Arithmetic-geometric mean: Difference between revisions

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@@ Line 1,549: / Line 1,549: @@
 =={{header|Lambdatalk}}==
 <syntaxhighlight lang="Scheme">
+{def eps 1e-15}
+-> eps
 {def agm
+  {lambda {:a :g}
- {def agm.r
-  {lambda {:an :gn :tol}
+   {if {> {abs {- :a :g}} {eps}}
-   {if {> {abs {- :an :gn}} :tol}
+    then {agm {/ {+ :a :g} 2}
-    then {agm.r {/ {+ :an :gn} 2} {sqrt {* :an :gn}} :tol}
+              {sqrt {* :a :g}}}
-    else :an }}}
+    else :a }}}
- {lambda {:a0 :g0}
-  {agm.r {/ {+ :a0 :g0} 2} {sqrt {* :a0 :g0}} 1e-15}}}
 -> agm
@@ Line 1,562: / Line 1,563: @@
 -> 0.8472130847939792
-Using the lib_BN library we compute 70 digits
+Multi-precision version using the lib_BN library
+{BN.DEC 70}
+->   70 digits
+{def EPS {BN./ 1 {BN.pow 10 45}}}
+-> EPS
 {def AGM
+  {lambda {:a :g}
- {def AGM.r
+   {if {= {BN.compare {BN.abs {BN.- :a :g}} {EPS}} 1}
-  {lambda {:an :gn :tol}
-   {if {= {BN.compare {BN.abs {BN.- :an :gn}} :tol} 1}
+    then {AGM {BN./ {BN.+ :a :g} 2}
-    then {AGM.r {BN./ {BN.+ :an :gn} 2}
+              {BN.sqrt {BN.* :a :g}}}
-                {BN.sqrt {BN.* :an :gn}}
+    else :a }}}
-                :tol}
-    else :an }}}
- {lambda {:a0 :g0}
-  {AGM.r {BN./ {BN.+ :a0 :g0} 2}
-         {BN.sqrt {BN.* :a0 :g0}}
-         {BN./ 1 {BN.pow 10 45}}}}}
 -> AGM
-{BN.DEC 70}
-->   70 digits
 {AGM 1 {BN./ 1 {BN.sqrt 2}}}
 -> 0.8472130847939790866064991234821916364814459103269421850605793726597339
 </syntaxhighlight>
 =={{header|LFE}}==