Created
May 4, 2020 13:52
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Version of https://github.com/nearform/node-cephes that works standalone in Google Apps Script
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| const TOTAL_STACK = 1024 * 1024; // 1MB | |
| const TOTAL_MEMORY = 2 * 1024 * 1024; // 1MB | |
| const WASM_PAGE_SIZE = 64 * 1024; // Defined in WebAssembly specs | |
| /** | |
| * Implementation of atob() according to the HTML and Infra specs, except that | |
| * instead of throwing INVALID_CHARACTER_ERR we return null. | |
| */ | |
| function atobb(data) { | |
| // Web IDL requires DOMStrings to just be converted using ECMAScript | |
| // ToString, which in our case amounts to using a template literal. | |
| data = `${data}`; | |
| // "Remove all ASCII whitespace from data." | |
| data = data.replace(/[ \t\n\f\r]/g, ""); | |
| // "If data's length divides by 4 leaving no remainder, then: if data ends | |
| // with one or two U+003D (=) code points, then remove them from data." | |
| if (data.length % 4 === 0) { | |
| data = data.replace(/==?$/, ""); | |
| } | |
| // "If data's length divides by 4 leaving a remainder of 1, then return | |
| // failure." | |
| // | |
| // "If data contains a code point that is not one of | |
| // | |
| // U+002B (+) | |
| // U+002F (/) | |
| // ASCII alphanumeric | |
| // | |
| // then return failure." | |
| if (data.length % 4 === 1 || /[^+/0-9A-Za-z]/.test(data)) { | |
| return null; | |
| } | |
| // "Let output be an empty byte sequence." | |
| let output = ""; | |
| // "Let buffer be an empty buffer that can have bits appended to it." | |
| // | |
| // We append bits via left-shift and or. accumulatedBits is used to track | |
| // when we've gotten to 24 bits. | |
| let buffer = 0; | |
| let accumulatedBits = 0; | |
| // "Let position be a position variable for data, initially pointing at the | |
| // start of data." | |
| // | |
| // "While position does not point past the end of data:" | |
| for (let i = 0; i < data.length; i++) { | |
| // "Find the code point pointed to by position in the second column of | |
| // Table 1: The Base 64 Alphabet of RFC 4648. Let n be the number given in | |
| // the first cell of the same row. | |
| // | |
| // "Append to buffer the six bits corresponding to n, most significant bit | |
| // first." | |
| // | |
| // atobLookup() implements the table from RFC 4648. | |
| buffer <<= 6; | |
| buffer |= atobLookup(data[i]); | |
| accumulatedBits += 6; | |
| // "If buffer has accumulated 24 bits, interpret them as three 8-bit | |
| // big-endian numbers. Append three bytes with values equal to those | |
| // numbers to output, in the same order, and then empty buffer." | |
| if (accumulatedBits === 24) { | |
| output += String.fromCharCode((buffer & 0xff0000) >> 16); | |
| output += String.fromCharCode((buffer & 0xff00) >> 8); | |
| output += String.fromCharCode(buffer & 0xff); | |
| buffer = accumulatedBits = 0; | |
| } | |
| // "Advance position by 1." | |
| } | |
| // "If buffer is not empty, it contains either 12 or 18 bits. If it contains | |
| // 12 bits, then discard the last four and interpret the remaining eight as | |
| // an 8-bit big-endian number. If it contains 18 bits, then discard the last | |
| // two and interpret the remaining 16 as two 8-bit big-endian numbers. Append | |
| // the one or two bytes with values equal to those one or two numbers to | |
| // output, in the same order." | |
| if (accumulatedBits === 12) { | |
| buffer >>= 4; | |
| output += String.fromCharCode(buffer); | |
| } else if (accumulatedBits === 18) { | |
| buffer >>= 2; | |
| output += String.fromCharCode((buffer & 0xff00) >> 8); | |
| output += String.fromCharCode(buffer & 0xff); | |
| } | |
| // "Return output." | |
| return output; | |
| } | |
| /** | |
| * A lookup table for atob(), which converts an ASCII character to the | |
| * corresponding six-bit number. | |
| */ | |
| function atobLookup(chr) { | |
| if (/[A-Z]/.test(chr)) { | |
| return chr.charCodeAt(0) - "A".charCodeAt(0); | |
| } | |
| if (/[a-z]/.test(chr)) { | |
| return chr.charCodeAt(0) - "a".charCodeAt(0) + 26; | |
| } | |
| if (/[0-9]/.test(chr)) { | |
