Calc (finance · statistics · exact math · engineering)

{
  "name": "Calc (finance \u00b7 statistics \u00b7 exact math \u00b7 engineering)",
  "description": "Deterministic calculations sold per request in AIC credits: loans, NPV/IRR, bonds, Black-Scholes, probability distributions, confidence intervals, power analysis, Welch t-test, exact integer arithmetic, IPv4 subnets, beam deflection. Same input, same bytes. Optional parameters left empty are treated as not given. Send exact decimals as strings (JSON numbers carry only double precision). Calculation tools only \u2014 not investment, tax, medical or design advice.",
  "version": "1.0.0",
  "supportedInterfaces": [
    {
      "url": "https://calc.star365.site/a2a",
      "protocolBinding": "JSONRPC",
      "protocolVersion": "1.0"
    }
  ],
  "provider": {
    "organization": "star365",
    "url": "https://star365.site"
  },
  "documentationUrl": "https://calc.star365.site/",
  "capabilities": {
    "streaming": false,
    "pushNotifications": false,
    "extensions": [
      {
        "uri": "https://github.com/google-agentic-commerce/a2a-x402/blob/main/spec/v0.2",
        "description": "x402 payments over A2A (payment-required \u2192 payment-submitted \u2192 payment-completed)",
        "required": true
      },
      {
        "uri": "https://aic.star365.site/spec/AIC-PROTOCOL-v0.md",
        "description": "settled in AIC credits via scheme aic-escrow",
        "required": true,
        "params": {
          "facilitator": "https://aic.star365.site/v0/x402",
          "network": "aic:credit",
          "payTo": "2ba7f612-4245-44ef-940a-1411f824baa9",
          "offers": [
            {
              "skill": "compound-fv-pv",
              "amount": "300",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/compound-fv-pv",
              "mimeType": "application/json",
              "queryParams": {
                "op": "future-value",
                "principal": "1000",
                "deposit": "0",
                "rate_pct": "5",
                "years": "10",
                "compounds_per_year": "12"
              }
            },
            {
              "skill": "npv-irr",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/npv-irr",
              "mimeType": "application/json",
              "queryParams": {
                "rate_pct": "8",
                "flows": "-1000,300,400,500"
              }
            },
            {
              "skill": "loan-schedule",
              "amount": "500",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/loan-schedule",
              "mimeType": "application/json",
              "queryParams": {
                "principal": "250000",
                "rate_pct": "4.5",
                "months": "360",
                "kind": "annuity"
              }
            },
            {
              "skill": "bond-ytm-duration",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/bond-ytm-duration",
              "mimeType": "application/json",
              "queryParams": {
                "face": "1000",
                "coupon_pct": "6",
                "years": "10",
                "m": "2",
                "y_pct": "8"
              }
            },
            {
              "skill": "black-scholes",
              "amount": "500",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/black-scholes",
              "mimeType": "application/json",
              "queryParams": {
                "S": "100",
                "K": "100",
                "T": "1",
                "r_pct": "5",
                "sigma_pct": "20",
                "q_pct": "0"
              }
            },
            {
              "skill": "prob-distribution",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/prob-distribution",
              "mimeType": "application/json",
              "queryParams": {
                "kind": "binom",
                "p1": "10",
                "p2": "0.3",
                "query": "le",
                "a": "3"
              }
            },
            {
              "skill": "confidence-interval",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/confidence-interval",
              "mimeType": "application/json",
              "queryParams": {
                "kind": "mean",
                "mean": "13.4875",
                "sd": "1.208822",
                "mu0": "12.5",
