Nutrition and veterinary science kernels
Human energy-balance and body-composition formulas (BMI, Mifflin-St Jeor BMR, TDEE, macros) alongside weight-based veterinary dosing, fluid therapy, and per-species reference constants for dogs, cats,
Two modules for weight-driven clinical arithmetic in two different patients. nutrition is human energy balance and body composition — the formulas behind a BMI reading, a daily calorie target, a macro split, and a cardio zone. veterinary is the small-animal-practice equivalent: a per-kg drug dose, a fluid-therapy rate, a caloric requirement, and a set of per-species reference constants (gestation length, normal heart-rate range, packed-cell volume, blood volume, anesthetic MAC) keyed by an integer species code. Both modules take and return plain Float64/Int/List[Float64] values — no structs, no status-code vocabulary — so every function is a single formula that either returns the right number or a visibly wrong one; neither module validates its inputs beyond what the arithmetic itself happens to guard against, which matters more here than in most of this corpus because a caller building a real dosing or diet tool on top of these numbers has no status code to check.
from algenta import MojoRuntime
runtime = MojoRuntime(mode="local")
runtime.execute("nutrition", "bmi", [70.0, 1.75])["result"]
# 22.857142857142858 -- BMI = weight_kg / height_m^2
runtime.execute("nutrition", "bmr_mifflin", [70.0, 175.0, 30, True])["result"]
# 1648.75 -- Mifflin-St Jeor, male: 10*70 + 6.25*175 - 5*30 + 5
runtime.execute("veterinary", "dose_mg", [25.0, 10.0])["result"]
# 250.0 -- a 25 kg dog at 10 mg/kgThe modules
nutrition
Human energy-balance and body-composition formulas: BMI and its WHO-style category, Mifflin-St Jeor BMR, activity-scaled TDEE, a caloric-deficit target, an Atwater-factor macro split, Devine ideal body weight, Deurenberg body-fat percentage, a water-intake rule of thumb, and heart-rate-based cardio metrics (max HR, target zone, VO2max estimate).
veterinary
Weight-based small-animal dosing and fluid therapy (drug dose, fluid rate, dehydration deficit, canine maintenance fluids, canine resting energy requirement) plus per-species reference constants — gestation length, normal heart-rate range, packed-cell-volume midpoint, blood-volume estimate, and anesthetic MAC — addressed by an integer species code that only one of the seven species-coded functions actually implements for all four species the module documents.
nutrition: energy balance and body composition
bmi(weight_kg, height_m)
weight_kg / height_m^2.
bmi_category(bmi_val)
WHO-style classification: 0 underweight (< 18.5), 1 normal (< 25.0), 2 overweight (< 30.0), 3 obese (>= 30.0).
bmr_mifflin(weight_kg, height_cm, age, is_male)
Mifflin-St Jeor: 10*W + 6.25*H - 5*A + 5 for men, 10*W + 6.25*H - 5*A - 161 for women.
tdee(bmr_val, activity_level)
bmr_val * activity_level. The docstring names the intended range as 1.2-1.9 (sedentary to very active); the function does not clamp or validate it.
caloric_deficit(tdee_val, target_loss_kg_per_week)
target_loss_kg_per_week * 7700 / 7 — the standard ~7700-kcal-per-kg-of-fat rule of thumb, spread over 7 days. tdee_val is accepted but never referenced in the arithmetic.
macro_split(calories, protein_pct, fat_pct)
[protein_g, fat_g, carb_g] from Atwater factors (protein and carb at 4 kcal/g, fat at 9 kcal/g). carb_pct = 1 - protein_pct - fat_pct is not clamped, so percentages that sum past 1.0 silently produce a negative carb figure rather than an error.
ideal_body_weight(height_cm, is_male)
Devine formula: 50 + 2.3*(inches - 60) for men, 45.5 + 2.3*(inches - 60) for women, where inches = height_cm / 2.54. The Devine formula is defined for adult heights at or above 60 inches (152.4 cm); below that the function still returns a number, just one the original formula was never validated for.