| return chr.charCodeAt(0) - "0".charCodeAt(0) + 52; | |
| } | |
| if (chr === "+") { | |
| return 62; | |
| } | |
| if (chr === "/") { | |
| return 63; | |
| } | |
| // Throw exception; should not be hit in tests | |
| return undefined; | |
| } | |
| const WASM_CODE = _base64ToArrayBuffer( | |
| 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| |
| "base64" | |
| ); | |
| function _base64ToArrayBuffer(base64) { | |
| var binary_string = atobb(base64); | |
| var len = binary_string.length; | |
| var bytes = new Uint8Array(len); | |
| for (var i = 0; i < len; i++) { | |
| bytes[i] = binary_string.charCodeAt(i); | |
| } | |
| return bytes.buffer; | |
| } | |
| class CephesWrapper { | |
| constructor(sync) { | |
| // Initialize the runtime's memory | |
| this._wasmMemory = new WebAssembly.Memory({ | |
| initial: TOTAL_MEMORY / WASM_PAGE_SIZE, | |
| maximum: TOTAL_MEMORY / WASM_PAGE_SIZE | |
| }); | |
| this._HEAP8 = new Int8Array(this._wasmMemory.buffer); | |
| this._HEAP16 = new Int16Array(this._wasmMemory.buffer); | |
| this._HEAP32 = new Int32Array(this._wasmMemory.buffer); | |
| this._HEAPF32 = new Float32Array(this._wasmMemory.buffer); | |
| this._HEAPF64 = new Float64Array(this._wasmMemory.buffer); | |
| // Compile and export program | |
| if (sync) { | |
| // compile synchronously | |
| const program = this._compileSync(); | |
| this._exportProgram(program); | |
| // create a dummy compile promise | |
| this.compiled = Promise.resolve(); | |
| } else { | |
| // create a singleton compile promise | |
| this.compiled = this._compileAsync().then(program => | |
| this._exportProgram(program) | |
| ); | |
| } | |
| } | |
| _AsciiToString(ptr) { | |
| let str = ""; | |
| while (1) { | |
| const ch = this._HEAP8[ptr++ >> 0]; | |
| if (ch === 0) return str; | |
| str += String.fromCharCode(ch); | |
| } | |
| } | |
| _mtherr(name /* char* */, code /* int */) { | |
| // from mtherr.c | |
| let codemsg = ""; | |
| switch (code) { | |
| case 1: | |
| codemsg = "argument domain error"; | |
| break; | |
| case 2: | |
| codemsg = "function singularity"; | |
| break; | |
| case 3: | |
| codemsg = "overflow range error"; | |
| break; | |
| case 4: | |
| codemsg = "underflow range error"; | |
| break; | |
| case 5: | |
| codemsg = "total loss of precision"; | |
| break; | |
| case 6: | |
| codemsg = "partial loss of precision"; | |
| break; | |
| case 33: | |
| codemsg = "Unix domain error code"; | |
| break; | |
| case 34: | |
| codemsg = "Unix range error code"; | |
| break; | |
| default: | |
| codemsg = "unknown error"; | |
| } | |
| const fnname = this._AsciiToString(name); | |
| const message = 'cephes reports "' + codemsg + '" in ' + fnname; | |
| // Restore stack to the STACKTOP before throwing. This only works because | |
| // all the exported cephes functions are plain functions. | |
| this.stackRestore(0); | |
| if (code == 1) { | |
| throw new RangeError(message); | |
| } else { | |
| throw new Error(message); | |
| } | |
| } | |
| _wasmImports() { | |
| return { | |
| env: { | |
| // cephes error handler | |
| _mtherr: this._mtherr.bind(this), | |
| // memory | |
| memory: this._wasmMemory, | |
| STACKTOP: 0, | |
| STACK_MAX: TOTAL_STACK | |
| } | |
| }; | |
| } | |
| _compileSync() { | |
| return new WebAssembly.Instance( | |
| new WebAssembly.Module(WASM_CODE), | |
| this._wasmImports() | |
| ); | |
| } | |
| _compileAsync() { | |
| return WebAssembly.instantiate(WASM_CODE, this._wasmImports()).then( | |
| results => results.instance | |
| ); | |
| } | |
| _exportProgram(program) { | |
| // export cephes functions | |
| for (const key of Object.keys(program.exports)) { | |
| if (key.startsWith("_cephes_")) { | |
| this[key] = program.exports[key]; | |
| } | |
| } | |
| // export special stack functions | |
| this.stackAlloc = program.exports.stackAlloc; | |
| this.stackRestore = program.exports.stackRestore; | |
| this.stackSave = program.exports.stackSave; | |
| } | |
| // export helper functions | |
| getValue(ptr, type) { | |
| type = type || "i8"; | |
| if (type.charAt(type.length - 1) === "*") type = "i32"; // pointers are 32-bit | |
| switch (type) { | |
| case "i1": | |
| return this._HEAP8[ptr >> 0]; | |
| case "i8": | |