                "n": "8",
                "level": "0.95"
              }
            },
            {
              "skill": "sample-size-power",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/sample-size-power",
              "mimeType": "application/json",
              "queryParams": {
                "kind": "ttest_ind",
                "effect": "0.5",
                "alpha": "0.05",
                "power": "0.8",
                "alt": "two",
                "ratio": "1"
              }
            },
            {
              "skill": "welch-ttest",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/welch-ttest",
              "mimeType": "application/json",
              "queryParams": {
                "a": "5.1,4.9,5.3,5",
                "b": "5.8,6.1,5.9,6.2,6"
              }
            },
            {
              "skill": "exact-integer-math",
              "amount": "300",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/exact-integer-math",
              "mimeType": "application/json",
              "queryParams": {
                "op": "modpow",
                "a": "4",
                "exp": "13",
                "mod": "497"
              }
            },
            {
              "skill": "ipv4-subnet",
              "amount": "300",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/ipv4-subnet",
              "mimeType": "application/json",
              "queryParams": {
                "cidr": "192.168.1.10/24"
              }
            },
            {
              "skill": "beam-deflection",
              "amount": "400",
              "maxTimeoutSeconds": 60,
              "method": "GET",
              "resource": "https://calc.star365.site/feed/beam-deflection",
              "mimeType": "application/json",
              "queryParams": {
                "case": "ss_udl",
                "span_m": "6",
                "w_N_per_m": "10000",
                "E_Pa": "200000000000",
                "I_m4": "0.0000833"
              }
            }
          ]
        }
      }
    ]
  },
  "defaultInputModes": [
    "application/json"
  ],
  "defaultOutputModes": [
    "application/json"
  ],
  "skills": [
    {
      "id": "compound-fv-pv",
      "name": "Compound interest: future value or present value",
      "description": "op=future-value: fields principal, rate_pct, years, compounds_per_year (1\u2013365; years \u00d7 compounds_per_year must be a whole number of periods) and optional deposit (added at the END of every compounding period, default 0): returns fv, total_principal, interest, periods. op=present-value: fields amount, rate_pct, years: discounts an amount due in N years with ANNUAL compounding (fields of the other op are refused, not ignored). Rate is a PERCENT (5.25 = 5.25%). Calculation tool only \u2014 no taxes or fees, not investment advice. Price 300 \u00b5AIC.",
      "tags": [
        "finance",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"compound-fv-pv\",\"op\":\"future-value\",\"principal\":\"1000\",\"rate_pct\":\"5\",\"years\":\"10\",\"compounds_per_year\":\"12\"}",
        "{\"skill\":\"compound-fv-pv\",\"op\":\"present-value\",\"amount\":\"10000\",\"rate_pct\":\"4\",\"years\":\"5\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "npv-irr",
      "name": "NPV and IRR of a cash-flow series",
      "description": "Net present value at a per-period percent rate and the internal rate of return of up to 30 cash flows (period 0 first; negative = outflow). IRR is returned only when it is unique (exactly one sign change); otherwise the request is refused before payment (no_sign_change / multiple_irr / no_converge). Rate is a PERCENT per period. Calculation tool only \u2014 not investment advice. Price 400 \u00b5AIC.",
      "tags": [
        "finance",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"npv-irr\",\"rate_pct\":\"8\",\"flows\":\"-1000,300,400,500\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "loan-schedule",
      "name": "Loan repayment summary (annuity or equal principal)",
      "description": "Monthly loan repayment: first and last installment (payment, principal, interest, balance), total interest and total paid, for an annuity (level payment) or equal-principal loan over 1\u20131200 months. Annual rate is a PERCENT (4.5 = 4.5%, at most 100). Principal at most 9999999.99. Amounts are rounded to 4 decimals. Long terms at high rates are refused with 422 ill_conditioned (rounding error of the annuity recursion grows with (1 + rate/12)^months; amplification above 1e5 is not sold). Fixed rate, no fees, no prepayment. Calculation tool only \u2014 not a loan offer or advice. Price 500 \u00b5AIC.",
