+         ;;     = (1 + d2)/[(1 + e^{-x})(1 + d')]
+         ;;     = [1/(1 + e^{-x})] (1 + d2)/(1 + d')
          ;;
          ;; where
          ;;
@@ -2129,15 +2129,14 @@ USA.
          ;;
          ;; By Lemma 2 this relative error is bounded by
          ;;
-         ;;     2|d0 - d'|
-         ;;      = 2|d0 - d0 e^{-x}/(1 + e^{-x})
+         ;;     2|d2 - d'|
+         ;;      = 2|d2 - d0 e^{-x}/(1 + e^{-x})
          ;;             - d1/(1 + e^{-x})
          ;;             - d0 d1 e^{-x}/(1 + e^{-x})|
-         ;;     <= 2|d0| + 2|d0 e^{-x}/(1 + e^{-x})|
+         ;;     <= 2|d2| + 2|d0 e^{-x}/(1 + e^{-x})|
          ;;             + 2|d1/(1 + e^{-x})|
          ;;             + 2|d0 d1 e^{-x}/(1 + e^{-x})|
-         ;;     <= 2|d0| + 2|d0| + 2|d1| + 2|d0 d1|
-         ;;     <= 4|d0| + 2|d1| + 2|d0 d1|
+         ;;     <= 2|d2| + 2|d0| + 2|d1| + 2|d0 d1|
          ;;     <= 6 eps + 2 eps^2.
          ;;
          (/ 1 (+ 1 (exp (- x)))))