| return this._HEAP8[ptr >> 0]; | |
| case "i16": | |
| return this._HEAP16[ptr >> 1]; | |
| case "i32": | |
| return this._HEAP32[ptr >> 2]; | |
| case "i64": | |
| return this._HEAP32[ptr >> 2]; | |
| case "float": | |
| return this._HEAPF32[ptr >> 2]; | |
| case "double": | |
| return this._HEAPF64[ptr >> 3]; | |
| default: | |
| throw new Error("invalid type for getValue: " + type); | |
| } | |
| return null; | |
| } | |
| writeArrayToMemory(array, buffer) { | |
| this._HEAP8.set(array, buffer); | |
| } | |
| } | |
| // execute syncronously = true | |
| // Async operation don't work properly in Apps Scripts | |
| // https://stackoverflow.com/questions/61190809/running-async-functions-on-google-apps-script | |
| const cephes = new CephesWrapper(true); | |
| // =========================== | |
| // Arithmetic and Algebraic | |
| // =========================== | |
| /** | |
| * Returns the sign bit | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_signbit(x) { | |
| return cephes._cephes_signbit(x); | |
| } | |
| /** | |
| * Check if Not-A-Number | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_isnan(x) { | |
| return cephes._cephes_isnan(x); | |
| } | |
| /** | |
| * Check if finite | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_isfinite(x) { | |
| return cephes._cephes_isfinite(x); | |
| } | |
| /** | |
| * Cube root | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cbrt(x) { | |
| return cephes._cephes_cbrt(x); | |
| } | |
| /** | |
| * Evaluate polynomial | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_polevl(x, coef, N) { | |
| return cephes._cephes_polevl(x, coef, N); | |
| } | |
| /** | |
| * Evaluate Chebyshev series | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_chbevl(x, array, n) { | |
| return cephes._cephes_chbevl(x, array, n); | |
| } | |
| /** | |
| * Round to nearest integer value | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_round(x) { | |
| return cephes._cephes_round(x); | |
| } | |
| /** | |
| * Extract exponent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_frexp(x) { | |
| return cephes._cephes_frexp(x); | |
| } | |
| /** | |
| * Add integer to exponent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ldexp(x, pw2) { | |
| return cephes._cephes_ldexp(x, pw2); | |
| } | |
| // =========================== | |
| // Exponential and Trigonometric | |
| // =========================== | |
| /** | |
| * Exponential of squared argument | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_expx2(x, sign) { | |
| return cephes._cephes_expx2(x, sign); | |
| } | |
| /** | |
| * Degrees, minutes, seconds to radians | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_radian(d, m, s) { | |
| return cephes._cephes_radian(d, m, s); | |
| } | |
| /** | |
| * Circular sine and cosine of argument in degrees | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_sincos(x, flg) { | |
| return cephes._cephes_sincos(x, flg); | |
| } | |
| /** | |
| * Circular cotangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cot(x) { | |
| return cephes._cephes_cot(x); | |
| } | |
| /** | |
| * Circular cotangent of argument in degrees | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cotdg(x) { | |
| return cephes._cephes_cotdg(x); | |
| } | |
| /** | |
| * Relative error approximations for log(1 + x) | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_log1p(x) { | |
| return cephes._cephes_log1p(x); | |
| } | |
| /** | |
| * Relative error approximations for exp(x) - 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_expm1(x) { | |
| return cephes._cephes_expm1(x); | |
| } | |
| /** | |
| * Relative error approximations for cos(x) - 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cosm1(x) { | |
| return cephes._cephes_cosm1(x); | |
| } | |
| /** | |
| * Arc cosine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_acos(x) { | |
| return cephes._cephes_acos(x); | |
| } | |
| /** | |
| * Arc hyperbolic cosine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_acosh(x) { | |
| return cephes._cephes_acosh(x); | |
| } | |
| /** | |
| * Arc hyperbolic sine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_asinh(xx) { | |
| return cephes._cephes_asinh(xx); | |