      "tags": [
        "finance",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"loan-schedule\",\"principal\":\"250000\",\"rate_pct\":\"4.5\",\"months\":\"360\",\"kind\":\"annuity\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "bond-ytm-duration",
      "name": "Bond price, yield to maturity, duration and convexity",
      "description": "Fixed-coupon bullet bond valued on a coupon date (first coupon exactly one period away, so NO accrued interest: clean = dirty price). Give face, coupon_pct, years, m (coupon payments per year: 1, 2, 4 or 12) and EXACTLY ONE of y_pct (yield \u2192 price) or price (price \u2192 yield, solved by bisection). Yields and rates are PERCENT, nominal annual compounded m times a year (per-period rate = y/m), not an effective annual rate. years \u00d7 m must be a whole number of coupon periods (m=12: use multiples of 0.25 years). Returns price, ytm_pct, current_yield_pct (annual coupon / price), premium (par|premium|discount), macaulay_years (PV-weighted average time of the cash flows, years), modified_years (macaulay / (1 + y/m), years) and convexity (d\u00b2P/dy\u00b2 / P, years\u00b2, y as a decimal fraction: price change \u2248 \u2212modified\u00b7\u0394y + \u00bd\u00b7convexity\u00b7\u0394y\u00b2 with \u0394y = 0.01 for 1 percentage point). Limits: face \u2264 9999999999.99, coupon_pct 0\u2013100, years \u2264 100, y_pct in (-99, 1000]. Fixed rate, no call/put, no credit risk, no day-count or settlement-date handling. If price is given, the returned price is that input. Calculation tool only \u2014 not investment advice. Price 400 \u00b5AIC.",
      "tags": [
        "finance",
        "bond",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"bond-ytm-duration\",\"face\":\"1000\",\"coupon_pct\":\"6\",\"years\":\"10\",\"m\":\"2\",\"y_pct\":\"8\"}",
        "{\"skill\":\"bond-ytm-duration\",\"face\":\"1000\",\"coupon_pct\":\"6\",\"years\":\"10\",\"m\":\"2\",\"price\":\"925.5\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "black-scholes",
      "name": "Black-Scholes price and Greeks (European option)",
      "description": "European call and put under Black-Scholes-Merton: constant volatility and rate, continuous dividend yield q, no early exercise. Inputs: S spot, K strike, T years to expiry, r_pct risk-free rate, sigma_pct volatility, q_pct dividend yield (default 0) \u2014 all PERCENT, annualised; r and q are continuously compounded. Returns d1, d2, call, put and the Greeks with the ENGINE'S conventions: delta{call,put} per 1 unit of S; gamma per 1 unit of S\u00b2; vega = \u2202V/\u2202\u03c3 per 1.00 change of volatility (20% \u2192 120%), so divide by 100 for one volatility point; theta{call,put} = \u2202V/\u2202t per YEAR (negative = time decay), divide by 365 for one calendar day; rho{call,put} = \u2202V/\u2202r per 1.00 change of r, divide by 100 for one percentage point (rho excludes any dividend-yield effect). Numbers are rounded to 10 significant digits; a value that is a small difference of larger terms (delta of a far out-of-the-money put, theta near a sign change) is accurate in absolute terms, so its low digits can be noise. Limits: S, K > 0 (\u2264 9 integer digits, 6 decimals); T \u2264 100; sigma_pct \u2264 500; |r_pct|, |q_pct| < 100. Refused before payment: sigma\u00b7\u221aT < 0.001, or |d1| or |d2| > 4 (extreme moneyness, where the price is a difference of near-equal terms or the normal CDF tail is not guaranteed). Calculation tool only \u2014 not trading, hedging or investment advice. Price 500 \u00b5AIC.",
      "tags": [
        "finance",
        "options",
        "black-scholes",
        "greeks",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"black-scholes\",\"S\":\"100\",\"K\":\"100\",\"T\":\"1\",\"r_pct\":\"5\",\"sigma_pct\":\"20\"}",
        "{\"skill\":\"black-scholes\",\"S\":\"42\",\"K\":\"40\",\"T\":\"0.5\",\"r_pct\":\"10\",\"sigma_pct\":\"20\",\"q_pct\":\"3\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "prob-distribution",
      "name": "Probability distribution: probabilities and quantiles (binomial, Poisson, normal, t, chi-square, F)",