body_fat_estimate(bmi_val, age, is_male)
Deurenberg (1991): 1.20*BMI + 0.23*age - 10.8*sex - 5.4, sex = 1 for male, 0 for female.
water_intake(weight_kg)
weight_kg * 0.033 liters/day — the common 33 mL/kg/day rule of thumb.
heart_rate_max(age)
220 - age (the Fox formula).
target_heart_rate(hr_max, intensity_low, intensity_high)
[hr_max*intensity_low, hr_max*intensity_high] — a percentage-of-max-HR zone, not the heart-rate-reserve (Karvonen) method, so it takes no resting heart rate.
vo2max_estimate(hr_rest, hr_max)
15.3 * (hr_max / hr_rest) (the Uth-Sørensen-Overgaard-Pedersen estimate). hr_rest = 0 divides by zero rather than being guarded.
The formulas are the textbook ones, not simplifications of them. Checking each against its published source: Mifflin-St Jeor's +5/-161 sex offset, Devine's 50/45.5 base weights and 2.3 per-inch slope, and Deurenberg's 1.20/0.23/10.8/5.4 coefficients all match the original equations exactly — nothing here is a rounded-off or partial reimplementation.
tests/mojo/test_wave60.mojo ("Wave 60 — Optics, Electrical Engineering, Nutrition Science", the 250-library-milestone wave) pins several of these against hand-worked values rather than just range-checking them: bmr_mifflin(70.0, 175.0, 30, True) must equal 1648.75 exactly (10*70 + 6.25*175 - 5*30 + 5), tdee(1800.0, 1.55) must equal 2790.0, and macro_split(2000.0, 0.3, 0.3) must split into protein_g = 150.0, fat_g = 66.667, carb_g = 200.0 — a split whose three components, fed back through the Atwater factors (150*4 + 66.667*9 + 200*4), sum back to 2000.0 kcal to within the test's own 0.1 tolerance.
macro_split's missing clamp is reachable with ordinary-looking inputs. A caller asking for a 40%-protein, 40%-fat plan — each individually plausible — gets carb_pct = 1 - 0.4 - 0.4 = 0.2, fine. But 60%-protein, 50%-fat (a caller stacking two "high" targets without checking they still sum under 1.0) gives carb_pct = -0.1, and macro_split returns that as a genuine negative carb_g rather than refusing — nothing in the function's def name or return type signals that the third slot can go negative.
veterinary: weight-based dosing and species reference constants
dose_mg(weight_kg, dose_per_kg)
weight_kg * dose_per_kg — a linear per-kg drug dose.
fluid_rate_ml_hr(total_ml, hours)
total_ml / hours.
fluid_deficit(weight_kg, dehydration_pct)
weight_kg * dehydration_pct / 100 * 1000 mL — the standard fluid-deficit estimate; dehydration_pct is taken as a whole number (8 for 8% dehydrated), not a fraction.
maintenance_fluid_dog(weight_kg)
60 * weight_kg mL/day. The module's own docstring calls this "simplified" — it is a flat per-kg rate rather than the allometric-scaling maintenance formulas (e.g. ~132 * weight^0.75) veterinary practice uses across a wider weight range.
caloric_requirement_dog(weight_kg)
70 * weight_kg^0.75 kcal/day — the standard interspecies Resting Energy Requirement (RER) allometric formula. Despite the _dog suffix, the 70*BW^0.75 equation itself is not dog-specific in veterinary nutrition (the same formula is the standard RER for cats and other mammals too); _dog names this module's one entry point for it, not a species restriction in the math. weight_kg^0.75 is computed as sqrt(sqrt(weight_kg^3)) via 20 fixed iterations of a private Newton's-method square root (_sqrt_approx), not a general power or logarithm routine.
body_condition_score_ideal(species_code)
Always returns 5.0 on the 1-9 BCS scale, regardless of species_code — the docstring's "Dog(0)=5.0, Cat(1)=5.0" describes the two species the rest of the module supports, but this particular function does not branch on its input at all.