| } | |
| /** | |
| * Arc hyperbolic tangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_atanh(x) { | |
| return cephes._cephes_atanh(x); | |
| } | |
| /** | |
| * Arcsine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_asin(x) { | |
| return cephes._cephes_asin(x); | |
| } | |
| /** | |
| * Arctangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_atan(x) { | |
| return cephes._cephes_atan(x); | |
| } | |
| /** | |
| * Quadrant correct arctangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_atan2(y, x) { | |
| return cephes._cephes_atan2(y, x); | |
| } | |
| /** | |
| * Cosine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cos(x) { | |
| return cephes._cephes_cos(x); | |
| } | |
| /** | |
| * Cosine of arg in degrees | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cosdg(x) { | |
| return cephes._cephes_cosdg(x); | |
| } | |
| /** | |
| * Exponential, base e | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_exp(x) { | |
| return cephes._cephes_exp(x); | |
| } | |
| /** | |
| * Exponential, base 2 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_exp2(x) { | |
| return cephes._cephes_exp2(x); | |
| } | |
| /** | |
| * Exponential, base 10 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_exp10(x) { | |
| return cephes._cephes_exp10(x); | |
| } | |
| /** | |
| * Hyperbolic cosine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_cosh(x) { | |
| return cephes._cephes_cosh(x); | |
| } | |
| /** | |
| * Hyperbolic sine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_sinh(x) { | |
| return cephes._cephes_sinh(x); | |
| } | |
| /** | |
| * Hyperbolic tangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_tanh(x) { | |
| return cephes._cephes_tanh(x); | |
| } | |
| /** | |
| * Logarithm, base e | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_log(x) { | |
| return cephes._cephes_log(x); | |
| } | |
| /** | |
| * Logarithm, base 2 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_log2(x) { | |
| return cephes._cephes_log2(x); | |
| } | |
| /** | |
| * Logarithm, base 10 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_log10(x) { | |
| return cephes._cephes_log10(x); | |
| } | |
| /** | |
| * Power | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_pow(x, y) { | |
| return cephes._cephes_pow(x, y); | |
| } | |
| /** | |
| * Integer Power | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_powi(x, nn) { | |
| return cephes._cephes_powi(x, nn); | |
| } | |
| /** | |
| * Sine | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_sin(x) { | |
| return cephes._cephes_sin(x); | |
| } | |
| /** | |
| * Sine of arg in degrees | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_sindg(x) { | |
| return cephes._cephes_sindg(x); | |
| } | |
| /** | |
| * Tangent | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_tan(x) { | |
| return cephes._cephes_tan(x); | |
| } | |
| /** | |
| * Tangent of arg in degrees | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_tandg(x) { | |
| return cephes._cephes_tandg(x); | |
| } | |
| // =========================== | |
| // Exponential integral | |
| // =========================== | |
| /** | |
| * Exponential integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ei(x) { | |
| return cephes._cephes_ei(x); | |
| } | |
| /** | |
| * Exponential integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_expn(n, x) { | |
| return cephes._cephes_expn(n, x); | |
| } | |
| /** | |
| * Hyperbolic cosine integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_shichi(x) { | |
| return cephes._cephes_shichi(x); | |
| } | |
| /** | |
| * Cosine integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_sici(x) { | |
| return cephes._cephes_sici(x); | |
| } | |
| // =========================== | |
| // Gamma | |
| // =========================== | |
| /** | |
| * Natural log of |beta|. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_lbeta(a, b) { | |
| return cephes._cephes_lbeta(a, b); | |
| } | |
| /** | |
| * Beta | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_beta(a, b) { | |
| return cephes._cephes_beta(a, b); | |
| } | |
| /** | |
| * Factorial | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_fac(i) { | |