      "description": "Cumulative / interval probabilities and quantiles. kind with p1/p2: binom (p1 = n trials 1\u2013100000, p2 = success probability 0\u20131), poisson (p1 = lambda > 0 up to 100000, p2 omitted), normal (p1 = mean, p2 = standard deviation > 0), t (p1 = degrees of freedom, integer 1\u20131000), chi2 (p1 = degrees of freedom, integer 1\u20131000), f (p1, p2 = numerator and denominator degrees of freedom, integers 1\u20131000). query: le = P(X \u2264 a); ge = P(X \u2265 a); between = P(a \u2264 X \u2264 b), bounds included; quantile = smallest integer k with P(X \u2264 k) \u2265 p (binom, poisson) or the x with P(X \u2264 x) = p (continuous), p from 0.000001 to 0.999999. For binom and poisson a and b must be integers. Returns value, mean and variance (the string \"undefined\" where the moment does not exist, e.g. t with 1 degree of freedom) and whether the distribution is discrete. Results are rounded to 7 significant digits: the engine uses jStat special functions that are only about 1e-8 accurate, so degrees of freedom above 1000, extreme tails, discrete quantiles whose p sits within 1e-8 of a cumulative probability and narrow intervals that are differences of nearly equal cumulative probabilities are refused before payment; probabilities below about 1e-300 print as 0. Calculation tool only \u2014 not statistical, medical or investment advice. Price 400 \u00b5AIC.",
      "tags": [
        "statistics",
        "probability",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"prob-distribution\",\"kind\":\"binom\",\"p1\":\"10\",\"p2\":\"0.3\",\"query\":\"le\",\"a\":\"3\"}",
        "{\"skill\":\"prob-distribution\",\"kind\":\"t\",\"p1\":\"12\",\"query\":\"quantile\",\"p\":\"0.975\"}",
        "{\"skill\":\"prob-distribution\",\"kind\":\"normal\",\"p1\":\"100\",\"p2\":\"15\",\"query\":\"between\",\"a\":\"85\",\"b\":\"110\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "confidence-interval",
      "name": "Confidence interval for a mean (t) or a proportion (Wald and Wilson), with an optional one-sample test",
      "description": "kind=mean: from summary statistics mean, sd (sample standard deviation, n \u2212 1), n (2\u20131000) and level (0.5 < level \u2264 0.999, up to 4 decimals, default 0.95): standard error, t critical value, margin of error and the interval mean \u00b1 t\u00b7se; with mu0 also the one-sample t statistic, degrees of freedom and two-sided p. kind=proportion: x successes of n trials (n up to 1e9) at level: p-hat, the Wald interval (clipped to [0,1]; unreliable for small n or extreme p, flagged by small_sample) and the Wilson interval; with p0 (0 < p0 < 1) also the z test against p0 (standard error under p0) and its two-sided p. Assumes a normal population (mean) or simple random sampling (proportion); no continuity correction, no exact (Clopper\u2013Pearson) interval. The mean results that rely on the t distribution (t critical value, margin, p) are rounded to 7 significant digits because the engine uses jStat (about 1e-8 accurate); sample sizes above 1000, |t| above 40, |z| above 30 and a mean more than 1e6 margins from zero are refused before payment. Calculation tool only \u2014 not statistical or medical advice. Price 400 \u00b5AIC.",
      "tags": [
        "statistics",
        "confidence-interval",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"confidence-interval\",\"kind\":\"mean\",\"mean\":\"13.4875\",\"sd\":\"1.208822\",\"n\":\"8\",\"level\":\"0.95\",\"mu0\":\"12.5\"}",
        "{\"skill\":\"confidence-interval\",\"kind\":\"proportion\",\"x\":\"45\",\"n\":\"120\",\"level\":\"0.95\",\"p0\":\"0.5\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "sample-size-power",
      "name": "Statistical power and required sample size (t tests, two proportions, correlation)",
