Clarified for various mathematical functions the defined input and ou…

…tput ranges. Mention that `NaN` is returned outside of the defined input range where possible.

CHANGELOG.md

@@ -8,7 +8,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 
-- Trigonometric functions: Clarified that NaN is returned outside of their defined input range and defined output ranges where possible.
+- Clarified for various mathematical functions the defined input and output ranges. Mention that `NaN` is returned outside of the defined input range where possible.
 
 ## [2.0.0-rc.1] - 2023-05-25
 

absolute.json

@@ -1,7 +1,7 @@
 {
     "id": "absolute",
     "summary": "Absolute value",
-    "description": "Computes the absolute value of a real number `x`, which is the \"unsigned\" portion of x and often denoted as *|x|*.\n\nThe no-data value `null` is passed through and therefore gets propagated.",
+    "description": "Computes the absolute value of a real number `x`, which is the \"unsigned\" portion of `x` and often denoted as *|x|*.\n\nThe no-data value `null` is passed through and therefore gets propagated.",
     "categories": [
         "math"
     ],
@@ -95,4 +95,4 @@
             "result": true
         }
     }
-}
+}

arccos.json

@@ -1,24 +1,26 @@
 {
     "id": "arccos",
     "summary": "Inverse cosine",
-    "description": "Computes the arc cosine of `x`. The arc cosine is the inverse function of the cosine so that *`arccos(cos(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated. `NaN` is returned for values < -1 and > 1.",
+    "description": "Computes the arc cosine of `x`. The arc cosine is the inverse function of the cosine so that *`arccos(cos(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated. `NaN` is returned for values outside of the allowed range.",
     "categories": [
         "math > trigonometric"
     ],
     "parameters": [
         {
             "name": "x",
-            "description": "A number.",
+            "description": "A number in the range *[-1, 1]*.",
             "schema": {
                 "type": [
                     "number",
                     "null"
-                ]
+                ],
+                "minimum": -1,
+                "maximum": 1
             }
         }
     ],
     "returns": {
-        "description": "The computed angle in radians.",
+        "description": "The computed angle in radians in the range *[0, π]*.",
         "schema": {
             "type": [
                 "number",

arcosh.json

@@ -1,24 +1,25 @@
 {
     "id": "arcosh",
     "summary": "Inverse hyperbolic cosine",
-    "description": "Computes the inverse hyperbolic cosine of `x`. It is the inverse function of the hyperbolic cosine so that *`arcosh(cosh(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated. `NaN` is returned for values < 1.",
+    "description": "Computes the inverse hyperbolic cosine of `x`. It is the inverse function of the hyperbolic cosine so that *`arcosh(cosh(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated. `NaN` is returned for values outside of the allowed range.",
     "categories": [
         "math > trigonometric"
     ],
     "parameters": [
         {
             "name": "x",
-            "description": "A number.",
+            "description": "A number in the range *[1, +∞)*.",
             "schema": {
                 "type": [
                     "number",
                     "null"
                 ]
-            }
+            },
+            "minimum": 1
         }
     ],
     "returns": {
-        "description": "The computed angle in radians.",
+        "description": "The computed angle in radians in the range *[0, +∞)*.",
         "schema": {
             "type": [
                 "number",

arcsin.json

@@ -8,17 +8,19 @@
     "parameters": [
         {
             "name": "x",
-            "description": "A number.",
+            "description": "A number in the range *[-1, 1]*.",
             "schema": {
                 "type": [
                     "number",
                     "null"
-                ]
+                ],
+                "minimum": -1,
+                "maximum": 1
             }
         }
     ],
     "returns": {
-        "description": "The computed angle in radians.",
+        "description": "The computed angle in radians in the range *[-π/2, π/2]*.",
         "schema": {
             "type": [
                 "number",

arctan.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed angle in radians.",
+        "description": "The computed angle in radians in the range *(−π/2, π/2)*.",
         "schema": {
             "type": [
                 "number",
@@ -41,4 +41,4 @@
             "title": "Inverse tangent explained by Wolfram MathWorld"
         }
     ]
-}
+}

artanh.json

@@ -1,14 +1,14 @@
 {
     "id": "artanh",
     "summary": "Inverse hyperbolic tangent",
-    "description": "Computes the inverse hyperbolic tangent of `x`. It is the inverse function of the hyperbolic tangent so that *`artanh(tanh(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated. `NaN` is returned for values <= -1 and >= 1.",
+    "description": "Computes the inverse hyperbolic tangent of `x`. It is the inverse function of the hyperbolic tangent so that *`artanh(tanh(x)) = x`*.\n\nWorks on radians only.\nThe no-data value `null` is passed through and therefore gets propagated.  `NaN` is returned for values outside of the allowed range.",
     "categories": [
         "math > trigonometric"
     ],
     "parameters": [
         {
             "name": "x",
-            "description": "A number.",
+            "description": "A number in the range *(-1, 1)*.",
             "schema": {
                 "type": [
                     "number",

cos.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed cosine of `x`.",
+        "description": "The computed cosine in the range *[-1, 1]*.",
         "schema": {
             "type": [
                 "number",

cosh.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed hyperbolic cosine of `x`.",
+        "description": "The computed hyperbolic cosine in the range *[1, +∞)*.",
         "schema": {
             "type": [
                 "number",