| return cephes._cephes_fac(i); | |
| } | |
| /** | |
| * Gamma | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_gamma(x) { | |
| return cephes._cephes_gamma(x); | |
| } | |
| /** | |
| * Logarithm of gamma function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_lgam(x) { | |
| return cephes._cephes_lgam(x); | |
| } | |
| /** | |
| * Incomplete beta integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_incbet(aa, bb, xx) { | |
| return cephes._cephes_incbet(aa, bb, xx); | |
| } | |
| /** | |
| * Inverse beta integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_incbi(aa, bb, yy0) { | |
| return cephes._cephes_incbi(aa, bb, yy0); | |
| } | |
| /** | |
| * Incomplete gamma integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_igam(a, x) { | |
| return cephes._cephes_igam(a, x); | |
| } | |
| /** | |
| * Complemented gamma integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_igamc(a, x) { | |
| return cephes._cephes_igamc(a, x); | |
| } | |
| /** | |
| * Inverse gamma integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_igami(a, y0) { | |
| return cephes._cephes_igami(a, y0); | |
| } | |
| /** | |
| * Psi (digamma) function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_psi(x) { | |
| return cephes._cephes_psi(x); | |
| } | |
| /** | |
| * Reciprocal Gamma | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_rgamma(x) { | |
| return cephes._cephes_rgamma(x); | |
| } | |
| // =========================== | |
| // Error function | |
| // =========================== | |
| /** | |
| * Error function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_erf(x) { | |
| return cephes._cephes_erf(x); | |
| } | |
| /** | |
| * Complemented error function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_erfc(a) { | |
| return cephes._cephes_erfc(a); | |
| } | |
| /** | |
| * Dawson's integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_dawsn(xx) { | |
| return cephes._cephes_dawsn(xx); | |
| } | |
| /** | |
| * Fresnel integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_fresnl(xxa) { | |
| return cephes._cephes_fresnl(xxa); | |
| } | |
| // =========================== | |
| // Bessel | |
| // =========================== | |
| /** | |
| * Airy | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_airy(x) { | |
| return cephes._cephes_airy(x); | |
| } | |
| /** | |
| * Bessel, order 0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_j0(x) { | |
| return cephes._cephes_j0(x); | |
| } | |
| /** | |
| * Bessel, order 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_j1(x) { | |
| return cephes._cephes_j1(x); | |
| } | |
| /** | |
| * Bessel, order n | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_jn(n, x) { | |
| return cephes._cephes_jn(n, x); | |
| } | |
| /** | |
| * Bessel, noninteger order | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_jv(n, x) { | |
| return cephes._cephes_jv(n, x); | |
| } | |
| /** | |
| * Bessel, second kind, order 0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_y0(x) { | |
| return cephes._cephes_y0(x); | |
| } | |
| /** | |
| * Bessel, second kind, order 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_y1(x) { | |
| return cephes._cephes_y1(x); | |
| } | |
| /** | |
| * Bessel, second kind, order n | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_yn(n, x) { | |
| return cephes._cephes_yn(n, x); | |
| } | |
| /** | |
| * Bessel, noninteger order | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_yv(v, x) { | |
| return cephes._cephes_yv(v, x); | |
| } | |
| /** | |
| * Modified Bessel, order 0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_i0(x) { | |
| return cephes._cephes_i0(x); | |
| } | |
| /** | |
| * Exponentially scaled i0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_i0e(x) { | |
| return cephes._cephes_i0e(x); | |
| } | |
| /** | |
| * Modified Bessel, order 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_i1(x) { | |
| return cephes._cephes_i1(x); | |
| } | |
| /** | |
| * Exponentially scaled i1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_i1e(x) { | |
| return cephes._cephes_i1e(x); | |
| } | |
| /** | |
| * Modified Bessel, nonint. order | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_iv(v, x) { | |