      "description": "Give exactly one of n (get the power at that sample size) or power (get the required sample size). kind: ttest_ind = independent two-sample t test (effect = Cohen d, n = size of group 1, group 2 = ratio \u00d7 n, ratio 0.1\u201310, default 1); ttest_one = one-sample or paired t test (effect = d of the differences); prop = two proportions by Cohen h with a normal approximation (p1, p2 in (0,1), p1 \u2260 p2, n = size of group 1, group 2 = ratio \u00d7 n); corr = correlation test by Fisher z (effect = r, 0 < |r| < 1, n \u2265 4). alpha is the significance level (0.0001 \u2264 alpha < 0.5); alt = two (default) or one (one-sided: for the t tests effect must be positive). Returns power, n (the continuous solution when solving, the input otherwise), nCeil (n rounded up), n2 (group 2 for ttest_ind and prop) and effect (d, Cohen h, or atanh r). t tests use the noncentral t distribution with both tails for two-sided tests. Results are rounded to 7 significant digits: the engine uses jStat (about 1e-8 to 1e-9 accurate), so t tests are limited to 4\u20131000 degrees of freedom, a target power above 0.999, a required n beyond the limit and a solution within 1e-6 (relative) of an integer are refused before payment. Planning approximation only \u2014 it ignores dropout, multiple comparisons and design effects and is not a study design or medical advice. Price 400 \u00b5AIC.",
      "tags": [
        "statistics",
        "power-analysis",
        "sample-size",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"sample-size-power\",\"kind\":\"ttest_ind\",\"effect\":\"0.5\",\"alpha\":\"0.05\",\"power\":\"0.8\"}",
        "{\"skill\":\"sample-size-power\",\"kind\":\"prop\",\"p1\":\"0.6\",\"p2\":\"0.4\",\"alpha\":\"0.05\",\"n\":\"100\"}",
        "{\"skill\":\"sample-size-power\",\"kind\":\"corr\",\"effect\":\"0.3\",\"alpha\":\"0.05\",\"power\":\"0.8\",\"alt\":\"two\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "welch-ttest",
      "name": "Welch's two-sample t-test (unequal variances)",
      "description": "Two-sided Welch t-test of two independent samples a and b (2\u201350 decimals each, comma-separated, sign allowed). Returns t = (mean(a) \u2212 mean(b)) / sqrt(sd_a\u00b2/n_a + sd_b\u00b2/n_b), Welch\u2013Satterthwaite df, the two-sided p, and per group n, mean, sd (n\u22121), se, median, min, max. Derived values carry 9 significant digits; p is rounded to 6 decimals (a reported p of 0 means p < 5e-7 \u2014 the engine's tail p is not reliable below ~1e-10 in relative terms: measured relative error 7e-7 at p=1e-10, 7% at 1e-15; its absolute error stays below 3e-8) (measured against scipy: largest error 5e-7 over 131 cases). Refused before payment: fewer than 2 values in a group (too_few), no variance in either group (no_variance), max|x| / SE above 100000 (ill_conditioned \u2014 center your data and ask again). Calculation tool only \u2014 it does not check the test's assumptions; not statistical or medical advice. Price 400 \u00b5AIC.",
      "tags": [
        "statistics",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"welch-ttest\",\"a\":\"5.1,4.9,5.3,5.0\",\"b\":\"5.8,6.1,5.9,6.2,6.0\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "exact-integer-math",
      "name": "Exact integer math: modpow, modinv, crt, binom, egcd",
      "description": "Exact big-integer arithmetic, results as decimal STRINGS (never rounded). op=modpow: a^exp mod mod (a may be negative; result in [0, mod); 0^0 = 1; exp \u2265 0, mod \u2265 1). op=modinv: inverse of a modulo mod (mod \u2265 2; refused 422 noinv if gcd(a mod mod, mod) \u2260 1). op=crt: Chinese remainder theorem for 1\u201310 congruences x \u2261 remainders[i] (mod moduli[i]) (moduli \u2265 1, not necessarily coprime; result x in [0, lcm) plus the combined modulus; refused 422 nosol if inconsistent). op=binom: C(n, k) for 0 \u2264 n, k \u2264 1000 (0 when k > n). op=egcd: gcd (\u2265 0), lcm (0 if a or b is 0) and B\u00e9zout coefficients x, y with a\u00b7x + b\u00b7y = gcd from the classic extended Euclidean algorithm on |a|, |b| (coefficients are not unique; (0,0) refused 422 zero). Integer arguments are decimal strings of at most 60 digits; lists are comma-separated. A result whose digits look like personal data to the delivery filter (a 13\u201319 digit string that passes a card-number check, or a 13-digit date-shaped number) is refused before payment with 422 result_unrepresentable \u2014 nothing is altered or charged. Calculation tool only \u2014 not cryptographic design or key-generation advice. Price 300 \u00b5AIC.",
      "tags": [
        "math",
        "number-theory",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"exact-integer-math\",\"op\":\"modpow\",\"a\":\"4\",\"exp\":\"13\",\"mod\":\"497\"}",
        "{\"skill\":\"exact-integer-math\",\"op\":\"crt\",\"remainders\":\"2,3,2\",\"moduli\":\"3,5,7\"}",
        "{\"skill\":\"exact-integer-math\",\"op\":\"binom\",\"n\":\"52\",\"k\":\"5\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "ipv4-subnet",