anesthesia_mac(species_code, agent_code)
Typical minimum alveolar concentration: Dog/isoflurane 1.3, Dog/sevoflurane 2.4, Cat/isoflurane 1.6, Cat/sevoflurane 3.1. The branch is species_code == 0 (Dog) vs. everything else (Cat) — Horse (2) and Cow (3), both named in the module's own species-code comment, silently receive Cat's MAC values.
gestation_period_days(species_code)
Dog 63, Cat 65, Horse 340, Cow 283 days; any other code returns 0.0.
heart_rate_normal_range_low(species_code) / heart_rate_normal_range_high(species_code)
Dog 60-140, Cat 120-220, Horse 28-44 bpm; Cow and any other code return 0.0 for both bounds.
packed_cell_volume_normal(species_code)
Dog 46.0, Cat 37.5; Horse, Cow, and any other code return 0.0.
blood_volume_estimate(weight_kg, species_code)
Dog 90 mL/kg, Cat 60 mL/kg; Horse, Cow, and any other code return 0.0 regardless of weight_kg.
Seven of the twelve functions take a species_code; only one of those seven covers all four species the module's header comment lists. The file opens with # Species codes: 0=Dog, 1=Cat, 2=Horse, 3=Cow, and gestation_period_days is the only species-coded function that actually branches on all four — every other one recognizes at most three (heart_rate_normal_range_low/_high, which cover Dog/Cat/Horse and fall through to 0.0 for Cow) or just two (packed_cell_volume_normal and blood_volume_estimate, Dog/Cat only; Horse and Cow both return 0.0). body_condition_score_ideal ignores species_code entirely.
anesthesia_mac is the one case where the fallback is a wrong number, not an obviously-empty one. Every other species-coded function's fallback for an unlisted species is 0.0 — a value a caller checking "did I get a real reading back" can catch. anesthesia_mac has no such tell: its if species_code == 0 branch means any non-zero code, including Horse (2) and Cow (3), falls through to the Cat branch and returns a real-looking MAC value (1.6 for isoflurane, 3.1 for sevoflurane) that belongs to a different species. anesthesia_mac(2, 0) — Horse, isoflurane — returns 1.6, Cat's value, with nothing in the return distinguishing it from a genuine Horse reading.
A worked chain from tests/mojo/test_wave86.mojo ("Wave 86 — Paper Science, Radar, Veterinary"), which pins exact values rather than just checking they're finite:
caloric_requirement_dog(10.0)'s expected value is independently reproducible outside the test file too: 70 * 10**0.75 == 393.6389276332444 and 70 * 5**0.75 == 234.0591067417477 in plain Python, matching the test's 393.64/234.06 comments to four significant figures — the module's sqrt-of-sqrt-of-cube approximation of a fractional power reproduces the closed-form result to full double precision for both weights checked.
Verification
mojo/tests/libs/test_nutrition.mojo and mojo/tests/libs/test_veterinary.mojo are auto-generated coverage smoke tests: each calls every function once with fixed placeholder arguments (0.5, small integers) and checks only that a Float64 result is finite, or that a list has non-negative length — they pin no specific numeric output and would not catch a sign error or a swapped coefficient.
The real numeric assertions live in the wave-suite files instead: tests/mojo/test_wave60.mojo pins bmi, bmr_mifflin, tdee, caloric_deficit, macro_split, water_intake, heart_rate_max, target_heart_rate, and vo2max_estimate against exact hand-computed values (plus range checks on ideal_body_weight and body_fat_estimate), and tests/mojo/test_wave86.mojo pins all twelve veterinary functions, including every species/agent combination anesthesia_mac, gestation_period_days, heart_rate_normal_range_low, heart_rate_normal_range_high, and packed_cell_volume_normal actually implement. The worked examples in this page are drawn from those pinned assertions, and the caloric_requirement_dog values were independently re-derived in plain Python (70 * w**0.75) to confirm the module's iterative square-root approximation of the fractional power is not losing precision anywhere the test tolerance would hide.
Next: see the full function list in the Runtime library catalog, or browse the Engine catalog for how nutrition and veterinary are exposed alongside every other engine.
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