exp.json

@@ -18,12 +18,13 @@
         }
     ],
     "returns": {
-        "description": "The computed value for *e* raised to the power of `p`.",
+        "description": "The computed value for *e* raised to the power of `p`. Value is in the range of *(0, +∞)*",
         "schema": {
             "type": [
                 "number",
                 "null"
-            ]
+            ],
+            "minimumExclusive": 0
         }
     },
     "examples": [
@@ -65,4 +66,4 @@
             "result": true
         }
     }
-}
+}

ln.json

@@ -1,19 +1,20 @@
 {
     "id": "ln",
     "summary": "Natural logarithm",
-    "description": "The natural logarithm is the logarithm to the base *e* of the number `x`, which equals to using the *log* process with the base set to *e*. The natural logarithm is the inverse function of taking *e* to the power x.\n\nThe no-data value `null` is passed through.\n\nThe computations follow [IEEE Standard 754](https://ieeexplore.ieee.org/document/8766229) whenever the processing environment supports it. Therefore, *`ln(0)`* results in ±infinity if the processing environment supports it or otherwise an exception is thrown.",
+    "description": "The natural logarithm is the logarithm to the base *e* of the number `x`, which equals to using the *log* process with the base set to *e*. The natural logarithm is the inverse function of taking *e* to the power x.\n\nThe no-data value `null` is passed through.\n\nThe computations follow [IEEE Standard 754](https://ieeexplore.ieee.org/document/8766229) whenever the processing environment supports it. Therefore, *`ln(0)`* results in -infinity if the processing environment supports it or otherwise an exception is thrown. `NaN` is returned for values outside of the allowed range.",
     "categories": [
         "math > exponential & logarithmic"
     ],
     "parameters": [
         {
             "name": "x",
-            "description": "A number to compute the natural logarithm for.",
+            "description": "A number to compute the natural logarithm for in the range *[0, +∞)*.",
             "schema": {
                 "type": [
                     "number",
                     "null"
-                ]
+                ],
+                "minimum": 0
             }
         }
     ],
@@ -64,4 +65,4 @@
             "result": true
         }
     }
-}
+}

log.json

@@ -1,19 +1,20 @@
 {
     "id": "log",
     "summary": "Logarithm to a base",
-    "description": "Logarithm to the base `base` of the number `x` is defined to be the inverse function of taking b to the power of x.\n\nThe no-data value `null` is passed through and therefore gets propagated if any of the arguments is `null`.\n\nThe computations follow [IEEE Standard 754](https://ieeexplore.ieee.org/document/8766229) whenever the processing environment supports it. Therefore, `log(0, 2)` results in ±infinity if the processing environment supports it or otherwise an exception is thrown.",
+    "description": "Logarithm to the base `base` of the number `x` is defined to be the inverse function of taking b to the power of x.\n\nThe no-data value `null` is passed through and therefore gets propagated if any of the arguments is `null`.\n\nThe computations follow [IEEE Standard 754](https://ieeexplore.ieee.org/document/8766229) whenever the processing environment supports it. Therefore, `log(0, 2)` results in -infinity if the processing environment supports it or otherwise an exception is thrown. `NaN` is returned for values outside of the allowed range.",
     "categories": [
         "math > exponential & logarithmic"
     ],
     "parameters": [
         {
             "name": "x",
-            "description": "A number to compute the logarithm for.",
+            "description": "A number to compute the logarithm for in the range *[0, +∞)*.",
             "schema": {
                 "type": [
                     "number",
                     "null"
-                ]
+                ],
+                "minimum": 0
             }
         },
         {
@@ -78,4 +79,4 @@
             "title": "IEEE Standard 754-2019 for Floating-Point Arithmetic"
         }
     ]
-}
+}

sgn.json

@@ -23,6 +23,12 @@
             "type": [
                 "number",
                 "null"
+            ],
+            "enum": [
+                -1,
+                0,
+                1,
+                null
             ]
         }
     },
@@ -104,4 +110,4 @@
             "result": true
         }
     }
-}
+}

sin.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed sine of `x`.",
+        "description": "The computed sine in the range *[-1, 1]*.",
         "schema": {
             "type": [
                 "number",

sinh.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed hyperbolic sine of `x`.",
+        "description": "The computed hyperbolic sine.",
         "schema": {
             "type": [
                 "number",
@@ -41,4 +41,4 @@
             "title": "Hyperbolic sine explained by Wolfram MathWorld"
         }
     ]
-}
+}

tan.json

@@ -18,7 +18,7 @@
         }
     ],
     "returns": {
-        "description": "The computed tangent of `x`.",
+        "description": "The computed tangent.",
         "schema": {
             "type": [
                 "number",

tanh.json

@@ -18,14 +18,14 @@
         }
     ],
     "returns": {
-        "description": "The computed hyperbolic tangent of `x`.",
+        "description": "The computed hyperbolic tangent in the range *(-1, 1)*.",
         "schema": {
             "type": [
                 "number",
                 "null"
             ],
-            "minimum": -1,
-            "maximum": 1
+            "minimumExclusive": -1,
+            "maximumExclusive": 1
         }
     },
     "examples": [