| return cephes._cephes_iv(v, x); | |
| } | |
| /** | |
| * Mod. Bessel, 3rd kind, order 0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_k0(x) { | |
| return cephes._cephes_k0(x); | |
| } | |
| /** | |
| * Exponentially scaled k0 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_k0e(x) { | |
| return cephes._cephes_k0e(x); | |
| } | |
| /** | |
| * Mod. Bessel, 3rd kind, order 1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_k1(x) { | |
| return cephes._cephes_k1(x); | |
| } | |
| /** | |
| * Exponentially scaled k1 | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_k1e(x) { | |
| return cephes._cephes_k1e(x); | |
| } | |
| /** | |
| * Mod. Bessel, 3rd kind, order n | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_kn(nn, x) { | |
| return cephes._cephes_kn(nn, x); | |
| } | |
| // Hypergeometric | |
| /** | |
| * Confluent hypergeometric | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_hyperg(a, b, x) { | |
| return cephes._cephes_hyperg(a, b, x); | |
| } | |
| /** | |
| * Gauss hypergeometric function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_hyp2f1(a, b, c, x) { | |
| return cephes._cephes_hyp2f1(a, b, c, x); | |
| } | |
| // =========================== | |
| // Elliptic | |
| // =========================== | |
| /** | |
| * Complete elliptic integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ellpe(x) { | |
| return cephes._cephes_ellpe(x); | |
| } | |
| /** | |
| * Incomplete elliptic integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ellie(phi, m) { | |
| return cephes._cephes_ellie(phi, m); | |
| } | |
| /** | |
| * Complete elliptic integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ellpk(x) { | |
| return cephes._cephes_ellpk(x); | |
| } | |
| /** | |
| * Incomplete elliptic integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ellik(phi, m) { | |
| return cephes._cephes_ellik(phi, m); | |
| } | |
| /** | |
| * Jacobian elliptic function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ellpj(u, m) { | |
| return cephes._cephes_ellpj(u, m); | |
| } | |
| // =========================== | |
| // Probability | |
| // =========================== | |
| /** | |
| * Beta distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_btdtr(a, b, x) { | |
| return cephes._cephes_btdtr(a, b, x); | |
| } | |
| /** | |
| * Exact Smirnov statistic, for one-sided test. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_smirnov(n, e) { | |
| return cephes._cephes_smirnov(n, e); | |
| } | |
| /** | |
| * Kolmogorov's limiting distribution of two-sided test. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_kolmogorov(y) { | |
| return cephes._cephes_kolmogorov(y); | |
| } | |
| /** | |
| * Functional inverse of Smirnov distribution. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_smirnovi(n, p) { | |
| return cephes._cephes_smirnovi(n, p); | |
| } | |
| /** | |
| * Functional inverse of Kolmogorov statistic for two-sided test. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_kolmogi(p) { | |
| return cephes._cephes_kolmogi(p); | |
| } | |
| /** | |
| * Inverse Negative binomial distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_nbdtri(k, n, p) { | |
| return cephes._cephes_nbdtri(k, n, p); | |
| } | |
| /** | |
| * Functional inverse of Student's t distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_stdtri(k, p) { | |
| return cephes._cephes_stdtri(k, p); | |
| } | |
| /** | |
| * Binomial distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_bdtr(k, n, p) { | |
| return cephes._cephes_bdtr(k, n, p); | |
| } | |
| /** | |
| * Complemented binomial | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_bdtrc(k, n, p) { | |
| return cephes._cephes_bdtrc(k, n, p); | |
| } | |
| /** | |
| * Inverse binomial | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_bdtri(k, n, y) { | |
| return cephes._cephes_bdtri(k, n, y); | |
| } | |
| /** | |
| * Chi square distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_chdtr(df, x) { | |
| return cephes._cephes_chdtr(df, x); | |
| } | |
| /** | |
| * Complemented Chi square | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_chdtrc(df, x) { | |