      "name": "IPv4 subnet calculator (CIDR, split, host-count sizing)",
      "description": "Given one IPv4 address with prefix in strict CIDR form a.b.c.d/p (octets 0-255 without leading zeros, prefix 0-32; no netmask form), returns network, broadcast, first/last usable host, mask, wildcard, usable host count, total addresses, legacy class (from the first octet of the given address) and RFC 1918 private flag, ALL ADDRESSES AS OCTET ARRAYS such as [192,168,1,0] (never dotted strings). Rules: usable hosts = 2^(32-p) - 2 (network and broadcast excluded); /31 = 2 usable hosts (RFC 3021 point-to-point, first_host = network, last_host = broadcast); /32 = 1 host (first_host = last_host = network). Optional, mutually exclusive: split=k divides the network into equal subnets of the new prefix p + ceil(log2 k), so k is rounded UP to the next power of two (count reports the real number; the first 16 subnets are listed, listed tells how many; refused with 422 if the new prefix would exceed 32); hosts=h returns the longest prefix holding h usable hosts (h=1 gives /32, h=2 gives /30, never /31) and whether such a subnet fits inside the given CIDR. Integer arithmetic, exact. Calculation tool only - not network design, security or address-allocation advice. Price 300 \u00b5AIC.",
      "tags": [
        "network",
        "ipv4",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"ipv4-subnet\",\"cidr\":\"192.168.1.10/24\"}",
        "{\"skill\":\"ipv4-subnet\",\"cidr\":\"10.0.0.0/16\",\"split\":\"4\"}",
        "{\"skill\":\"ipv4-subnet\",\"cidr\":\"10.0.0.0/8\",\"hosts\":\"500\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    },
    {
      "id": "beam-deflection",
      "name": "Beam reactions, moments, shear and maximum deflection (6 standard cases)",
      "description": "Linear-elastic Euler-Bernoulli beam of constant EI in SI units only (metres, newtons, pascals, m^4). case: ss_udl = simply supported, uniform load w (N/m); ss_point = simply supported, point load P (N) at a_m from the left support (a_m must be between span_m/1000 and span_m*(1-1/1000)); cant_point = cantilever fixed at x=0, point load P at the free end x=L; cant_udl = cantilever, uniform load w; ff_udl = both ends fully fixed, uniform load w; cont2_udl = two equal spans L (total 2L, supports at x=0, L, 2L), uniform load w on both. Give w_N_per_m for *_udl cases and P_N for *_point cases (the other one is refused). Returns support reactions (x_m from the left end, upward force_N; fixed-end moments are not in reactions but are max_negative_moment_Nm), max_positive_moment_Nm (sagging, >= 0), max_negative_moment_Nm (hogging, reported as a negative number or 0), max_shear_N (largest absolute shear), max_deflection_m (downward, positive) and max_deflection_x_m (position of the maximum, found numerically, 6 significant digits, other values 12; for cont2_udl the two spans mirror each other and the position in the first span is given). Valid only for small deflections; E_Pa is in pascals (steel about 200000000000) and I_m4 in m^4 - the tool does not check that the numbers are physically plausible, and refuses results of 1e12 or more. Self-weight, shear deformation, load factors and design codes are NOT included. Calculation tool only - not structural design advice. Price 400 \u00b5AIC.",
      "tags": [
        "engineering",
        "structural",
        "calculation",
        "deterministic"
      ],
      "examples": [
        "{\"skill\":\"beam-deflection\",\"case\":\"ss_udl\",\"span_m\":\"6\",\"w_N_per_m\":\"10000\",\"E_Pa\":\"200000000000\",\"I_m4\":\"0.0000833\"}",
        "{\"skill\":\"beam-deflection\",\"case\":\"ss_point\",\"span_m\":\"4\",\"P_N\":\"1000\",\"a_m\":\"1.5\",\"E_Pa\":\"200000000000\",\"I_m4\":\"0.0001\"}",
        "{\"skill\":\"beam-deflection\",\"case\":\"cont2_udl\",\"span_m\":\"4\",\"w_N_per_m\":\"1000\",\"E_Pa\":\"200000000000\",\"I_m4\":\"0.0001\"}"
      ],
      "inputModes": [
        "application/json"
      ],
      "outputModes": [
        "application/json"
      ]
    }
  ],
  "signatures": [
    {
      "protected": "eyJhbGciOiJFZERTQSIsInR5cCI6IkpPU0UiLCJraWQiOiJhZ2VudDoyYmE3ZjYxMi00MjQ1LTQ0ZWYtOTQwYS0xNDExZjgyNGJhYTkifQ",
      "signature": "aGu72QvqdLgTsJB8ddUty5_9iLGErd53kAWKNCOBNybR7MGd8MGsUUsaNF4X4-BFA4nbEHvDORGTkuzMtxzkAA"
    }
  ]
}