| return cephes._cephes_chdtrc(df, x); | |
| } | |
| /** | |
| * Inverse Chi square | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_chdtri(df, y) { | |
| return cephes._cephes_chdtri(df, y); | |
| } | |
| /** | |
| * F distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_fdtr(ia, ib, x) { | |
| return cephes._cephes_fdtr(ia, ib, x); | |
| } | |
| /** | |
| * Complemented F | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_fdtrc(ia, ib, x) { | |
| return cephes._cephes_fdtrc(ia, ib, x); | |
| } | |
| /** | |
| * Inverse F distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_fdtri(ia, ib, y) { | |
| return cephes._cephes_fdtri(ia, ib, y); | |
| } | |
| /** | |
| * Gamma distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_gdtr(a, b, x) { | |
| return cephes._cephes_gdtr(a, b, x); | |
| } | |
| /** | |
| * Complemented gamma | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_gdtrc(a, b, x) { | |
| return cephes._cephes_gdtrc(a, b, x); | |
| } | |
| /** | |
| * Negative binomial distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_nbdtr(k, n, p) { | |
| return cephes._cephes_nbdtr(k, n, p); | |
| } | |
| /** | |
| * Complemented negative binomial | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_nbdtrc(k, n, p) { | |
| return cephes._cephes_nbdtrc(k, n, p); | |
| } | |
| /** | |
| * Normal distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ndtr(a) { | |
| return cephes._cephes_ndtr(a); | |
| } | |
| /** | |
| * Inverse normal distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_ndtri(y0) { | |
| return cephes._cephes_ndtri(y0); | |
| } | |
| /** | |
| * Poisson distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_pdtr(k, m) { | |
| return cephes._cephes_pdtr(k, m); | |
| } | |
| /** | |
| * Complemented Poisson | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_pdtrc(k, m) { | |
| return cephes._cephes_pdtrc(k, m); | |
| } | |
| /** | |
| * Inverse Poisson distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_pdtri(k, y) { | |
| return cephes._cephes_pdtri(k, y); | |
| } | |
| /** | |
| * Student's t distribution | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_stdtr(k, t) { | |
| return cephes._cephes_stdtr(k, t); | |
| } | |
| // =========================== | |
| // Miscellaneous | |
| // =========================== | |
| /** | |
| * Integral of Planck's black body radiation formula | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_plancki(w, T) { | |
| return cephes._cephes_plancki(w, T); | |
| } | |
| /** | |
| * Complemented Planck radiation integral | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_planckc(w, T) { | |
| return cephes._cephes_planckc(w, T); | |
| } | |
| /** | |
| * Planck's black body radiation formula | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_planckd(w, T) { | |
| return cephes._cephes_planckd(w, T); | |
| } | |
| /** | |
| * Wavelength, w, of maximum radiation at given temperature T. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_planckw(T) { | |
| return cephes._cephes_planckw(T); | |
| } | |
| /** | |
| * Dilogarithm | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_spence(x) { | |
| return cephes._cephes_spence(x); | |
| } | |
| /** | |
| * Riemann Zeta function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_zetac(x) { | |
| return cephes._cephes_zetac(x); | |
| } | |
| /** | |
| * Two argument zeta function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_zeta(x, q) { | |
| return cephes._cephes_zeta(x, q); | |
| } | |
| /** | |
| * Struve function | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_struve(v, x) { | |
| return cephes._cephes_struve(v, x); | |
| } | |
| // =========================== | |
| // Polynomials and Power Series | |
| // =========================== | |
| /** | |
| * Evaluate polynomial when coefficient of x is 1.0. | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_p1evl(x, coef, N) { | |
| return cephes._cephes_p1evl(x, coef, N); | |
| } | |
| /** | |
| * The polylogarithm of order n | |
| * | |
| * @customfunction | |
| */ | |
| function cephes_polylog(n, x) { | |
| return cephes._cephes_polylog(n, x); | |
| } |
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